notes11 - Serial Correlation in Time Series Models ECON 399...

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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 period’s 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 period’s residuals are given by u t = ρu t- 1 + e t • We assume that e t is normally distributed with a mean of zero • We hope that | ρ | < 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 period’s 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 ρ = 0 u t = ρu t- 1 + e t (1) • If ρ 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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notes11 - Serial Correlation in Time Series Models ECON 399...

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