Estimation and forecasting of time dependent parameter models using reliable software

Until recently, the dominant paradigm in the analysis and forecasting of nonstationary time series has been the approach proposed originally by Box and Jenkins in 1970, which involves the en bloc processing of time series data that have been reduced to stationarity by pre-processing, using techniques such as differencing and use of transformation. A more flexible and widely applicable alternative, which is now favored in many different scientific disciplines, is to analyse the time series directly in their non stationary form using recursive estimation and fixed interval smoothing. Here, the estimates of model parameters or state variables are updated sequentially, so allowing for the estimation of the time variable or state dependent parameters that can be used to characterise models of nonstationary systems. This paper provides an introduction to the latest techniques, developed by the author using MATLAB tool box, in optimal recursive estimation and concentrates on the simplest class of models for nonstationary systems; namely time variable parameter, or Vector Auto Regressive Moving Averages with eXogenous variables (VARMAX), Generalised AutoRegressive Conditional Heteroscedastic (GARCH) errors, as well as the closely related time variable parameter version of the State Space time dependant (SDP) models. In all cases, the utility of these methods is demonstrated through example