Testing for drift in a time series

  • Fabio Busetti
  • 4


    Mendeley users who have this article in their library.
  • N/A


    Citations of this article.


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.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

There are no full text links


  • Fabio Busetti

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free