Bootstrap Tests for Fractional Cointegration: A Reappraisal of the Relationship Between Government Popularity and Economic Performance in the UK
The paper proposes a new model of fractional cointegration, and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap. In these procedures, ARFIMA time series models fitted to the data, with resampled residuals, are used to simulate the null hypothesis of non-cointegration. The simulations are used to determine p-values for alternative test statistics, including the F goodness-of-fit statistic, the Durbin-Watson, and estimates of the residual d. The tests are applied to the hypothesis that UK government support, shown in previous work to be a nonstationary fractional process, is not explained by indicators of economic performance. The power properties of the tests are studied by simulations of artificial cointegrating relationships based on the sample data. The tests based solely on the regression residuals, which are shown to be inconsistent for nonstationary alternatives, perform poorly relative to the test based on the F statistic.
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