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Testing for Drift in a Time Series


  • Busettti, F.
  • Harvey, A.


The paper presents various tests for assessing whether a time series is subject to drift. We first consider departures from the null hypothesis of no drift against the alternative of a deterministic and/or a non-stationary stochastic drift with initial value zero. We show that the standard t-test on the mean of first differences achieves high power in both directions of the alternative hypothesis and it seems preferable to locally best invariant tests specifically designed to test against a non-stationary drift. The test may be modified, parametrically or nonparametrically to deal with serial correlation. Tests for the null hypothesis of a non-stationary drift are then examined. The simple t-statistic, now standardized by the square root of the sample size, is again a viable alternative, but this time there is no need to correct for serial correlation. We present the asymptotic distribution of the test, provide critical values and compare its performance with that of the standard augmented Dickey-Fuller test procedures. We show that the t-test does not suffer from the large size distortion of the augmented Dickey-Fuller test for cases in which the variance of the nonstationary drift, the signal, is small compared to that of the stationary part of the model. The use of the tests is illustrated with data on global warming and electricity consumption.

Suggested Citation

  • Busettti, F. & Harvey, A., 2002. "Testing for Drift in a Time Series," Cambridge Working Papers in Economics 0237, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:0237
    Note: EM

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    Cited by:

    1. Fabio Busetti & Silvia Fabiani & Andrew Harvey, 2006. "Convergence of Prices and Rates of Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 863-877, December.
    2. Busetti, Fabio & Harvey, Andrew, 2008. "Testing For Trend," Econometric Theory, Cambridge University Press, vol. 24(01), pages 72-87, February.

    More about this item


    Cramér-von Mises distribution; locally best invariant test; stochastic trend; unit root; unobserved components;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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