Modelling exchange rate volatility with random level shifts

ABSTRACT

Recent literature has shown that the volatility of exchange rate returns displays long memory features. It has also been shown that if a short memory process is contaminated by level shifts, the estimate of the long memory parameter tends to be upward biased. In this article, we directly estimate a random level shift model to the logarithm of the absolute returns of five exchange rates series, in order to assess whether random level shifts (RLSs) can explain this long memory property. Our results show that there are few level shifts for the five series, but once they are taken into account the long memory property of the series disappears. We also provide out-of-sample forecasting comparisons, which show that, in most cases, the RLS model outperforms popular models in forecasting volatility. We further support our results using a variety of robustness checks.

KEYWORDS:

• Random level shifts
• long-memory
• forecasting
• volatility

JEL CLASSIFICATION:

• C22
• F37

Acknowledgements

We thank Rasmus Varneskov for sharing his code to estimate the models analysed in Varneskov and Perron (2015) and two referees for useful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Given the relatively large nuber of breaks due to the long span of data available, note that for CAD/USD we use only the last 4500 observations and for GBP/USD the last 5000.

² For the estimation, we used the Matlab codes based on MS_Regress, the MATLAB Package for Markov Regime Switching Models by Marcelo Perlin.