# Parameter estimation by maximum likelihood The function returns the MLE of unknown parameters in the specification of a state space model. ```r 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/](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 ```r 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")] ```

dlmMLE function