11 Autocorrelation and ARCH
In time-series data the disturbance in one period is usually related to the disturbance in the next. Shocks persist: a strike, a cold winter or a change in consumer confidence affects several months, not one. Omitted variables that move slowly, such as tastes or technology, leave a slowly moving pattern in the residuals. A misspecified functional form or missing dynamics does the same, and so does the interpolation used to construct monthly or quarterly series from annual data. The disturbances then violate the assumption \(\Cov (u_t, u_s) = 0\) for \(t \neq s\). This section works out what that does to least squares, how to detect it, how to estimate the model efficiently or with valid standard errors, and how to forecast. It ends with a different kind of time dependence, in the variance rather than the mean: autoregressive conditional heteroscedasticity.
11.2 Consequences for least squares
11.3 Testing for autocorrelation
11.4 Estimation with autocorrelated disturbances
11.5 Forecasting with autocorrelated disturbances
11.6 Autoregressive conditional heteroscedasticity
11.7 Autocorrelation in software
11.8 Practice Problems
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