This software provides Fortran 90-Splus functions and Matlab programs to fit Time-Varying Autoregressive (TVAR) models with a fixed order using a Bayesian Dynamic Linear Model (DLM) framework. The evolution of parameters in time is defined through a Random Walk and with standard Normal-Inverse Gamma priors on model coefficients and variances. Using a DLM algorithm for sequential and retrospective smoothing, the software computes posterior estimates of the AR coefficients and variances at each time. The main focus is on inference on latent component structure defined through the time-varying characteristic roots of the process.

Basically, the software is organised in three parts and particularly for the Fortran-Splus version each one is defined as follows. A program named "grid.90", computes the log-likelihood and mean square error (MSE) of a DLM-TVAR for a desired grid of values for model order and discount factors for the evolution of parameters. As output, the combination of order-discount factors that maximises the log-likelihood and minimises the MSE are reported and both can be used for further analysis. The second part consists of a program named "tvar.90" which fits the TVAR model for any specification of model order and discount factors. "tvar.90" computes and saves posterior means for model parameters and has the additional option of generating samples from the posterior distribution of the parameters at each time. Finally, the program named "decomp.90", reads the output for "tvar.90" and produces posterior inference on latent component structure with component ordering via the amplitude, periodicity or corresponding moduli for characteristic-component roots. Furthermore, the Splus functions summarise the output of the Fortran programs offering different graphical displays. Some involve plots of the data with the time-varying latent components, time trajectories for moduli and frequency of the associated characteristic roots which can also include 95 % posterior intervals at selected time points.

The software is designed for a Unix environment and the Fortran version requires LAPACK, public domain software for matrix algebra. On the other hand, the MATLAB version is free-standing and permits time-varying spectral inference. The software comes with 3 data sets and tutorial examples. The data sets are: an Electro-Encephalogram (EEG) trace, an oxygen-isotope time series and a series of non-stationary sea level pressures. Particularly for the EEG data, the Matlab version offers the possibility of contour/surface plotting of the EEG channels and related inferences over a graphical representation of the head of a person. As the authors of the software point out, the Matlab version requires further upgrading.

This a very general software for modelling time series within a linear-non stationary context that incorporates model selection through a formal likelihood exploration. Although all the emphasis is in latent structure rather than aspects as forecasting, it offers a diversity of analysis for component modelling that range from simple computation of posterior moments to exploration via direct Monte Carlo simulation of posterior distributions. Additionally, component structure can be studied with a variety of orderings so properly handles for identifiability issues that naturally arise in DLM-TVAR models. The software is free, occupies approximately 99 Kb of disk space and is available to the public domain from

www.isds.duke.edu/~mw/tvar.html,