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Journal of Business & Economic Statistics
ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20
Multivariate Stochastic Volatility via Wishart
Processes: A Comment
Wolfgang Rinnergschwentner , Gottfried Tappeiner & Janette Walde
To cite this article: Wolfgang Rinnergschwentner , Gottfried Tappeiner & Janette Walde (2012) Multivariate Stochastic Volatility via Wishart Processes: A Comment, Journal of Business & Economic Statistics, 30:1, 164-164, DOI: 10.1080/07350015.2012.634358
To link to this article: http://dx.doi.org/10.1080/07350015.2012.634358
Published online: 22 Feb 2012.
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Multivariate Stochastic Volatility via Wishart
Processes: A Comment
Wolfgang R
INNERGSCHWENTNERDepartment of Statistics, University of Innsbruck, Innsbruck A-6020 (wolfgang.rinnergschwentner@uibk.ac.at)
Gottfried T
APPEINERDepartment of Economic Theory, Economic Policy and Economic History, University of Innsbruck, Innsbruck A-6020 (gottfried.tappeiner@uibk.ac.at)
Janette W
ALDEDepartment of Statistics, University of Innsbruck, Innsbruck A-6020 (janette.walde@uibk.ac.at)
This comment refers to an error in the methodology for estimating the parameters of the model developed by Philipov and Glickman for modeling multivariate stochastic volatility via Wishart processes. For estimation they used Bayesian techniques. The derived expressions for the full conditionals of the model parameters as well as the expression for the acceptance ratio of the covariance matrix are erroneous. In this erratum all necessary formulae are given to guarantee an appropriate implementation and application of the model.
KEY WORDS: Bayesian time series; Stochastic covariance; Time-varying correlation; Markov Chain Monte Carlo.
This comment refers to an error in the methodology for esti-mating the parameters of the model developed by Philipov and Glickman (2006) for modeling multivariate stochastic volatil-ity via Wishart processes. For estimation they used Bayesian techniques. There is an error in the derivation of the conditional posterior distribution forA−1. It contains the term tr(S−1
t
−1
t+1)
(cf. p. 327), where tr(A) is defined as the trace of matrixA. This expression is simplified to
tr
tion appears to be an erroneous application of the properties of the trace of a matrix. However, this derivation cannot be achieved
with known mathematical methods (Horn and Johnson1985).
Since the erroneous term in the conditional posterior ofA−1
appears in the conditional posterior distributions of the
param-eters ν and d, and in the acceptance ratio of −1
t , they are
also specified incorrectly. The correct expressions for all full conditionals as well as for the acceptance ratio of−1
t are
Using the correct expression of the sampler for A−1 the
MCMC sampler becomes more complex, because the full con-ditional ofA−1
no longer follows a known distribution. Philipov and Glickman (2006) drew the values forA−1
directly from a Wishart distribution and employ a simple Gibbs sampler. Now the Gibbs sampler must be combined with a Metropolis Hastings algorithm.
[Received August 2010. Accepted September 2011.]
REFERENCES
Horn, R., and Johnson, C. (1985), Matrix Analysis, Cambridge, MA: Cam-bridge University Press. [164]
Philipov, A., and Glickman, M. (2006), “Multivariate Stochastic Volatility via Wishart Processes,” Journal of Business and Economic Statistics, 24, 313–328. [164]
© 2012American Statistical Association Journal of Business & Economic Statistics
January 2012, Vol. 30, No. 1
DOI:10.1080/07350015.2012.634358
164
