tailieunhanh - KInh tế ứng dụng_ Lecture 9: Autocorrelation

Autocorrelation (also called serial correlation) is violation of the assumption that the error terms are not correlated, ., with autocorrelation E(∈i, ∈j) ≠ 0 (∈i ≠ ∈j). That is, the error in the period t is not independent of previous errors. Since we do not know the population line, we do not know the actual errors (∈s), but we estimate them by the residuals (e). Hence a look at the residual plot for a regression that (i) has no autocorrelation; (ii) has positive autocorrelation, and, (iii) has negative autocorrelation. The positive autocorrelation is the common problem in economics. . | Applied Econometrics 1 Autocorrelation Applied Econometrics Lecture 9 Autocorrelation It is never possible to step twice into the same river 1 Introduction Autocorrelation also called serial correlation is violation of the assumption that the error terms are not correlated . with autocorrelation E ei ej 0 ei ej . That is the error in the period t is not independent of previous errors. Since we do not know the population line we do not know the actual errors es but we estimate them by the residuals e . Hence a look at the residual plot for a regression that i has no autocorrelation ii has positive autocorrelation and iii has negative autocorrelation. The positive autocorrelation is the common problem in economics. 2 Consequences of autocorrelation Ordinary least squares OLS estimates in presence of autocorrelation will not have the desirable statistical properties. With positive autocorrelation the standard errors are too low underestimated . This adversely affects the t statistics overestimated so we may reject the null when it is in fact valid. Likewise the R2 and related F - statistic are likely to be overestimated. 3 Detecting autocorrelation There are many ways to check for autocorrelation such as 1 looking at the residual plot 2 observing the correlogram 3 using the runs tests and 4 using the Durbin - Watson statistic. This section presents the runs tests and Durbin - Watson tests. Runs test Autocorrelation can show up in the residual plot. A non - autocorrelation error should jump around the mean zero in a random manner. With positive autocorrelation we are most likely to get with economic data the error is more likely to stay above or below the mean for successive observations. with negative autocorrelation it will jump above and below very frequently . We can formalize this approach in the runs test by counting the number of runs in the data. A run is defined as the succession of positive or negative residual even just one observation counts as a run