Aspects of multilinear algebra in statistical analysis of seasonal multivariate time series

Abstract: Representations of concepts from multivariate statistics are studied using multilinear algebra. Applications are given to the analysis of seasonal multivariate time series. The first paper concerns a class of permutation matrices which are representations of permutation operators on tensor spaces. In the second paper, the derivation of moments and cumulants of Hilbert space valued random variables are studied. Relations between moments and cumulants - as vector space elements - are given which generalize well-known results for scalar random variables. Representations of differentials are discussed and results for differentials of matrix valued functions with matrix arguments are derived. Moments and cumulants of the non-central Wishart distribution are given. in the third paper, seasonal multivariate time series are investigated using the concepts described in the first two papers. Estimators of unknown parameters are given and their asymptotic distributions are derived. Test statistics for testing homogeneity in time and independence of subprocesses are given and also their asymptotic distributions.