dlmForecast function

Prediction and simulation of future observations

The function evaluates the expected value and variance of future observations and system states. It can also generate a sample from the distribution of future observations and system states.

dlmForecast(mod, nAhead = 1, method = c("plain", "svd"), sampleNew = FALSE)

Arguments

• mod: an object of class "dlm", or a list with components m0, C0, FF, V, GG, and W, defining the model and the parameters of the prior distribution. mod can also be an object of class "dlmFiltered", such as the output from dlmFilter.

• nAhead: number of steps ahead for which a forecast is requested.

• method: method="svd" uses singular value decomposition for the calculations. Currently, only method="plain"

  is implemented.

• sampleNew: if sampleNew=n for an integer n, them a sample of size n from the forecast distribution of states and observables will be returned.

Returns

A list with components

a	matrix of expected values of future states
R	list of variances of future states
f	matrix of expected values of future observations
Q	list of variances of future observations
newStates	list of matrices containing the simulated future values
	of the states. Each component of the list corresponds
	to one simulation.
newObs	same as newStates , but for the observations.

The last two components are not present if sampleNew=FALSE.

Note

The function is currently entirely written in and is not particularly fast. Currently, only constant models are allowed.

Examples

## Comparing theoretical prediction intervals with sample quantiles
set.seed(353)
n <- 20; m <- 1; p <- 5
mod <- dlmModPoly() + dlmModSeas(4, dV=0)
W(mod) <- rwishart(2*p,p) * 1e-1
m0(mod) <- rnorm(p, sd=5)
C0(mod) <- diag(p) * 1e-1
new <- 100
fore <- dlmForecast(mod, nAhead=n, sampleNew=new)
ciTheory <- (outer(sapply(fore$Q, FUN=function(x) sqrt(diag(x))), qnorm(c(0.1,0.9))) +
             as.vector(t(fore$f)))
ciSample <- t(apply(array(unlist(fore$newObs), dim=c(n,m,new))[,1,], 1,
                    FUN=function(x) quantile(x, c(0.1,0.9))))
plot.ts(cbind(ciTheory,fore$f[,1]),plot.type="s", col=c("red","red","green"),ylab="y")
for (j in 1:2) lines(ciSample[,j], col="blue")
legend(2,-40,legend=c("forecast mean", "theoretical bounds", "Monte Carlo bounds"),
       col=c("green","red","blue"), lty=1, bty="n")

Author(s)

Giovanni Petris GPetris@uark.edu