Exponential GARCH Model with Exogenous Covariate for South Sudanese Pounds—USD Exchange Rate Volatility: On the Effects of Conflict on Volatility

Abstract

The empirical models that explain the variation in exchange rate on the ground of macroeconomic fundamentals only are usually bias on the account of omitted variable hence, they cannot decently explain variations in exchange rate. However, if socio-political determinants, like civil wars, violence are incorporated in simple time series specification, the variations of exchange rate can be understood better. Apparently in developing countries like South Sudan where socio-political problems like conflict are most prevalent, the subject remains largely under-explored. This paper therefore, applies ARMA (p, q)-EGARCH (p, q) model with exogenous covariate for SSP-USD exchange rate volatility to examine the effect of conflict as an exogenous variable on exchange rate volatility. The proposed model is ARMA (1, 2)-EGARCH (1, 1) class of models with exogenous covariate in both mean and volatility equations. An empirical application of the proposed model is demonstrated by incorporating the conflict index as covariate in both mean and volatility equations of the proposed model. Parameter estimation was performed using maximum likelihood estimation method. The estimation results with classical maximum likelihood estimation method suggested that exchange rate volatility was persistent as evidenced by higher values of the coefficient of the parameter that accounts for persistence ( β ) in conditional volatility. Furthermore, the parameter for leverage effect in our models was found to be significant. The results showed that the effects of conflict on volatility of SSP-USD was found positive and statistically significant in both equations indicating that higher prevalence of conflict makes the exchange rate to be more volatile.

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“…ARIMA-X( p , i , q ) is an extension of the standard univariate ARIMA( p , i , q ) but the former incorporates exogenous variables which may be crucial in determining the forecast value of the stationary stock returns (Bierens, 1987; Choudhry, 1995; Engle and Patton, 2001). Consequently, following Bierens (1987) and Kur et al (2021), this paper uses ARIMA model that incorporates exogenous variables, ARIMA-X( p , i , q ), to build the conditional mean equation generally specified as follows: where y t is the response variable which must be stationary; ψ 0 is the constant intercept; ϕ i , φ k and θ j are the coefficients of the autoregressive term, k exogenous variables and the moving average respectively; p and q are the lag limits of the autoregressive and the moving average variables respectively; r denotes the number of exogenous variables; x tk represents r number of exogenous variables and ε t is the white-noised residual.…”

“…ARIMA-X(p,i,q) is an extension of the standard univariate ARIMA (p,i,q) but the former incorporates exogenous variables which may be crucial in determining the forecast value of the stationary stock returns (Bierens, 1987;Choudhry, 1995;Engle and Patton, 2001). Consequently, following Bierens (1987) and Kur et al (2021), this paper uses ARIMA model that incorporates exogenous variables, ARIMA-X(p, i, q), to build the conditional mean equation generally specified as follows:…”