Description Details Note Author(s) References See Also Examples

This packages provides a Markov chain Monte Carlo (MCMC) sampler for fully Bayesian estimation of latent factor stochastic volatility models. Sparsity can be achieved through the usage of Normal-Gamma priors on the factor loadings matrix.

In recent years, multivariate factor stochastic volatility (SV) models have been increasingly used to analyze financial and economic time series because they can capture joint (co-)volatility dynamics by a small number of latent time-varying factors. The main advantage of such a model is its parsimony, as all variances and covariances of a time series vector are governed by a low-dimensional common factor with the components following independent SV models. For problems of this kind, MCMC is a very efficient estimation method, it is however associated with a considerable computational burden when the number of assets is moderate to large. To overcome this, the latent volatility states are drawn "all without a loop" (AWOL), ancillarity-sufficiency interweaving strategies (ASIS) are applied to sample the univariate components as well as the factor loadings. Thus, this package can be applied directly estimate time-varying covariance and correlation matrices for medium-and high-dimensional time series. To guarantee sparsity, a hierarchical Normal-Gamma prior can be used for the factor loadings matrix which shrinks the unnecessary factor loadings towards zero.

This package is currently in active development; the interface of some of the functions might change. Moreover, even though I tried to carefully check everything, factorstochvol may still contain typos, inconsistencies, or even bugs. Your comments and suggestions are warmly welcome!

Gregor Kastner gregor.kastner@wu.ac.at

Kastner, G., Frühwirth-Schnatter, S., and Lopes, H.F. (2017).
Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models.
*Journal of Computational and Graphical Statistics*, **26**(4), 905–917,
doi: 10.1080/10618600.2017.1322091.

Kastner, G. (2019). Sparse Bayesian Time-Varying Covariance Estimation
in Many Dimensions. *Journal of Econometrics*, **210**(1), 98–115.
doi: 10.1016/j.jeconom.2018.11.007.

Kastner, G. and Frühwirth-Schnatter, S. (2014). Ancillarity-Sufficiency
Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic
Volatility Models. *Computational Statistics and Data Analysis*,
doi: 10.1016/j.csda.2013.01.002.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | ```
set.seed(1)
# simulate data from a (small) factor SV model:
sim <- fsvsim(series = 5, factors = 2)
# estimate the model (CAVEAT: only few draws!)
res <- fsvsample(sim$y, factors = 2, draws = 2000, burnin = 500)
# plot implied volas overtime:
voltimeplot(res)
# plot correlation matrix at some points in time:
par(mfrow = c(2,2))
corimageplot(res, seq(1, nrow(sim$y), length.out = 4),
fsvsimobj = sim, plotCI = 'circle',
plotdatedist = -2)
# plot (certain) covariances and correlations over time
par(mfrow = c(2,1))
covtimeplot(res, 1)
cortimeplot(res, 1)
# plot (all) correlations over time
corplot(res, fsvsimobj = sim, these = 1:10)
# plot factor loadings
par(mfrow = c(1,1))
facloadpointplot(res, fsvsimobj = sim)
facloadpairplot(res)
facloadcredplot(res)
facloaddensplot(res, fsvsimobj = sim)
# plot latent log variances
logvartimeplot(res, fsvsimobj = sim, show = "fac")
logvartimeplot(res, fsvsimobj = sim, show = "idi")
# plot communalities over time
comtimeplot(res, fsvsimobj = sim, show = 'joint')
comtimeplot(res, fsvsimobj = sim, show = 'series')
``` |

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