State Space Methods in Ox/SsfPack

Abstract

The use of state space models and their inference is illustrated using the package SsfPack for Ox. After a rather long introduction that explains the use of SsfPack and many of its functions, four case-studies illustrate the practical implementation of the software to real world problems through short sample programs. The first case consists in the analysis of the well-known (at least to time series analysis experts) Nile data with a local level model. The other case-studies deal with ARIMA and RegARIMA models applied to the (also well-known) Airline time series, structural time series models applied to the Italian industrial production index and stochastic volatility models applied to the FTSE100 index. In all applications inference on the model (hyper-) parameters is carried out by maximum likelihood, but in one case (stochastic volatility) also an MCMC-based approach is illustrated. Cubic splines are covered in a very short example as well.

Keywords

• ARIMA
• Kalman filter
• state space methods
• unobserved components
• Gibbs sampling
• Ox
• SsfPack