The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model

Abstract

Abstract We study temporal volatility patterns in seven nominal dollar spot exchange rates, all of which display strong evidence of autoregressive conditional heteroskedasticity (ARCH). We first formulate and estimate univariate models, the results of which are subsequently used to guide specification of a multivariate model. The key element of our multivariate approach is exploitation of factor structure, which facilitates tractable estimation via a substantial reduction in the number of parameters to be estimated. Such a latent-variable model is shown to provide a good description of multivariate exchange rate movements: the ARCH effects capture volatility clustering, and the factor structure captures commonality in volatility movements across exchange rates. In this paper we specify and estimate a multivariate time-series model with an underlying latent variable whose innovations display autoregressive conditional heteroskedasticity (ARCH). Various aspects of this factor-analytic approach are sketched in Diebold (1986) and Diebold and Nerlove (1987); here we provide a more complete exposition, propose a new estimation procedure, and present a detailed substantive application to movements in seven major dollar spot exchange rates. To guide multivariate specification, we begin with a univariate analysis and relate the results to apparent random walk behaviour, leptokurtic unconditional distributions and convergence to normality under temporal aggregation.