This study looks at a possible combination of both the ARMA and ARCH-types models to form a single model such as ARMA-ARCH that will completely model the linear and non-linear features of financial data. The data used for this study are daily closing share prices of First Bank of Nigeria plc from January 4, 2000 to December 31, 2013 and were obtained from the Nigerian Stock Exchange. The share price series was found to be nonstationary while the returns series which is the first difference of log of the share price series was found to be stationary. This study provides evidence to show that ARMA(2,2) model is found to be adequate in the modeling the linear dependence in the returns of First Bank of Nigeria while the ARCH(1) model is adequate in modeling the changing conditional variance in the returns of First Bank of Nigeria. Therefore, combining the two models results in a single ARMA(2,2)-ARCH(1) model that completely models the returns series of First Bank of Nigeria.
Keywords: ARMA model; ARCH model; linear dependence; conditional variance; First Bank of Nigeria
IntroductionLinear time series models are not good models for describing certain characteristics of a volatility series in that in ARMA models, it is assumed that linear dependence is present in the observations. Also, assumption of homoscedasticity is not appropriate when using financial data. For instance, returns typically exhibit linear dependence as such ARMA models are natural candidates for modeling the linear dependence in financial data. However, financial data frequently exhibit volatility clustering leading to the violation of the assumption of constant variance thus making a way for the