Econometrica: Jan 1990, Volume 58, Issue 1

A General Approach to the Limiting Distribution for Estimators in Time Series Regression with Nonstable Autoregressive Errors

https://doi.org/0012-9682(199001)58:1<145:AGATTL>2.0.CO;2-4
p. 145-163

Katsuto Tanaka, Seiji Nabeya

We consider the time series regression model where the error term follows a nonstable autoregressive process, and present a general approach for deriving the limiting distribution of a normalized estimator for the autoregressive parameter. The present approach is quite straightforward and leads us to an accurate evaluation of the distribution function, unlike the other approaches suggested in the literature. Our methodology is illustrated and percent points are tabulated. The present approach produces a good approximation method for the finite sample distribution and also provides an accurate evaluation of the limiting powers of some unit root tests under a sequence of local alternatives.

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