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

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  • 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.

Suggested Citation

  • Naoya Katayama, 2004. "Seasonally and Fractionally Differenced Time Series (revised, August 2006)," Hi-Stat Discussion Paper Series d03-11, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:hstdps:d03-11
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    More about this item

    Keywords

    Fractional differencing; Lagrange multiplier test; Long memory; Seasonal differencing; Seasonal persistence;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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