Use of Partial Cumulative Sum to Detect Trends and Change Periods for Nonlinear Time Series

Because the structural change of a time series from one pattern to another may not switch at once but rather experience a period of adjustment, conventional change point detection may be inappropriate under some circumstances. Furthermore, changes in time series often occur gradually so that there is a certain amount of fuzziness in the change point. For this, considerable research has focused on the theory of change period detection for improved model performance. However, a change period in some small time interval may appear to be negligible noise in a larger time interval. In this paper, we propose an approach to detect trends and change periods with fuzzy statistics using partial cumulative sums. By controlling the parameters, we can filter the noises and discover suitable change periods. Having discovered the change periods, we can proceed to identify the trends in the time series. We use simulations to test our approach. Our results show that the performance of our approach is satisfactory.