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一橋大学

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一橋大学経済研究所

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アジア長期経済統計プロジェクト

Global Economic History Network

政府統計ミクロデータの試行的提供

ICPSR データアーカイブ

AMU and AMU Deviation indicators

Seasonally and Fractionally Differenced Time Series


Naoya Katayama


January 2004
revised August 2006


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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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