# 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. ```r 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 ```r ## 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

dlmForecast function