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Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes

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  • DUFOUR, Jean-Marie
  • TORRÈS, Olivier

Abstract

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.

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File URL: http://hdl.handle.net/1866/336
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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2000-12.

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Length: 34 pages
Date of creation: 2000
Date of revision:
Handle: RePEc:mtl:montde:2000-12

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Keywords: time series; Markov ocess; autoregressive ocess; autocorrelation; dynamic model; distributed lag model; two-sided autoregression; intercalary indendence; exact test; finite-same test; Ogawara-Hannan; investment;

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References

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  1. Campbell, Bryan & Dufour, Jean-Marie, 1997. "Exact Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 151-73, February.
  2. Savin, N.E., 1984. "Multiple hypothesis testing," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 14, pages 827-879 Elsevier.
  3. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Tests in Single Equation Autoregressive Distributed Lag Models," Cahiers de recherche 9549, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. Marc Hallin & Jean-Marie Dufour & Ivan Mizera, 1998. "Generalized run tests for heteroscedastic time series," ULB Institutional Repository 2013/2077, ULB -- Universite Libre de Bruxelles.
  5. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-94, March.
  6. N.E. Savin & Allan Wurtz, 1996. "The Effect of Nuisance Parameters on the Power of LM Tests in Logit and Probit Models," Econometrics 9606002, EconWPA.
  7. Craig Burnside & Martin Eichenbaum, 1994. "Small Sample Properties of Generalized Method of Moments Based Wald Tests," NBER Technical Working Papers 0155, National Bureau of Economic Research, Inc.
  8. Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
  9. Miyazaki, Shigetaka & Griffiths, William E., 1984. "The properties of some covariance matrix estimators in linear models with AR(1) errors," Economics Letters, Elsevier, vol. 14(4), pages 351-356.
  10. Maasoumi, Esfandiar, 1992. "Fellow's opinion : Rules of thumb and pseudo-science," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 1-4.
  11. Dufour, J.-M., 1986. "Nonlinear hypotheses, inequality restrictions and non-nested hypotheses: Exact simultaneous tests in linear regressions," CORE Discussion Papers 1986016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. DeJong, David N. & Nankervis, John C. & Savin, N. E. & Whiteman, Charles H., 1992. "The power problems of unit root test in time series with autoregressive errors," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 323-343.
  13. Park, Rolla Edward & Mitchell, Bridger M., 1980. "Estimating the autocorrelated error model with trended data," Journal of Econometrics, Elsevier, vol. 13(2), pages 185-201, June.
  14. Nankervis, John C & Savin, N E, 1996. "The Level and Power of the Bootstrap t Test in the AR(1) Model with Trend," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 161-68, April.
  15. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
  16. Burnside, Craig & Eichenbaum, Martin S, 1996. "Small-Sample Properties of GMM-Based Wald Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 294-308, July.
  17. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
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Citations

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Cited by:
  1. Dufour, J.M. & Khalaf, L. & Bernard, J.T. & Genest, I., 2001. "Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects," Cahiers de recherche 2001-08, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Gossner, Olivier & Schlag, Karl H., 2013. "Finite-sample exact tests for linear regressions with bounded dependent variables," Journal of Econometrics, Elsevier, vol. 177(1), pages 75-84.
  3. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Exact tests for contemporaneous correlation of disturbances in seemingly unrelated regressions," Journal of Econometrics, Elsevier, vol. 106(1), pages 143-170, January.
  4. Luger, Richard, 2003. "Exact non-parametric tests for a random walk with unknown drift under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 115(2), pages 259-276, August.
  5. Jean-Marie Dufour & Abdeljelil Farhat, 2001. "Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions," CIRANO Working Papers 2001s-56, CIRANO.

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