The reason is that it is much more difficult to

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somewhat imprecise results here. The reason is that it is much more difficult to characterize meaningfully “well behaved” data in a time series context. Thus, for example, in contrast to the sharp result that produces the White robust estimator, the theory underlying the Newey- West robust estimator is somewhat ambiguous in its requirement of a bland statement about “how far one must go back in time until correlation becomes unimportant.” ™  14/45
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Part 15: Generalized Regression Applications The Familiar AR(1) Model t =  t-1 + ut , | | < 1 . This characterizes the disturbances, not the regressors. A general characterization of the mechanism producing  history + current innovations  Analysis of this model in particular. The mean and variance and autocovariance  Stationarity. Time series analysis.  Implication: The form of 2 ; Var[] vs. Var[u].  Other models for autocorrelation - less frequently used – AR(1) is the workhorse. ™  15/45
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Part 15: Generalized Regression Applications Building the Model p Prior view: A feature of the data n “Account for autocorrelation in the data.” n Different models, different estimators p Contemporary view: Why is there autocorrelation? n What is missing from the model? n Build in appropriate dynamic structures n Autocorrelation should be “built out” of the model n Use robust procedures (Newey-West) instead of elaborate models specifically for the autocorrelation. ™  16/45
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Part 15: Generalized Regression Applications Model Misspecification ™  17/45
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Part 15: Generalized Regression Applications Implications for Least Squares Familiar results: Consistent, unbiased, inefficient, asymptotic normality The inefficiency of least squares:  Difficult to characterize generally. It is worst in “low frequency” i.e., long period (year) slowly evolving data.  Can be extremely bad. GLS vs. OLS, the efficiency ratios can be 3 or more. A very important exception - the lagged dependent variable yt = xt + yt-1 + t. t = t-1 + ut,. Obviously, Cov[yt-1 ,t ]  0, because of the form of t. How to estimate? IV Should the model be fit in this form? Is something missing? Robust estimation of the covariance matrix - the Newey-West estimator. ™  18/45
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Part 15: Generalized Regression Applications GLS and FGLS Theoretical result for known - i.e., known . Prais- Winsten vs. Cochrane-Orcutt. FGLS estimation: How to estimate ? OLS residuals as usual - first autocorrelation. Many variations, all based on correlation of et and et-1 ™  19/45
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Part 15: Generalized Regression Applications Testing for Autocorrelation A general proposition: There are several tests. All are functions of the simple autocorrelation of the least squares residuals. Two used generally, Durbin-Watson and Lagrange Multiplier The Durbin - Watson test. d 2(1 - r). Small values of d lead to rejection of NO AUTOCORRELATION: Why are the bounds necessary?
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