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

Listed author(s):
  • Vinod, H.D.
  • Shenton, L.R.

For a first-order autoregressive AR(1) model with zero initial value, x i = ax i−1 ,_, + e i , 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|

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 12 (1996)
Issue (Month): 03 (August)
Pages: 481-499

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Handle: RePEc:cup:etheor:v:12:y:1996:i:03:p:481-499_00
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