Testing for seasonal unit roots by frequency domain regression
AbstractThis paper develops univariate seasonal unit root tests based on spectral regression estimators. An advantage of the frequency domain approach is that it enables serial correlation to be treated non-parametrically. We demonstrate that our proposed statistics have pivotal limiting distributions under both the null and near seasonally integrated alternatives when we allow for weak dependence in the driving shocks. This is in contrast to the popular seasonal unit root tests of, among others, Hylleberg et al. (1990) which treat serial correlation parametrically via lag augmentation of the test regression. Moreover, our analysis allows for (possibly infinite order) moving average behaviour in the shocks, while extant large sample results pertaining to the Hylleberg et al. (1990) type tests are based on the assumption of a finite autoregression. The size and power properties of our proposed frequency domain regression-based tests are explored and compared for the case of quarterly data with those of the tests of Hylleberg et al. (1990) in simulation experiments.
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Bibliographic InfoPaper provided by University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 10/02.
Date of creation: Sep 2010
Date of revision:
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Seasonal unit root tests; moving average; frequency domain regression; spectral density estimator; Brownian motion;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-03-20 (All new papers)
- NEP-ETS-2010-03-20 (Econometric Time Series)
- NEP-FMK-2010-03-20 (Financial Markets)
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