A New Asymmetric GARCH Model: Testing, Estimation and Application

Hatemi-J, Abdulnasser (2013): A New Asymmetric GARCH Model: Testing, Estimation and Application.

Abstract

Since the seminal work by Engle (1982), the autoregressive conditional heteroscedasticity (ARCH) model has been an important tool for estimating the time-varying volatility as a measure of risk. Numerous extensions of this model have been put forward in the literature. The current paper offers an alternative approach for dealing with asymmetry in the underlying volatility model. Unlike previous papers that have dealt with asymmetry, this paper suggests to explicitly separate the positive shocks from the negative ones in the ARCH modeling approach. A test statistic is suggested for testing the null hypothesis of no asymmetric ARCH effects. In case the null hypothesis is rejected, the model can be estimated by using the maximum likelihood method. The suggested asymmetric volatility approach is applied to modeling separately the potential time-varying volatility in markets that are rising or falling by using the changes in the world market stock price index.

• Item Type: MPRA Paper
• Language: English
• Keywords: GARCH; Asymmetry; Modelling volatility; Hypothesis testing, World stock price index.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; G - Financial Economics > G1 - General Financial Markets > G10 - General

References

Apergis N. and S. Miller (2005) Money volatility and output volatility: any asymmetric effects?: Evidence from conditional measures of volatility, Journal of Economic Studies, 32, 511-523.

Bollerslev, T. (1986) Generalized autoregressive conditional heteroscedasticity, Journal of Econometrics, 31, 309-328.

Bollerslev, T., Chou, R. Y. and Kroner, K. F. (1992) ARCH modelling in finance: a review of the theory and empirical evidence. Journal of Econometrics, 52(5), 5-59.

Bollerslev T. and Zhou H. (2006) Volatility puzzles: a unified framework for gauging return-volatility regression, Journal of Econometrics, 131, 123–50.

Brooks C. (1997) GARCH Modelling in Finance: A Review of the Software Options, Economic Journal, 107, 1271-1276.

Ding, Z. Granger, C.W.J. and Engle R.F. (1993) A long memory property of stock market returns and a new model, Journal of Empirical Finance, 1, 83–106.

Engle R. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of UK inflation, Econometrica, 50, 987-1008.

Engle R. (1995) ARCH Selected readings, advanced texts in econometrics, Oxford University Press.

Engle R. (2002) New frontiers for arch models, Journal of Applied Econometrics, 17(5), 425-446.

Engle R. and Kroner K. (1995) Multivariate simultaneous generalized ARCH, Econometric Theory, 11, 122-150.

Francq, C. and Zakoian, J.M. (2010) GARCH Models: Structure, Statistical Inference and Financial Applications, Wiley.

Francq, C. and Zakoian, J.M. (2012) Strict stationarity testing and estimation of explosive and stationary GARCH models, Econometrica, 80, 821–861.

Mandelbrot B. (1963) The variation of certain speculative prices, Journal of Business, 36, 394-419.

Nelson D. (1991) Conditional heteroskedasticity in asset returns: a new approach, Econometrica, 59, 347–70.

Poon, S.H. and Granger, C.W.J. (2003) Forecasting Volatility in Financial Markets: A Review, Journal of Economic Literature, 41, 478-539.

Zakoian, J.M. (1994) Threshold heteroskedastic models, Journal of Economic Dynamics and Control, 18(5), 931-955.