| One major interest of financial time series analysis is to identify changepoints of trends and recognize patterns that can be used for classification and clustering of time series. Because of the large amounts of data, nonlinear relationship of the data elements, and the presence of random noise, some method of data reduction is necessary. The data reduction, however, must preserve the important characteristics of the original data. Many representation methods in the time domain or frequency domain have been suggested to accomplish efficient extraction of information. These include, for example, piecewise linear approximation, symbolic representation, and discrete wavelet transformation (DWT). However, most of the existing methods do not take into consideration time information of trends and/or depend on user-defined parameters, for example the number of segments for piecewise approximation.;We introduce alternating trend smoothing (ATS) and piecewise band smoothing (PBS) for data representation based on up/down direction change as it has h (step size) additional data points and linear regression using small sets of current data points respectively. The proposed method is flexible and interpretable in the sense that it allows the acquisition and addition of new data points (online method) to detect meaningful trends and changepoints.;Changepoints are confirmed once new data points stray far enough outside of the band, creating a reduced dataset of changepoints to utilize. Next, we define patterns from the reduced data which preserve trends and the length of a trends duration. In addition to the definition of patterns, some distance metrics are suggested as similarity measures that are suitable for reduced data by our data representation. Finally, we demonstrate applications of clustering, classification, indexing, and prediction using methods suggested, and discuss conclusions and future work. |
