A0157
Title: Understanding fluctuations through multivariate circulant singular spectrum analysis
Authors: Pilar Poncela - Universidad Autonoma de Madrid (Spain) [presenting]
Eva Senra - Universidad de Alcala (Spain)
Juan Bogalo - University of Alcala (Spain)
Abstract: The decomposition of multichannel signals into their underlying components is a problem of key interest in many disciplines. It involves the analysis of nonlinear and nonstationary time series. After extracting the underlying latent components, the need is to identify their frequencies of oscillation. Many successful multivariate methods identify the frequencies after the decomposition problem has been solved. However, they might face difficulties matching extracted components with frequencies. Multivariate circulant singular spectrum analysis (MCiSSA) is developed, a self-identifying procedure for the frequencies without the need to further process the data. Seeing MSSA procedures as a generalization of principal components that includes series and their lags, the key is the use of block circulant matrices instead of the variance-covariance matrix, which matches eigenvalues with frequencies. MCiSSA performs a double diagonalization of that block circulant matrix that uncovers cross-section relations per frequency. The procedure works well in synthetic examples with latent signals modulated in amplitude and/or frequency. Finally, MCiSSA is applied to real data, firstly to energy commodity prices that are dominated by European gas at all frequencies. The second application shows the growing trend of temperatures in 12 South European cities and their changing pattern in seasonality.
