stsm-package: Structural Time Series Models

In stsm: Structural Time Series Models

Description

This package provides algorithms to fit structural time series models by maximum likelihood.

Details

As witnessed in the special issue of the Journal of Statistical Software (Commandeur et al., 2011), the prevalent procedure to fit a structural time series model is as follows: 1) choose arbitrary starting values for the parameters, 2) evaluate the log-likelihood function by means of the Kalman filter, 3) obtain a new set of parameter values that lead to a higher value of the log-likelihood function by means of the L-BFGS-B algorithm, 4) iterate the searching procedure until a predetermined degree of convergence. Considering that there are several packages in R to run the Kalman filter (see for instance Tusell, 2011 and the documentation in package KFKSDS) and that the optim function in the stats package provides and interface to the L-BFGS-B and to other optimization algorithms, fitting a structural time series model may seem a simple procedure that requires little more than translating the matrices of the state space form of the model into the syntax of the chosen interface.

In practice, the process is not always that straightforward. As stated in the documentation of StructTS, optimization of structural models is a lot harder than many of the references admit. There are several details that should be taken into account when implementing the procedure described above, (L<c3><b3>pez-de-Lacalle, 2013).

There are not many packages in R that provide alternative procedures to fit structural models. It is probably a consequence of the widespread believe that all that is needed to carry out and analysis with structural time series models is an implementation of the Kalman filter together with a general purpose optimization algorithm.

The package stsm implements specific algorithms to fit models in the framework of the basic structural time series model. The following enhancements to general purpose optimization algorithms are implemented: scoring algorithm based on analytical derivatives, maximization of the time or frequency domain likelihood function, automatic choice of the optimal step size, concentration of a parameter, implementation of the original and a modified version of the expectation-maximization algorithm.

References

Commandeur, J.J.F., Koopman, S.J. and Ooms, M. (2011). ‘Statistical Software for State Space Methods’, Journal of Statistical Software, Vol. 41, No. 1, http://www.jstatsoft.org/v41/i01/.

Durbin, J. and Koopman, S.J. (2001). Time Series Analysis by State Space Methods. Oxford University Press.

Harvey, A.C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.

L<c3><b3>pez-de-Lacalle, J. (2013). ‘101 Variations on a Maximum Likelihood Procedure for a Structural Time Series Model.’ Unpublished manuscript.

Tusell. F. (2011). ‘Kalman Filtering in R.’ Journal of Statistical Software, Vol. 39, No. 2. http://www.jstatsoft.org/v39/i02/.

Author(s)

Javier L<c3><b3>pez-de-Lacalle [e-mail]

stsm documentation built on May 2, 2019, 7:39 a.m.