Autocorrelation in Linear Regression: Identification, Consequences, and Detection, Summaries of Economics

Download Autocorrelation in Linear Regression: Identification, Consequences, and Detection and more Summaries Economics in PDF only on Docsity! REGRESSION DIAGNOSTIC III: AUTOCORRELATION AUTOCORRELATION  One of the assumptions of the classical linear regression (CLRM) is that the covariance between ui, the error term for observation i, and uj, the error term for observation j, is zero.  Reasons for autocorrelation include: The possible strong correlation between the shock in time t with the shock in time t+1 More common in time series data DURBIN-WATSON (d) TEST  The Durbin-Watson d statistic is defined as: DURBIN-WATSON (d) TEST ASSUMPTIONS  Assumptions of DW test are:  1. The regression model includes an intercept term.  2. The regressors are fixed in repeated sampling.  3. The error term follows the first-order autoregressive (AR-1) scheme:  4. The error term is normally distributed.  5. The regressors do not include the lagged value(s) of the dependent variable, Yt. First-Order Autocorrelation (AR-1 PROCESS) The simplest and most commonly observed is the first-order autocorrelation. Consider the multiple regression model: Yt=β1+β2X2t+β3X3t+β4X4t+…+βkXkt+ut in which the current observation of the error term ut is a function of the previous (lagged) observation of the error term: ut=ρut-1+et DW DECISION RULES aa aa inconclusive inconclusive — oe Seeeereen iil een iil nese Ue Ce Failto Om) A Toi] ahah a CTF] correlation aL DW DECISION RULES  If the statistic lies near the value 2, there is no serial correlation.  But if the statistic lies in the vicinity of 0, there is positive serial correlation.  The closer the d is to zero, the greater the evidence of positive serial correlation.  If it lies in the vicinity of 4, there is evidence of negative serial correlation  Role of thumb the usual range of DW test statistics is 1.5-2.5 DRAWBACKS OF THE DW TEST 1. It may give inconclusive results 2. It is not applicable when a lagged dependent variable is used 3. It can’t take into account higher order of autocorrelation