Abstract
In this paper, we propose multivariate stochastic volatility models with a spherical parameterization of a Cholesky decomposition to make a time-dependent correlation matrix be positive definite without any constraints. An attractive feature of our model is that it can be easily fit using the R package NIMBLE. In addition to the spherical transformation, we introduce a multivariate L measure as a Bayesian model comparison criterion to assess the fit of different models. We present extensive simulation studies to examine the empirical performance of the proposed method and illustrate the methodology on time series of energy usage in a science building on the main campus of the University of Connecticut.Please confirm if the inserted city and country name is correct. Amend if necessary.RightPlease confirm if the corresponding author is correctly identified. Amend if necessary.Right
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Acknowledgements
We would like to thank the editor and two reviewers for their valuable comments. We thank the staff of the Department of Facilities at the University of Connecticut for providing the energy usage data. Dr. Chen’s research was partially supported by NIH Grants #GM70335 and #P01CA142538.
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Appendices
Appendix A: Trace plots for convergence diagnostics
In order to check the convergence of the MCMC algorithm, we get two random MCMC samples from a simulation replicate. The trace plots shown in Fig. 5 confirm that our proposed method has good convergence.
Trace plots for one replicate in simulation study
Appendix B: Marginal likelihood comparison
In order to check the performance of the marginal likelihood for model selection, we present selection results for Scenario 1 in Simulation III. We generate data from the SP-DMSV model. We fit both the SP-DMSV and FSV models, and compute the marginal likelihood under each model fit on the 2000 posterior samples. We have 100 replicates in Scenario 1. The logarithms of differences is shown in Fig. 6.
Boxplot for differences of marginal likelihood
Appendix C: Posterior estimates with credible bands
The posterior estimates with 95% credible bands for the last 50 time points are shown in Fig. 7.
Posterior estimates for last 50 time points with 95% credible bands (first row: variance (\(\sigma ^2_1.\sigma ^2_2,\sigma ^2_3\)); second row: correlation (\(\rho _{12},\rho _{13},\rho _{23}\)))
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Hu, G., Chen, MH. & Ravishanker, N. Bayesian analysis of spherically parameterized dynamic multivariate stochastic volatility models. Comput Stat 38, 845–869 (2023). https://doi.org/10.1007/s00180-022-01266-9
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DOI: https://doi.org/10.1007/s00180-022-01266-9