A STUDY ON THE NIGERIAN NAIRA PER US-DOLLAR EXCHANGE RATE USING ARFIMA-GARCH AND ARFIMA-FIGARCH MODELS
A STUDY ON THE NIGERIAN NAIRA PER US-DOLLAR EXCHANGE RATE USING ARFIMA-GARCH AND ARFIMA-FIGARCH MODELS
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Date
2023-04
Authors
AHMAD, MAIMUNA ALIYU
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Abstract
Autoregressive Fractionally Integrated Moving Average (ARFIMA) model is widely used in the study of long memory processes but it is not suitable for series exhibiting high periods of volatility. Exchange rate series are characterized by periods of stability followed by periods of instability in volatility which can be modeled by Autoregressive Conditional Heteroskedastic (ARCH) model. A parsimonious generalization of the ARCH model is Generalized ARCH (GARCH), but still, neither ARCH nor GARCH can handle the presence of long memory in volatility. This research investigated the presence of long memory both in mean and volatility of the Nigerian Naira per US-Dollar exchange rate series using the hybrid models of ARFIMA, GARCH and Fractionally Integrated GARCH (FIGARCH) origins. Long memory tests were carried out on fractionally differenced and volatility series. The result of GPH estimator indicated the existence of significant Long Memory in the exchange rate data. Classical ARFIMA model was fitted to the data but the results showed the presence of serial autocorrelation and ARCH effects, signifying the limitations of fitting the ARFIMA model. Hybrid ARFIMA models with conditional variance following GARCH and FIGARCH processes were then respectively fitted to the exchange rate series with much improvement in model fitting. Autocorrelation of residuals and ARCH effects were insignificant showing the adequacy of the fitted hybrid models. At the end of the research, the forecasting performance measures of the fitted ARFIMA-GARCH and ARFIMA-FIGARCH models were determined in terms of RMSE. ARFIMA-GARCH demonstrated a better performance.
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A DISSERTATION SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA-NIGERIA, IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTER OF SCIENCE DEGREE IN STATISTICS DEPARTMENT OF STATISTICS, AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA