Turning point detection using non-parametric statistical surveillance

Abstract

Turning point detection is important in many areas. One application is forecasting the time of the next tum in the business cycle, by detection of a tum in leading economic indicators. Another application is detection of a peak in the human menstrual cycle. In both these applications we make continual observation of the time series with the goal of detecting the turning point in the cycle as soon as possible. At each time, an alarm statistic and alarm limits are used in making a decision as to whether the time series has reached a turning point. The alarm statistic and the alarm-limit are based on the maximum likelihood ratio technique for surveillance. No parametric function is assumed for the cycle, but a non-parametric estimation procedure is used.

The shape of the turning point has an impact on the performance of the method for turning point detection. The influence of some turning point characteristics (slopes and smoothness of curve) is evaluated both theoretically and by simulation studies. The simulations are used to demonstrate the effect of the slopes (both pre-peak and post-peak). Results from the simulation study show that the false alarm probability increases for a non-smooth curve and that the detection probability is sensitive to the shape of the curve just around the turning point. In the theoretical investigation, it is shown that the expected delay of an alarm is shorter for a steeper post-peak slope. The method is also evaluated by applying it to a set of Swedish data.