Modelling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized Arch Model

TLDR

The study proposes a multivariate time‑series model that allows time‑varying conditional variances and covariances while keeping conditional correlations constant. The model extends the seemingly unrelated regression framework by modeling each conditional variance as a univariate GARCH process, enabling heteroskedasticity and allowing comparison of estimates across pre‑EMS and post‑EMS periods. Applied to five European‑US dollar exchange rates, the model shows that currency comovements were significantly higher after the EMS inception compared to the pre‑EMS free‑float period.

Abstract

A multivariate time series model with time varying conditional variances and covariances but with constant conditional correlations is proposed. In a multivariate regression framework, the model is readily interpreted as an extension of the seemingly unrelated regression (SUR) model allowing for heteroskedasticity. Each of the conditional variances are parameterized as a univariate generalized autoregressive conditional heteroskedastic (GARCH) process. The descriptive validity of the model is illustrated for a set of 5 nominal European-US dollar exchange rates following the inception of the European Monetary System (EMS). EMS results are compared to estimates obtained for the same model using data over the pre-EMS period, July 1973 to March 1979. When compared to the pre-EMS free float period, the comovements between the currencies are found to be significantly higher over the later period.