Time Series Modelling of Daily Log-Price Ranges for Sf/Usd and Usd/Gbp

Abstract

The aim of this paper is to model the dynamic evolution of daily log-price ranges for two foreign exchange rates, SF/USD and USD/GBP. Following Chou (2001),we adopt the CARR model, which is identical to the ACD model of Engle & Russell (1998). Log-price ranges are highly efficient measures of daily volatilities and hence our empirical results provide insights into the volatility dynamics for SF/USD and USD/GBP. We find that both series are highly persistent, and in particular, USD/GBP calls for a long memory specification in the form of a fractionally integrated CARR model. Semi-parametric and parametric models are estimated, and the parametric (fractionally integrated) CARR with a Gamma distribution is the preferred model. However, the estimation results of the simple semi-parametric procedure (QMLE) are virtually identical to the results of the preferred parametric models.

Keywords: Daily Price Range, Foreign Exchange Rate Volatility, Persistency, CARR, FICARR

JEL Classification: C22, G15