Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein–Uhlenbeck processes

Griffin, Jim E.; Steel, Mark F. J.

doi:10.1016/j.csda.2009.06.008

Cited by 18 publications

(13 citation statements)

References 20 publications

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“…It is possible for supOU processes to display not only short-range dependence but also long-range dependence. SupOU processes have found many applications, especially in finance where positive supOU processes are used in models for stochastic volatility; see [9,11,12,23,33,38,39].…”

Section: Introductionmentioning

confidence: 99%

The unusual properties of aggregated superpositions of Ornstein–Uhlenbeck type processes

Grahovac¹,

Leonenko²,

Sikorskii³

et al. 2019

Bernoulli

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Section: Introductionmentioning

confidence: 99%

The unusual properties of aggregated superpositions of Ornstein–Uhlenbeck type processes

Grahovac¹,

Leonenko²,

Sikorskii³

et al. 2019

Bernoulli

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“…X s dW s , J 0 = 0, and (W s ) s∈R + is a standard Brownian motion independent of the process (X s ) s∈R + which is a non-negative supOU process. Some examples of applications of the supOU SV model can be found in [12,32,49].…”

Section: Introductionmentioning

confidence: 99%

Weak dependence and GMM estimation of supOU and mixed moving average processes

Curato¹,

Stelzer²

2019

Electron. J. Statist.

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We consider a mixed moving average (MMA) process X driven by a Lévy basis and prove that it is weakly dependent with rates computable in terms of the moving average kernel and the characteristic quadruple of the Lévy basis. Using this property, we show conditions ensuring that sample mean and autocovariances of X have a limiting normal distribution. We extend these results to stochastic volatility models and then investigate a Generalized Method of Moments estimator for the supOU process and the supOU stochastic volatility model after choosing a suitable distribution for the mean reversion parameter. For these estimators, we analyze the asymptotic behavior in detail.An important example of MMA are the supOU processes studied in [3,10,25,27]. In the univariate case, assume |x|>1 log(|x|) ν(dx) < ∞ and R − − 1 A π(dA) < ∞, where ν is a Lévy measure and π is the probability distribution on R − of the random parameter A, see Definition 2.1 for details. If Λ is a Lévy basis on R with those characteristics, then the processis called a supOU process. Whereas a non-Gaussian Ornstein-Uhlenbeck process necessarily exhibits autocorrelation e ah for h ∈ N, the supOU process has a flexible dependence structure. For example, its autocorrelations can show a polynomial decay depending on the probability distribution π. Moreover, when a discrete probability distribution π for the random parameter A is considered, we obtain a popular model used, for example, in stochastic volatility models [3], in modeling fractal activity times [36,37] and in astrophysics [35].MMA processes can also be used, under suitable conditions, as building blocks for more complex models. We study in this paper the class of MMA stochastic volatility models. An example of the class is the supOU SV model, defined in [10,11], where the log-price process (of some financial asset) is defined for t ∈ R + as

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“…The hyperparameter a = 1 and the mean a/b = 3 which give a prior mass on a reasonable range of values. In parametric case when F J is an exponential distribution with mean 1/γ, then γ is given a vague prior Ga(0.001, 0.001) as in Griffin and Steel (2010). Similarly, if F J is given a Pólya tree prior, then the scale γ of the exponential centering distribution is given the same prior distribution.…”

Section: Further Specification Of the Bayesian Modelmentioning

confidence: 99%

“…Under certain conditions, the sum in Equation (2) can be extended to an integral. The probabilistic background is developed by Barndorff-Nielsen (2001) and Barndorff-Nielsen and Leonenko (2005), and an MCMC method for Bayesian inference is discussed by Griffin and Steel (2010). Unlike the superposition in Equation (2), these continuous superpositions can be constructed so that σ 2 (t) has long memory.…”

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confidence: 99%

Inference in Infinite Superpositions of Non-Gaussian Ornstein-Uhlenbeck Processes Using Bayesian Nonparametic Methods

Griffin

2010

Journal of Financial Econometrics

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This paper describes a Bayesian nonparametric approach to volatility estimation. Volatility is assumed to follow a superposition of an infinite number of Ornstein-Uhlenbeck processes driven by a compound Poisson process with a parametric or nonparametric jump size distribution. This model allows a wide range of possible dependencies and marginal distributions for volatility. The properties of the model and prior specification are discussed, and a Markov chain Monte Carlo algorithm for inference is described. The model is fitted to daily returns of four indices: the Standard and Poors 500, the NASDAQ 100, the FTSE 100, and the Nikkei 225.

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Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein–Uhlenbeck processes

Cited by 18 publications

References 20 publications

The unusual properties of aggregated superpositions of Ornstein–Uhlenbeck type processes

The unusual properties of aggregated superpositions of Ornstein–Uhlenbeck type processes

Weak dependence and GMM estimation of supOU and mixed moving average processes

Inference in Infinite Superpositions of Non-Gaussian Ornstein-Uhlenbeck Processes Using Bayesian Nonparametic Methods

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