The Statistical Distribution of Daily Exchange Rate Price Changes: Dependent Vs Independent Models

This study evaluates recently reported, conflicting, models for the probability distributions of daily exchange rate price changes. The conflicting conclusions arise from differing data sets, noncomparable evaluation criteria, and failures to directly compare the candidate models. This study evaluates the mixed jump diffusion model, a discrete mixture of normals distribution model, and four alternative forms of the generalized autoregressive conditional heteroscedastic (GARCH) model. We estimate parameters for each model using maximum likelihood techniques; the goodness-of-fit for the models is measured using Schwarz’s criteria. In contrast to some recently published results, none of our autoregressive conditional variance models dominated the others; also none of these models consistently dominated the two models that assume returns are independent. In the cases where there is significant first-order heteroscedasticity in the data set, the GARCH models are superior only 50% of the time. In the most recent subperiod (Jan 88 Dec 92) tests show that for three of the four currencies the first-order heteroscedasticities are less pronounced than in prior periods. Curiously, first-order GARCH parameters are significant in cases where tests for first-order heteroscedasticity are not significant; this result suggests that our models may be misspecified. Results indicate that independence should not be overlooked, and future research should not focus on the search for the perfect GARCH model, but attempt to develop models that incorporate the pronounced volatility clustering found in exchange rate price series and the independent behavior that exists in the data. These conclusions are consistent with recent findings related to high frequency (intra-daily) returns.