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 here…

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") # add fan 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)

Speechless! Anyway, well done mate.

Happy new year Guy!

Any plan to visit Southampton soon? Maybe then I can have a chance to be talked through some of the clever stuff you don’t stop doing. I’m getting closer to conduct my sensitivity analysis so expect more bugs from this end.

Check you later,

Rich

________________________________ De : Guy Abel À : rkapend@yahoo.fr Envoyé le : Mardi 15 janvier 2013 16h26 Objet : [New post] tsbugs Package

WordPress.com gjabel posted: “My tsbugs package has gone up on CRAN. The functions 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 foun”

Hi Rich, Yep, coming over next week. I will come by for a chat. Guy

I expected that the code for prediction to be:

#forecasts

for(t in 98:107){

y.new[t] ~ dnorm(y.mean[t], isigma2)

}

and not the outcome code:

#forecasts

for(t in 98:107){

y.new[t] <- y[t]

}

Is this a bug or I missed something?

Thanks, great tool!

Pablo

I think that the likelihood for the forecast period (98-107) already has been made by this part:

#likelihood

for(t in 3:107){

y[t] ~ dnorm(y.mean[t], isigma2)

}

Then the y values for the forecast period (98-107) are copied into a new variable y.new just to make it ieasier to plot the forecast separately using fan(ynew.pn).

Thanks Pablo.

I think our code for the forecasts are broadly equivalent. Both of our stochastic y.new[t] is generated from the same time dependent mean and variance as my y[t]. However, in the BUGS model I have only set up random nodes for future values once (in the first for loop of the BUGS script, where WinBUGS or OpenBUGS will see the NA’s in the data as missing) and then relabeled them in the forecast chunk of the BUGS code. This works, as using the ar.bugs function the data is modified to add on the right amount of NA’s at the end of the series so BUGS treats them as random nodes (in the top loop). You can see the data (that is used in the data argument on the R2OpenBUGS bugs command) by entering ar2$data into the R console. If I did not modify the data, then I would need a new loop for forecasted values (like the one you propose). Hope this makes sense?

Thanks!

Basically you are following the forecasting style of arima() function in R.

Thanks a lot for making this package! This certainly lowers the threshold for using MCMC modelling for a lot of users.