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Abstract
This paper considers spurious regression between two different types of seasonal time series: one with a deterministic seasonal component and the other with a stochastic seasonal component. When one type of seasonal time series is regressed on the other type and they are independent of each other, the phenomenon of spurious regression occurs. Asymptotic properties of the regression coefficient estimator and the associated regression ‘t-ratio’ are studied. A Monte Carlo simulation study is conducted to confirm the phenomenon of spurious regression and spurious rejection of seasonal cointegration for finite samples.
Acknowledgements
Byeongchan Seong's research was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund; KRF-2006-331-C00052). Sung K. Ahn's work was supported by the Korea Research Foundation Grant (KRF-2005-070-C00022) funded by the Korean Government (MOEHRD).
Notes
†See Johansen Citation14 for the concepts regarding the sequential cointegrating rank test.
‡It would be interesting for future studies to investigate in a future study how the empirical size of a cointegration test depends on these nuisance parameters.