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

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Author Info
Nabeya, Seiji
Tanaka, Katsuto
Abstract

The authors consider the time series regression model where the error term follows a nonstable autoregressive process and present a general approach for delivering the limiting distribution of a normalized estimator for the autoregressive parameter. The present approach is quite straightforward and leads them to an accurate evaluation of the distribution function, unlike the other approaches suggested in the literature. The authors' 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. Copyright 1990 by The Econometric Society.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 58 (1990)
Issue (Month): 1 (January)
Pages: 145-63
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Handle: RePEc:ecm:emetrp:v:58:y:1990:i:1:p:145-63

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  1. María Presno & Anna López, 2003. "Testing for stationarity in series with a shift in the mean. A fredholm approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 12(1), pages 195-213, June. [Downloadable!] (restricted)
  2. Graham Elliott & James H. Stock, 1992. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," NBER Technical Working Papers 0122, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. James H. Stock, 1991. "Confidence Intervals for the Largest Autoresgressive Root in U.S. Macroeconomic Time Series," NBER Technical Working Papers 0105, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, EconWPA. [Downloadable!]
  5. Ulrich K. Müller, 2002. "Size and Power of Tests for Stationarity in Highly Autocorrelated Time Series," University of St. Gallen Department of Economics working paper series 2002 2002-26, Department of Economics, University of St. Gallen. [Downloadable!]
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