Research ArticleOpen AccessGoogle Scholar indexed
Limit Theory of Model Order Change-Point Estimator for GARCH Models
Pan-African University Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya
Machakos University, Machakos, Kenya
Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
- 1 Pan-African University Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya
- 2 Machakos University, Machakos, Kenya
- 3 Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Journal of Mathematical Finance·Volume 08 (2018)·Pages 426–445·Published 29 March 2018·DOI10.4236/jmf.2018.82027
Copy link · social · email
Abstract
The limit theory of a change-point process which is based on the Manhattan distance of the sample autocorrelation function with applications to GARCH processes is examined. The general theory of the sample autocovariance and sample autocorrelation functions of a stationary GARCH process forms the basis of this study. Specifically the point processes theory is utilized to obtain their weak convergence limit at different lags. This is further extended to the change-point process. The limits are found to be generally random as a result of the infinite variance.
KeywordsAutocorrelation FunctionChange-PointConvergenceGARCHManhattan DistanceModel OrderPoint ProcessRegular VariationWeak Limit
- Chinzara, Z. (2010) Macroeconomic Uncertainty and Emerging Market Stock Market Volatility: The Case for South Africa. Working Paper 187, 1-19.
- Matteo Manera, M.N. and Vignati, I. (2012) Financial Speculation in Energy and Agriculture Futures Markets: A Multivariate Garch Approach. International Association for Energy Economics, 3.
- Mikosch, T. and Starica, C. (2004) Nonstationarities in Financial Time Series, the Long-Range Dependence and the Igarch Effects. Review of Economics and Statistics, 86, 378-390. https://doi.org/10.1162/003465304323023886
- Yau, C.Y. and Zhao, Z. (2015) Inference for Multiple Change Points in Time Series via Likelihood Ratio Scan Statistics. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78, 895-916. https://doi.org/10.1111/rssb.12139
- Lee, T., Kim, M. and Baek, C. (2014) Tests for Volatility Shifts in Garch against Long Range Dependence. Journal of Time Series Analysis, 36, 127-153. https://doi.org/10.1111/jtsa.12098
- Na, O., Lee, J. and Lee, S. (2011) Change Point Detection in Copula Arma Garch Models. Journal of Time Series Analysis, 33, 554-569. https://doi.org/10.1111/j.1467-9892.2011.00763.x
- Alemohammad, N., Rezakhah, S. and Alizadeh, S.H. (2016) Markov Switching Component Garch Model Stability and Forecasting. Communications in Statistics Theory and Statistics, 45, 4332-4348. https://doi.org/10.1080/03610926.2013.841934
- Irungu, I., Mwita, P. and Waititu, A. (2018) Consistency of the Model Order Change-Point Estimator for Garch Models. Journal of Mathematical Finance, 8, 266-282. https://doi.org/10.4236/jmf.2018.82018
- Bartkiewicz, K., Jakubowski, A., Mikosch, T. and Wintenberger, O. (2011) Stable Limits for Sums of Dependent Infinite Variance Random Variables. Probabability Theory Related Fields, 150, 337-372. https://doi.org/10.1007/s00440-010-0276-9
- Davis, R.A. and Resnick, S.I. (2011) Limit Theory for the Sample Covariance and Correlation Functions of Moving Averages. Annals of Statistics, 14, 533-558. https://doi.org/10.1214/aos/1176349937
- Davis, R.A. and Resnick, S.I. (1996) Limit Theory for Bilinear Processes with Heavy-Tailed Noise. Annals of Statistics, 6, 1191-1210. https://doi.org/10.1214/aoap/1035463328
- Mikosch, T. and Starica, C. (2000) Limit Theory for the Sample Autocorrelations and Extremes of a Garch (1,1) Process. Annals of Statistics, 28, 1427-1451.