References
-
Bellini, F. and Bottolo, L. (2007). Stationarity domains for
$\delta$ -power GARCH process with heavy tails. Statistics and probability Letters, 77, 1418-1427. https://doi.org/10.1016/j.spl.2007.02.012 - Bollerslev, T. (1986). Generalized autoregressive conditional hetero- skedasticity. Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
- Bougerol, P. and Picard, N. M. (1992). Stationarity of GARCH processes and of some nonnegative time series. Journal of Econometrics, 52, 115-127. https://doi.org/10.1016/0304-4076(92)90067-2
- 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. https://doi.org/10.1016/0927-5398(93)90006-D
- Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987-1007. https://doi.org/10.2307/1912773
- Hwang, S. Y. and Kim, T. Y. (2004). Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure. Stochastic Processes and their Applications, 110, 295-314. https://doi.org/10.1016/j.spa.2003.11.001
- Kingman, J. F. C. (1973). Subadditive ergodic theory. Annals of Probability, 1, 883-909. https://doi.org/10.1214/aop/1176996798
- Kesten, H. and Spitzer, F. (1984). Convergence in distribution of products of random matrices. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete, 67, 363-386. https://doi.org/10.1007/BF00532045
- Lee, O. and Shin, D. W. (2004). Strict stationarity and mixing properties of asymmetric power GARCH models allowing a signed volatility. Economics Letters, 84, 167-173. https://doi.org/10.1016/j.econlet.2003.11.021
- Ling, S. (1999). On the probabilistic properties of a double threshold ARMA conditional heteroskedastic model. Journal of Applied Probability, 36, 688-705. https://doi.org/10.1239/jap/1032374627
- Ling, S. and McAleer, M. (2002). Necessary and sufficient conditions for GARCH(r,s) and asymmetric power GARCH(r,s) models. Econometric Theory, 18, 722-729.
- Meyn, S. P. and Tweedie, R. L. (1993). Markov chains and stochastic stability, Springer, London.
- Tweedie, R. L. (2001). Drift conditions and invariant measures for Markov chains. Stochastic Processes and their Applications, 92, 345-354. https://doi.org/10.1016/S0304-4149(00)00085-5