A Score Test for Seasonal Fractional Integration and Cointegration
This paper develops a time domain score statistic for testing fractional integration at zero and seasonal frequencies in quarterly time series models. Further, it introduces the notion of fractional cointegration at different frequencies between two seasonally integrated, I(1) series. In testing problem involving seasonal fractional cointegration, it is argued that the alternative hypothesis is one-sided for which the usual score test may not be appropriate. Therefore, based on the ideas in Silvapulle and Silvapulle (1995), a one-sided score statistics is constructed. A simulation study finds that the score statistic generally has desirable size and power properties in finite samples. The score statistics are applied to the quarterly Australian consumption function. The income and consumption series are found to be I(1) at zero and seasonal frequencies and these two series are not fractionally cointegrated at any frequency.
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