Autoregressive moving average model for matrix time series

Abstract

In the paper, the autoregressive moving average model for matrix time series (MARMA) is investigated. The properties of the MARMA model are investigated by using the conditional least square estimation, the conditional maximum likelihood estimation, the projection theorem in Hilbert space and the decomposition technique of time series, which include necessary and sufficient conditions for stationarity and invertibility, model parameter estimation, model testing and model forecasting.

Keywords:

• Matrix time series
• autoregressive moving average model
• bilinear model
• statistical inference

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper is partially supported by the basic scientific research business expenses of Universities in Xinjiang, China [Grant Number XQZX20230057] and the National Natural Science Foundation of China [Grant Number 11671142].