Multivariate Stochastic Variance Models

Harvey, Andrew; Ruiz, Esther; Shephard, Neil

doi:10.2307/2297980

Cited by 1,116 publications

(861 citation statements)

References 30 publications

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“…To benchmark the ASV-DPM sampler, we apply it to 1,000 returns generated with Harvey et al (1994) parametric, asymmetric, stochastic volatility model…”

Section: Results With Quasi-return Datamentioning

confidence: 99%

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Jensen

Maheu

2012

SSRN Journal

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In this paper, we extend the parametric, asymmetric, stochastic volatility model (ASV), where returns are correlated with volatility, by flexibly modeling the bivariate distribution of the return and volatility innovations nonparametrically. Its novelty is in modeling the joint, conditional, return-volatility distribution with an infinite mixture of bivariate Normal distributions with mean zero vectors, but having unknown mixture weights and covariance matrices. This semiparametric ASV model nests stochastic volatility models whose innovations are distributed as either Normal or Student-t distributions, plus the response in volatility to unexpected return shocks is more general than the fixed asymmetric response with the ASV model. The unknown mixture parameters are modeled with a Dirichlet process prior. This prior ensures a parsimonious, finite, posterior mixture that best represents the distribution of the innovations and a straightforward sampler of the conditional posteriors. We develop a Bayesian Markov chain Monte Carlo sampler to fully characterize the parametric and distributional uncertainty. Nested model comparisons and out-ofsample predictions with the cumulative marginal-likelihoods, and one-day-ahead, predictive logBayes factors between the semiparametric and parametric versions of the ASV model shows the semiparametric model projecting more accurate empirical market returns. A major reason is how volatility responds to an unexpected market movement. When the market is tranquil, expected volatility reacts to a negative (positive) price shock by rising (initially declining, but then rising when the positive shock is large). However, when the market is volatile, the degree of asymmetry and the size of the response in expected volatility is muted. In other words, when times are good, no news is good news, but when times are bad, neither good nor bad news matters with regards to volatility. JEL classification: C11, C14, C53, C58

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“…To benchmark the ASV-DPM sampler, we apply it to 1,000 returns generated with Harvey et al (1994) parametric, asymmetric, stochastic volatility model…”

Section: Results With Quasi-return Datamentioning

confidence: 99%

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Jensen

Maheu

2012

SSRN Journal

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“…That is, the observations are a zero-mean process with time-varying log-variance that one wants to estimate. The SV model is popular in the study of nonlinear state-space models (due to the estimation challenges that it presents [15,[48][49][50]) and is of interest in finance (due to its applicability in the study of stock returns [17,[51][52][53]). …”

Section: Practical Applicationmentioning

confidence: 99%

“…However, as reported in [56], these methods fail when addressing the SV model since they are unable to update their prior beliefs for such model (the Kalman gain is always null). Alternatives based on transformations of the model have been suggested ( [15,50]) but, as reported in [33], they fall short when compared to SMC methods. Furthermore, the SV model has been in use in econometrics for a long time [53], as it is of interest in estimating the risk involved in financial transactions.…”

Section: Practical Applicationmentioning

confidence: 99%

Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

Urteaga

Bugallo

Djurić

2017

EURASIP J. Adv. Signal Process.

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We consider the problem of sequential inference of latent time-series with innovations correlated in time and observed via nonlinear functions. We accommodate time-varying phenomena with diverse properties by means of a flexible mathematical representation of the data. We characterize statistically such time-series by a Bayesian analysis of their densities. The density that describes the transition of the state from time t to the next time instant t + 1 is used for implementation of novel sequential Monte Carlo (SMC) methods. We present a set of SMC methods for inference of latent ARMA time-series with innovations correlated in time for different assumptions in knowledge of parameters. The methods operate in a unified and consistent manner for data with diverse memory properties. We show the validity of the proposed approach by comprehensive simulations of the challenging stochastic volatility model.

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“…When f 50, model (1a,b) becomes the basic LMSV model in Harvey (1998); if d50 and ufu,1, we obtain the ARSV (AutoRegressive SV) model in Harvey et al (1994); when hd50, f 51j or hf 50, d51j, model (1a,b) becomes the RWSV (Random Walk SV) model. Notice that in the last case, the parameters of the ARLMSV model are not identified.…”

Section: Qml Estimation Of Lmsv Modelsmentioning

confidence: 99%

“…4. Consequently, we have first estimated the ARSV model by the QML method of Harvey et al (1994). The estimated parameters together with their standard deviations, computed using the formulae in Ruiz (1994) and Harvey and Shephard (1993), appear in Table 2.…”

Section: Finite Sample Properties Of Qml Estimatormentioning

confidence: 99%

Finite sample properties of a QML estimator of stochastic volatility models with long memory

Pérez

Ruiz

2001

Economics Letters

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Multivariate Stochastic Variance Models

Cited by 1,116 publications

References 30 publications

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

Finite sample properties of a QML estimator of stochastic volatility models with long memory

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