Maximum Likelihood Estimation
Maximum likelihood estimation.
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estMaxLik(obj1, obj2=NULL, ...) ## S3 method for class 'TSmodel' estMaxLik(obj1, obj2, algorithm="optim", algorithm.args=list(method="BFGS", upper=Inf, lower=-Inf, hessian=TRUE), ...) ## S3 method for class 'TSestModel' estMaxLik(obj1, obj2=TSdata(obj1), ...) ## S3 method for class 'TSdata' estMaxLik(obj1, obj2, ...)
an object of class TSmodel, TSdata or TSestModel
TSdata or a TSmodel to be fitted with obj1.
the algorithm ('optim', or 'nlm' ) to use for maximization.
arguments for the optimization algorithm.
arguments passed on to other methods.
obj2 should specify a
obj1 is a
NULL, then the data is extracted from
TSmodel object is used to specify both the initial parameter
values and the model structure (the placement of the parameters
in the various arrays of the TSmodel). Estimation attempts to minimimize the
negative log likelihood (as returned by
l ) of the given model
structure by adjusting the
parameter values. A
TSmodel can also have constant values in
some array elements, and these are not changed. (See
fixConstants regarding setting of constants.)
With the number of parameter typically used in multivariate time series
models, the default maximum number of iterations may not be enough. Be sure to
check for convergence (a warning is printed at the end, or use
on the result). The maximum iterations is passed to the estimation algorithm
algorithm.args, but the elements of that list will depend on the
algorithm (so see the help for the alogrithm).
The example below is for the default
The value returned is an object of class TSestModel with additional
est$converged, which is TRUE or FALSE indicating convergence,
est$converceCode, which is the code returned by the estimation algorithm,
est$results, which are detailed results returned by the estimation
algorithm. The hessian and gradient in results could potentially
be used for restarting in the case of non-convergence, but that has not
yet been implemented.
Maximum likelihood estimation of multivariate time series models tends to be
problematic, even when a good structure and good starting parameter values
are known. This is especially true for state space models. Also, it seems that
in-sample fit is often obtained at the expense of out-of-sample forecasting
ability. If a prior model structure is not important then the
estimation method may be preferable.
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