Special classes of multivariate generalized autoregressive conditional heteroscedasticity models for volatility series

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.

Bollerslev, T., Engle, R.F. and Wooldridge, J.M. (1988). A Capital Asset Pricing Model with Time-Varying Covariances, The Journal of Political Economy, 96, 116-131.

Chepngetich Mercy and John Kihoro (2015). Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series, Science Journal ofApplied Mathematics and Statistics, 3(3), 124-135.

Engle, R.F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50(4), 987-1007.

Engle, R.F, Ng, V.K. and Rothschild, M. (1990). Asset Pricing with a Factor ARCH Covariance Structure: Empirical Estimates for Treasury Bills, Journal of Econometrics, 45, 213-238.

Engle, R.F. and Ng, V.K. (1993). Measuring and Testing the Impact of News on Volatility, Journal of Finance, 48(5), 1749 – 1778.

Engle, R.F. and Kroner K.F. (1995). Multivariate Simultaneous Generalised ARCH, Econometric Theory, 11, 122-150.

Eric, Z. and Jiahui, W. (2006). Modelling Financial Time Series with S-PLUS, Springer, New York.

Gujarati, D.N. and Porter, D.C. (2009). Basic Econometrics, Fifth Edition, Irwin McGraw-Hill, London.

Hansson, B. and Hordahl (1998). Testing the Conditional CAPM Using Multivariate GARCH-M, Applied Financial Economics, 8, 377-388.

Kawakastsu, H. (2006). Matrix Exponential GARCH, Journal of Econometrics, 134, 95-128.

Lanne, M. and Saikkonen, P. (2007). A Multivariate Generalised Orthogonal Factor GARCH Model, Journal of Business and Economic Statistics, 25, 61-75.

Luc, B., Sebastien L. and Jeroen, V.K.R. (2006). Multivariate GARCH Models: A Survey, Journal of Applied Econometrics, 21, 79-109.

Mittnik, S. (1989). Multivariate Time Series Analysis with State Space, Computers Math. Application, 17(8/9), 1189-1201.

Silvennoinen, A. and Ter􀜽̈svirta, T. (2009). Multivariate GARCH Models: Handbook of Financial Time Series, Springer, Berlin, Heidelberg.

Sentana, E. (1998). The Chats Between Conditionally Heteroscedasticity Factor Models and for GARCH Model, Econometric Journal, 1, 1-9.

Usoro, A.E. and John, E.E (2019). Volatility of Internally Generated Revenue and Effects of its Major Components: A case of Akwa Ibom State, Nigeria, American Journal of Theoretical and Applied Statistics, 8(6), 276-286.

Usoro, A.E., Ikpang, N.I. and George, E.U. (2020). Volatility Measure of Nigeria Crude Oil Production as a Tool to Investigate Production Variability, African Journal of Mathematics and Computer Science Research, 13(1), 1-16.

Van Der W.R. (2007). Go-GARCH: A Multivariate Generalised Orthogonal GARCH Model. Journal of Applied Econometrics, 17, 549-564.

Vrantos, I.D., Dellaportas, P. and Politis, D.N. (2003). A Full Factor Multivariate GARCH Model, Econometrics Journal, 6, 312-334.

Wikipedia (2012). Vector Autoregressive Models.