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Unformatted text preview: Serial Correlation in Time Series Models ECON 399 Neil Hepburn Contents 1 The Nature of Serial Correlation 1 2 Detection of Serial Correlation 2 2.1 Testing When Regressors are not Strictly Exogenous . . . . . . . 4 2.2 Higher Order Autocorrelation . . . . . . . . . . . . . . . . . . . . 5 3 Remedial Measures 5 1 The Nature of Serial Correlation The Nature of Serial Correlation Serial correlation exists when the residuals in one time period are affected by residuals in one or more previous time periods Serial Correlation is often referred to as Autocorrelation The number of previous periods that affect the current residuals is referred to as the order An AR(1) process has only the previous periods residuals influencing the current residuals, an AR(2) process has two lags, and so on. An AR(q) Process In an AR(1) process, the current periods residuals are given by u t = u t- 1 + e t We assume that e t is normally distributed with a mean of zero We hope that | | < 1 1 2 Detection of Serial Correlation Detection of Serial Correlation Just as with heteroscedasticity there are fairly straight forward tests for serial correlation The simplest to understand is the Breusch-Godfrey test The null hypothesis is that there is no serial correlation This test involves regressing current residuals on previous periods resid- uals (up to the order of autocorrelation being tested) The Breusch-Godfrey Test Under the null hypothesis, when we estimate the following we should have = 0 u t = u t- 1 + e t (1) If 6 = 0, then we have a problem with autocorrelation The problem that we face is that simply estimating Equation (1) will not be efficient There is a simple way around this Testing When All Regressors are Strictly Exogenous The simplest case to think about is one where the regressors are strictly exogenous There are no lagged dependent variables None of the x s are endogenous regressors The Breusch-Godfrey test can be done by regressing the current period residuals on the original regressors and the lagged residuals...
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- Spring '11