Bartlett‐type modified test for moving seasonality with applications

Abstract

Socioeconomic time series are often presented in a seasonally adjusted form so that the underlying short-term trend can be more easily analysed, and current socioeconomic conditions can be easily assessed. As a first step towards seasonally adjusting a series, it is essential to test for a changing (moving) seasonal pattem against a stable seasonal pattern over time. To test for moving seasonality, Sutradhar and Dagum have applied a modified Bartlett test to trend-free data consisting of seasonality only. In general, however, such trend-free or detrended data appear to consist of seasonality plus irregular components. This makes the estimation of the parameters more complicated than was the case for Sutradhar and Dagum. We discuss this estimation problem in the present paper in connection with three Canadian export series. As Sutradhar and Dagum did, we then develop a modified Bartlett test under the new set-up and apply the test for testing for moving seasonality in the three Canadian export series.