tsbugs (version 1.2.1)

rv.bugs: Create BUGS Script of a Random Variance Shift Model

Description

Create BUGS script of an Random Variance (RV) shift model similar to that of McCulloch and Tsay (1991). 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 some parameters.

Usage

rv.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)", 
		rv.tol0.prior = "dgamma(0.000001,0.000001)", rv.eps.prior = "dbeta(1, 100)", 
		rv.ilambda2.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. Default is 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 this is set to a normal distribution with mean 0 and tolerance 1 (dnorm(0,1)). The same prior is used for all autoregressive terms.

rv.tol0.prior

Prior distribution for the time-specific tolerance of the first data point, from which potential future shifts are based on. This must be a distribution of syntax recognisable to BUGS. By default this is set to a uninformative gamma distribution.

rv.eps.prior

Prior distribution for the epsilon term (the probability of the variance shift). This must be a distribution of syntax recognisable to BUGS and in theory restricted to generate values between 0 and 1, although no check is made to ensure users specify distributions as such. By default this argument is set to a beta distribution with a small probability for a variance shift (dbeta(1,100)).

rv.ilambda2.prior

Prior for the inverse of the squared lambda term of a variance shift model. The lambda represents the magnitude (on the log scale) of average variance shifts, thus ilambda2 in a BUGS model is a similar to a tolerance on the shifts in the variance, and hence must be positive. By default this is set to a gamma distribution (dgamma(0.01,0.01)).

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 random variance shift model adapted from McCulloch and Tsay (1991). Prior distributions for the tolerance of the initial data point, the probability of the variance shift, and the magnitude of average variance shifts can be specified. by users to differ from their default values. User specified prior distributions should be set up using BUGS syntax. For example, dnorm is a normal distribution with mean and tolerance (not variance) arguments.

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

McCulloch, R. E. and R. S. Tsay (1993). Bayesian Inference and Prediction for Mean and Variance Shifts in Autoregressive Time Series. Journal of the American Statistical Association 88 (423), 968--978.

See Also

ar.bugs, sv.bugs

Examples

# NOT RUN {
# Create AR(0)-SV model for population growth rate
r <- ts(ew[2:167]/ew[1:166]-1, start=1841)
y <- diff(r) 
plot(y, type = "l")
rv0 <- rv.bugs(y)
print(rv0)

# AR(2)-RV model with alternative priors
rv2 <- rv.bugs(y, rv.eps.prior = "dbeta(1,20)")
print(rv2)

# AR(0)-RV model with posterior simulations
rv0 <- rv.bugs(y, sim = TRUE)
print(rv0) 

# }
# NOT RUN {
  # Run in OpenBUGS
  writeLines(rv0$bug, "rv0.txt")
  library("R2OpenBUGS")
  
  # Run model (can take some time, depending on data length)
  rv0.bug <- bugs(data = rv0$data,
  				 inits = list(inits(rv0)), 
  				 param = c(nodes(rv0, "prior")$name, "y.sim", "y.new"), 
  				 model = "rv0.txt", 
  				 n.iter = 11000, n.burnin = 1000, n.chains = 1)
  
  # Plot the parameters posteriors and traces
  library("coda")
  param.mcmc <- as.mcmc(rv0.bug$sims.matrix[, nodes(rv0, "prior")$name])
  plot(param.mcmc)
  
  # Plot posterior simulations using fanplot
  library("fanplot")
  y.mcmc <- rv0.bug$sims.list$y.sim
  y.pn <- pn(y.mcmc, st = start(y)[1])
  plot(y, type = "n")
  fan(y.pn)
  lines(y)
  
  # Plot volatility
  h.mcmc <- rv0.bug$sims.list$h
  h.pn <- pn(h.mcmc, st = start(y)[1])
  sigma.pn <- pn(sims = sqrt(exp(h.mcmc)), st = start(y)[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)
  plot(NULL, type = "n", xlim = tsp(sigma.pn)[1:2], ylim = range(sigma.pn[, 1:95]), main = "sigma_t")
  fan(sigma.pn) 
# }