چكيده فارسي :
Many Time series data are ubiquitous. As such, they have motivated many works in machine learning and data analysis fields for classification and clustering of temporal data. While several clustering methods for univariate time series exist, and a few for multivariate series, most are based on distance and/or dissimilarity measures that do not utilize the time dependency information that is inherent to time series data. To explore and highlight the main dynamic structure of a set of multivariate time series, we extend the use of standard variance-covariance matrices for non-time series data in principal component analysis to the use of cross-autocorrelation matrices at time lags k = 1,2,.... This is also achieved by combining the principles of both canonical correlation analysis and principal component analysis for time series to obtain a new type of covariance/correlation matrix for a principal component analysis to produce a so-called principal component time series. Simulations and real data are used to study the effectiveness of the new procedure to show the benefits of the extended autocorrelation and cross-autocorrelation functions in exploring the main structural features of multiple time series.
