Tag Archives: GARCH

Modelling the Volatilities of Nigeria Exchange Rate, Inflation Rate, and the Stock Exchange using Time Series Models (Published)

This research modelled the volatilities of Exchange rate, Inflation rate and Nigeria stock exchange. The research fit time series models; Autoregressive Conditional Heteroskedastic (ARCH) model, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, and Exponential GARCH (EGARCH) model, using the monthly data on Exchange rate, Inflation rate, and Stock exchange from January 1990 to December 2017. The return series of the variables shows periods of low and high volatilities, which signify volatility clustering. The parameters of the three variables were estimated and compared using each of univariate GARCH (1, 1) model under consideration i.e. GARCH (1, 1), EGARCH (1, 1) and GJR-GARCH (1, 1) models. Furthermore, the three variables were compared using the GARCH (1, 1) model and it was discovered that Nigeria stock exchange have the best performance, followed by inflation rate and exchange rate in that order.  based on the assumption of 5% level of significant for GARCH (1, 1) model, most of the parameters of the Stock exchange are significant with a p-value less than 0.05, for Exchange rate only the constant (Cst1) and a_1 parameters is significant, for Inflation both Alpha1 and Beta1 are significant. EGARCH (1, 1) indicate that Nigeria stock exchange just as GARCH (1, 1) have the best performance, followed by inflation rate and exchange rate in that order. Only Exchange Rate has leverage volatility effect out of the three variables based on the result from EGARCH model.

Citation: Nasiru M.O., Ajayi A.A., Mustapha A.K  (2021) Modelling the Volatilities of Nigeria Exchange Rate, Inflation Rate, and the Stock Exchange using Time Series Models, International Journal of Mathematics and Statistics StudiesVol.9, No.4, pp.1-13

Keywords: EGARCH, Exchange Rate, GARCH, Inflation Rate, arch, stock exchange


The objective of the paper is to empirically examine the static and dynamic short-run and long-run interaction between the prices (and their volatility)  of natural gas, crude oil, propane and heating oil   in the  US economy, using the Toda and Yamamoto (1995) procedure of Granger’s Causality. Long-run equilibrium relationship is examined using Johansen’s maximum likelihood procedure. The price volatility spill over is also examined between the energy markets using ARCH model. The relationship between prices of energy products may have several implications for the pricing of their derivative products and risk management. This study also examines the efficiency of these markets using the Lo-Mackinlay and Chow-Denning’s (1993) multiple variance ratio tests.   The study uses daily timeseries data from 7th January 1997 to 4th April 2012. To avoid non-stationarity in the variables, all prices are converted into returns form. Based on this data, we found that the return on Henry Hub Natural gas is , well explained by the explanatory variables such as the return of WTI crude oil, Heating oil, propane and the  past values (two days lags) of its own  return. The study found that there is bidirectional causality between Henry Hub Natural Gas return and Heating Oil return. Unidirectional causality is found between three pairs of energy products and the causality runs from Propane return to Crude Oil return, Crude Oil return to Heating Oil return and Heating Oil return to Propane return. Surprisingly, we did not find any causal relationship between Henry Hub Natural Gas return and WTI crude oil return. .There exists a long run equilibrium relationship between the each pair of commodities except between Henry Hub Natural gas and WTI crude oil price. Bidirectional volatility spillover is found between Henry Hub natural gas return and heating oil return, Henry Hub natural gas return and Propane return, WTI crude oil return and Heating Oil return, WTI crude oil return and Propane return. The result from efficient market hypothesis reveals that the energy market in the U.S. does not seem to follow the weak form of efficiency during the study period

Keywords: EGARCH, GARCH, Heating oil, Natural Gas, Toda and Yamamoto causality, Vector Auto Regression, crude oil, volatility clustering, volatility spike