Stationarity of Garch processes and of some nonnegative time series

Bougerol, Philippe; Picard, Nico

doi:10.1016/0304-4076(92)90067-2

Cited by 482 publications

(313 citation statements)

References 13 publications

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“…These general results can, however, for this model be considerably reduced; cf. Nelson (1990) and Bougerol and Picard (1992a). The multivariate regular variation of this model was derived by Basrak et al (2002b), and Mikosch and Stȃricȃ (2000).…”

Section: Arch(1) and Garch(11) Processesmentioning

confidence: 99%

High-level dependence in time series models

2009

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We present several notions of high-level dependence for stochastic processes, which have appeared in the literature. We calculate such measures for discrete and continuous-time models, where we concentrate on time series with heavy-tailed marginals, where extremes are likely to occur in clusters. Such models include linear models and solutions to random recurrence equations; in particular, discrete and continuous-time moving average and (G)ARCH processes. To illustrate our results we present a small simulation study.

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Section: Arch(1) and Garch(11) Processesmentioning

confidence: 99%

High-level dependence in time series models

2009

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“…The return process r t following the model defined in Eqs. (1) 7 and (2) is strictly stationary if the following condition holds (see, Bougerol and Picard, 1992),…”

Section: Introductionmentioning

confidence: 99%

A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation

Ausín

Galeano

Ghosh

2014

European Journal of Operational Research

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Financial time series analysis deals with the understanding of data collected on financial markets. Several parametric distribution models have been entertained for describing, estimating and predicting the dynamics of financial time series. Alternatively, this article considers a Bayesian semiparametric approach. In particular, the usual parametric distributional assumptions of the GARCH-type models are relaxed by entertaining the class of location-scale mixtures of Gaussian distributions with a Dirichlet process prior on the mixing distribution, leading to a Dirichlet process mixture model. The proposed specification allows for a greater exibility in capturing both the skewness and kurtosis frequently observed in financial returns. The Bayesian model provides statistical inference with finite sample validity. Furthermore, it is also possible to obtain predictive distributions for the Value at Risk (VaR), which has become the most widely used measure of market risk for practitioners. Through a simulation study, we demonstrate the performance of the proposed semiparametric method and compare results with the ones from a normal distribution assumption. We also demonstrate the superiority of our proposed semiparametric method using real data from the Bombay Stock Exchange Index (BSE-30) and the Hang Seng Index (HSI). In particular, the usual parametric distributional assumptions of the GARCH-type models are relaxed by entertaining the class of location-scale mixtures of Gaussian distributions with a Dirichlet process prior on the mixing distribution, leading to a Dirichlet process mixture model. The proposed specification allows for a greater flexibility in capturing both the skewness and kurtosis frequently observed in financial returns. The Bayesian model provide statistical inference with finite sample validity. Furthermore, it is also possible to obtain predictive distributions for the Value at Risk (VaR), which has become the most widely used measure of market risk for practitioners. Through a simulation study, we demonstrate the performance of the proposed semiparametric method and compare results with the ones from a normal distribution assumption. We also demonstrate the superiority of our proposed semiparametric method using real data from the Bombay Stock Exchange Index (BSE-30) and the Hang Seng Index (HSI).

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“…In [22] (see also [26] and [23]), Bougerol and Picard derived a necessary and sufficient condition for the existence of a strictly stationary solution to the linear stochastic recurrent equation…”

Section: A Strict Stationarity Conditionmentioning

confidence: 99%

Concepts of and tools for Nonlinear Time‐Series Modelling

Amendola

Francq

2009

Handbook of Computational Econometrics

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Tools and approaches are provided for nonlinear time series modelling in econometrics. A wide range of topics is covered, including probabilistic properties, statistical inference and computational methods. The focus is on the applications but the ideas of the mathematical arguments are also provided. Techniques and concepts are illustrated by various examples, Monte Carlo experiments and a real application. 1

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Stationarity of Garch processes and of some nonnegative time series

Cited by 482 publications

References 13 publications

High-level dependence in time series models

High-level dependence in time series models

A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation

Concepts of and tools for Nonlinear Time‐Series Modelling

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