On a matrix-valued autoregressive model

Many data sets in biology, medicine, and other biostatistical areas deal with matrix-valued time series. The case of a single univariate time series is very well developed in the literature; and single multi-variate series (i.e., vector time series) though less well studied have also been developed. A class of matrix time series models is introduced for dealing with situations where there are multiple sets of multi-variate time series data. Explicit expressions for a matrix autoregressive model along with its cross-autocorrelation functions are derived. Stationarity conditions are also provided. Least squares estimators and maximum likelihood estimators of the model parameters and their asymptotic properties are derived. Results are illustrated through simulation studies and a real data application.