Analysis of Exchange Rates via Multivariate Bayesian Factor Stochastic Volatility Models
Multivariate factor stochastic volatility (SV) models are increasingly used for the analysis of multivariate financial and economic time series because they can capture the volatility dynamics by a small number of latent factors. The main advantage of suc
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Analysis of Exchange Rates via Multivariate Bayesian Factor Stochastic Volatility Models Gregor Kastner, Sylvia Frühwirth-Schnatter, and Hedibert F. Lopes
Abstract Multivariate factor stochastic volatility (SV) models are increasingly used for the analysis of multivariate financial and economic time series because they can capture the volatility dynamics by a small number of latent factors. The main advantage of such a model is its parsimony, as the variances and covariances of a time series vector are governed by a low-dimensional common factor with the components following independent SV models. For high-dimensional problems of this kind, Bayesian MCMC estimation is a very efficient estimation method; however, it is associated with a considerable computational burden when the dimensionality of the data is moderate to large. To overcome this, we avoid the usual forward-filtering backward-sampling (FFBS) algorithm by sampling “all without a loop” (AWOL), consider various reparameterizations such as (partial) noncentering, and apply an ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation at a univariate level, which can be applied directly to heteroskedasticity estimation for latent variables such as factors. To show the effectiveness of our approach, we apply the model to a vector of daily exchange rate data.
G. Kastner () • S. Frühwirth-Schnatter WU Vienna University of Economics and Business, Institute for Statistics and Mathematics, Welthandelsplatz 1, 1020 Wien, Austria e-mail: [email protected]; [email protected] H.F. Lopes The University of Chicago, Booth School of Business, 5807 South Woodlawn Avenue, Chicago IL 60637, USA e-mail: [email protected] 181 E. Lanzarone and F. Ieva (eds.), The Contribution of Young Researchers to Bayesian Statistics, Springer Proceedings in Mathematics & Statistics 63, DOI 10.1007/978-3-319-02084-6__35, © Springer International Publishing Switzerland 2014
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35.1 Introduction In the recent years, factor SV models have been progressively applied to important problems in financial econometrics such as asset allocation and asset pricing. These models extend standard factor pricing models such as the arbitrage pricing theory and the capital asset pricing model. As opposed to factor SV models, standard factor pricing models do not attempt to model the dynamics of the volatilities of the asset returns and usually assume that the covariance matrix Σt ≡ Σ is constant. Empirical evidence suggests that multivariate factor SV models are a promising approach for modeling multivariate time-varying volatility, explaining excess asset returns, and generating optimal portfolio strategies. Following [1], the model reads 1/2
yt = Λft + Σt 1/2
ft = V t
ut ,
t ,
t ∼ Nm (0, Im ) ,
ut ∼ Nr (0, Ir ) ,
(1) (2)
where for t = 1, . . . , T , the vector yt = (y1t , . . . , ymt ) consists of (potentially demeaned) log returns of m observed time series, Σt = Diag(exp(h1t ), . . . , exp(hmt )), Vt = Diag(exp(hm+1
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