Modelling the Dependency between Inflation and Exchange Rate Using Copula

Abstract

In this paper, we propose a copula approach in measuring the dependency between inflation and exchange rate. In unveiling this dependency, we first estimated the best GARCH model for the two variables. Then, we derived the marginal distributions of the standardised residuals from the GARCH. The Laplace and generalised t distributions best modelled the residuals of the GARCH(1,1) models, respectively, for inflation and exchange rate. These marginals were then used to transform the standardised residuals into uniform random variables on a unit interval [0, 1] for estimating the copulas. Our results show that the dependency between inflation and exchange rate in Ghana is approximately 7%.

A Copula-Based Approach for Modelling the Dependence between Inflation and Exchange Rate in Kenya

“…There are three widely used methods for evaluating dependence: linear correlation, spearman Rho, and Kendall's tau. Kendall's tau is particularly popular in copula analyses [11]. With Copula C, Kendall's tau for any two random variables X and Y can be written as:…”

“…The estimate of copula parameters can indeed be divided into parametric [11] (such as maximum likelihood), semiparametric (such as the maximum pseudo-likelihood technique [17], SCOMDY [18] (Semiparametric Copula-Based Multivariate Dynamic Models), etc. ), and non-parametric methods.…”

“…The copula model configuration requires accurate marginal distribution specification. If the model of the marginal distributions has not been correctly specified, the copula model will be incorrectly Additionally, to obtain the best fitted marginal distribution, [11], amongst many others, used the parsimonious GARCH (1, 1) model.…”

“…Two researchers [11] and [12] used copulas to model the relationship between inflation and exchange rate. When modeling the relationship between inflation and exchange rates, [12] used data from European banks between 2000 and 2016; [11] used Ghanaian data between 2000 and 2018. Our research departs from their research in three ways.…”

“…1. For estimating the marginal distribution, we employed the ARMA + GARCH model as opposed to [11] who used GARCH. [11] used GARCH because it is well known to capture the volatility and [12] used SARIMA because their data exhibited the presence of seasonality.…”