Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 2 3 4 5 6 7 | ```
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)
``` |

`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 |

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

`beg` |
Starting value for which data are considered onwards (and including) in the likelihood of the BUGS model. By default this is the |

`mean.prior` |
Prior for mean term (not used if mean.centre is not set to |

`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 ( |

`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 ( |

`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 ( |

`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. |

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).

`bug ` |
A BUGS model of type |

`data ` |
The data to be used with the model. This might extend the original data passed to the function with |

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

Guy J. Abel

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 | ```
# 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))
## End(Not run)
``` |

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