## The tsbugs package for R

I have/will update this post as I expanded the tsbugs package.

My tsbugs package has gone up on CRAN. I decided not to write a vignette for the submission, as it would have involved doing some estimation in BUGS via R2WinBUGS or R2OpenBUGS and running into some problems when submitted the package. Instead I thought I would post a quick guide below. Note, the package code is on my github if you would like to contribute more models to the package…

The functions in the tsbugs package are aimed to automate the writing of time series models to run in WinBUGS or OpenBUGS. I created these functions a while back when I was doing some work on model averaging for time series models. I found it a lot easier to build R functions to write the BUGS models than the more error-inducing process of copy and pasting BUGS scripts, and then making slight alterations to create new models. It also allowed me to add arguments to specify different lag lengths, prior distributions, variance assumptions and data lengths. Below are examples for three types of time series models; autorgressive models with constant variance, stochastic volatility and random variance shift models.

Autoregressive Models

The `ar.bugs` command builds a BUGS script for autoregressive (AR) models ready to use in R2OpenBUGS. For example, consider the `LakeHuron` data.

```LH <- LakeHuron
par(mfrow=c(2,1))
plot(LH, main="Level (ft)")
plot(diff(LH), main="Differenced Level")
```

We can construct a AR(1) model for this data (after differencing the data to obtain a stationary mean) as such:

```library("tsbugs")
ar1 <- ar.bugs(y=diff(LH), ar.order=1)
print(ar1)
```

The `ar.bugs` function allows for alternative specifications for prior distributions, forecasts and the inclusion of mean term:

```ar2 <- ar.bugs(y=diff(LH), ar.order=2, ar.prior="dunif(-1,1)",
var.prior="dgamma(0.001,0.001)", k = 10,
mean.centre = TRUE)
print(ar2)
```

The tsbugs objects can be used with R2OpenBUGS to easily run models from R. This is made even easier using the `inits` and `nodes` functions (also in the tsbugs package). For example:

```writeLines(ar2\$bug, "ar2.txt")
library("R2OpenBUGS")
ar2.bug <- bugs(data = ar2\$data,
inits = list(inits(ar2)),
param = c(nodes(ar2, "prior")\$name, "y.new"),
model = "ar2.txt",
n.iter = 11000, n.burnin = 1000, n.chains = 1)
```

Note, 1) the model is written to a .txt file (as required by R2OpenBUGS), 2) the data used is part of the `tsbugs` object. The `ar.bugs` command cleans the data and adds missing values at the end of the series for foretasted values, 3) the initial values offered by the inits function are very crude, and with more complicated data or models, users might be better off specifying there own list of initial values. The parameter traces and posterior distributions can be plotted using the coda package:

```library("coda")
param.mcmc <- as.mcmc(ar2.bug\$sims.matrix[,nodes(ar2, "prior")\$name])
plot(param.mcmc[,1:4])
```

The fanplot package can be used to plot the entire series of posterior predictive distributions. We may also plot (after deriving using the `diffinv` function) the posterior predictive distributions of the lake level:

```# derive future level
ynew.mcmc <- ar2.bug\$sims.list\$y.new
lhnew.mcmc <- apply(ynew.mcmc, 1, diffinv, xi = tail(LH,1))
lhnew.mcmc <- t(lhnew.mcmc[-1,])

# plot differenced
par(mfrow=c(2,1))
plot(diff(LH) ,xlim=k0+c(-50,10), main="Differenced Level")

library("fanplot")
k0 <- end(LH)[1]
fan(ynew.mcmc, start=k0+1, rcex=0.5)

# plot undifferenced
plot(LH, xlim=k0+c(-50,10), main="Level")
fan(lhnew.mcmc, start=k0+1, rcex=0.5)
```

Stochastic Volatility Models

The `sv.bugs` command builds a BUGS script for stochastic volatility SV models ready to use in R2OpenBUGS. For example, consider the `svpdx` data.

```# plot
plot(svpdx\$pdx, type = "l",
main = "Return of Pound-Dollar exchange rate data
from 2nd October 1981 to 28th June 1985",
cex.main = 0.8)
```

We can construct a AR(0)-SV model for this data, and also obtain posterior simulations using the `sv.bugs` command:

```y <- svpdx\$pdx
sv0 <- sv.bugs(y, sim=TRUE)
print(sv0)
```

This model closely matches those presented in
Meyer and Yu (2002). There are further options in the tsbugs package to incorporate different priors that do not involve transformations such as those for `psi1` above. Using R2OpenBUGS we can fit the model,

```# decent initial value for variance in first period
init <- inits(sv0, warn=FALSE)
init\$psi0 <- log(var(y))
# write bug
writeLines(sv0\$bug, "sv0.txt")
# might take a while to compile
sv0.bug <- bugs(data = sv0\$data,
inits = list(init),
param = c(nodes(sv0, "prior")\$name,"y.sim","h"),
model = "sv0.txt",
n.iter = 11000, n.burnin = 1000, n.chains = 1)
```

The volatility and estimates can be easily extracted,

```h.mcmc <- sv0.bug\$sims.list\$h
```

Which allows us to directly view the estimated volatility process or the time-dependent standard deviation using the fanplot package,

```# plot
plot(NULL, xlim = c(1, 945)+c(0,40), ylim = c(-4,2),
main="Estimated Volatility from SV Model")
# fan
fan(h.mcmc, type = "interval")
```

We can also plot the posterior simulations from the model:

```# derive percentiles
y.mcmc <- sv0.bug\$sims.list\$y.sim
# plot
plot(NULL, type = "l", xlim = c(1, 945)+c(0,20),
ylim = range(y),
main = "Posterior Model Simulations and Data")
fan(y.mcmc)
lines(y)
```

Random Variance Shift Models

The `rv.bugs` command builds a BUGS script for random variance (RV) shift models, similar to that of McCulloch and Tsay (1993) ready to use in R2OpenBUGS. Consider the `ew` data.

```r <- ts(ew[2:167]/ew[1:166]-1, start=1841)
y <- diff(r)
plot(y, main="Difference in England and Wales
Population Growth Rate")
```

We can create a BUGS script to fit a RV model to this data, including posterior simulations, using the `rv.bugs` command:

```rv0<-rv.bugs(y, sim=TRUE)
print(rv0)
```

and then run the script in R2OpenBUGS (this can take a couple of hours):

```# decent inital value for variance in first period
init <- inits(rv0, warn=FALSE)
init\$isig02<-sd(y)^-2
# write bug
writeLines(rv0\$bug,"rv0.txt")
# might take a while to compile
rv0.bug <- bugs(data = rv0\$data,
inits = list(init),
param = c(nodes(rv0, "prior")\$name,"y.sim",
"h","delta","beta"),
model = "rv0.txt",
n.iter = 11000, n.burnin = 1000, n.chains = 1)
```

We can plot the posterior simulations from the model using the fanplot package:

```# derive percentiles
y0 <- tsp(y)[1]
y.mcmc <- rv0.bug\$sims.list\$y.sim

# plot
plot(NULL, xlim=tsp(y)[1:2]+c(-5,5), ylim = range(y),
main="Posterior Simulations")
fan(y.mcmc, start = y0, rlab=c(10,50,90), llab=TRUE)
lines(y)
```

Alongside the posterior distributions of the standard deviations,

```# derive sigma
h.mcmc <- rv0.bug\$sims.list\$h
sigma.mcmc <- sqrt(exp(h.mcmc))
# plots
plot(NULL, xlim =tsp(y)[1:2]+c(-5,5), ylim = c(0,0.008),
main="Standard Deviation")
fan(sigma.mcmc, start = y0, rlab=c(5,50,95), llab = c(5,50,95))
```

The posterior distributions of the probability of a variance shift and multiplier effect of the shift in variance (`delta[t]` and `beta[t]` in the BUGS model) can also be plotted. Note, when there is no variance shift, the posterior of the `beta[t]` is similar to the prior distribution.

```#extract data
delta.mcmc <- rv0.bug\$sims.list\$delta
beta.mcmc <- rv0.bug\$sims.list\$beta

# plots
par(mfrow=c(2,1))
plot(NULL, xlim = tsp(y)[1:2]+c(-5,5), ylim = c(0,1),
main="Probability of Variance Change Point")
fan(delta.mcmc, start=y0, ln = NULL, rlab = NULL)

plot(NULL, xlim = tsp(y)[1:2]+c(-5,5), ylim = c(-2,2),
main="Variance Multiplier")
fan(beta.mcmc, start=y0)
```