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The Finite-Sample Properties of Autoregressive Approximations of Fractionally-Integrated and Non-Invertible Processes

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  • S. D. Grose

    ()

  • D. S. Poskitt

    ()

Abstract

This paper investigates the empirical properties of autoregressive approximations to two classes of process for which the usual regularity conditions do not apply; namely the non-invertible and fractionally integrated processes considered in Poskitt (2006). In that paper the theoretical consequences of fitting long autoregressions under regularity conditions that allow for these two situations was considered, and convergence rates for the sample autocovariances and autoregressive coefficients established. We now consider the finite-sample properties of alternative estimators of the AR parameters of the approximating AR(h) process and corresponding estimates of the optimal approximating order h. The estimators considered include the Yule-Walker, Least Squares, and Burg estimators.

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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 15/06.

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Length: 35 pages
Date of creation: Jun 2006
Date of revision:
Handle: RePEc:msh:ebswps:2006-15

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Keywords: Autoregression; autoregressive approximation; fractional process;

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References

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  1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
  2. D. Poskitt, 2007. "Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(4), pages 697-725, December.
  3. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
  4. John Barkoulas & Christopher F. Baum, 2003. "Long-Memory Forecasting of U.S. Monetary Indices," Boston College Working Papers in Economics 558, Boston College Department of Economics.
  5. Baillie, Richard T. & Chung, Sang-Kuck, 2002. "Modeling and forecasting from trend-stationary long memory models with applications to climatology," International Journal of Forecasting, Elsevier, vol. 18(2), pages 215-226.
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Cited by:
  1. D.S. Poskitt & Simone D. Grose & Gael M. Martin, 2013. "Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes," Monash Econometrics and Business Statistics Working Papers 25/13, Monash University, Department of Econometrics and Business Statistics.
  2. D.S. Poskitt & Gael M. Martin & Simone D. Grose, 2012. "Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap," Monash Econometrics and Business Statistics Working Papers 8/12, Monash University, Department of Econometrics and Business Statistics.

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