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Estimation for Autoregressive Time Series with a Root Near 1

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  • Roy, Anindya
  • Fuller, Wayne A

Abstract

Estimators for the parameters of autoregressive time series are compared, emphasizing processes with a unit root or a root close to 1. The approximate bias of the sum of the autoregressive coefficients is expressed as a function of the test for a unit root. This expression is used to construct an estimator that is nearly unbiased for the parameter of the first-order scalar process. The estimator for the first-order process has a mean squared error that is about 40% of that of ordinary least squares for the process with a unit root and a constant mean, and the mean squared error is smaller than that of ordinary least squares for about half of the parameter space. The maximum loss of efficiency is 6n[superscript -1] in the remainder of the parameter space. The estimation procedure is extended to higher-order processes by modifying the estimator of the sum of the autoregressive coefficients. Limiting results are derived for the autoregressive process with a mean that is a linear trend.

Suggested Citation

  • Roy, Anindya & Fuller, Wayne A, 2001. "Estimation for Autoregressive Time Series with a Root Near 1," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 482-493, October.
    • Handle: RePEc:bes:jnlbes:v:19:y:2001:i:4:p:482-93
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