University of Birmingham

Regression-Based Unit Root Tests with Recursive Mean Adjustment for Seasonal and Non-Seasonal Time Series

Email address: R.Taylor@bham.ac.uk

Abstract:
This paper considers tests for (seasonal) unit roots in a univariate time series pro-cess. We construct test statistics which are similar with respect to both the initial values of the process and the possibility of (differential seasonal) drift under the (sea-sonal) unit root null. In contrast to existing approaches, where similar inference is obtained by (seasonally) de-meaning and (seasonally) de-trending the process, utiliz-ing all available sample data, we adopt the technique of recursive (seasonal) de-meaning and (seasonal) de-trending of the process. Representations are derived for the limiting distributions of the proposed test statistics under both the (seasonal) unit root null and under near (seasonal) integration. In the non-seasonal case the asymptotic local power of the proposed statistic is compared with the QD de-trended DF tests of Elliott et al. (1996) and Elliott (1999), and found to outperform both of these approaches in the case where the initial observation is drawn from the stationary distribution of the process. We also ¯nd in the case of quarterly data that our proposed statistics display superior ¯nite sample size and power properties to the conventional seasonal unit root statistics of Hylleberg et al. (1990) and variants of such tests constructed using simple symmetric least squares and weighted symmetric least squares estimation.

PDF file of paper: taylor.pdf

Session: Time Series Analysis

Time: Friday, 6 July, 8:45am - 10:15am

Room: B