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Journal of Applied Mathematics
Volume 2016, Article ID 5061749, 9 pages
Research Article

A Three-State Markov-Modulated Switching Model for Exchange Rates

Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria

Received 30 July 2016; Revised 26 September 2016; Accepted 5 October 2016

Academic Editor: Wei-Chiang Hong

Copyright © 2016 Idowu Oluwasayo Ayodeji. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Several authors have examined the long swings hypothesis in exchange rates using a two-state Markov switching model. This study developed a model to investigate long swings hypothesis in currencies which may exhibit a -state pattern. The proposed model was then applied to euros, British pounds, Japanese yen, and Nigerian naira. Specification measures such as AIC, BIC, and HIC favoured a three-state pattern in Nigerian naira but a two-state one in the other three currencies. For the period January 2004 to May 2016, empirical results suggested the presence of asymmetric swings in naira and yen and long swings in euros and pounds. In addition, taking as the benchmark for smoothing probabilities, choice models provided a clear reading of the cycle in a manner that is consistent with the realities of the movements in corresponding exchange rate series.