Multivariate Stochastic Volatility: A Review

By Manabu Asai, Michael Mcaleer, Jun Yu. 2006

365 citations recorded by the source corpus.

The literature on multivariate stochastic volatility (MSV) models has developed significantly over the last few years. This paper reviews the substantial literature on specification, estimation, and evaluation of MSV models. A wide range of MSV models is presented according to various categories, namely, (i) asymmetric models, (ii) factor models, (iii) time-varying correlation models, and (iv) alternative MSV specifications, including models based on the matrix exponential transformation, the Cholesky decomposition, and the Wishart autoregressive process. Alternative methods of estimation, including quasi-maximum likelihood, simulated maximum likelihood, and Markov chain Monte Carlo methods, are discussed and compared. Various methods of diagnostic checking and model comparison are also reviewed.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/d121bd7ac91e06fa439134982a3ac51cb6e6d3ad

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Citations in the corpus

Exchange Rates and Oil Prices: A Multivariate Stochastic Volatility Analysis (2012, neutral): “Benassy-Querea, Mignonb, and Penot (2007), Coudert, Mignon, and Penot (2007), Chen and Chen (2007), Ayadi (2005), Chaudhuri and Daniel (1998) and Krugman (1984) all provide evidence supporting this view.”
Multivariate High-Frequency-Based Volatility (HEAVY) Models (2012, background): “(2006) and Asai et al. (2006), where the focus in the latter is on multivariate stochastic volatility.”
Realized Volatility: A Review (2008, methodology): “…by the Riskmetrics methodology (Morgan, 1996) (see McAleer, 2005 for a recent exposition of a wide range of univariate and multivariate, conditional and stochastic, models of volatility, and Asai et al. (2006) for a review of the growing literature on multivariate stochastic volatility models).”
Bayesian Multivariate Time Series Methods for Empirical Macroeconomics (2010, neutral): “Discussions of various approaches can be found in Asai et al. (2006), and Chib et al. (2006, 2009) and the reader is referred to these papers for complete treatments. In this section, we will describe two approaches popular in macroeconomics. The first was popularized by Cogley and Sargent (2005), t”
A Generalized Dynamic Conditional Correlation Model: Simulation and Application to Many Assets (2009, background): “, Asai et al. (2006) for a recent review. By now, there are many variants of multivariate GARCH models available, see Bauwens et al. (2006). The current benchmark models seem to be the Constant Conditional Correlation (CCC) model of Bollerslev (1990) and its extensions, e.”
Modelling and Forecasting Multivariate Realized Volatility (2011, neutral): “(2009), and the model of Bauer and Vorkink (2007), who employ the matrix log transformation to guarantee positive definiteness of the forecast, are among the few proposed approaches for the dynamics of the whole realized covariance matrix.”
Autoregressive Conditional Duration Models in Finance: A Survey of the Theoretical and Empirical Literature (2008, background): “See, for instance, Shephard (2005) for a collection of important papers on this subject, Broto and Ruiz (2004) for a survey of estimation methods for univariate SV models as well as Asai et al. (2006) for a recent review on multivariate SV models.”
Multivariate stochastic volatility (2009, methodology): “αt+1 = μ + Φ(αt − μ )+ ηt, (Φ : diagonal), αt =v ech(At) ,η t ∼N p(p+1)/2(0, Σηη), as suggested in Asai et al. (2006) .”
Generalized dynamic factor models and volatilities: estimation and forecasting (2017, neutral): “In factor models for volatilities (approach(i)), common factors are 1We refer to the surveys by Bauwens et al. (2006), Asai et al. (2006), and Silvennoinen and Teräsvirta (2009) for comprehensive reviews of the subject.”
A multivariate Ornstein-Uhlenbeck type stochastic volatility model (2009, background): “Keywords: Barndorff-Nielsen-Shephard (BNS) stochastic volatility model; Lévy process; matrix subordinator; multivariate stochastic volatility; Ornstein-Uhlenbeck type process; state-space representation”
A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries (2008, background): “McAleer (2005) gives a recent exposition of a wide range of univariate and multivariate, conditional and stochastic, models f volatility, and Asai, McAleer, and Yu (2006) provide a review of the rapidly growing literatureon multivariate stochastic volatility models.”