Volatility Behaviour of Currency Exchange Rates in Selected Countries: Long Memory Effect

Abstract

In financial econometrics, models of long memory, such as ARFIMA models, are compared to short memory models, such as ARIMA models. Given that the researchers were empirically desirous of determining the volatility behaviour of exchange rate returns on African currencies in exchange for the United States dollar, we went beyond ARIMA modeling to test for the incidence or otherwise of fractional integration of all the currencies of selected countries in view of data availability. Hence, the order of integration test was carried out. Three different models of ARFIMA (1, d, q) were subjected to selection isometrics, and the best model was determined on the basis of the smallest ACF, AIC, and SBC values. The chosen models were estimated using the iterative algorithm, which encompasses the conditional maximum likelihood. The existence of a fractional integration was established for exchange rate returns for all the currencies. The study found an incidence of robust long-term memory in the volatility of currencies in selected countries, indicating that shocks to the exchange rates of BWP, KES, EGP, NGN, and TND in relation to the US dollar decay at a slow rate over time. In effect, the volatility in the currency exchange rates of the countries researched is long-lasting. The study also established that the ARFIMA (1, 0.0291, 1), ARFIMA (1, 0.250, 1), ARFIMA (1, 0.016, 1), and ARFIMA (1, 0.338, 1) models are the dominant models for analyzing the daily inter-temporal dynamics associated with the exchange rate returns of BWP, KES, EGP, and TND. Only for the Naira/dollar exchange rate, we found the ARFIMA (1, 0.197, 2) model to be the best. The robustness check of our estimates was ascertained when we estimated the hybrid ARFIMA (p,d,q)-GARCH (1,1) models that were highly significant with larger values of log-likelihood. So, we recommended the ARFIMA (1, d, 2) model for analyzing the long-term volatility of the Naira/dollar exchange rate returns, while the ARFIMA (1, d, 1) model should be applied in analyzing the exchange rate return dynamics of the currencies of the other countries researched. The research findings are significant because they pave the way for policymakers around the exchange rates of the researched countries to determine whether their exchange rate volatility is long-lasting, to use a model-based framework instead of observing only trends, and to revise their policies on exchange rates accordingly.