EconometricanalysisTimeSeriesData文件材料.ppt

* * * * * * * * * * * * * * * Applied Econometrics William Greene Department of Economics Stern School of Business Applied Econometrics 26. Time Series Data For example,… In parts… Studying the Frequency Domain Cannot identify the number of terms Cannot identify frequencies from the time series Deconstructing the variance, autocovariances and autocorrelations Contributions at different frequencies Apparent large weights at different frequencies Using Fourier transforms of the data Does this provide “new” information about the series? Autocorrelation in Regression Yt = b’xt + εt Cov(εt, εt-1) ≠ 0 Ex. RealConst = a + bRealIncome + εt U.S. Data, quarterly, 1950-2000 Autocorrelation How does it arise? What does it mean? Modeling approaches Classical – direct: “Corrective” Estimation that accounts for autocorrelation Inference in the presence of autocorrelation Contemporary – structural Model the source Incorporate the time series aspect in the model Stationary Time Series zt = b1yt-1 + b2yt-2 + … + bPyt-P + et Autocovariance: γk = Cov[yt,yt-k] Autocorrelation: ?k = γk / γ0 Stationary series: γk depends only on k, not on t Weak stationarity: E[yt] is not a function of t, E[yt * yt-s] is not a function of t or s, only of |t-s| Strong stationarity: The joint distribution of [yt,yt-1,…,yt-s] for any window of length s periods, is not a function of t or s. A condition for weak stationarity: The smallest root of the characteristic polynomial: 1 - b1z1 - b2z2 - … - bPzP = 0, is greater than one. The unit circle Complex roots Example: yt = ?yt-1 + ee, 1 - ?z = 0 has root z = 1/ ?, | z | 1 = | ? | 1. Stationary vs. Nonstationary Series OLS vs. GLS OLS Unbiased? Consistent: (Except in the presence of a lagged dependent variable) Inefficient GLS Consistent and efficient +----------------------------------------------------+ | Ordinary least squares regression | | LHS=REALCONS Mean = 2999.436 | | Autocorrel Durbin-Wat