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On the structure of generalized threshold arch processes

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  • Gonçalves, E.
  • Mendes-Lopes, N.

Abstract

The aim of this paper is to develop probabilistic studies, useful for applications, namely in what concerns the implementation and validation of subsequent statistical methods. More precisely, we establish new conditions on the stationarity and ergodicity of the GTARCH model and obtain a unique representation of its conditional volatility in terms of present and past observations. A minimal definition of a GTARCH process is then deduced.

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  • Gonçalves, E. & Mendes-Lopes, N., 2010. "On the structure of generalized threshold arch processes," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 573-580, April.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:573-580
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    References listed on IDEAS

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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Gonçalves, Esmeralda & Leite, Joana & Mendes-Lopes, Nazaré, 2009. "A mathematical approach to detect the Taylor property in TARCH processes," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 602-610, March.
    3. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    5. 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.
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    1. 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.

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