dlmSmooth function

DLM smoothing

The function apply Kalman smoother to compute smoothed values of the state vectors, together with their variance/covariance matrices.

dlmSmooth(y, ...)
## Default S3 method:
dlmSmooth(y, mod, ...)
## S3 method for class 'dlmFiltered'
dlmSmooth(y, ..., debug = FALSE)

Arguments

• y: an object used to select a method.
• ...: futher arguments passed to or from other methods.
• mod: an object of class "dlm".
• debug: if debug=FALSE, faster C code will be used, otherwise all the computations will be performed in R.

Details

The default method returns means and variances of the smoothing distribution for a data vector (or matrix) y and a model mod.

dlmSmooth.dlmFiltered produces the same output based on a dlmFiltered object, typically one produced by a call to dlmFilter.

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

Returns

A list with components - s: Time series (or matrix) of smoothed values of the state vectors. The series starts one time unit before the first observation.

• U.S: See below.

• D.S: Together with U.S, it gives the SVD of the variances of the smoothing errors.

Warning

The observation variance V in mod must be nonsingular.

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.

Giovanni Petris (2010), An R Package for Dynamic Linear Models. Journal of Statistical Software, 36(12), 1-16. https://www.jstatsoft.org/v36/i12/.

Petris, Petrone, and Campagnoli, Dynamic Linear Models with R, Springer (2009).

Author(s)

Giovanni Petris GPetris@uark.edu

See Also

See dlm for a description of dlm objects, dlmSvd2var to obtain a variance matrix from its SVD, dlmFilter for Kalman filtering, dlmMLE for maximum likelihood estimation, and dlmBSample for drawing from the posterior distribution of the state vectors.

Examples

s <- dlmSmooth(Nile, dlmModPoly(1, dV = 15100, dW = 1470))
plot(Nile, type ='o')
lines(dropFirst(s$s), col = "red")

## Multivariate
set.seed(2)
tmp <- dlmRandom(3, 5, 20)
obs <- tmp$y
m <- tmp$mod
rm(tmp)

f <- dlmFilter(obs, m)
s <- dlmSmooth(f)
all.equal(s, dlmSmooth(obs, m))