Monotonicity aspects on seasonal adjustment

Abstract

Monotonicity is an important property in time series analysis. It is often of interest to know if the seasonal adjustment method used has altered the monotonicity or changed the time of turning points in a time series that exhibits cycles. The issue of whether the monotonicity of the trend cycle component of the original non-stationary time series is preserved after the series has been adjusted is treated in this report. The time of a turning point is defined as the time when the cycle changes from recession to expansion (or vice versa). In this report seasonal adjustment with moving average methods is analysed from monotonicity aspects. The time series is assumed to consist of three additive components: a trend cycle part, a seasonal part and a stochastic error part. No parametric model is assumed for the trend cycle. The behaviour of the adjusted series is analysed for two cases: a monotonically increasing trend cycle and a trend cycle with a peak. If the trend cycle is monotonic within the entire observed section the monotonicity is preserved. Unimodality is preserved but not always the time of the turning point.