J. Dorfman

The following product is developed by J. Dorfman, a third party developer, for use with GAUSS. Technical support is provided directly through the developer.


State Space Aoki Time Series

SSATS 2.0 is a set of preprogrammed GAUSS procedures that perform all the tasks necessary to and associated with the specification, estimation, and forecasting of multivariate state space time series models. A standard state space model takes the form:


yt = Cz t + et (observation equation)
zt+1 = Az t + Bet (state equation)


where yt is an (m x 1) vector of the time series to be modeled and/or forecast, z tis the (n x 1) state vector, e t is an (m x 1) vector of stochastic innovations (error terms), and A, B, and C are parameter matrices to be estimated.


Masanao Aoki developed a particularly successful algorithm to estimate such models based on the balanced representation and relying heavily on results from linear systems theory. SSATS 2.0 will let a researcher easily begin to implement the techniques laid out in Aoki’s book, State Space Modeling of Time Series (Springer-Verlag, 1987, 1990).


SSATS will be useful to any researcher who is interested in empirical work on multivariate dynamic systems. SSATS is a valuable tool for anyone involved in the specification, estimation, and forecasting of multivariate (or univariate) time series models. The procedures can be used on their own, combined into a single command program, or used selectively in conjunction with other time series methods to aid in specification or forecast evaluation.


SSATS 2.0 provides procedures to easily accomplish such tasks as:

Scale and center data prior to estimation

Choose the model specification (model order of the time series),


Estimate the model coefficients A, B, and C

Estimate covariance matrices of parameter matrices, data series, errors, and states

Evaluate model specification with diagnostic tools

Produce in-sample and out-of-sample forecasts

Evaluate forecasting performance including a variety of summary statistics.


All of the forecasting evaluation procedures can be used with forecasts generated by any methods; they are not restricted to use with state space models. Similarly, the model specification procedures and statistical tests included can be used to identify the model order of a time series even if the researcher then estimates a VAR or VARMA model instead of a state space model.


The SSATS 2.0 procedure module comes with:

19 procedures


A complete user’s guide containing descriptions and examples for all procedures


A primer on state space models, the Aoki estimation algorithm, and tips and guidance on how to successfully model and forecast multivariate time series using state space models


A sample program showing how to combine the procedures into a complete implementation of the procedures to specify a model, estimate it, produce forecasts, and evaluate the model’s performance


A sample data set and demo output to allow researchers to insure that the programs are working properly on their systems.


Platform: Windows, LINUX, UNIX


Requires: GAUSS Mathematical & Statistical System v3.2 and above.