On monotonicity and early warnings with applications in economics

Abstract

In this report a method for monitoring time series with cycles is presented. It is a nonparametric approach for detecting the turning point of the cycles. Time series of business indicators often exhibit cycles that can not easily be modelled with a parametric function. Forecasting the turning points is important to economic and political decisions. One approach to forecasting the business cycles is to use a leading indicator. The method presented in this report uses statistical surveillance to detect the turning points of a leading indicator. Statistical surveillance is a methodology for detecting a change in the underlying process as soon as possible. Observations on the leading indicator are gathered once a month and the change in the process is a turning point. Only a part of a series that contains one turning point at most will be investigated. The time series is assumed to consist of two additive components: a trend cycle part and a stochastic error part. No parametric model is assumed for the trend cycle, estimation is instead made by robust regression under different monotonicity restrictions. The aim is to detect a turning point as soon as possible, not to predict the value of the time series at the turning point. Evaluation of this surveillance method is done by means of simulation. The number of false alarms and the delay time are analysed. The evaluation shows that if there is no turning point then the median time to the first false alarm is five years, whereas if there is a turning point after three years, the median time to an alarm is 3 months.