factorstochvol-package: Bayesian Estimation of (Sparse) Latent Factor Stochastic Volatility Models through MCMC

Description

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.

Arguments

Author

Gregor Kastner gregor.kastner@wu.ac.at

Details

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.

References

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, tools:::Rd_expr_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. tools:::Rd_expr_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, tools:::Rd_expr_doi("10.1016/j.csda.2013.01.002").

Examples

Run this code

# \donttest{
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')
# }