dlm (version 1.1-2)

dlmForecast: Prediction and simulation of future observations

Description

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.

Usage

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

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.

Value

• A list with components ll{ 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.

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")