Implementation of the Estimating Functions Approach in Asset Returns Volatility Forecasting Using First Order Asymmetric GARCH Models
ABSTRACT
This paper implements the method of estimating functions (EF) in the modelling and forecasting of financial returns volatility. This estimation approach incorporates higher order moments which are common in most financial time series, into modelling, leading to a substantial gain of information and overall efficiency benefits. The two models considered in this paper provide a better in-sample-fit under the estimating functions approach relative to the traditional maximum likely-hood estimation (MLE) approach when fitted to empirical time series. On this ground, the EF approach is employed in the first order EGARCH and GJR-GARCH models to forecast the volatility of two market indices from the USA and Japanese stock markets. The loss functions, mean square error (MSE) and mean absolute error (MAE), have been utilized in evaluating the predictive ability of the EGARCH vis-à-vis the GJR-GARCH model.
This paper implements the method of estimating functions (EF) in the modelling and forecasting of financial returns volatility. This estimation approach incorporates higher order moments which are common in most financial time series, into modelling, leading to a substantial gain of information and overall efficiency benefits. The two models considered in this paper provide a better in-sample-fit under the estimating functions approach relative to the traditional maximum likely-hood estimation (MLE) approach when fitted to empirical time series. On this ground, the EF approach is employed in the first order EGARCH and GJR-GARCH models to forecast the volatility of two market indices from the USA and Japanese stock markets. The loss functions, mean square error (MSE) and mean absolute error (MAE), have been utilized in evaluating the predictive ability of the EGARCH vis-à-vis the GJR-GARCH model.
Cite this paper
Mutunga, T. , Islam, A. and Orawo, L. (2015) Implementation of the Estimating Functions Approach in Asset Returns Volatility Forecasting Using First Order Asymmetric GARCH Models. Open Journal of Statistics, 5, 455-464. doi: 10.4236/ojs.2015.55047.
Mutunga, T. , Islam, A. and Orawo, L. (2015) Implementation of the Estimating Functions Approach in Asset Returns Volatility Forecasting Using First Order Asymmetric GARCH Models. Open Journal of Statistics, 5, 455-464. doi: 10.4236/ojs.2015.55047.
References
[1] Lars, K.M. (2002) GARCH-Modelling: Theoretical Survey, Model Implementation and Robustness Analysis. Masters Thesis, Royal Institute of Technology (KTH), Stockholm. [2] Bollerslev, T., Chou, R. and Kroner, K.F. (1992) ARCH Modelling in Finance: A Review of the Theory and Empirical Evidence. Journal of Econometrics, 52, 5-59.
http://dx.doi.org/10.1016/0304-4076(92)90064-X [3] Chappel, D., Padmore, J. and Pidgeon, J. (1998) A Note on ERM Membership and the Efficiency of the London Stock Exchange. Applied Economics Letters, 5, 19-23.
http://dx.doi.org/10.1080/758540120 [4] Janne, K. (2012) GARCH models for Foreign Exchange Rates. Bachelors Thesis, Aalto University, Aalto. [5] Li, Y. (2013) GARCH Models for Forecasting Volatilities of Three Major Stock Indicies Using Both Frequentist and Bayesian Approach. Masters Thesis, Ball State University, Muncie, IN. [6] Su, D. and Fleisher, B.M. (1998) Risk, Return and Regulation in Chinese Stock Markets. Journal of Economics and Business, 50, 239-256.
http://dx.doi.org/10.1016/S0148-6195(98)00002-2 [7] Kalu, O.E. (2010) Modelling Stock Returns Volatility in Nigeria Using GARCH Models. MPRA (Munich Personal RePEc Archive) Paper No. 23432. [8] Olweny, T. (2011) Modelling Volatility of Short-term Interest Rates in Kenya. International Journal of Business and Social Science, 2, 289-303. [9] Suliman, Z.S. and Peter, W. (2012) Modelling Stock Market Volatility using Univariate GARCH Models: Evidence from Sudan and Egypt. International Journal of Economics and Finance, 4, 161-176. [10] Wagalla, A., Nassiuma, D.K., Islam, A.S. and Mwangi, J.W. (2012) Volatility Modelling of the Nairobi Stock Exchange Returns Using the ARCH-Type Models. International Journal of Applied Science and Technology, 2, 165-174. [11] Mwangi, J.W. (2007) Parameter Estimation for Nonlinear Time Series Models Using Estimating Functions. PhD Thesis, Egerton University, Kenya. [12] Neelabh, R. (2009) Conditional Heteroscedastic Time Series Models with Asymmetry and Structural Breaks. PhD Thesis, University of Pune, Pune. [13] Mutunga, T.N., Islam, A.S. and Orawo, L.A. (2014) Estimation of Asymmetric GARCH Models: The Estimating Functions Approach. International Journal of Applied Science and Technology, 4, 198-209. [14] Godambe, V.P. and Thompson, M.E. (1989) An Extension of the Quasi-Likelihood Estimation. Journal of Statistical Planning and Inference, 22, 137-172.
http://dx.doi.org/10.1016/0378-3758(89)90106-7 [15] Black, F. (1976) Studies of Stock Price Volatility Changes. Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economics Statistics Section, Boston, 25-26 August 1976, 177-181. [16] Engle, R.F. and Ng, V.K. (1993) Measuring and Testing the Impact of News on Volatility. Journal of Finance, 48, 1749-1778.
http://dx.doi.org/10.1111/j.1540-6261.1993.tb05127.x [17] Wu, G. (2001) The Determinants of Asymmetric Volatility. Review of Financial Studies, 14, 837-859.
http://dx.doi.org/10.1093/rfs/14.3.837 [18] Blair, B., Poon, S. and Taylor, S.J. (2002) Asymmetric and Crash Effects in Stock Volatility for the S&P 100 Index and Its Constituents. Applied Financial Economics, 12, 319-329.
http://dx.doi.org/10.1080/09603100110090154 [19] Nelson, D.B. (1991) Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59, 347-370.
http://dx.doi.org/10.2307/2938260 [20] Glosten, L.R., Jagannathan, R. and Runkle, D. (1993) On the Relation between the Expected Value and the Volatility of Nominal Excess Returns on Stocks. Journal of Finance, 48, 1779-1801.
http://dx.doi.org/10.1111/j.1540-6261.1993.tb05128.x [21] Godambe, V.P. (1960) An Optimum Property of Regular Maximum Likelihood Equations. Annals of Mathematical Statistics, 31, 1208-1211.
http://dx.doi.org/10.1214/aoms/1177705693 [22] Jorion, P. (1996) Risk and Turnover in the Foreign Exchange Market. In: Frankel, J.A., Galli, G. and Giovannini, A., Eds., The Microstructure of Foreign Exchange Markets, NBER Chapters, National Bureau of Economic Research, Inc., Cambridge, 19-40.
[1] Lars, K.M. (2002) GARCH-Modelling: Theoretical Survey, Model Implementation and Robustness Analysis. Masters Thesis, Royal Institute of Technology (KTH), Stockholm. [2] Bollerslev, T., Chou, R. and Kroner, K.F. (1992) ARCH Modelling in Finance: A Review of the Theory and Empirical Evidence. Journal of Econometrics, 52, 5-59.
http://dx.doi.org/10.1016/0304-4076(92)90064-X [3] Chappel, D., Padmore, J. and Pidgeon, J. (1998) A Note on ERM Membership and the Efficiency of the London Stock Exchange. Applied Economics Letters, 5, 19-23.
http://dx.doi.org/10.1080/758540120 [4] Janne, K. (2012) GARCH models for Foreign Exchange Rates. Bachelors Thesis, Aalto University, Aalto. [5] Li, Y. (2013) GARCH Models for Forecasting Volatilities of Three Major Stock Indicies Using Both Frequentist and Bayesian Approach. Masters Thesis, Ball State University, Muncie, IN. [6] Su, D. and Fleisher, B.M. (1998) Risk, Return and Regulation in Chinese Stock Markets. Journal of Economics and Business, 50, 239-256.
http://dx.doi.org/10.1016/S0148-6195(98)00002-2 [7] Kalu, O.E. (2010) Modelling Stock Returns Volatility in Nigeria Using GARCH Models. MPRA (Munich Personal RePEc Archive) Paper No. 23432. [8] Olweny, T. (2011) Modelling Volatility of Short-term Interest Rates in Kenya. International Journal of Business and Social Science, 2, 289-303. [9] Suliman, Z.S. and Peter, W. (2012) Modelling Stock Market Volatility using Univariate GARCH Models: Evidence from Sudan and Egypt. International Journal of Economics and Finance, 4, 161-176. [10] Wagalla, A., Nassiuma, D.K., Islam, A.S. and Mwangi, J.W. (2012) Volatility Modelling of the Nairobi Stock Exchange Returns Using the ARCH-Type Models. International Journal of Applied Science and Technology, 2, 165-174. [11] Mwangi, J.W. (2007) Parameter Estimation for Nonlinear Time Series Models Using Estimating Functions. PhD Thesis, Egerton University, Kenya. [12] Neelabh, R. (2009) Conditional Heteroscedastic Time Series Models with Asymmetry and Structural Breaks. PhD Thesis, University of Pune, Pune. [13] Mutunga, T.N., Islam, A.S. and Orawo, L.A. (2014) Estimation of Asymmetric GARCH Models: The Estimating Functions Approach. International Journal of Applied Science and Technology, 4, 198-209. [14] Godambe, V.P. and Thompson, M.E. (1989) An Extension of the Quasi-Likelihood Estimation. Journal of Statistical Planning and Inference, 22, 137-172.
http://dx.doi.org/10.1016/0378-3758(89)90106-7 [15] Black, F. (1976) Studies of Stock Price Volatility Changes. Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economics Statistics Section, Boston, 25-26 August 1976, 177-181. [16] Engle, R.F. and Ng, V.K. (1993) Measuring and Testing the Impact of News on Volatility. Journal of Finance, 48, 1749-1778.
http://dx.doi.org/10.1111/j.1540-6261.1993.tb05127.x [17] Wu, G. (2001) The Determinants of Asymmetric Volatility. Review of Financial Studies, 14, 837-859.
http://dx.doi.org/10.1093/rfs/14.3.837 [18] Blair, B., Poon, S. and Taylor, S.J. (2002) Asymmetric and Crash Effects in Stock Volatility for the S&P 100 Index and Its Constituents. Applied Financial Economics, 12, 319-329.
http://dx.doi.org/10.1080/09603100110090154 [19] Nelson, D.B. (1991) Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59, 347-370.
http://dx.doi.org/10.2307/2938260 [20] Glosten, L.R., Jagannathan, R. and Runkle, D. (1993) On the Relation between the Expected Value and the Volatility of Nominal Excess Returns on Stocks. Journal of Finance, 48, 1779-1801.
http://dx.doi.org/10.1111/j.1540-6261.1993.tb05128.x [21] Godambe, V.P. (1960) An Optimum Property of Regular Maximum Likelihood Equations. Annals of Mathematical Statistics, 31, 1208-1211.
http://dx.doi.org/10.1214/aoms/1177705693 [22] Jorion, P. (1996) Risk and Turnover in the Foreign Exchange Market. In: Frankel, J.A., Galli, G. and Giovannini, A., Eds., The Microstructure of Foreign Exchange Markets, NBER Chapters, National Bureau of Economic Research, Inc., Cambridge, 19-40.