Testing for Drift in a Time Series

Fabio Busetti and Andrew Harvey

Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge

Abstract: 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.

Keywords: Cramér-von Mises distribution; locally best invariant test; stochastic trend; unit root; unobserved components (search for similar items in EconPapers)
JEL-codes: C22 C52 (search for similar items in EconPapers)
Pages: 20
Date: 2002-12
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-rmg
Note: EM
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://files.econ.cam.ac.uk/repec/cam/pdf/wp0237.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:0237

Access Statistics for this paper

More papers in Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge
Bibliographic data for series maintained by Jake Dyer ().