Detecting Major Extrema in Streaming Time Series

Time series are formed from data points collected over time. The prominent data points of time series are often minima or maxima; hence they have special values. Moreover, they are virtually turning points that change trend of time series. These prominent data points play an important role in determining the characteristics of time series so they are called important data points or major extrema. There are many methods to detect major extrema in time series in static context; however, in streaming context there have almost been no methods to carry out this task so far. In the paper, we propose a method for detecting major extrema in streaming time series. The method is of low computational time in identifying major extrema as soon as a newly in-coming data point of streaming time series is collected. The experimental results demonstrate that the proposed method exactly detects major extrema on the fly. Furthermore, the method could identify correlation of streaming time series thanks to their major extrema. An interesting application of the proposed method is to enable the task of online forecasting to predict future data points of streaming time series based on similarity search using major extrema.