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Tests for Stochastic Seasonality Applied to Daily Financial Time Series

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We develop tests for seasonal unit roots for daily data by extending the methodology of Hylleberg et al. (‘Seasonal Integration and Cointegration’, Journal of Econometrics, Vol. 44 (1990), No. 1–2, pp. 215–238) and apply our tests to UK and US daily stock market indices. We also investigate a suggestion by Franses and Romijn (‘Periodic Integration in Quarterly Macroeconomic Variables’, International Journal of Forecasting, Vol. 9 (1993), No. 4, pp. 467–476) and Franses (‘A Multivariate Approach to Modelling Univariate Seasonal Time Series’, Journal of Econometrics, Vol. 63 (1994), No. 1, pp. 133–151) and create a price series for each day of the week and test for cointegration amongst these series. Our Monte Carlo experiments indicate that the Hylleberg et al. procedure is robust to autoregressive conditional heteroscedasticity type errors, while the Franses and Romijn procedure is less so. Finally, we employ Harvey’s (Time Series Models, Hemel Hempstead, Harvester Wheatsheaf, 1993) basic structural model to test for the presence of stationary stochastic seasonality. Our results suggest that we can reject the existence of seasonal unit roots at the daily frequency in both of these markets; however, we do find evidence of stationary stochastic seasonality.
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Document Type: Original Article

Affiliations: 1: University of Southampton, 2: ISMA Centre, University of Reading

Publication date: 01 January 1999

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