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. A 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 exist 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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 21 (2002)
Issue (Month): 1 ()
|Contact details of provider:|| Web page: http://www.tandfonline.com/LECR20|
|Order Information:||Web: http://www.tandfonline.com/pricing/journal/LECR20|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Abadir, Karim M., 1993. "Ols Bias in a Nonstationary Autoregression," Econometric Theory, Cambridge University Press, vol. 9(01), pages 81-93, January.
- Perron, P. & Phillips, P.C.B., 1986.
"Does Gnp Have a Unit Root? a Reevaluation,"
Cahiers de recherche
8640, Universite de Montreal, Departement de sciences economiques.
- 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.
- 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, 1986.
"Regression Theory for Near-Integrated Time Series,"
Cowles Foundation Discussion Papers
781R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1987.
- 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.
- 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.
- 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.
- 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.).
- 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.
- 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.
- Knight, J.L. & Satchell, S.E., 1993. "Asymptotic Expansions for Random Walks with Normal Errors," Econometric Theory, Cambridge University Press, vol. 9(03), pages 363-376, June.
- 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.
- repec:cup:etheor:v:9:y:1993:i:3:p:363-76 is not listed on IDEAS
- repec:cup:etheor:v:9:y:1993:i:1:p:81-93 is not listed on IDEAS
- 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.
When requesting a correction, please mention this item's handle: RePEc:taf:emetrv:v:21:y:2002:i:1:p:89-119. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.