A spectral approach to seasonal filtering
N. E. Tuckwell · ANU Open Research (Australian National University) · 1968
An important requirement in analysing a time series generated by an unknown stochastic process is to look for measurable periodicities. Considering an economic time series as a finite realisation from this process, a contributing source of variation within the data is usually the seasonal component. If the amplitude of this known periodic oscillation can be accurately estimated, the variation attributable to the seasonal can be removed from the series, so making the problems of forecasting and control less difficult. To achieve this end, a series is often considered in the frequency rather than time domain. Chapter 1 outlines the reasons for adopting this frequency, or spectral, approach to time series analysis and briefly introduces some of the formulae and estimation procedures used. In Chapter 2 a model purporting to represent an economic time series is presented and the seasonal component, considered as a sum over a. specified number of frequency band signals. A method of estimation, or filter, designed to allow for a changing seasonal pattern is described and illustrated with an example. Chapter 3 discusses the problems associated with this estimation procedure and the flexibility which it permits in allowing the analyst to calculate the seasonal for any given data interval. The conclusions in this chapter have been arrived at by examining a number of different series, although for the purposes of this thesis results have only been given with reference to a single example. In Chapter 4, filters designed to estimate the trend component of a series are discussed with particular emphasis being placed on a method which does not lose observations in the transformation. Further seasonal problems are dealt , with in Chapter 5, while Chapter 6 covers the means of numerical solution used in deriving seasonally adjusted figures.