Bolla, Marianna: Reduction of High Frequency and High …

Előadás címe: Reduction of High Frequency and High Dimensional Time Series Cross-Sectionally and Longitudinally

Helyszín: Online,

Időpont: 2020.06.29., 14:40 – 15:00

Kivonat: Having high frequency, high dimensional time series, we want to find latent driving forces behind the strongly connected components, for example, finding the underlying signals detected by many sensors. This cross-sectional reduction of dimensionality is the task of dynamic factor analysis. In case of regular time series, this reduction can be done in the innovation subspaces by the block Cholesky decomposition of the block Toeplitz matrix of the autocovariance matrices up to a certain order.  As the rank of the spectral density matrix at any frequency is equal to the dimension of the innovation subspaces, an equivalent solution is obtained with the spectral decomposition of these matrices at the Fourier frequencies. At the same time, we are able to make compression in the frequency domain by using complex Wishart matrices. This extends to a compression longitudinally, in particular, when the sensors record the components of the time series in different units of the time.