TESTING FOR TREND; TESTING FOR TREND; FABIO BUSETTI AND ANDREW HARVEY

The paper examines various tests for assessing whether a time series model requires a slope component. We first consider the simple t-test on the mean of first differences and show that it achieves high power against the alternative hypothesis of a stochastic nonstationary slope and also against a p...

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Bibliographic Details
Published in:Econometric theory 2008-02, Vol.24 (1), p.72
Main Authors: Busetti, Fabio, Harvey, Andrew
Format: Article
Language:English
Subjects:
Econometrics
Hypotheses
Hypothesis testing
Monte Carlo simulation
Nonparametric statistics
Normal distribution
Power
Stochastic models
Test methods
Time series
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Summary:The paper examines various tests for assessing whether a time series model requires a slope component. We first consider the simple t-test on the mean of first differences and show that it achieves high power against the alternative hypothesis of a stochastic nonstationary slope and also against a purely deterministic slope. The test may be modified, parametrically or nonparametrically, to deal with serial correlation. Using both local limiting power arguments and finite-sample Monte Carlo results, we compare the t-test with the nonparametric tests of Vogelsang (1998, Econometrica 66, 123-148) and with a modified stationarity test. Overall the t-test seems a good choice, particularly if it is implemented by fitting a parametric model to the data. When standardized by the square root of the sample size, the simple t-statistic, with no correction for serial correlation, has a limiting distribution if the slope is stochastic. We investigate whether it is a viable test for the null hypothesis of a stochastic slope and conclude that its value may be limited by an inability to reject a small deterministic slope. [PUBLICATION ABSTRACT]
ISSN:0266-4666
1469-4360