567 – Computing with Time Series Data
Complexity of Continuous Functions and Segmentation of Time Series
Boris Darkhovsky
Russian Academy of Sciences
Alexandra Piryatinska
San Francisco State University
In many applications time series are sequences of connected, distinct segments which are generated by their own individual mechanisms. To analyze such series it is necessary to split them into these segments. If time series is generated by stochastic mechanisms, then the segmentation problem can be reduced to the classical change-point detection problem. However it is not the case for deterministic or mixed mechanisms. A new approach to this problem based on the novel concept of the complexity of a continuous function is proposed. The complexity of a continuous function is defined as the fraction of the function values necessary to recover the original function via a certain fixed family of approximation methods without exceeding a given error. Complexity parameters are used as diagnostic sequences to find the change-points of the original time series.
