M-Estimation for Nearly Non-Stationary Autoregressive Time Series.
WASHINGTON UNIV SEATTLE DEPT OF STATISTICS
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The nearly nonstationary first order autoregression is a sequence of processes where the autoregressive coefficient tends to 1 as n approaches infinity. M-estimates of the autoregressive coefficient are considered. The process is allowed to be nongaussian, but a 2 delta moment condition is assumed. The limiting distribution is not the usual normal limit but is characterized as a ratio of two stochastic integrals. The asymptotically most efficient M-estimate is not given by maximum likelihood. However, it is shown that the loss of efficiency in using maximum likelihood is no worse than about 20 whereas the usual least squares estimator can have arbitrarily low efficiency. Keywords M estimation time series, autoregressive non stationary.
- Statistics and Probability