This chapter examines a number of different topics relating to structural time series models. The first two sections deal with certain fundamental questions concerning trend and seasonality, and provide a justification of the statistical models adopted and the reasons for the shortcomings of certain other approaches. Various extensions of the trend and seasonal components of structural models are also considered.

Section 6.3 looks at the consequences of different observation and model timing intervals and shows that the principal structural models are relatively robust to changes in the observation timing interval. Data irregularities are examined in section 6.4. The Kaiman filter is an invaluable tool for handling such problems as missing observations, outliers and data revisions, and the structural approach appears to be the natural way to tackle model formulation.

The potential of state space methods for handling various types of non-linearity and structural change is explored in section 6.5, while the last section sets up models appropriate for dealing with count data and qualitative observations. Again it is argued that the structural approach is the natural way to proceed.

Trends, detrending and unit roots

This section discusses various aspects of trends. The first two sub-sections focus on the fundamental definition of a trend and the way in which a series may be decomposed into a trend and other components. It is assumed that the series in question do not contain components, such as seasonal and daily effects, which tend to repeat their pattern within a given time period.