Exact Moments for Autor1egressive and Random walk Models for a Zero or Stationary Initial Value

Hrishikesh Vinod and L.R. Shenton

Econometric Theory, 1996, vol. 12, issue 3, 481-499

Abstract: For a first-order autoregressive AR(1) model with zero initial value, xi = axi−1,_, + ei, we provide the bias, mean squared error, skewness, and kurtosis of the maximum likelihood estimator â. Brownian motion approximations by Phillips (1977, Econometrica 45, 463–485; 1978, Biometrika 65, 91–98; 1987, Econometrica 55, 277–301), Phillips and Perron (1988, Biometrika 75, 335–346), and Perron (1991, Econometric Theory 7, 236–252; 1991, Econometrica 59, 211–236), among others, yield an elegant unified theory but do not yield convenient formulas for calibration of skewness and kurtosis. In addition to the usual stationary case |α|

Date: 1996
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