Characterizing Common Seasonality in Multivariate Time Series

• Activity Number: 601
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Fabio Nieto*+ and Daniel Peña and Dagoberto Saboyá
• Companies: Universidad Nacional De Colombia and Universidad Carlos III de Madrid and Universidad Nacional de Colombia
• Keywords: Dynamic common factors ; Multivariate time series ; Seasonality

Abstract

In the field of multivariate time series analysis, dynamic common factors, as stochastic processes, have been analyzed under the assumptions that they can be either stationary or nonstationary or either seasonal or nonseasonal. The issue of seasonality is of main concern because it is well known that a deseasonalized time series may exhibit spurious characteristics; specifically, in showing cycles the original data do not contain. Hence, when using seasonal time series, it is appropriate to take into account directly the seasonal characteristic in the modeling process. In this paper, the problem of determining different types of pure common seasonality in a multivariate observable stochastic process is considered. In this case, clusters of time series are obtained, where the clustering source is the kind of seasonality. The main results consist in (i) obtaining the asymptotic behavior of the sequence of the so-called sample generalized autocovariance matrices and (ii) in analyzing the finite-sample behavior of the eigenvalue sequences of those autocovariance matrices. This last empirical tool is very useful for determining the number of pure seasonal stochastic mechanisms