stochvolTMB

stochvolTMB is a package for fitting stochastic volatility (SV) models to time series data. It is inspired by the package stochvol, but parameter estimates are obtained through optimization and not MCMC, leading to significant speed up. It is built on Template Model Builder for fast and efficient estimation. The latent volatility is integrated out of the likelihood using the Laplace approximation and automatic differentiation (AD) is used for accurate evaluation of derivatives.

Four distributions for the observational error are implemented:

• Gaussian - The classic SV model with Gaussian noise
• t - t-distributed noise for heavy tail returns
• Leverage - Extending the Gaussian model by allowing observed returns to be correlated with the latent volatility
• Skew-Gaussian - Skew-Gaussian distributed noise for asymmetric returns

Installation

To install the current stable release from CRAN, use

install.packages("stochvolTMB")

To install the current development version, use

# install.packages("devtools")
devtools::install_github("JensWahl/stochvolTMB")

If you would also like to build and view the vignette locally, use

devtools::install_github("JensWahl/stochvolTMB", dependencies = TRUE, build_vignettes = TRUE)

Example

The main function for estimating parameters is estimate_parameters:

library(stochvolTMB, warn.conflicts = FALSE)

# load s&p500 data from 2005 to 2018
data(spy)

# find the best model using AIC 
gaussian <- estimate_parameters(spy$log_return, model = "gaussian", silent = TRUE)
t_dist <- estimate_parameters(spy$log_return, model = "t", silent = TRUE)
skew_gaussian <- estimate_parameters(spy$log_return, model = "skew_gaussian", silent = TRUE)
leverage <- estimate_parameters(spy$log_return, model = "leverage", silent = TRUE)

AIC(gaussian, t_dist, skew_gaussian, leverage)
#>               df       AIC
#> gaussian       3 -23430.57
#> t_dist         4 -23451.69
#> skew_gaussian  4 -23440.87
#> leverage       4 -23608.85
# The leverage model stand out with an AIC for below the other models

# get parameter estimates with standard error
estimates <- summary(leverage)
head(estimates, 10)
#>       parameter     estimate    std_error     z_value       p_value
#>  1:     sigma_y  0.008338425 0.0004163323  20.0282918  3.121840e-89
#>  2:     sigma_h  0.273445746 0.0182642070  14.9716736  1.124552e-50
#>  3:         phi  0.967720808 0.0043682334 221.5359687  0.000000e+00
#>  4:         rho -0.748692587 0.0322489934 -23.2159986 3.138829e-119
#>  5: log_sigma_y -4.786880902 0.0499293705 -95.8730474  0.000000e+00
#>  6: log_sigma_h -1.296652044 0.0667927998 -19.4130512  5.986433e-84
#>  7:   phi_logit  4.110208379 0.1375465458  29.8823090 3.341130e-196
#>  8:   rho_logit -1.939946750 0.1467666528 -13.2178987  6.916940e-40
#>  9:           h -0.536253306 0.5182212112  -1.0347961  3.007641e-01
#> 10:           h -0.207810839 0.4245275458  -0.4895108  6.244801e-01
#>            type
#>  1: transformed
#>  2: transformed
#>  3: transformed
#>  4: transformed
#>  5:       fixed
#>  6:       fixed
#>  7:       fixed
#>  8:       fixed
#>  9:      random
#> 10:      random

## plot estimated volatility with 95 % confidence interval
plot(leverage, include_ci = TRUE, dates = spy$date)

Shiny app

By running demo() you start a shiny application where you can visually inspect the effect of choosing different models and parameter configurations

demo()