A Closer Look at Two Approaches for Analysis and Classification of Nonstationary Time Series

We summarize the relevant aspects of the two approaches for the analysis and classification of several nonstationary time series presented in this book. In Gao et al. (2009), the interest lies in grouping several time series into clusters according to their time-scale characteristics. In Prado (2009), the goal is to estimate the probability that a given time series, from a large collection of them, is a realization from one of multiple processes that can be characterized in terms of their quasi-periodic structure. The methodology of Gao et al. (2009) assumes that there is a known number of clusters G and so, at the end of the analysis, each time series is assigned to one of these clusters. Moreover, the method assumes that there is no training data available (i.e., the group membership of all time series in the data is not known). Prado (2009) assumes that there is a known number of states K and estimates the probability that each time series is a realization from the process that underlines each of the k states for k = 1:K. Both methodologies take into account the spectral characteristics of the time series.