The past ten years have witnessed some major developments in the field of time series analysis. The twin assumptions of linearity and stationarity which underlie so much of conventional time series analysis have finally been abandoned, and the subject has moved in a new direction. This new direction is, of course, the study of non-linear models, and it is this area, together with the treatment of spectral analysis of non-stationary processes, which forms the substance of this book. Non-linear models offer both great excitement and great challenges. The mathematical ideas
involved are much more complex than those of linear models, and the statistical problems of model identification and parameter estimation are similarly more intricate. However, once these nettles are grasped, the richness of the new models is quite fascinating. Experience so far gained has shown that even simple non-linear models can capture types of time series behaviour which it would be impossible to describe with linear models.