dlmMLE function

Parameter estimation by maximum likelihood

The function returns the MLE of unknown parameters in the specification of a state space model.

dlmMLE(y, parm, build, method = "L-BFGS-B", ..., debug = FALSE)

Arguments

• y: a vector, matrix, or time series of data.
• parm: vector of initial values - for the optimization routine - of the unknown parameters.
• build: a function that takes a vector of the same length as parm and returns an object of class dlm, or a list that may be interpreted as such.
• method: passed to optim.
• ...: additional arguments passed to optim and build.
• debug: if debug=TRUE, the likelihood calculations are done entirely in R, otherwise C functions are used.

Details

The evaluation of the loglikelihood is done by dlmLL. For the optimization, optim is called. It is possible for the model to depend on additional parameters, other than those in parm, passed to build via the ... argument.

Returns

The function dlmMLE returns the value returned by optim.

References

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).

Warning

The build argument must return a dlm with nonsingular observation variance V.

Author(s)

Giovanni Petris GPetris@uark.edu

See Also

dlmLL, dlm.

Examples

data(NelPlo)
### multivariate local level -- seemingly unrelated time series
buildSu <- function(x) {
  Vsd <- exp(x[1:2])
  Vcorr <- tanh(x[3])
  V <- Vsd %o% Vsd
  V[1,2] <- V[2,1] <- V[1,2] * Vcorr
  Wsd <- exp(x[4:5])
  Wcorr <- tanh(x[6])
  W <- Wsd %o% Wsd
  W[1,2] <- W[2,1] <- W[1,2] * Wcorr
  return(list(
              m0 = rep(0,2),
              C0 = 1e7 * diag(2),
              FF = diag(2),
              GG = diag(2),
              V = V,
              W = W))
}

suMLE <- dlmMLE(NelPlo, rep(0,6), buildSu); suMLE
buildSu(suMLE$par)[c("V","W")]
StructTS(NelPlo[,1], type="level") ## compare with W[1,1] and V[1,1]
StructTS(NelPlo[,2], type="level") ## compare with W[2,2] and V[2,2]

## multivariate local level model with homogeneity restriction
buildHo <- function(x) {
  Vsd <- exp(x[1:2])
  Vcorr <- tanh(x[3])
  V <- Vsd %o% Vsd
  V[1,2] <- V[2,1] <- V[1,2] * Vcorr
  return(list(
              m0 = rep(0,2),
              C0 = 1e7 * diag(2),
              FF = diag(2),
              GG = diag(2),
              V = V,
              W = x[4]^2 * V))
}

hoMLE <- dlmMLE(NelPlo, rep(0,4), buildHo); hoMLE
buildHo(hoMLE$par)[c("V","W")]