AM  Vol.10 No.3 , March 2019
Application of Iterative Approaches in Modeling the Efficiency of ARIMA-GARCH Processes in the Presence of Outliers
Abstract: The study explored both Box and Jenkins, and iterative outlier detection procedures in determining the efficiency of ARIMA-GARCH-type models in the presence of outliers using the daily closing share price returns series of four prominent banks in Nigeria (Skye (Polaris) bank, Sterling bank, Unity bank and Zenith bank) from January 3, 2006 to November 24, 2016. The series consists of 2690 observations for each bank. The data were obtained from the Nigerian Stock Exchange. Unconditional variance and kurtosis coefficient were used as criteria for measuring the efficiency of ARIMA-GARCH-type models and our findings revealed that kurtosis is a better criterion (as it is a true measure of outliers) than the unconditional variance (as it can be depleted or amplified by outliers). Specifically, the strength of this study is in showing the applicability and relevance of iterative methods in time series modeling.
Cite this paper: Akpan, E. , Lasisi, K. , Adamu, A. and Rann, H. (2019) Application of Iterative Approaches in Modeling the Efficiency of ARIMA-GARCH Processes in the Presence of Outliers. Applied Mathematics, 10, 138-158. doi: 10.4236/am.2019.103012.

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

[2]   Francq, C. and Zakoian, J. (2010) GARCH Models: Structure, Statistical Inference and Financial Applications. 1st Edition, John Wiley & Sons Ltd., Chichester, 19-220.

[3]   Moffat, I.U. and Akpan, E.A. (2018) Modeling Heteroscedasticity of Discrete-Time Series in the Face of Excess Kurtosis. Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, 18, 23-32.

[4]   Feng, L. and Shi, Y. (2017) A Simulation Study on the Distributions of Disturbances in GARCH Model. Cogent Economics and Finance, 5, Article ID: 1355503.

[5]   Cain, M.K., Zhang, Z. and Yuan, K. (2017) Univariate and Multivariate Skewness and Kurtosis for Measuring Nonnormality: Prevalence Influence and Estimation. Behavior Research Methods, 49, 1716-1735.

[6]   Fiori, A.M. and Beltrami, D. (2014) Right and Left Kurtosis Measures: Large Sample Estimation and an Application to Financial Returns. STAT, 3, 95-108.

[7]   Westfall, P. H. (2014) Kurtosis as Peakness, 1905-2014. R.I.P. The American Statistician, 68, 191-195.

[8]   Akpan, E.A., Lasisi, K.E and Adamu, A. (2018) Modeling Heteroscedasticity in the Presence of Outliers in Discrete-Time Stochastic Series. Academic Journal of Applied Mathematical Sciences, 4, 61-76.

[9]   Akpan, E.A. and Moffat, I.U. (2017) Detection and Modeling of Asymmetric GARCH Effects in a Discrete-Time Series. International Journal of Statistics and Probability, 6, 111-119.

[10]   Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (2008) Time Series Analysis: Forecasting and Control. 3rd Edition, John Wiley & Sons, Hoboken, NJ, 5-22.

[11]   Engle, R.F. (1982) Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflations. Econometrica, 50, 987-1007.

[12]   Bollerslev, T. (1986) Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics, 31, 307-327.

[13]   Tsay, R.S. (2010) Analysis of Financial Time Series. 3rd Edition, John Wiley & Sons Inc., New York, 97-140.

[14]   Nelson, D.B. (1991) Conditional Heteroscedasticity of Asset Returns. A New Approach. Econometrica, 59, 347-370.

[15]   Glosten, L.R., Jagannathan, R. and Runkle, D. (1993) On the Relation between the expected Values and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance, 48, 1779-1801.

[16]   Moffat, I.U. and Akpan, E.A. (2017) Identification and Modeling of Outliers in a Discrete-Time Stochastic Series. American Journal of Theoretical and Applied Statistics, 6, 191-197.

[17]   Sanchez, M.J. and Pena, D. (2003) The Identification of Multiple Outliers in ARIMA Models. Communications in Statistics-Theory and Methods, 32, 1265-1287.

[18]   Wei, W.W.S. (2006) Time Series Analysis Univariate and Multivariate Methods. 2nd Edition, Addison-Wesley, New York, 3-59.

[19]   Chen, C. and Liu, L.M. (1993) Joint Estimation of Model Parameters and Outlier Effects in Time Series. Journal of the American Statistical Association, 8, 284-297.

[20]   Chang, I., Tiao, G.C. and Chen, C. (1988) Estimation of Time Series Parameters in the Presence of Outliers. Technometrics, 30, 193-204.

[21]   Carnero, M.A., Pena, D and Ruiz, E. (2012) Estimating GARCH Volatility in the Presence of Outliers. Economics Letters, 114, 86-90.