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Testing for Drift in a Time Series


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  • 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.

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Bibliographic Info

Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0237.

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Length: 20
Date of creation: Dec 2002
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Handle: RePEc:cam:camdae:0237

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Related research

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

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Cited by:
  1. Fabio Busetti & Silvia Fabiani & Andrew Harvey, 2006. "Convergences of prices and rates of inflation," Temi di discussione (Economic working papers) 575, Bank of Italy, Economic Research and International Relations Area.
  2. Busetti, Fabio & Harvey, Andrew, 2008. "Testing For Trend," Econometric Theory, Cambridge University Press, vol. 24(01), pages 72-87, February.


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