tailieunhanh - Lecture Advanced Econometrics (Part II) - Chapter 9: Autocorrelation

Lecture "Advanced Econometrics (Part II) - Chapter 9: Autocorrelation" presentation of content: Properties of ols estimator under autocorrelation, disturnabce rprocess, estimation under autocorrelation. | Advanced Econometrics Chapter 9 Autocorrelation Chapter 9 AUTOCORRELATION Non-zero correlation between errors at different observations E stst 0 t s violated assumption 4 E sể ơỀI because the off-diagonals 0. Example log Qt P1 2 log Kt Mog Lt St t 1 2 . T In recession Qị more than inputs St 0 In boom QỲ more than inputs St 0 Autocorrelation also called serial correlation can exist in any research study in which the order of the observations has some meaning it occur most frequently in time-series data. Pure serial correlation is caused by the underlying distribution of the error term of the true specification of an equation. Impure serial correlation is caused by a specification error such as an omitted variable or incorrect functional form. We here study about the pure serial correlation. Nam T. Hoang University of New England - Australia 1 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 9 Autocorrelation I. PROPERTIES OF OLS ESTIMATOR UNDER AUTOCORRELATION à 1. Pols is still unbiased. à 2. Pols is still consistent. 3. Pols is longer best efficient it is less efficient than Pglsvariances. 4. VarCov Pols Ơ2 X X -1 so the standard errors of Pj 5 are biased downward and inconsistent because they are based on incorrect formula. 5. t-statistic R2 overall F-statistics upward. II. DISTURBANCE PROCESS For testing or treatment we need to make more explicit assumption about the type of autocorrelation. The most common is first order autoregressive process AR 1 . St pst -1 ut ut satisfies all classical assumptions. E ut 0 E u ut ƠJ E utu5 0 t s p coefficient of autocorrelation. p stationary of St. Covariance stationary of St the mean variance and all autocovariances of St are constant. Autocovariances Cov st st_ s X Cov st 5 st X a Q t t - 5 Ys Y- 5 So Cov st st-5 X does not depend on t only depend on s. St pst-1 ut p pst-2 ut-1 ut p -2 pip-1 ut Nam T. Hoang University of New England - Australia 2 University of Economics - HCMC - Vietnam Advanced .