SV.mcmc: Fit Bayesian Stochastic Volatility Model

In astsa: Applied Statistical Time Series Analysis

Fit Bayesian Stochastic Volatility Model

Description

Fits a stochastic volatility model to a univariate time series of returns.

Usage

SV.mcmc(y, nmcmc = 1000, burnin = 100, init = NULL, hyper = NULL, tuning = NULL, 
         sigma_MH = NULL, npart = NULL, mcmseed = NULL)

Arguments

y	single time series of returns
nmcmc	number of iterations for the MCMC procedure
burnin	number of iterations to discard for the MCMC procedure
init	initial values of (phi, sigma, beta) - default is c(0.9, 0.5, .1)
hyper	hyperparameters for bivariate normal distribution of (phi, sigma); user inputs (mu_phi, mu_q, sigma_phi, sigma_q, rho) - default is c(0.9, 0.5, 0.075, 0.3, -0.25)
tuning	tuning parameter - default is .03
sigma_MH	covariance matrix used for random walk Metropolis; it will be scaled by tuning in the script - default is matrix(c(1,-.25,-.25,1), nrow=2, ncol=2)
npart	number of particles used in particle filter - default is 10
mcmseed	seed for mcmc - default is 90210

Details

The log-volatility process is x_t and the returns are y_t. The SV model is

x_t = φ x_{t-1} + σ w_t \qquad y_t = β \exp\{\frac{1}{2} x_t\}ε_t

where w_t and ε_t are independent standard normal white noise.

The model is fit using a technique described in the paper listed below (in the Source section) where the state parameters (φ, σ) are sampled simultaneously with a bivariate normal prior specified in the arguments init and hyper.

Two graphics are returned: (1) the three parameter traces [with effective sample sizes (ESS)], their ACFs, and their histograms with the .025, .5, and .975 quantiles displayed, and (2) the log-volatility posterior mean along with corresponding .95 credible intervals.

Value

Returned invisibly:

phi	vector of sampled state AR parameter
sigma	vector of sampled state error stnd deviation
beta	vector of sampled observation error scale
log.vol	matrix of sampled log-volatility
options	values of the input arguments

Note

Except for the data, all the other inputs have defaults. The time to run and the acceptance rate are returned at the end of the analysis. The acceptance rate should be around 28% and this can be adjusted using the tuning parameter.

Author(s)

D.S. Stoffer

Source

Gong & Stoffer (2021). A note on efficient fitting of stochastic volatility models. Journal of Time Series Analysis, 42(2), 186-200. https://github.com/nickpoison/Stochastic-Volatility-Models

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 
#--   A minimal example  --##
myrun <- SV.mcmc(sp500w)   # results in object myrun - don't forget it 

str(myrun)                 # an easy way to see the default input options

## End(Not run)

astsa documentation built on Jan. 10, 2023, 1:11 a.m.