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Stationarity of stable power-GARCH processes

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  • Mittnik, Stefan
  • Paolella, Marc S.
  • Rachev, Svetlozar T.

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  • Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2002. "Stationarity of stable power-GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 97-107, January.
    • Handle: RePEc:eee:econom:v:106:y:2002:i:1:p:97-107
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    1. Groenendijk, Patrick A. & Lucas, Andre & de Vries, Casper G., 1995. "A note on the relationship between GARCH and symmetric stable processes," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 253-264, September.
    2. Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-285, July-Sept.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
    5. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    6. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    7. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. McCulloch, J. Huston, 1985. "Interest-risk sensitive deposit insurance premia : Stable ACH estimates," Journal of Banking & Finance, Elsevier, vol. 9(1), pages 137-156, March.
    10. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    11. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
    12. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    13. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
    14. de Vries, Casper G., 1991. "On the relation between GARCH and stable processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 313-324, June.
    15. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
    16. Mittnik, Stefan & Paolella, Marc S., 2003. "Prediction of Financial Downside-Risk with Heavy-Tailed Conditional Distributions," CFS Working Paper Series 2003/04, Center for Financial Studies (CFS).
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    Cited by:

    1. Xing Yu, 2012. "The optimal portfolio model based on multivariate t distribution with linear weighted sum method," E3 Journal of Business Management and Economics., E3 Journals, vol. 3(1), pages 044-047.
    2. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    3. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc, 2006. "Accurate value-at-risk forecasting based on the normal-GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2295-2312, December.
    4. Paolella, Marc S. & Taschini, Luca, 2008. "An econometric analysis of emission allowance prices," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2022-2032, October.
    5. Alex Huang, 2013. "Value at risk estimation by quantile regression and kernel estimator," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 225-251, August.
    6. Rombouts Jeroen V. K. & Bouaddi Mohammed, 2009. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-32, May.
    7. Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Fabozzi, Frank J., 2013. "CVaR sensitivity with respect to tail thickness," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 977-988.
    8. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
    9. Alex Yi-Hou Huang & Tsung-Wei Tseng, 2009. "Forecast of value at risk for equity indices: an analysis from developed and emerging markets," Journal of Risk Finance, Emerald Group Publishing, vol. 10(4), pages 393-409, August.
    10. Sun, Wei & Rachev, Svetlozar & Fabozzi, Frank J., 2007. "Fractals or I.I.D.: Evidence of long-range dependence and heavy tailedness from modeling German equity market returns," Journal of Economics and Business, Elsevier, vol. 59(6), pages 575-595.
    11. Huang, Alex YiHou, 2010. "An optimization process in Value-at-Risk estimation," Review of Financial Economics, Elsevier, vol. 19(3), pages 109-116, August.
    12. Kirt C. Butler & Katsushi Okada, 2008. "Higher-Order Terms in Bivariate Returns to International Stock Market Indices," Multinational Finance Journal, Multinational Finance Journal, vol. 12(1-2), pages 127-155, March-Jun.
    13. Sio Chong U & Jacky So & Deng Ding & Lihong Liu, 2016. "An efficient Fourier expansion method for the calculation of value-at-risk: Contributions of extra-ordinary risks," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-27, March.
    14. Wei Sun & Svetlozar Rachev & Frank Fabozzi & Petko Kalev, 2009. "A new approach to modeling co-movement of international equity markets: evidence of unconditional copula-based simulation of tail dependence," Empirical Economics, Springer, vol. 36(1), pages 201-229, February.
    15. Calzolari, Giorgio & Halbleib, Roxana & Parrini, Alessandro, 2014. "Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 158-171.
    16. Peter A. Zadrozny, 2005. "Necessary and Sufficient Restrictions for Existence of a Unique Fourth Moment of a Univariate GARCH(p,q) Process," CESifo Working Paper Series 1505, CESifo Group Munich.
    17. Paolella, Marc S. & Polak, Paweł, 2015. "ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 282-297.
    18. Frank Fabozzi & Borjana Racheva-Iotova & Stoyan Stoyanov, 2006. "An empirical examination of the return distribution characteristics of agency mortgage pass-through securities," Applied Financial Economics, Taylor & Francis Journals, vol. 16(15), pages 1085-1094.
    19. Christian Francq & Simos G. Meintanis, 2016. "Fourier-type estimation of the power GARCH model with stable-Paretian innovations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(4), pages 389-424, May.
    20. Huang, Alex YiHou & Peng, Sheng-Pen & Li, Fangjhy & Ke, Ching-Jie, 2011. "Volatility forecasting of exchange rate by quantile regression," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 591-606, October.
    21. Gonçalves, E. & Leite, J. & Mendes-Lopes, N., 2012. "On the probabilistic structure of power threshold generalized arch stochastic processes," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1597-1609.
    22. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
    23. Bekaert, Geert & Engstrom, Eric & Ermolov, Andrey, 2015. "Bad environments, good environments: A non-Gaussian asymmetric volatility model," Journal of Econometrics, Elsevier, vol. 186(1), pages 258-275.
    24. Bellini, Fabio & Bottolo, Leonardo, 2007. "Stationarity domains for [delta]-power Garch process with heavy tails," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1418-1427, July.
    25. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.

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