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Seasonally and Fractionally Differenced Time Series (revised, August 2006)

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Author Info
Naoya Katayama
Abstract

This paper deals with a generalized seasonally integrated autoregressive moving average (SARIMA) model, which allows the two differencing parameters to take on fractional values. After investigating the basic properties of the model, we examine the asymptotic properties of the estimators and statistics without assuming normality. It is shown that the standard asymptotic results hold for the tests and the estimators; that is, the conditional sum of squares estimator is strongly consistent and tends towards normality, the Lagrange multiplier (LM) test and the Wald test statistics are more powerful than the old Portmanteau test statistics, and Godfrey's LM test is also applicable. The finite behaviour of the tests and estimators is also examined by simulations, and the source of differences in behaviour is made clear in terms of the asymptotic theory.

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File URL: http://hi-stat.ier.hit-u.ac.jp/research/discussion/2003/pdf/D03-11.pdf
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Publisher Info
Paper provided by Institute of Economic Research, Hitotsubashi University in its series Hi-Stat Discussion Paper Series with number d03-11.

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Date of creation: Jan 2004
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Handle: RePEc:hst:hstdps:d03-11

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Related research
Keywords: Fractional differencing; Lagrange multiplier test; Long memory; Seasonal differencing; Seasonal persistence;

Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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  1. Paramsothy Silvapulle, 2001. "A Score Test For Seasonal Fractional Integration And Cointegration," Econometric Reviews, Taylor and Francis Journals, vol. 20(1), pages 85-104. [Downloadable!] (restricted)
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  2. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August. [Downloadable!]
  3. Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.
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This page was last updated on 2009-11-15.

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