predict.svdraws function

Prediction of Future Returns and Log-Volatilities

Simulates draws from the predictive density of the returns and the latent log-volatility process. The same mean model is used for prediction as was used for fitting, which is either a) no mean parameter, b) constant mean, c) AR(k) structure, or d) general Bayesian regression. In the last case, new regressors need to be provided for prediction.

## S3 method for class 'svdraws'
predict(object, steps = 1L, newdata = NULL, ...)

Arguments

• object: svdraws or svldraws object.
• steps: optional single number, coercible to integer. Denotes the number of steps to forecast.
• newdata: only in case d) of the description corresponds to input parameter designmatrix in svsample. A matrix of regressors with number of rows equal to parameter steps.
• ...: currently ignored.

Returns

Returns an object of class svpredict, a list containing three elements: - vol: mcmc.list object of simulations from the predictive density of the standard deviations sd_(n+1),...,sd_(n+steps)

• h: mcmc.list object of simulations from the predictive density of h_(n+1),...,h_(n+steps)

• y: mcmc.list object of simulations from the predictive density of y_(n+1),...,y_(n+steps)

Note

You can use the resulting object within plot.svdraws (see example below), or use the list items in the usual coda methods for mcmc objects to print, plot, or summarize the predictions.

Examples

# Example 1
## Simulate a short and highly persistent SV process 
sim <- svsim(100, mu = -10, phi = 0.99, sigma = 0.2)

## Obtain 5000 draws from the sampler (that's not a lot)
draws <- svsample(sim$y, draws = 5000, burnin = 100,
  priormu = c(-10, 1), priorphi = c(20, 1.5), priorsigma = 0.2)

## Predict 10 days ahead
fore <- predict(draws, 10)

## Check out the results
summary(predlatent(fore))
summary(predy(fore))
plot(draws, forecast = fore)

# Example 2
## Simulate now an SV process with an AR(1) mean structure
len <- 109L
simar <- svsim(len, phi = 0.93, sigma = 0.15, mu = -9)
for (i in 2:len) {
  simar$y[i] <- 0.1 - 0.7 * simar$y[i-1] + simar$vol[i] * rnorm(1)
}

## Obtain 7000 draws
drawsar <- svsample(simar$y, draws = 7000, burnin = 300,
  designmatrix = "ar1", priormu = c(-10, 1), priorphi = c(20, 1.5),
  priorsigma = 0.2)

## Predict 7 days ahead (using AR(1) mean for the returns)
forear <- predict(drawsar, 7)

## Check out the results
plot(forear)
plot(drawsar, forecast = forear)

## Not run:

# Example 3
## Simulate now an SV process with leverage and with non-zero mean
len <- 96L
regressors <- cbind(rep_len(1, len), rgamma(len, 0.5, 0.25))
betas <- rbind(-1.1, 2)
simreg <- svsim(len, rho = -0.42)
simreg$y <- simreg$y + as.numeric(regressors %*% betas)

## Obtain 12000 draws
drawsreg <- svsample(simreg$y, draws = 12000, burnin = 3000,
  designmatrix = regressors, priormu = c(-10, 1), priorphi = c(20, 1.5),
  priorsigma = 0.2, priorrho = c(4, 4))

## Predict 5 days ahead using new regressors
predlen <- 5L
predregressors <- cbind(rep_len(1, predlen), rgamma(predlen, 0.5, 0.25))
forereg <- predict(drawsreg, predlen, predregressors)

## Check out the results
summary(predlatent(forereg))
summary(predy(forereg))
plot(forereg)
plot(drawsreg, forecast = forereg)
## End(Not run)

See Also

plot.svdraws, volplot.