Stochastic volatility models for exchange rates and their estimation using quasi-maximum-likelihood methods: an application to the South African Rand

M. Kulikova and D. Taylor

Journal of Applied Statistics, 2013, vol. 40, issue 3, 495-507

Abstract: This paper is concerned with the volatility modeling of a set of South African Rand (ZAR) exchange rates. We investigate the quasi-maximum-likelihood (QML) estimator based on the Kalman filter and explore how well a choice of stochastic volatility (SV) models fits the data. We note that a data set from a developing country is used. The main results are: (1) the SV model parameter estimates are in line with those reported from the analysis of high-frequency data for developed countries; (2) the SV models we considered, along with their corresponding QML estimators, fit the data well; (3) using the range return instead of the absolute return as a volatility proxy produces QML estimates that are both less biased and less variable; (4) although the log range of the ZAR exchange rates has a distribution that is quite far from normal, the corresponding QML estimator has a superior performance when compared with the log absolute return.

Date: 2013
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DOI: 10.1080/02664763.2012.740791

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