Distribution of the Least Squares Estimator in a First-Order Autoregressive Model
This paper investigates the finite sample distribution of the least squares estimator of the autoregressive parameter in a first-order autoregressive model. Uniform asymptotic expansion for the distribution applicable to both stationary and nonstationary cases is obtained. Accuracy of the approximation to the distribution by a first few terms of this expansion is then investigated. It is found that the leading term of this expansion approximates well the distribution. The approximation is, in almost all cases, accurate to the second decimal place throughout the distribution. In the literature, there exists a number of approximations to this distribution which are specifically designed to apply in some special cases of this model. The present approximation compares favorably with those approximations and in fact, its accuracy is, with almost no exception, as good as or better than these other approximations. Convenience of numerical computations seems also to favor the present approximations over the others. An application of the finding is illustrated with examples.
|Date of creation:||23 Oct 1996|
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- Perron, P., 1987.
"The Calculation of the Limiting Distribution of the Least Squares Estimator in Near-Integrated Model,"
Cahiers de recherche
8748, Universite de Montreal, Departement de sciences economiques.
- Perron, Pierre, 1989. "The Calculation of the Limiting Distribution of the Least-Squares Estimator in a Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 5(02), pages 241-255, August.
- Peter C.B. Phillips & Pierre Perron, 1986.
"Testing for a Unit Root in Time Series Regression,"
Cowles Foundation Discussion Papers
795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
- Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
- repec:cup:etheor:v:7:y:1991:i:2:p:236-52 is not listed on IDEAS
- Perron, Pierre & Phillips, Peter C. B., 1987.
"Does GNP have a unit root? : A re-evaluation,"
Elsevier, vol. 23(2), pages 139-145.
- Schwert, G. William, 1987. "Effects of model specification on tests for unit roots in macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 20(1), pages 73-103, July.
- Perron, Pierre, 1991.
"A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case without an Intercept,"
Econometric Society, vol. 59(1), pages 211-36, January.
- Perron,P., 1988. "A Continuous Time Approximation To The Unstable First- Order Autoregressive Process: The Case Without An Intercept," Papers 337, Princeton, Department of Economics - Econometric Research Program.
- Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
- Perron, Pierre, 1991. "A Continuous Time Approximation to the Stationary First-Order Autoregressive Model," Econometric Theory, Cambridge University Press, vol. 7(02), pages 236-252, June.
- repec:cup:etheor:v:11:y:1995:i:2:p:306-30 is not listed on IDEAS
- Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-85, March.
- Francis X. Diebold & Marc Nerlove, 1988. "Unit roots in economic time series: a selective survey," Finance and Economics Discussion Series 49, Board of Governors of the Federal Reserve System (U.S.).
- Satchell, Stephen Ellwood, 1984. "Approximation to the Finite Sample Distribution for Nonstable First Order Stochastic Difference Equations," Econometrica, Econometric Society, vol. 52(5), pages 1271-89, September.
- Phillips, Peter C B, 1988.
"Regression Theory for Near-Integrated Time Series,"
Econometric Society, vol. 56(5), pages 1021-43, September.
- Tsui, Albert K. & Ali, Mukhtar M., 1994. "Exact distributions, density functions and moments of the last squares estimator in a first-order autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 17(4), pages 433-454, May.
- Larsson, Rolf, 1995. "The Asymptotic Distributions Of Some Test Statistics in Near-Integrated AR Processes," Econometric Theory, Cambridge University Press, vol. 11(02), pages 306-330, February.
- Stock, James H. & Watson, Mark W., 1989. "Interpreting the evidence on money-income causality," Journal of Econometrics, Elsevier, vol. 40(1), pages 161-181, January.
- Nabeya, Seiji & Tanaka, Katsuto, 1990. "A General Approach to the Limiting Distribution for Estimators in Time Series Regression with Nonstable Autoregressive Errors," Econometrica, Econometric Society, vol. 58(1), pages 145-63, January.
- Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
- James H. Stock & Mark W. Watson, 1987. "Interpreting Evidence on Money-Income Causality," NBER Working Papers 2228, National Bureau of Economic Research, Inc.
- Cryer, Jonathan D. & Nankervis, John C. & Savin, N.E., 1989. "Mirror-Image and Invariant Distributions in ARMA Models," Econometric Theory, Cambridge University Press, vol. 5(01), pages 36-52, April.
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