dlmFilter: DLM filtering

Description

The functions applies Kalman filter to compute filtered values of the state vectors, together with their variance/covariance matrices. By default the function returns an object of class "dlmFiltered". Methods for residuals and tsdiag for objects of class "dlmFiltered" exist.

Usage

dlmFilter(y, mod, debug = FALSE, simplify = FALSE)

Arguments

The data. y can be a vector, a matrix, a univariate or multivariate time series.

mod

An object of class dlm, or a list with components m0, C0, FF, V, GG, W, and optionally JFF, JV, JGG, JW

debug

If FALSE, faster C code will be used, otherwise all the computations will be performed in R.

simplify

See value below.

Value

A list with the components described below. If simplify is FALSE, the returned list has class "dlmFiltered".
yThe input data, coerced to a matrix. This is present only if simplify is FALSE.
modThe argument mod (possibly simplified).
mTime series (or matrix) of filtered values of the state vectors. The series starts one time unit before the first observation.
U.CSee below.
D.CTogether with U.C, it gives the SVD of the variances of the estimation errors. The variance of $m[t,]-theta[t,]$ is given by U.C[[t]] %*% diag(D.C[t,]^2) %*% t(U.C[[t]]).
aTime series (or matrix) of predicted values of the state vectors given the observations up and including the previous time unit.
U.RSee below.
D.RTogether with U.R, it gives the SVD of the variances of the prediction errors. The variance of $a[t,]-theta[t,]$ is given by U.R[[t]] %*% diag(D.R[t,]^2) %*% t(U.R[[t]]).
fTime series (or matrix) of one-step-ahead forecast of the observations.

Details

The calculations are based on the singular value decomposition (SVD) of the relevant matrices. Variance matrices are returned in terms of their SVD.

References

Zhang, Y. and Li, X.R., Fixed-interval smoothing algorithm based on singular value decomposition, Proceedings of the 1996 IEEE International Conference on Control Applications.

Examples

Run this code

nileBuild <- function(par) {
  dlmModPoly(1, dV = exp(par[1]), dW = exp(par[2]))
}
nileMLE <- dlmMLE(Nile, rep(0,2), nileBuild); nileMLE$conv
nileMod <- nileBuild(nileMLE$par)
unlist(nileMod[c("V","W")])
nileFilt <- dlmFilter(Nile, nileMod)
nileSmooth <- dlmSmooth(nileFilt)
plot(cbind(Nile, nileFilt$m[-1], nileSmooth$s[-1]), plot.type='s',
     col=c("black","red","blue"), ylab="Level", main="Nile river", lwd=c(1,2,2))

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