In this paper, we focused on Multivariate Generalised Autoregressive Conditional Heteroscedasticity models for volatility series using response vector of variances. The paper aimed at developing alternative multivariate GARCH models characterised by either autoregressive or moving average process. Isolated Multivariate Generalised Conditional Heteroscedasticity, ISO-MGARCH (p,0) models and Isolated Multivariate Generalised Conditional Heteroscedasticity, ISO-MGARCH(0, q) models are identified from MGARCH (p, q) model under specific conditions. To ascertain the models applicability, the isolated univariate and multivariate GARCH (2,0) models were fitted to volatility measures of Nigeria average, urban and rural consumer price indices from January 1995 to December 2019. The volatility series were subjected to autocorrelation and partial autocorrelation checks as applicable to stationary autoregressive moving average process, where single autoregressive and moving average models are identified under certain conditions. This justified the isolation of pure autoregressive and pure moving average MGARCH models. Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Schwarz’s Information criterion (SIC) compare the isolated multivariate GARCH models with the existing univariate GARCH models, and the results revealed the same comparative advantage in capturing volatility series.
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