Final Review for Package for Analysis of Space-Time Ecological Series | LATIN 1, Exams of Latin language

Download Final Review for Package for Analysis of Space-Time Ecological Series | LATIN 1 and more Exams Latin language in PDF only on Docsity! Package ‘pastecs’ April 19, 2009 Title Package for Analysis of Space-Time Ecological Series Version 1.3-8 Date 2009-25-23 Author Frederic Ibanez <ibanez@obs-vlfr.fr>, Philippe Grosjean <phgrosjean@sciviews.org> & Michele Etienne <etienne@obs-vlfr.fr> Description Regulation, decomposition and analysis of space-time series. The pastecs library is a PNEC-Art4 and IFREMER (Benoit Beliaeff <Benoit.Beliaeff@ifremer.fr>) initiative to bring PASSTEC 2000 (http://www.obs-vlfr.fr/~enseigne/anado/passtec/passtec.htm) functionnalities to R. URL http://www.sciviews.org/pastecs Maintainer Philippe Grosjean <phgrosjean@sciviews.org> Encoding latin1 License GPL (>= 2) Depends boot, stats Repository CRAN Date/Publication 2009-02-23 11:20:40 R topics documented: .gleissberg.table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 abund . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 AutoD2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 bnr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 buysbal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 daystoyears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 decaverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 deccensus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 decdiff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1 2 .gleissberg.table decevf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 decloess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 decmedian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 decreg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 disjoin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 disto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 escouf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 extract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 first . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 GetUnitText . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 is.tseries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 last . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 local.trend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 marbio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 marphy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 match.tol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 pennington . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 pgleissberg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 regarea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 regconst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 reglin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 regspline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 regul . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 regul.adj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 regul.screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 releve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 specs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 stat.desc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 stat.pen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 stat.slide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 trend.test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 tsd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 tseries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 turnogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 turnpoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 vario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Index 71 .gleissberg.table Table of probabilities according to the Gleissberg distribution Description The table of probabilities to have 0 to n-2 extrema in a series, for n=3 to 50 (for n > 50, the Gleissberg distribution is approximated with a normal distribution AutoD2 5 Examples data(bnr) bnr.abd <- abund(bnr) summary(bnr.abd) plot(bnr.abd, dpos=c(105, 100)) bnr.abd$n <- 26 # To identify a point on the graph, use: bnr.abd$n <- identify(bnr.abd) lines(bnr.abd) bnr2 <- extract(bnr.abd) names(bnr2) AutoD2 AutoD2, CrossD2 or CenterD2 analysis of a multiple time-series Description Compute and plot multiple autocorrelation using Mahalanobis generalized distance D2. AutoD2 uses the same multiple time-series. CrossD2 compares two sets of multiple time-series having same size (same number of descriptors). CenterD2 compares subsamples issued from a single multivariate time-series, aiming to detect discontinuities. Usage AutoD2(series, lags=c(1, nrow(series)/3), step=1, plotit=TRUE, add=FALSE, ...) CrossD2(series, series2, lags=c(1, nrow(series)/3), step=1, plotit=TRUE, add=FALSE, ...) CenterD2(series, window=nrow(series)/5, plotit=TRUE, add=FALSE, type="l", level=0.05, lhorz=TRUE, lcol=2, llty=2, ...) Arguments series regularized multiple time-series series2 a second set of regularized multiple time-series lags minimal and maximal lag to use. By default, 1 and a third of the number of observations in the series respectively step step between successive lags. By default, 1 window the window to use for CenterD2. By default, a fifth of the total number of observations in the series plotit if TRUE then also plot the graph add if TRUE then the graph is added to the current figure type The type of line to draw in the CenterD2 graph. By default, a line without points level The significance level to consider in the CenterD2 analysis. By default 5% lhorz Do we have to plot also the horizontal line representing the significance level on the graph? 6 AutoD2 lcol The color of the significance level line. By default, color 2 is used llty The style for the significance level line. By default: llty=2, a dashed line is drawn ... additional graph parameters Value An object of class ’D2’ which contains: lag The vector of lags D2 The D2 value for this lag call The command invoked when this function was called data The series used type The type of ’D2’ analysis: ’AutoD2’, ’CrossD2’ or ’CenterD2’ window The size of the window used in the CenterD2 analysis level The significance level for CenterD2 chisq The chi-square value corresponding to the significance level in the CenterD2 analysis units.text Time units of the series, nicely formatted for graphs WARNING If data are too heterogeneous, results could be biased (a singularity matrix appears in the calcula- tions). Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) References Cooley, W.W. & P.R. Lohnes, 1962. Multivariate procedures for the behavioural sciences. Whiley & sons. Dagnélie, P., 1975. Analyse statistique à plusieurs variables. Presses Agronomiques de Gembloux. Ibanez, F., 1975. Contribution à l’analyse mathématique des évènements en écologie planctonique: optimisations méthodologiques; étude expérimentale en continu à petite échelle du plancton côtier. Thèse d’état, Paris VI. Ibanez, F., 1976. Contribution à l’analyse mathématique des évènements en écologie planctonique. Optimisations méthodologiques. Bull. Inst. Océanogr. Monaco, 72:1-96. Ibanez, F., 1981. Immediate detection of heterogeneities in continuous multivariate oceanographic recordings. Application to time series analysis of changes in the bay of Villefranche sur mer. Lim- nol. Oceanogr., 26:336-349. Ibanez, F., 1991. Treatment of the data deriving from the COST 647 project on coastal benthic ecology: The within-site analysis. In: B. Keegan (ed), Space and time series data analysis in coastal benthic ecology, p 5-43. bnr 7 See Also mahalanobis, acf Examples data(marphy) marphy.ts <- as.ts(as.matrix(marphy[, 1:3])) AutoD2(marphy.ts) marphy.ts2 <- as.ts(as.matrix(marphy[, c(1, 4, 3)])) CrossD2(marphy.ts, marphy.ts2) # This is not identical to: CrossD2(marphy.ts2, marphy.ts) marphy.d2 <- CenterD2(marphy.ts, window=16) lines(c(17, 17), c(-1, 15), col=4, lty=2) lines(c(25, 25), c(-1, 15), col=4, lty=2) lines(c(30, 30), c(-1, 15), col=4, lty=2) lines(c(41, 41), c(-1, 15), col=4, lty=2) lines(c(46, 46), c(-1, 15), col=4, lty=2) text(c(8.5, 21, 27.5, 35, 43.5, 57), 11, labels=c("Peripheral Zone", "D1", "C", "Front", "D2", "Central Zone")) # Labels time(marphy.ts)[marphy.d2$D2 > marphy.d2$chisq] bnr A data frame of 163 benthic species measured across a transect Description The bnr data frame has 103 rows and 163 columns. Each column is a separate species observed at least once in one of all stations. Several species are very abundant, other are very rare. Usage data(bnr) Source Unpublished dataset. 10 daystoyears or the date will not be correctly converted! In R, you can also use a POSIXt for- mat specification like "%d-%m%Y" for instance (see ?strptime for a com- plete description of POSIXt format specification. In both Splus and R, you can also use "mon" for abbreviated months like "mon d Y" for "Apr 20 1965", and "month" for fully-spelled months like "d month Y" for "24 September 2003" xmin The minimum value for the "days" time-scale Details The "years" time-scale uses one unit for each year. We deliberately "linearized" time in this time- scale and each year is considered to have exactly 365.25 days. There is thus no adjustment for lep years. Indeed, a small shift (less than one day) is introduced. This could result, for some dates, especially the 31st December, or 1st January of a year to be considered as belonging to the next, or previous year, respectively! Similarly, one month is considered to be 1/12 year, no mather if it has 28, 29, 30 or 31 days. Thus, the same warning applies: there are shifts in months introduced by this linearization of time! This representation simplifies further calculations, especially regarding seasonal effects (a quarter is exactly 0.25 units for instance), but shifts introduced in time may or may not be a problem for your particular application (if exact dates matters, do not use this; if shifts of up to one day is not significant, there is no problem, like when working on long-term biological series with years as units). Notice that converting it back to "days", using yearstodays() restablishes exact dates without errors. So, no data is lost, it just a conversion to a simplified (linearized) calendar! Value A numerical vector of the same length as x with the converted time-scale Author(s) Philippe Grosjean (〈phgrosjean@sciviews.org〉), Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉) See Also buysbal Examples # A vector with a "days" time-scale (25 values every 30 days) A <- (1:25)*30 # Convert it to a "years" time-scale, using 23/05/2001 (d/m/Y) as first value B <- daystoyears(A, datemin="23/05/2001", dateformat="d/m/Y") B # Convert it back to "days" time-scale yearstodays(B, xmin=30) # Here is an example showing the shift introduced, and its consequence: C <- daystoyears(unclass(as.Date(c("1970-1-1","1971-1-1","1972-1-1","1973-1-1"), format = "%Y-%m-%d"))) C decaverage 11 decaverage Time series decomposition using a moving average Description Decompose a single regular time series with a moving average filtering. Return a ’tsd’ object. To decompose several time series at once, use tsd() with the argument method="average" Usage decaverage(x, type="additive", order=1, times=1, sides=2, ends="fill", weights=NULL) Arguments x a regular time series (’rts’ under S+ and ’ts’ under R) type the type of model, either type="additive" (by default), or type="multiplicative" order the order of the moving average (the window of the average being 2*order+1), centered around the current observation or at left of this observation depending upon the value of the sides argument. Weights are the same for all observa- tions within the window. However, if the argument weights is provided, it supersedes order. One can also use order="periodic". In this case, a deseasoning filter is calculated according to the value of frequency times The number of times to apply the method (by default, once) sides If 2 (by default), the window is centered around the current observation. If 1, the window is at left of the current observation (including it) ends either "NAs" (fill first and last values that are not calculable with NAs), or "fill" (fill them with the average of observations before applying the filter, by default), or "circular" (use last values for estimating first ones and vice versa), or "peri- odic" (use entire periods of contiguous cycles, deseasoning) weights a vector indicating weight to give to all observations in the window. This argu- ment has the priority over order Details This function is a wrapper around the filter() function and returns a ’tsd’ object. However, it offers more methods to handle ends. Value A ’tsd’ object Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) 12 deccensus References Kendall, M., 1976. Time-series. Charles Griffin & Co Ltd. 197 pp. Laloire, J.C., 1972. Méthodes du traitement des chroniques. Dunod, Paris, 194 pp. Malinvaud, E., 1978. Méthodes statistiques de l’économétrie. Dunod, Paris. 846 pp. Philips, L. & R. Blomme, 1973. Analyse chronologique. Université Catholique de Louvain. Vander ed. 339 pp. See Also tsd, tseries, deccensus, decdiff, decmedian, decevf, decreg, decloess Examples data(marbio) ClausoB.ts <- ts(log(marbio$ClausocalanusB + 1)) ClausoB.dec <- decaverage(ClausoB.ts, order=2, times=10, sides=2, ends="fill") plot(ClausoB.dec, col=c(1, 3, 2), xlab="stations") # A stacked graph is more representative in this case plot(ClausoB.dec, col=c(1, 3), xlab="stations", stack=FALSE, resid=FALSE, lpos=c(53, 4.3)) deccensus Time decomposition using the CENSUS II method Description The CENSUS II method allows to decompose a regular time series into a trend, a seasonal compo- nent and residuals, according to a multiplicative model Usage deccensus(x, type="multiplicative", trend=FALSE) Arguments x A single regular time serie (a ’rts’ object under S+ and a ’ts’ object under R) with a "years" time scale (one unit = one year) and a complete number of cycles (at least 3 complete years) type The type of model. This is for compatibility with other decxxx() functions, but only a multiplicative model is allowed here trend If trend=TRUE a trend component is also calculated, otherwise, the decompo- sition gives only a seasonal component and residuals decevf 15 See Also tsd, tseries, decaverage, deccensus, decmedian, decevf, decreg, decloess Examples data(marbio) ClausoB.ts <- ts(log(marbio$ClausocalanusB + 1)) ClausoB.dec <- decdiff(ClausoB.ts, lag=1, order=2, ends="fill") plot(ClausoB.dec, col=c(1, 4, 2), xlab="stations") decevf Time series decomposition using eigenvector filtering (EVF) Description The eigenvector filtering decomposes the signal by applying a principal component analysis (PCA) on the original signal and a certain number of copies of it incrementally lagged, collected in a mul- tivariate matrix. Reconstructing the signal using only the most representative eigenvectors allows filtering it. Usage decevf(x, type="additive", lag=5, axes=1:2) Arguments x a regular time series (’rts’ under S+ and ’ts’ under R) type the type of model, either type="additive" (by default), or type="multiplicative" lag The maximum lag used. A PCA is run on the matrix constituted by vectors lagged from 0 to lag. The defaulf value is 5, but a value corresponding to no significant autocorrelation, on basis of examination of the autocorrelation plot obtained by acf in the library ’ts’ should be used (Lag at first time the autocorrelation curve crosses significance lines multiplied by the frequency of the series). axes The principal axes to use to reconstruct the filtered signal. For instance, to use axes 2 and 4, use axes=c(2,4). By default, the first two axes are considered (axes=1:2) Value a ’tsd’ object Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) 16 decloess References Colebrook, J.M., 1978. Continuous plankton records: zooplankton and environment, North-East Atlantic and North Sea 1948-1975. Oceanologica Acta, 1:9-23. Ibanez, F. & J.C. Dauvin, 1988. Long-term changes (1977-1987) on a muddy fine sand Abra alba - Melinna palmate population community from the Western English Channel. J. Mar. Prog. Ser., 49:65-81. Ibanez, F., 1991. Treatment of data deriving from the COST 647 project on coastal benthic ecology: The within-site analysis. In: B. Keegan (ed.) Space and time series data analysis in coastal benthic ecology. Pp. 5-43. Ibanez, F. & M. Etienne, 1992. Le filtrage des séries chronologiques par l’analyse en composantes principales de processus (ACPP). J. Rech. Océanogr., 16:27-33. Ibanez, F., J.C. Dauvin & M. Etienne, 1993. Comparaison des évolutions à long-terme (1977-1990) de deux peuplements macrobenthiques de la Baie de Morlaix (Manche Occidentale): relations avec les facteurs hydroclimatiques. J. Exp. Mar. Biol. Ecol., 169:181-214. See Also tsd, tseries, decaverage, deccensus, decmedian, decdiff, decreg, decloess Examples data(releve) melo.regy <- regul(releve$Day, releve$Melosul, xmin=9, n=87, units="daystoyears", frequency=24, tol=2.2, methods="linear", datemin="21/03/1989", dateformat="d/m/Y") melo.ts <- tseries(melo.regy) acf(melo.ts) # Autocorrelation is not significant after 0.16 # That corresponds to a lag of 0.16*24=4 (frequency=24) melo.evf <- decevf(melo.ts, lag=4, axes=1) plot(melo.evf, col=c(1, 4, 2)) # A superposed graph is better in the present case plot(melo.evf, col=c(1, 4), xlab="stations", stack=FALSE, resid=FALSE, lpos=c(0, 60000)) decloess Time series decomposition by the LOESS method Description Compute a seasonal decomposition of a regular time series using a LOESS method (local polyno- mial regression) Usage decloess(x, type="additive", s.window=NULL, s.degree=0, t.window=NULL, t.degree=2, robust=FALSE, trend=FALSE) decloess 17 Arguments x a regular time series (’rts’ under S+ and ’ts’ under R) type the type of model. This is for compatibility purpose. The only model type that is accepted for this method is type="additive". For a multiplicative model, use deccensus() instead s.window the width of the window used to extract the seasonal component. Use an odd value equal or just larger than the number of annual values (frequency of the time series). Use another value to extract other cycles (circadian, lunar,...). Using s.window="periodic" ensures a correct value for extracting a seasonal component when the time scale is in years units s.degree the order of the polynome to use to extract the seasonal component (0 or 1). By default s.degree=0 t.window the width of the window to use to extract the general trend when trend=TRUE (indicate an odd value). If this parameter is not provided, a reasonable value is first calculated, and then used by the algorithm. t.degree the order of the polynome to use to extract the general trend (0, 1 or 2). By default t.degree=2 robust if TRUE a robust regression method is used. Otherwise (FALSE), by default, a classical least-square regression is used trend If TRUE a trend is calculated (under R only). Otherwise, the series is decom- posed into a seasonal component and residuals only Details This function uses the stl() function for the decomposition. It is a wrapper that create a ’tsd’ object Value a ’tsd’ object Author(s) Philippe Grosjean (〈phgrosjean@sciviews.org〉), Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉) References Cleveland, W.S., E. Grosse & W.M. Shyu, 1992. Local regression models. Chapter 8 of Statistical Models in S. J.M. Chambers & T.J. Hastie (eds). Wadsworth & Brook/Cole. Cleveland, R.B., W.S. Cleveland, J.E. McRae, & I. Terpenning, 1990. STL: A seasonal-trend de- composition procedure based on loess. J. Official Stat., 6:3-73. See Also tsd, tseries, decaverage, deccensus, decmedian, decdiff, decevf, decreg 20 decreg References Frontier, S., 1981. Méthodes statistiques. Masson, Paris. 246 pp. Kendall, M., 1976. Time-series. Charles Griffin & Co Ltd. 197 pp. Legendre, L. & P. Legendre, 1984. Ecologie numérique. Tome 2: La structure des données écologiques. Masson, Paris. 335 pp. Malinvaud, E., 1978. Méthodes statistiques de l’économétrie. Dunod, Paris. 846 pp. Sokal, R.R. & F.J. Rohlf, 1981. Biometry. Freeman & Co, San Francisco. 860 pp. See Also tsd, tseries, decaverage, deccensus, decdiff, decevf, decmedian, decloess Examples data(marphy) density <- ts(marphy[, "Density"]) plot(density) Time <- time(density) # Linear model to represent trend density.lin <- lm(density ~ Time) summary(density.lin) xreg <- predict(density.lin) lines(xreg, col=3) density.dec <- decreg(density, xreg) plot(density.dec, col=c(1, 3, 2), xlab="stations") # Order 2 polynomial to represent trend density.poly <- lm(density ~ Time + I(Time^2)) summary(density.poly) xreg2 <- predict(density.poly) plot(density) lines(xreg2, col=3) density.dec2 <- decreg(density, xreg2) plot(density.dec2, col=c(1, 3, 2), xlab="stations") # Fit a sinusoidal model on seasonal (artificial) data tser <- ts(sin((1:100)/12*pi)+rnorm(100, sd=0.3), start=c(1998, 4), frequency=24) Time <- time(tser) tser.sin <- lm(tser ~ I(cos(2*pi*Time)) + I(sin(2*pi*Time))) summary(tser.sin) tser.reg <- predict(tser.sin) tser.dec <- decreg(tser, tser.reg) plot(tser.dec, col=c(1, 4), xlab="stations", stack=FALSE, resid=FALSE, lpos=c(0, 4)) plot(tser.dec, col=c(1, 4, 2), xlab="stations") # One can also use nonlinear models (see 'nls') # or autoregressive models (see 'ar' and others in 'ts' library) disjoin 21 disjoin Complete disjoined coded data (binary coding) Description Transform a factor in separate variables (one per level) with a binary code (0 for absent, 1 for present) in each variable Usage disjoin(x) Arguments x a vector containing a factor data Details Use cut() to transform a numerical variable into a factor variable Value a matrix containing the data with binary coding Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) References Fromentin J.-M., F. Ibanez & P. Legendre, 1993. A phytosociological method for interpreting plank- ton data. Mar. Ecol. Prog. Ser., 93:285-306. Gebski, V.J., 1985. Some properties of splicing when applied to non-linear smoothers. Comput. Stat. Data Anal., 3:151-157. Grandjouan, G., 1982. Une méthode de comparaison statistique entre les répartitions des plantes et des climats. Thèse d’Etat, Université Louis Pasteur, Strasbourg. Ibanez, F., 1976. Contribution à l’analyse mathématique des événements en Ecologie planctonique. Optimisations méthodologiques. Bull. Inst. Océanogr. Monaco, 72:1-96. See Also buysbal, cut 22 disto Examples # Artificial data with 1/5 of zeros Z <- c(abs(rnorm(8000)), rep(0, 2000)) # Let the program chose cuts table(cut(Z, breaks=5)) # Create one class for zeros, and 4 classes for the other observations Z2 <- Z[Z != 0] cuts <- c(-1e-10, 1e-10, quantile(Z2, 1:5/5, na.rm=TRUE)) cuts table(cut(Z, breaks=cuts)) # Binary coding of these data disjoin(cut(Z, breaks=cuts))[1:10, ] disto Compute and plot a distogram Description A distogram is an extension of the variogram to a multivariate time-series. It computes, for each observation (with a constant interval h between each observation), the euclidean distance normated to one (chord distance) Usage disto(x, max.dist=nrow(x)/4, plotit=TRUE, disto.data=NULL) Arguments x a matrix, a data frame or a multiple time-series max.dist the maximum distance to calculate. By default, it is the third of the number of observations (that is, the number of rows in the matrix) plotit If plotit=TRUE then the graph of the distogram is plotted disto.data data coming from a previous call to disto(). Call the function again with these data to plot the corresponding graph Value A data frame containing distance and distogram values Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) extract 25 Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉), Benjamin Planque (〈Benjamin.Planque@ifremer.fr〉), Jean-Marc Fromentin (〈Jean.Marc.Fromentin@ifremer.fr〉) References Cambon, J., 1974. Vecteur équivalent à un autre au sens des composantes principales. Application hydrologique. DEA de Mathématiques Appliquées, Université de Montpellier. Escoufier, Y., 1970. Echantillonnage dans une population de variables aléatoires réelles. Pub. Inst. Stat. Univ. Paris, 19:1-47. Jabaud, A., 1996. Cadre climatique et hydrobiologique du lac Léman. DEA d’Océanologie Bi- ologique Paris. See Also abund Examples data(marbio) marbio.esc <- escouf(marbio) summary(marbio.esc) plot(marbio.esc) # The x-axis has short labels. For more info., enter: marbio.esc$vr # Define a level at which to extract most significant variables marbio.esc$level <- 0.90 # Show it on the graph lines(marbio.esc) # This can also be done interactively on the plot using: # marbio.esc$level <- identify(marbio.esc) # Finally, extract most significant variables marbio2 <- extract(marbio.esc) names(marbio2) extract Extract a subset of the original dataset Description ‘extract’ is a generic function for extracting a part of the original dataset according to an analysis...) Usage extract(e, n, ...) 26 first Arguments e An object from where extraction is performed n The number of elements to extract ... Additional arguments affecting the extraction Value A subset of the original dataset contained in the extracted object See Also abund, regul, tsd, turnogram, turnpoints first Get the first element of a vector Description Extract the first element of a vector. Useful for the turnogram() function Usage first(x, na.rm=FALSE) Arguments x a numerical vector na.rm if na.rm=TRUE, then the first non-missing value (if any) is returned. By de- fault, it is FALSE and the first element (whatever its value) is returned Value a numerical value Author(s) Philippe Grosjean (〈phgrosjean@sciviews.org〉), Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉) See Also last, turnogram Examples a <- c(NA, 1, 2, NA, 3, 4, NA) first(a) first(a, na.rm=TRUE) GetUnitText 27 GetUnitText Format a nice time units for labels in graphs Description This is an internal function called by some plot() methods. Considering the time series ’units’ attribute and the frequency of the observations in the series, the function returns a string with a pertinent time unit. For instance, if the unit is ’years’ and the frequency is 12, then data are monthly sampled and GetUnitText() returns the string "months" Usage GetUnitText(series) Arguments series a regular time series (a ’rts’ object in Splus, or a ’ts’ object in R) Value a string with the best time unit for graphs Author(s) Philippe Grosjean (〈phgrosjean@sciviews.org〉), Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉) See Also daystoyears, yearstodays Examples timeser <- ts(1:24, frequency=12) # 12 observations per year if (exists("is.R") && is.function(is.R) && is.R()) { # We are in R attr(timeser, "units") <- "years" # time in years for 'ts' object } else { # We are in Splus attr(attr(timeser, "tspar"), "units") <- "years" # Idem for Splus 'rts' object } GetUnitText(timeser) # formats unit (1/12 year=months) 30 local.trend Details With local.trend(), you can: - detect changes in the mean value of a time series - determine the date of occurence of such changes - estimate the mean values on homogeneous intervals Value a ’local.trend’ object is returned. It has the method identify() Note Once transitions are identified with this method, you can use stat.slide() to get more detailed information on each phase. A smoothing of the series using running medians (see decmedian()) allows also to detect various levels in a time series, but according to the median statistic. Under R, see also the ’strucchange’ package for a more complete, but more complex, implementation of cumsum applied to time series. Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) References Ibanez, F., J.M. Fromentin & J. Castel, 1993. Application de la méthode des sommes cumulées à l’analyse des séries chronologiques océanographiques. C. R. Acad. Sci. Paris, Life Sciences, 316:745-748. See Also trend.test, stat.slide, decmedian Examples data(bnr) # Calculate and plot cumsum for the 8th series bnr8.lt <- local.trend(bnr[,8]) # To identify local trends, use: # identify(bnr8.lt) # and click points between which you want to compute local linear trends... marbio 31 marbio Several zooplankton taxa measured across a transect Description The marbio data frame has 68 rows (stations) and 24 columns (taxonomic zooplankton groups). Abundances are expressed in no per cubic meter of seawater. Usage data(marbio) Format This data frame contains the following columns giving abundance of: Acartia Acartia clausi - herbivorous AdultsOfCalanus Calanus helgolandicus (adults) - herbivorous Copepodits1 Idem (copepodits 1) - omnivorous Copepodits2 Idem (copepodits 2) - omnivorous Copepodits3 Idem (copepodits 3) - omnivorous Copepodits4 Idem (copepodits 4) - omnivorous Copepodits5 Idem (copepodits 5) - omnivorous ClausocalanusA Clausocalanus size class A - herbivorous ClausocalanusB Clausocalanus size class B - herbivorous ClausocalanusC Clausocalanus size class C - herbivorous AdultsOfCentropages Centropages tipicus (adults) - omnivorous JuvenilesOfCentropages Centropages typicus (juv.) - omnivorous Nauplii Nauplii of copepods - filter feeders Oithona Oithona sp. - carnivorous Acanthaires Various species of acanthaires - misc Cladocerans Various species of cladocerans - carnivorous EchinodermsLarvae Larvae of echinoderms - filter feeders DecapodsLarvae Larvae of decapods - omnivorous GasteropodsLarvae Larvae of gastropods - filter feeders EggsOfCrustaceans Eggs of crustaceans - misc Ostracods Various species of ostracods - omnivorous Pteropods Various species of pteropods - herbivorous Siphonophores Various species of siphonophores - carnivorous BellsOfCalycophores Bells of calycophores - misc 32 marphy Details This dataset corresponds to a single transect sampled with a plankton net across the Ligurian Sea front in the Mediterranean Sea, between Nice (France) and Calvi (Corsica). The transect extends from the Cap Ferrat (close to Nice) to about 65 km offshore in the direction of Calvi (along a bearing of 123°). 68 regularly spaced samples where collected on this transect. For more information about the water masses and their physico-chemical characteristics, see the marphy dataset. Source Boucher, J., F. Ibanez & L. Prieur (1987) Daily and seasonal variations in the spatial distribution of zooplankton populations in relation to the physical structure in the Ligurian Sea Front. Journal of Marine Research, 45:133-173. References Fromentin, J.-M., F. Ibanez & P. Legendre (1993) A phytosociological method for interpreting plankton data. Marine Ecology Progress Series, 93:285-306. See Also marphy marphy Physico-chemical records at the same stations as for marbio Description The marphy data frame has 68 rows (stations) and 4 columns. They are seawater measurements at a deep of 3 to 7 m at the same 68 stations as marbio. Usage data(marphy) Format This data frame contains the following columns: Temperature Seawater temperature in °C Salinity Salinity in g/kg Fluorescence Fluorescence of chlorophyll a Density Excess of volumic mass of the seawater in g/l pennington 35 Usage pennington(x, calc="all", na.rm=FALSE) Arguments x a numerical vector calc indicate which estimator(s) should be calculated. Use: "mean", "var", "mean.var" or "all" (by default) for the mean, the variance, the variance of the mean or all these three statitics, respectively na.rm if na.rm=TRUE, missing data are eliminated first. If it is FALSE (by default), any missing value in the series leads to NA as the result for the statistic Details A complex problem in marine ecology is the notion of zero. In fact, the random sampling of a fish population often leads to a table with many null values. Do these null values indicate that the fish was absent or do we have to consider these null values as missing data, that is, that the fish was rare but present and was not caught by the net? For instance, for 100 net trails giving 80 null values, how to estimate the mean? Do we have to divide the sum of fishes caught by 100 or by 20? Pennington (1983) applied in this case the probabilistic theory of Aitchison (1955). The later es- tablished a method to estimate mean and variance of a random variable with a non-null probability to present zero values and whose the conditional distribution corresponding to its non-null values follows a Gaussian curve. In practice, a lognormal distribution is found most of the time for non- null values in fishes population. It is also often the case for the plankton, after our own experience. pennington() calculates thus statistics for such conditional lognormal distributions. Value a single value, or a vector with "mean", "var" and "mean.var" if the argument calc="all" Note For multiple series, or for getting more statistics on the series, use stat.pen(). Use stat.slide() for obtaining statistics calculated separately for various intervals along the time for a time series Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) References Aitchison, J., 1955. On the distribution of a positive random variable having a discrete probability mass at the origin. J. Amer. Stat. Ass., 50:901-908. Pennington, M., 1983. Efficient estimations of abundance for fish and plankton surveys. Biometrics, 39:281-286. See Also stat.pen, stat.slide 36 pgleissberg Examples data(marbio) pennington(marbio[, "Copepodits2"]) pennington(marbio[, "Copepodits2"], calc="mean", na.rm=TRUE) pgleissberg Gleissberg distribution probability Description The Gleissberg distribution gives the probability to have k extrema in a series of n observations. This distribution is used in the turnogram to determine if monotony indices are significant (see turnogram()) Usage pgleissberg(n, k, lower.tail=TRUE, two.tailed=FALSE) Arguments n the number of observations in the series k the number of extrema in the series, as calculated by turnpoints() lower.tail if lower.tail=TRUE (by default) and two.tailed=FALSE, the left-side probability is returned. If it is FALSE, the right-side probability is returned two.tailed if two.tailed=TRUE, the two-sided probability is returned. By default, it is FALSE and a one-sided probability is returned (left or right, depending on the value of lower.tail Value a value giving the probability to have k extrema in a series of n observations Note The Gleissberg distribution is asymptotically normal. For n > 50, the distribution is approximated by a Gaussian curve. For lower n values, the exact probability is returned (using data in the variable .gleissberg.table Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) References Dallot, S. & M. Etienne, 1990. Une méthode non paramétrique d’analyse des séries en océanogra- phie biologique: les tournogrammes. Biométrie et océanographie - Société de biométrie, 6, Lille, 26-28 mai 1986. IFREMER, Actes de colloques, 10:13-31. Johnson, N.L. & Kotz, S., 1969. Discrete distributions. J. Wiley & sons, New York, 328 pp. regarea 37 See Also .gleissberg.table, turnpoints, turnogram Examples # Until n=50, the exact probability is returned pgleissberg(20, 10, lower.tail=TRUE, two.tailed=FALSE) # For higher n values, it is approximated by a normal distribution pgleissberg(60, 33, lower.tail=TRUE, two.tailed=FALSE) regarea Regulate a series using the area method Description Transform an irregular time series in a regular time series, or fill gaps in regular time series using the area method Usage regarea(x, y=NULL, xmin=min(x), n=length(x), deltat=(max(x) - min(x))/(n - 1), rule=1, window=deltat, interp=FALSE, split=100) Arguments x a vector with time in the irregular series. Missing values are allowed y a vector of same length as x and holding observations at corresponding times xmin allows to respecify the origin of time in the calculated regular time series. By default, the origin is not redefined and it is equivalent to the smallest value in x n the number of observations in the regular time series. By default, it is the same number than in the original irregular time series (i.e., length(x) deltat the time interval between two observations in the regulated time series rule the rule to use for extrapolated values (outside of the range in the initial irregular time series) in the regular time series. With rule=1 (by default), these entries are not calculated and get NA; with rule=2, these entries are extrapolated window size of the window to use for interpolation. By default, adjacent windows are used (window=deltat) interp indicates if matching observations in both series must be calculated (interp=TRUE), or if initial observations are used "as is" in the final regular series (interp=FALSE, by default) split a parameter to optimise calculation time and to avoid saturation of the memory. Very long time series are splitted into smaller subunits. This is transparent for the user. The default value of split=100 should be rarely changed. Give a lower value if the program fails and reports a memory problem during calcula- tion 40 reglin See Also regul, regarea, reglin, regspline, regul.screen, regul.adj, tseries, is.tseries, approxfun Examples data(releve) reg <- regconst(releve$Day, releve$Melosul) plot(releve$Day, releve$Melosul, type="l") lines(reg$x, reg$y, col=2) reglin Regulation of a series using a linear interpolation Description Transform an irregular time series in a regular time series, or fill gaps in regular time series using a linear interpolation Usage reglin(x, y=NULL, xmin=min(x), n=length(x), deltat=(max(x) - min(x))/(n - 1), rule=1) Arguments x a vector with time in the irregular series. Missing values are allowed y a vector of same length as x and holding observations at corresponding times xmin allows to respecify the origin of time in the calculated regular time series. By default, the origin is not redefined and it is equivalent to the smallest value in x n the number of observations in the regular time series. By default, it is the same number than in the original irregular time series (i.e., length(x) deltat the time interval between two observations in the regulated time series rule the rule to use for extrapolated values (outside of the range in the initial irregular time series) in the regular time series. With rule=1 (by default), these entries are not calculated and get NA; with rule=2, these entries are extrapolated Details Observed values are connected by lines and interpolated values are obtained from this "polyline". Value An object of type ’regul’ is returned. It has methods print(), summary(), plot(), lines(), identify(), hist(), extract() and specs(). regspline 41 Note This function uses approx() for internal calculations Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) See Also regul, regarea, regconst, regspline, regul.screen, regul.adj, tseries, is.tseries, approxfun Examples data(releve) reg <- reglin(releve$Day, releve$Melosul) plot(releve$Day, releve$Melosul, type="l") lines(reg$x, reg$y, col=2) regspline Regulation of a time series using splines Description Transform an irregular time series in a regular time series, or fill gaps in regular time series using splines Usage regspline(x, y=NULL, xmin=min(x), n=length(x), deltat=(max(x) - min(x))/(n - 1), rule=1, periodic=FALSE) Arguments x a vector with time in the irregular series. Missing values are allowed y a vector of same length as x and holding observations at corresponding times xmin allows to respecify the origin of time in the calculated regular time series. By default, the origin is not redefined and it is equivalent to the smallest value in x n the number of observations in the regular time series. By default, it is the same number than in the original irregular time series (i.e., length(x) deltat the time interval between two observations in the regulated time series rule the rule to use for extrapolated values (outside of the range in the initial irregular time series) in the regular time series. With rule=1 (by default), these entries are not calculated and get NA; with rule=2, these entries are extrapolated 42 regspline periodic indicates if the time series should be considered as periodic (periodic=TRUE, first value must be equal to the last one). If this is the case, first and second derivates used to calculate spline segments around first and last observations use data in the other extreme of the series. In the other case (periodic=FALSE (by default), derivates for extremes observations are considered to be equal to zero Details Missing values are interpolated using cubic splines between observed values. Value An object of type ’regul’ is returned. It has methods print(), summary(), plot(), lines(), identify(), hist(), extract() and specs(). Note This function uses spline() for internal calculations. However, interpolated values are not al- lowed to be higher than the largest initial observation or lower than the smallest one. Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) References Lancaster, P. & K. Salkauskas, 1986. Curve and surface fitting. Academic Press, England, 280 pp. See Also regul, regarea, regconst, reglin, regul.screen, regul.adj, tseries, is.tseries, splinefun Examples data(releve) reg <- regspline(releve$Day, releve$Melosul) plot(releve$Day, releve$Melosul, type="l") lines(reg$x, reg$y, col=2) regul 45 rule the rule to use for extrapolated values (observations in the final regular time series that are outside the range of observed values in the initial time series). With rule=1 (by default), these entries are not calculated and get NA; with rule=2, these entries are extrapolated (avoid using this option, or use with extreme care!!!) f parameter for the "constant" regulation method. Coefficient giving more weight to the observation at left (f=0, by default), to the observation at right (f=1), or give an intermediate weight to both of these observations (0 < f < 1) during the interpolation (see reglin() periodic parameter for the "spline" regulation method. Indicate if the time series should be considered as periodic (periodic=TRUE, first value must be equal to the last one). If this is the case, first and second derivates used to calculate spline segments around first and last observations use data in the other extreme of the series. In the other case (periodic=FALSE, by default), derivates for extremes observations are considered to be equal to zero window parameter for the "area" regulation method. Size of the window to consider (see regarea()). By default, the mean interval between observations in the initial irregular time series is used. Give the same value as for deltat for working with adjacent windows split other parameter for the "area" method. To optimise calculation time and to avoid to saturate memory, very long time series are splitted into smaller sub- units (see regarea()). This is transparent for the user. The default value of split=100 should be rarely changed. Give a lower value if the program fails and reports a memory problem during calculation specs a specs.regul object returned by the function specs() applied to a regul object. Allows to collect parameterization of the regul() function and to ap- ply them to another regulation reg A regul object as obtained after using the regul() function series the series to plot. By default, series=1, corresponding to the first (or possibly the unique) series in the regul object col (1) for plot(): the two colors to use to draw respectively the initial irregular series and the final regulated series. col=c(1,2) by default. (2) for hist(): the three colors to use to represent respectively the fist bar (exact coincidence), the middle bars (coincidence in a certain tolerance window) and the last bar (values always interpolated). By default, col=c(4,5,2) lty the style to use to draw lines for the initial series and the regulated series, respec- tively. The default style is used for both lines if this argument is not provided plot.pts if plot.pts=TRUE (by default) then points are also drawn for the regulated series (+). Those points that match observations in the initial irregular series, and are not interpolated, are further marked with a circle leg do we add a legend to the graph? By default, leg=FALSE, no legend is added llab the labels to use for the initial irregular and the final regulated series, respec- tively. By default, it is "initial" for the first one and the name of the regu- lation method used for the second one (see methods argument) 46 regul lpos the position of the top-left corner of the legend box (x,y), in the graph coordi- nates ... additional graph parameters label the character to use to mark points interactively selected on the graph. By de- fault, label="#" nclass the number of classes to calculate in the histogram. This is indicative and this value is automatically adjusted to obtain a nicely-formatted histogram. By de- fault, nclass=30 plotit If plotit=TRUE then the histogram is plotted. Otherwise, it is only calculated Details Several irregular time series (for instance, contained in a data frame) can be treated at once. Specify a vector with "constant", "linear", "spline" or "area" for the argument methods to use a different regulation method for each series. See corresponding fonctions (regconst(), reglin(), regspline() and regarea()), respectively, for more details on these methods. Arguments can be saved in a specs object and reused for other similar regulation processes. Func- tions regul.screen() and regul.adj() are useful to chose best time interval in the com- puted regular time series. If you want to work on seasonal effects in the time series, you will better use a "years" time-scale (1 unit = 1 year), or convert into such a scale. If initial time unit is "days" (1 unit = 1 day), a conversion can be operated at the same time as the regulation by specifying units="daystoyears". Value An object of type ’regul’ is returned. It has methods print(), summary(), plot(), lines(), identify(), hist(), extract() and specs(). Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) References Lancaster, P. & K. Salkauskas, 1986. Curve and surface fitting. Academic Press, England, 280 pp. Fox, W.T. & J.A. Brown, 1965. The use of time-trend analysis for environmental interpretation of limestones. J. Geol., 73:510-518. Ibanez, F., 1991. Treatment of the data deriving from the COST 647 project on coastal benthic ecology: The within-site analysis. In: B. Keegan (ed). Space and Time Series Data Analysis in Coastal Benthic Ecology. Pp 5-43. Ibanez, F. & J.C. Dauvin, 1988. Long-term changes (1977-1987) on a muddy fine sand Abra alba - Melinna palmata population community from the Western English Channel. J. Mar. Ecol. Prog. Ser., 49:65-81. See Also regul.screen, regul.adj, tseries, is.tseries, regconst, reglin, regspline, regarea, daystoyears regul.adj 47 Examples data(releve) # The series in this data frame are very irregularly sampled in time: releve$Day length(releve$Day) intervals <- releve$Day[2:61]-releve$Day[1:60] intervals range(intervals) mean(intervals) # The series must be regulated to be converted in a 'rts' or 'ts object rel.reg <- regul(releve$Day, releve[3:8], xmin=9, n=63, deltat=21, tol=1.05, methods=c("s","c","l","a","s","a"), window=21) rel.reg plot(rel.reg, 5) specs(rel.reg) # Now we can extract one or several regular time series melo.ts <- extract(rel.reg, series="Melosul") is.tseries(melo.ts) # One can convert time-scale from "days" to "years" during regulation # This is most useful for analyzing seasonal cycles in a second step melo.regy <- regul(releve$Day, releve$Melosul, xmin=6, n=87, units="daystoyears", frequency=24, tol=2.2, methods="linear", datemin="21/03/1989", dateformat="d/m/Y") melo.regy plot(melo.regy, main="Regulation of Melosul") # In this case, we have only one series in 'melo.regy' # We can use also 'tseries()' instead of 'extract()' melo.tsy <- tseries(melo.regy) is.tseries(melo.tsy) regul.adj Adjust regulation parameters Description Calculate and plot an histogram of the distances between interpolated observations in a regulated time series and closest observations in the initial irregular time series. This allows to optimise the tol parameter Usage regul.adj(x, xmin=min(x), frequency=NULL, deltat, tol=deltat, tol.type="both", nclass=50, col=c(4, 5, 2), plotit=TRUE, ...) Arguments x a vector with times corresponding to the observations in the irregular initial time series 50 regul.screen tol it is possible to tolerate some differences in the time between two matching observations (in the original irregular series and in the regulated series). If tol=0 both values must be strictly identical; a higher value allows some fuzzy matching. tol must be a round fraction of deltat and cannot be higher than it, otherwise, it is adjusted to the closest acceptable value. By default, tol=deltat/5 tol.type the type of window to use for the time-tolerance: "left", "right", "both" (by default) or "none". If tol.type="left", corresponding x values are seeked in a window ]xregul-tol, xregul]. If tol.type="right", they are seeked in the window [xregul, xregul+tol[. If tol.type="both", then they are seeked in the window ]xregul-tol, xregul+tol]. If several observations are in this window, the closest one is used. Finally, if tol.type="none", then all observations in the regulated time series are interpolated (even if exactly matching observations exist!) Details Whatever the efficiency of the interpolation procedure used to regulate an irregular time series, a matching, non-interpolated observation is always better than an interpolated one! With very ir- regular time series, it is often difficult to decide which is the better regular time-scale in order to interpolate as less observations as possible. regul.screen() tests various combinations of number of observation, interval between two observations and position of the first observation and allows to choose the combination that best matches the original irregular time series. To choose also an optimal value for tol, use regul.adj() concurrently. Value A list containing: tol a vector with the adjusted values of tol for the various values of deltat n a table indicating the maximum value of n for all combinations of deltat and xmin to avoid any extrapolation nbr.match a table indicating the number of matching observations (in the tolerance win- dow) for all combinations of deltat and xmin nbr.exact.match a table indicating the number of exactly matching observations (with a tolerance window equal to zero) for all combinations of deltat and xmin Author(s) Philippe Grosjean (〈phgrosjean@sciviews.org〉), Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉) See Also regul.adj, regul releve 51 Examples data(releve) # This series is very irregular, and it is difficult # to choose the best regular time-scale releve$Day length(releve$Day) intervals <- releve$Day[2:61]-releve$Day[1:60] intervals range(intervals) mean(intervals) # A combination of xmin=1, deltat=22 and n=61 seems correct # But is it the best one? regul.screen(releve$Day, xmin=0:11, deltat=16:27, tol=1.05) # Now we can tell that xmin=9, deltat=21, n=63, with tol=1.05 # is a much better choice! releve A data frame of six phytoplankton taxa followed in time at one station Description The releve data frame has 61 rows and 8 columns. Several phytoplankton taxa were numbered in a single station from 1989 to 1992, but at irregular times. Usage data(releve) Format This data frame contains the following columns: Day days number, first observation being day 1 Date strings indicating the date of the observations in "dd/mm/yyyy" format Astegla the abundance of Asterionella glacialis Chae the abundance of Chaetoceros sp Dity the abundance of Ditylum sp Gymn the abundance of Gymnodinium sp Melosul the abundance of Melosira sulcata + Paralia sulcata Navi the abundance of Navicula sp Source Belin, C. & B. Raffin, 1998. Les espèces phytoplanctoniques toxiques et nuisibles sur le littoral français de 1984 à 1995, résultats du REPHY (réseau de surveillance du phytoplancton et des phycotoxines). Rapport IFREMER, RST.DEL/MP-AO-98-16. IFREMER, France. 52 stat.desc specs Collect parameters ("specifications") from one object to use them in another analysis Description ‘specs’ is a generic function for reusing specifications included in an object and applying them in another similar analysis Usage specs(x, ...) Arguments x An object that has "specs" data ... Additional arguments (redefinition of one or several parameters) Value A ‘specs’ object that has the print method and that can be entered as an argument to functions using similar "specifications" See Also regul, tsd stat.desc Descriptive statistics on a data frame or time series Description Compute a table giving various descriptive statistics about the series in a data frame or in a sin- gle/multiple time series Usage stat.desc(x, basic=TRUE, desc=TRUE, norm=FALSE, p=0.95) stat.slide 55 See Also stat.slide, stat.desc Examples data(marbio) stat.pen(marbio[,c(4, 14:16)], basic=TRUE, desc=TRUE) stat.slide Sliding statistics Description Statistical parameters are not constant along a time series: mean or variance can vary each year, or during particular intervals (radical or smooth changes due to a pollution, a very cold winter, a shift in the system behaviour, etc. Sliding statistics offer the potential to describe series on successive blocs defined along the space-time axis Usage stat.slide(x, y, xcut=NULL, xmin=min(x), n=NULL, frequency=NULL, deltat=1/frequency, basic=FALSE, desc=FALSE, norm=FALSE, pen=FALSE, p=0.95) ## S3 method for class 'stat.slide': plot(statsl, stat="mean", col=c(1, 2), lty=c(par("lty"), par("lty")), leg=FALSE, llab=c("series", stat), lpos=c(1.5, 10), ...) ## S3 method for class 'stat.slide': lines(statsl, stat="mean", col=3, lty=1, ...) Arguments x a vector with time data y a vector with observation at corresponding times xcut a vector with the position in time of the breaks between successive blocs. xcut=NULL by default. In the later case, a vector with equally spaced blocs is constructed using xmin, n and frequency or deltat. If a value is provided for xcut, then it supersedes all these other parameters xmin the minimal value in the time-scale to use for constructing a vector of equally spaced breaks n the number of breaks to use frequency the frequency of the breaks in the time-scale deltat the bloc interval touse for constructing an equally-spaced break vector. deltat is 1/frequency 56 stat.slide basic do we have to return basic statistics (by default, it is FALSE)? These are: the number of values (nbr.val), the number of null values (nbr.null), the number of missing values (nbr.na), the minimal value (min), the maximal value (max), the range (range, that is, max-min) and the sum of all non-missing values (sum) desc do we have to return descriptive statistics (by default, it is FALSE)? These are: the median (median), the mean (mean), the standard error on the mean (SE.mean), the confidence interval of the mean (CI.mean) at the p level, the vari- ance (var), the standard deviation (std.dev) and the variation coefficient (coef.var) defined as the standard deviation divided by the mean norm do we have to return normal distribution statistics (by default, it is FALSE)? the skewness coefficient g1 (skewness), its significant criterium (skew.2SE, that is, g1/2.SEg1; if skew.2SE > 1, then skewness is significantly different than zero), kurtosis coefficient g2 (kurtosis), its significant criterium (kurt.2SE, same remark than for skew.2SE), the statistic of a Shapiro-Wilk test of normality (normtest.W) and its associated probability (normtest.p) pen do we have to return Pennington and other associated statistics (by default, it is FALSE)? pos.median, pos.mean, pos.var, pos.std.dev, respectively the median, the mean, the standard deviation and the variance, considering only non-null values; geo.mean, the geometric mean that is, the exponential of the mean of the logarithm of the observations, excluding null values. pen.mean, pen.var, pen.std.dev, pen.mean.var, respectively the mean, the variance, the standard de- viation and the variance of the mean after Pennington’s estimators (see pennington()) p the probability level to use to calculate the confidence interval on the mean (CI.mean). By default, p=0.95 statsl a ’stat.slide’ object, as returned by the function stat.slide() stat the statistic to plot on the graph. You can use "min", "max", "median", "mean" (by default), "pos.median", "pos.mean", "geo.mean" and "pen.mean". The other statistics cannot be superposed on the graph of the series in the current version of the function col the colors to use to plot the initial series and the statistics, respectively. By default, col=c(1,2) lty the style to use to draw the original series and the statistics. The default style is used if this argument is not provided leg if leg=TRUE, a legend box is drawn on the graph llab the labels to use for the legend. By default, it is "series" and the corresponding statistics provided in stat, respectively lpos the position of the top-left corner (x,y) of the legend box in the graph coordi- nates. By default lpos=c(1.5,10) ... additional graph parameters Details Available statistics are the same as for stat.desc() and stat.pen(). The Shapiro-Wilk test of normality is not available yet in Splus and it returns ’NA’ in this environment. If not a priori known, successive blocs can be identified using either local.trend() or decmedian() (see respective functions for further details) trend.test 57 Value An object of type ’stat.slide’ is returned. It has methods print(), plot() and lines(). Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) See Also stat.desc, stat.pen, pennington, local.trend, decmedian Examples data(marbio) # Sliding statistics with fixed-length blocs statsl <- stat.slide(1:68, marbio[, "ClausocalanusA"], xmin=0, n=7, deltat=10) statsl plot(statsl, stat="mean", leg=TRUE, lpos=c(55, 2500), xlab="Station", ylab="ClausocalanusA") # More information on the series, with predefined blocs statsl2 <- stat.slide(1:68, marbio[, "ClausocalanusA"], xcut=c(0, 17, 25, 30, 41, 46, 70), basic=TRUE, desc=TRUE, norm=TRUE, pen=TRUE, p=0.95) statsl2 plot(statsl2, stat="median", xlab="Stations", ylab="Counts", main="Clausocalanus A") # Median lines(statsl2, stat="min") # Minimum lines(statsl2, stat="max") # Maximum lines(c(17, 17), c(-50, 2600), col=4, lty=2) # Cuts lines(c(25, 25), c(-50, 2600), col=4, lty=2) lines(c(30, 30), c(-50, 2600), col=4, lty=2) lines(c(41, 41), c(-50, 2600), col=4, lty=2) lines(c(46, 46), c(-50, 2600), col=4, lty=2) text(c(8.5, 21, 27.5, 35, 43.5, 57), 2300, labels=c("Peripheral Zone", "D1", "C", "Front", "D2", "Central Zone")) # Labels legend(0, 1900, c("series", "median", "range"), col=1:3, lty=1) # Get cuts back from the object statsl2$xcut trend.test Test if an increasing or decreasing trend exists in a time series Description Test if the series has an increasing or decreasing trend, using a non-parametric Spearman test be- tween the observations and time 60 tsd default, series=NULL. It is also possible to use negative indices. In this case, all series are extracted, except those ones stack graphs of each component are either stacked (stack=TRUE, by default), or superposed on the same graph stack=FALSE resid do we have to plot also the "residuals" components (resid=TRUE, by default) or not? Usually, in a stacked graph, you would like to plot the residuals, while in a superposed graph, you would not labels the labels to use for all y-axes in a stacked graph, or in the legend for a su- perposed graph. By default, the names of the components ("trend", "seasonal", "deseasoned", "filtered", "residuals", ...) are used leg only used when stack=FALSE. Do we plot a legend (leg=TRUE or not? lpos position of the upper-left corner of the legend box in the graph coordinates (x,y). By default, leg=c(0,0) n the number of series to extract (from series 1 to series n). By default, n equals the number of series in the ’tsd’ object. If both series and components arguments are NULL, all series and components are extracted and this method has exactly the same effect as tseries components the names or indices of the components to extract. If components=NULL (by default), then all components of the selected series are extracted. It is also possible to specify negative indices. In this case, all components are extracted, except those ones Details To eliminate trend from a series, use "diff" or use "loess" with trend=TRUE. If you know the shape of the trend (linear, exponential, periodic, etc.), you can also use it with the "reg" (regres- sion) method. To eliminate or extract seasonal components, you can use "loess" if the seasonal component is additive, or "census" if it is multiplicative. You can also use "average" with argument order="periodic" and with either an additive or a multiplicative model, although the later method is often less powerful than "loess" or "census". If you want to extract a seasonal cycle with a given shape (for instance, a sinusoid), use the "reg" method with a fitted sinusoidal equation. If you want to identify levels in the series, use the "median" method. To smooth the series, you can use preferably the "evf" (eigenvector filtering), or the "average" methods, but you can also use "me- dian". To extract most important components from the series (no matter if they are cycles -seasonal or not-, or long-term trends), you should use the "evf" method. For more information on each of these methods, see online help of the corresponding decXXXX() functions. Value An object of type ’tsd’ is returned. It has methods print(), summary(), plot(), extract() and specs(). Note If you have to decompose a single time series, you could also use the corresponding decXXXX() function directly. In the case of a multivariate regular time series, tsd() is more convenient because it decompose all times series of a set at once! tsd 61 Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) References Kendall, M., 1976. Time-series. Charles Griffin & Co Ltd. 197 pp. Laloire, J.C., 1972. Méthodes du traitement des chroniques. Dunod, Paris, 194 pp. Legendre, L. & P. Legendre, 1984. Ecologie numérique. Tome 2: La structure des données écologiques. Masson, Paris. 335 pp. Malinvaud, E., 1978. Méthodes statistiques de l’économétrie. Dunod, Paris. 846 pp. Philips, L. & R. Blomme, 1973. Analyse chronologique. Université Catholique de Louvain. Vander ed. 339 pp. See Also tseries, decdiff, decaverage, decmedian, decevf, decreg, decloess, deccensus Examples data(releve) # Regulate the series and extract them as a time series object rel.regy <- regul(releve$Day, releve[3:8], xmin=6, n=87, units="daystoyears", frequency=24, tol=2.2, methods="linear", datemin="21/03/1989", dateformat="d/m/Y") rel.ts <- tseries(rel.regy) # Decompose all series in the set with the "loess" method rel.dec <- tsd(rel.ts, method="loess", s.window=13, trend=FALSE) rel.dec plot(rel.dec, series=5, col=1:3) # An plot series 5 # Extract "deseasoned" components rel.des <- extract(rel.dec, series=3:6, components="deseasoned") rel.des[1:10,] # Further decompose these components with a moving average rel.des.dec <- tsd(rel.des, method="average", order=2, times=10) plot(rel.des.dec, series=3, col=c(2, 4, 6)) # In this case, a superposed graph is more appropriate: plot(rel.des.dec, series=3, col=c(2,4), stack=FALSE, resid=FALSE, labels=c("without season cycle", "trend"), lpos=c(0, 55000)) # Extract residuals from the latter decomposition rel.res2 <- extract(rel.des.dec, components="residuals") 62 tseries tseries Convert a ’regul’ or a ’tsd’ object into a time series Description Regulated series contained in a ’regul’ object or components issued from a time series decompo- sition with ’tsd’ are extracted from their respective object and converted into uni- or multivariate regular time series (’rts’ objects in Splus and ’ts’ objects in R) Usage tseries(x) Arguments x A ’regul’ or ’tsd’ object Value an uni- or multivariate regular time series Note To extract some of the time series contained in the ’regul’ or ’tsd’ objects, use the extract() method Author(s) Philippe Grosjean (〈phgrosjean@sciviews.org〉), Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉) See Also is.tseries, regul, tsd Examples data(releve) rel.regy <- regul(releve$Day, releve[3:8], xmin=6, n=87, units="daystoyears", frequency=24, tol=2.2, methods="linear", datemin="21/03/1989", dateformat="d/m/Y") # This object is not a time series is.tseries(rel.regy) # FALSE # Extract all time series contained in the 'regul' object rel.ts <- tseries(rel.regy) # Now this is a time series is.tseries(rel.ts) # TRUE turnogram 65 mean of the three observation, or the median value, or the sum,... One can also decide not to aggregate observations, but to drop some of them. Hence, one can take only the first or the last observation of the group. All these options can be choosen by defining the argument FUN=.... A simple turnogram correspond to the change of the monotony index with the scale of observation, stating always from the first observation. One could also decide to start from the second, or the third observation for an aggregation of the observations three by three... and result could be somewhat different. A complete turnogram investigates all possibles combinations (observation scale versus starting point for the aggregation) and trace the maximal, minimal and mean curves for the change of the monotony index. It is thus more informative than the simple turnogram. However, it takes much more time to compute. The most obvious use of the turnogram is for the pretreatment of continuously sampled data. It helps in deciding which is the optimal sampling interval for the series to bear as most information as pos- sible while keeping the dataset as small as possible. It is also interesting to compare the turnogram with other functions like the variogram (see vario()) or the spectrogram (see spectrum()). Value An object of type ’turnogram’ is returned. It has methods print(), summary(), plot(), identify() and extract(). Author(s) Frédéric Ibanez (〈ibanez@obs-vlfr.fr〉), Philippe Grosjean (〈phgrosjean@sciviews.org〉) References Dallot, S. & M. Etienne, 1990. Une méthode non paramétrique d’analyse des series en océanogra- phie biologique: les tournogrammes. Biométrie et océanographie - Société de biométrie, 6, Lille, 26-28 mai 1986. IFREMER, Actes de colloques, 10:13-31. Johnson, N.L. & Kotz, S., 1969. Discrete distributions. J. Wiley & sons, New York, 328 pp. Kendall, M.G., 1976. Time-series, 2nd ed. Charles Griffin & co, London. Wallis, W.A. & G.H. Moore, 1941. A significance test for time series. National Bureau of Economic Research, tech. paper n°1. See Also pgleissberg, turnpoints, first, last, vario, spectrum Examples data(bnr) # Let's transform series 4 into a time series (supposing it is regular) bnr4 <- as.ts(bnr[, 4]) plot(bnr4, type="l", main="bnr4: raw data", xlab="Time") # A simple turnogram is calculated bnr4.turno <- turnogram(bnr4) summary(bnr4.turno) # A complete turnogram confirms that "level=3" is a good value: turnogram(bnr4, complete=TRUE) 66 turnpoints # Data with maximum info. are extracted (thus taking 1 every 3 observations) bnr4.interv3 <- extract(bnr4.turno) plot(bnr4, type="l", lty=2, xlab="Time") lines(bnr4.interv3, col=2) title("Original bnr4 (dotted) versus max. info. curve (plain)") # Choose another level (for instance, 6) and extract the corresponding series bnr4.turno$level <- 6 bnr4.interv6 <- extract(bnr4.turno) # plot both extracted series on top of the original one plot(bnr4, type="l", lty=2, xlab="Time") lines(bnr4.interv3, col=2) lines(bnr4.interv6, col=3) legend(70, 580, c("original", "interval=3", "interval=6"), col=1:3, lty=c(2, 1, 1)) # It is hard to tell on the graph which series contains more information # The turnogram shows us that it is the "interval=3" one! turnpoints Analyze turning points (peaks or pits) Description Determine the number and the position of extrema (turning points, either peaks or pits) in a regular time series. Calculate the quantity of information associated to the observations in this series, according to Kendall’s information theory Usage turnpoints(x) ## S3 method for class 'turnpoints': summary(turnp) ## S3 method for class 'turnpoints': plot(turnp, level=0.05, lhorz=TRUE, lcol=2, llty=2, ...) ## S3 method for class 'turnpoints': lines(turnp, max=TRUE, min=TRUE, median=TRUE, col=c(4, 4, 2), lty=c(2, 2, 1), ...) ## S3 method for class 'turnpoints': extract(turnp, n, no.tp=0, peak=1, pit=-1) Arguments x a vector or a time series turnp a ’turnpoints’ object, as returned by the function turnpoints() level the significant level to draw on the graph if lhorz=TRUE. By default, level=0.05, which corresponds to a 5% p-value for the test lhorz if lhorz=TRUE (by default), an horizontal line indicating significant level is drawn on the graph lcol the color to use to draw the significant level line, by default, color 2 is used turnpoints 67 llty the style to use for the significant level line. By default, style 2 is used (dashed line) ... Additional graph parameters max do we plot the maximum envelope line (by default, yes) min do we plot the minimum envelope line (by default, yes) median do we plot the median line inside the envelope (by default, yes) col a vector of three values for the color of the max, min, median lines, respectively. By default col=c(4,4,2) lty a vector of three values for the style of the max, min, median lines, respectively. By default lty=c(2,2,1), that is: dashed, dashed and plain lines n the number of points to extract. By default n=length(turnp), all points are extracted no.tp extract gives a vector representing the position of extrema in the original series. no.tp represents the code to use for points that are not an extremum, by default ’0’ peak the code to use to flag a peak, by default ’1’ pit the code to use to flag a pit, by default ’-1’ Details This function tests if the time series is purely random or not. Kendall (1976) proposed a series of tests for this. Moreover, graphical methods using the position of the turning points to draw automatically envelopes around the data are implemented, and also the drawing of median points between these envelopes. With a purely random time series, one expect to find, on average, a turning point (peak or pit that is, an observation that is preceeded and followed by, respectively, lower or higher observations) every 1.5 observation. Given it is impossible to determine if first and last observation are turning point, it gives: E(p) = 2/3 ∗ (n− 2) with p, the number of observed turning points and n the number of observations. The variance of p is: var(p) = (16 ∗ n− 29)/90 Ibanez (1982) demonstrated that P(t), the probability to observe a turning point at time t is: P (t) = 2 ∗ (1/n(t− 1)! ∗ (n− 1)!) where P is the probability to observe a turning point at time t under the null hypothesis that the time series is purely random, and thus, the distribution of turning points follows a normal distribution. The quantity of information I associated with this probability is: 70 vario References David, M., 1977. Developments in geomathematics. Tome 2: Geostatistical or reserve estimation. Elsevier Scientific, Amsterdam. 364 pp. Delhomme, J.P., 1978. Applications de la théorie des variables régionalisées dans les sciences de l’eau. Bull. BRGM, section 3 n°4:341-375. Matheron, G., 1971. La théorie des variables régionalisées et ses applications. Cahiers du Centre de Morphologie Mathématique de Fontainebleau. Fasc. 5 ENSMP, Paris. 212 pp. See Also disto Examples data(bnr) vario(bnr[, 4]) Index ∗Topic chron regarea, 36 regconst, 38 reglin, 39 regspline, 40 regul, 42 regul.adj, 46 regul.screen, 48 ∗Topic datasets .gleissberg.table, 2 bnr, 6 marbio, 30 marphy, 31 releve, 50 ∗Topic distribution .gleissberg.table, 2 pgleissberg, 35 ∗Topic htest AutoD2, 4 trend.test, 56 turnogram, 62 ∗Topic loess tsd, 58 ∗Topic manip disjoin, 20 first, 25 last, 27 match.tol, 32 regarea, 36 regconst, 38 reglin, 39 regspline, 40 regul, 42 tseries, 61 ∗Topic methods extract, 24 specs, 51 ∗Topic multivariate abund, 2 AutoD2, 4 disto, 21 escouf, 22 ∗Topic nonparametric tsd, 58 ∗Topic smooth decaverage, 10 deccensus, 11 decdiff, 13 decevf, 14 decloess, 15 decmedian, 17 decreg, 18 regarea, 36 regconst, 38 reglin, 39 regspline, 40 regul, 42 tsd, 58 ∗Topic ts AutoD2, 4 buysbal, 7 daystoyears, 8 decaverage, 10 deccensus, 11 decdiff, 13 decevf, 14 decloess, 15 decmedian, 17 decreg, 18 disto, 21 GetUnitText, 26 is.tseries, 27 local.trend, 28 match.tol, 32 regarea, 36 regconst, 38 reglin, 39 regspline, 40 71 72 INDEX regul, 42 regul.adj, 46 regul.screen, 48 stat.desc, 51 stat.pen, 53 stat.slide, 54 trend.test, 56 tsd, 58 tseries, 61 turnogram, 62 turnpoints, 65 vario, 68 ∗Topic univar pennington, 33 .gleissberg.table, 2, 36 abund, 2, 24, 25 acf, 6 approxfun, 39, 40 AutoD2, 4 bnr, 6 buysbal, 7, 9, 20 CenterD2 (AutoD2), 4 CrossD2 (AutoD2), 4 cut, 20 daystoyears, 8, 8, 26, 45 decaverage, 10, 12, 14–16, 18, 19, 60 deccensus, 11, 11, 14–16, 18, 19, 60 decdiff, 11, 12, 13, 15, 16, 18, 19, 60 decevf, 11, 12, 14, 14, 16, 18, 19, 60 decloess, 11, 12, 14, 15, 15, 18, 19, 60 decmedian, 11, 12, 14–16, 17, 19, 29, 56, 60 decreg, 11, 12, 14–16, 18, 18, 60 disjoin, 20 disto, 21, 69 escouf, 4, 22 extract, 24 extract.abund (abund), 2 extract.escouf (escouf), 22 extract.regul (regul), 42 extract.tsd (tsd), 58 extract.turnogram (turnogram), 62 extract.turnpoints (turnpoints), 65 first, 25, 28, 64 GetUnitText, 26 hist.regul (regul), 42 identify.abund (abund), 2 identify.escouf (escouf), 22 identify.local.trend (local.trend), 28 identify.regul (regul), 42 identify.turnogram (turnogram), 62 is.tseries, 27, 37, 39–41, 45, 61 last, 25, 27, 64 lines.abund (abund), 2 lines.escouf (escouf), 22 lines.regul (regul), 42 lines.stat.slide (stat.slide), 54 lines.turnpoints (turnpoints), 65 local.trend, 28, 56, 57 mahalanobis, 6 marbio, 30, 32 marphy, 31, 31 match.tol, 32 pennington, 33, 56 pgleissberg, 2, 35, 64 plot.abund (abund), 2 plot.escouf (escouf), 22 plot.regul (regul), 42 plot.stat.slide (stat.slide), 54 plot.tsd (tsd), 58 plot.turnogram (turnogram), 62 plot.turnpoints (turnpoints), 65 print.abund (abund), 2 print.escouf (escouf), 22 print.regul (regul), 42 print.specs.regul (regul), 42 print.specs.tsd (tsd), 58 print.stat.slide (stat.slide), 54 print.summary.abund (abund), 2 print.summary.escouf (escouf), 22 print.summary.regul (regul), 42 print.summary.tsd (tsd), 58 print.summary.turnogram (turnogram), 62 print.summary.turnpoints (turnpoints), 65 print.tsd (tsd), 58