A local unit root test in mean for financial time series

Abstract

A common financial trading strategy involves exploiting mean-reverting behaviour of paired asset prices. Since a unit root test can be used to determine which pairs of assets appear to exhibit mean-reverting behaviour, we propose a new Bayesian unit root to detect the presence of a local unit root vs. mean-reverting nonlinear smooth transition heteroskedastic alternative hypotheses. This test procedure is based on the posterior odds. For simultaneous estimation and inference, we employ an adaptive Bayesian Markov chain Monte Carlo scheme, which utilizes a mixture prior specification to solve the likelihood identification problem of the smoothing parameter and the autoregressive coefficient with a unit root. The size and power properties of the proposed method are examined via a simulation study. An empirical study examines the mean-reverting behaviour of price differential between stock and future.

Keywords:

• Bayesian hypothesis testing
• smooth transition
• GARCH
• mean reversion
• unit-root test
• Markov chain Monte Carlo method
• posterior odds ratio

Acknowledgements

The authors thank the referee for his insightful comments to improve the quality of the paper. The authors thank Dr Shu-Yu Chen for her preliminary computational work on this project that did not make the current version of the paper.

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Cathy Chen's research is funded by the Ministry of Science and Technology, Taiwan (NSC 101-2118-M-035-006-MY2, MOST 103-2118-M-035-002-MY2). Sangyeol Lee's research is funded in part by the National Research Foundation of Korea (NRF) (MEST No. 2012R1A2A2A01046092).