svm {bssm}

Stochastic Volatility Model

Description

Constructs a simple stochastic volatility model with Gaussian errors and first order autoregressive signal. See the main vignette for details.

Usage

svm(y, mu, rho, sd_ar, sigma)

Arguments

y

A numeric vector or a ts object of observations.

mu

A prior for mu parameter of transition equation. Should be an object of class bssm_prior.

rho

A prior for autoregressive coefficient. Should be an object of class bssm_prior.

sd_ar

A prior for the standard deviation of noise of the AR-process. Should be an object of class bssm_prior.

sigma

A prior for sigma parameter of observation equation, internally denoted as phi. Should be an object of class bssm_prior. Ignored if mu is provided. Note that typically parametrization using mu is preferred due to better numerical properties and availability of better Gaussian approximation. Most notably the global approximation approach does not work with sigma parameterization as sigma is not a parameter of the resulting approximate model.

Value

An object of class svm.

Examples

data("exchange")
y <- exchange[1:100] # for faster CRAN check
model <- svm(y, rho = uniform(0.98, -0.999, 0.999),
 sd_ar = halfnormal(0.15, 5), sigma = halfnormal(0.6, 2))

obj <- function(pars) {
   -logLik(svm(y, 
     rho = uniform(pars[1], -0.999, 0.999),
     sd_ar = halfnormal(pars[2], 5),
     sigma = halfnormal(pars[3], 2)), particles = 0)
}
opt <- optim(c(0.98, 0.15, 0.6), obj, 
  lower = c(-0.999, 1e-4, 1e-4),
  upper = c(0.999, 10, 10), method = "L-BFGS-B")
pars <- opt$par
model <- svm(y, 
  rho = uniform(pars[1],-0.999,0.999),
  sd_ar = halfnormal(pars[2], 5),
  sigma = halfnormal(pars[3], 2))

# alternative parameterization  
model2 <- svm(y, rho = uniform(0.98,-0.999, 0.999),
 sd_ar = halfnormal(0.15, 5), mu = normal(0, 0, 1))

obj2 <- function(pars) {
   -logLik(svm(y, 
     rho = uniform(pars[1], -0.999, 0.999),
     sd_ar = halfnormal(pars[2], 5),
     mu = normal(pars[3], 0, 1)), particles = 0)
}
opt2 <- optim(c(0.98, 0.15, 0), obj2, lower = c(-0.999, 1e-4, -Inf),
  upper = c(0.999, 10, Inf), method = "L-BFGS-B")
pars2 <- opt2$par
model2 <- svm(y, 
  rho = uniform(pars2[1],-0.999,0.999),
  sd_ar = halfnormal(pars2[2], 5),
  mu = normal(pars2[3], 0, 1))

# sigma is internally stored in phi
ts.plot(cbind(model$phi * exp(0.5 * fast_smoother(model)), 
  exp(0.5 * fast_smoother(model2))), col = 1:2)