A taxonomy of seasonal patterns

Abstract

Seasonal adjustment is a widely applied methodology and a common part of standard practice at many National Statistical Offices. For this reason, it is important there is a robust understanding of the characteristics of the actual data being labelled as seasonal components. The intention of this work was to document and categorise the range of seasonal patterns that appear in time-series data. Measures utilising elements of time series and seasonal adjustment theory were developed, and combined with existing measures from past literature, to characterise elements of the seasonal patterns. A selection of time series data, drawn from New Zealand, Australia, the United Kingdom, Canada and the United States of America, was first collected. X-12 ARIMA, the most common method for determining seasonal patterns, was then utilised to estimate the seasonal component of each time series. Cluster analysis methods were then applied to the measures to provide a number of different partitions of the time series data. After splitting the datasets by the sampling frequency and the seasonal adjustment decomposition used, six different groups of measures were calculated and clusters produced. While some of the approaches were not completely successful, others produced results that identified a number of interesting characteristics of some of the time series datasets. While most series were dominated by an annual cycle, some were found to have strong cycles repeating every three months, with some six month cycles also being detected. Series were found to be evolving at different rates, though difficulties in quantifying this evolution were evident. Additionally, there was no indication that the strength of the three main components, as measured by component ratios, affected any of the other traits of the seasonal pattern.