tsbugs (version 1.2.1)

sv.bugs: Create BUGS Script of a Stochastic Volatility (SV) Model

Description

Create BUGS script of an SV time series model, similar those in Meyer and Yu (2002). Options allow for the inclusion of a different lag orders for the mean term, forecasts, posterior simulations from the model and alternative specification of prior distributions on each parameters.

Usage

sv.bugs(y, ar.order = 0, k = NULL, sim = FALSE, mean.centre = FALSE, beg = ar.order + 1, 
		mean.prior = ar.prior, ar.prior = "dnorm(0,1)", 
		sv.order = 1, 
		sv.mean.prior1 = "dnorm(0,0.001)", sv.mean.prior2 = NULL, 
		sv.ar.prior1 = "dunif(0,1)", sv.ar.prior2 = NULL, 
		sv.tol.prior = "dgamma(0.01,0.01)",
space = FALSE)

Arguments

y

Data to be used for the BUGS model.

ar.order

AR order of the mean process for BUGS model.

k

Length of forecast horizon to be included in the BUGS model.

sim

Enable posterior simulations to be included in the BUGS model. Default is FALSE.

mean.centre

Include a term to centre the data on its mean value. Default is FALSE.

beg

Starting value for which data are considered onwards (and including) in the likelihood of the BUGS model. By default this is the ar.order+1 but if comparing models of different orders, users may wish to set all beg to the same value.

mean.prior

Prior for mean term (not used if mean.centre is not set to TRUE). The distribution should be stated in BUGS syntax. By default, the same prior as the autoregressive terms are used.

ar.prior

Prior for autoregressive terms. The distribution should be stated in BUGS syntax. By default set to a normal distribution with mean 0 and tolerance 1 (dnorm(0,1)). The same prior is used for all autoregressive terms.

sv.order

AR order of the volatility process for BUGS model.

sv.mean.prior1

Prior distribution for the mean volatility term. The distribution should be stated in BUGS syntax. By default set to a normal distribution with mean 0 and tolerance 0.001 (dnorm(0,0.001)), as in Meyer and Yu (2002).

sv.mean.prior2

Alternative prior for mean volatility term. The distribution set here will be transformed by taking the negative logarithm. The distribution should be stated in BUGS syntax.

sv.ar.prior1

Prior for autoregressive terms of the volatility process. The distribution set here will be transformed by doubling and then subtracting 1 as in Meyer and Yu (2002). The distribution syntax must be recognisable to BUGS. By default set to a uniform distribution with bounds 0 and 1 (dunif(0,1)).

sv.ar.prior2

Alternative prior for autoregressive terms of the volatility process. The distribution should be stated in BUGS syntax.

sv.tol.prior

Prior for the tolerance of the volatility. The distribution should be stated in BUGS syntax. By default set to a uninformative gamma distribution.

space

Include some additional empty lines to seperate the likelihood, priors, forcasts and simulation components of the BUGS model.

Value

bug

A BUGS model of type tsbugs.

data

The data to be used with the model. This might extend the original data passed to the function with k unknown future values to be forecast.

info

Additional information on the length of the data, variance type and line numbers of certain parts of the BUGS model.

Details

This function create BUGS scripts of an SV time series model, similar those in Meyer and Yu (2002). Prior distributions should be set up using BUGS syntax. For example, dnorm is a normal distribution with mean and tolerance (not variance) arguments. Prior distributions for the mean and autoregressive parameter in the volatility process can be specified directly in sv.mean.prior1 and sv.ar.prior1 respectively. In sv.mean.prior2 the prior is given on the mean variance, and then transformed to the mean volatility. In sv.ar.prior2 the prior is given on the positive scale as illustrated in Meyer and Yu (2002). Only one set of prior distributions are allowed (i.e. either sv.ar.prior1 or sv.ar.prior2 should specified by the user).

The data y, can contain missing values. Note, if missing values are close the beginning of the series when a high order model for the mean process is specified (i.e. the second data point is missing and a AR(4) is specified) the user with have to set a high starting point for model to be fitted on (beg) for the BUGS model to function (i.e. 7).

References

Meyer, R. and J. Yu (2002). BUGS for a Bayesian analysis of stochastic volatility models. Econometrics Journal 3 (2), 198--215.

See Also

ar.bugs, rv.bugs

Examples

# NOT RUN {
# Create AR(0)-SV model for svpdx
y <- svpdx$pdx
plot(y, type = "l")
sv0 <- sv.bugs(y)
print(sv0)

# AR(1)-SV model with AR(2) structure in the volatility
sv1 <- sv.bugs(y, ar.order = 1, sv.order = 2)
print(sv1)

# AR(0)-SV model with alternative prior
sv0 <- sv.bugs(y, sv.ar.prior2 = "dunif(-1,1)")
print(sv0)

# AR(0)-SV model with forecast and posterior simulations
sv0 <- sv.bugs(y, k = 10, sim = TRUE)
print(sv0) 

# }
# NOT RUN {
  # Run in OpenBUGS
  writeLines(sv0$bug, "sv0.txt")
  library("R2OpenBUGS")
  
  sv0.bug <- bugs(data = sv0$data,
  				  inits = list(inits(sv0)),
  				  param = c(nodes(sv0, "prior")$name, "y.sim", "y.new"), 
  				  model = "sv0.txt", 
  				  n.iter = 20000, n.burnin = 10000, n.chains = 1)
  
  # Plot the parameters posteriors and traces
  library("coda")
  param.mcmc <- as.mcmc(sv0.bug$sims.matrix[, nodes(sv0, "prior")$name])
  plot(param.mcmc)
  
  # Plot posterior simulations using fanplot
  library("fanplot")
  y.mcmc <- sv0.bug$sims.list$y.sim
  y.pn <- pn(y.mcmc, st = 1)
  plot(y, type = "n")
  fan(y.pn)
  lines(y)
  
  # Plot forecast using fanplot
  ynew.mcmc <- sv0.bug$sims.list$y.new
  ynew.pn <- pn(ynew.mcmc, st = sv0$info$n + 1)
  plot(y, type = "n", xlim = sv0$info$n + c(-100, 20))
  fan(ynew.pn)
  lines(y)
  
  # Plot volatility
  h.mcmc <- sv0.bug$sims.list$h
  h.pn <- pn(h.mcmc, st = 1)
  sigma.pn <- pn(sims = sqrt(exp(h.mcmc)), st = 1)
  par(mfrow = c(2, 1), mar = rep(2, 4))
  plot(NULL, type = "n", xlim = tsp(h.pn)[1:2], ylim = range(h.pn[, 5:95]), main = "h_t")
  fan(h.pn)
  abline(v = length(y))
  plot(NULL, type = "n", xlim = tsp(sigma.pn)[1:2], ylim = range(sigma.pn[, 1:95]), main = "sigma_t")
  fan(sigma.pn)
  abline(v = length(y)) 
# }