On a matrix‐valued autoregressive model
针对生物、医学等领域中出现的矩阵值时间序列数据，提出了一类矩阵自回归模型，给出了模型表达式、平稳性条件、参数估计方法及其渐近性质，并通过模拟和实际数据验证了模型的有效性。
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.