Volatility Analysis of Exchange Rate with Correlated Errors: A Sliding Data Matrix Approach

Author:

Mettle Felix Okoe1ORCID,Kallah-Dagadu Gabriel1ORCID,Aidoo Emmanuel1ORCID,Debrah Godwin1ORCID,Arku Dennis1ORCID

Affiliation:

1. Department of Statistics and Actuarial Science, University of Ghana, Legon, Ghana

Abstract

The main objective of this study is to propose a method of analysing the volatility of a seemingly random walk time series with correlated errors without transforming the series as performed traditionally. The proposed method involves the computation of moving volatilities based on sliding and cumulative data matrices. Our method rests on the assumption that the number of subperiods for which the series is available is the same for all periods and on the assumption that the series observations in each subperiod for all the periods under consideration are a random sample from a particular distribution. The method was successfully implemented on a simulated dataset. A paired sample t -test, Wilcoxon signed rank test, repeated measures (ANOVA), and Friedman tests were used to compare the volatilities of the traditional method and the proposed method under both sliding and cumulative data matrices. It was found that the differences among the average volatilities of the traditional method and sliding and cumulative matrix methods were insignificant for the simulated series that follow the random walk theorem. The implementation of the method on exchange rates for Canada, China, South Africa, and Switzerland resulted in adjudging South Africa to have the highest fluctuating exchange rates and hence the most unstable economy.

Publisher

Hindawi Limited

Subject

Applied Mathematics

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