Determining The Number of Factors in Two-Way Factor Model of High-Dimensional Matrix-Variate Time Series: A White-Noise based Method for Serial Correlation Models

In this paper, we study a new two-way factor model for high-dimensional matrix-variate time series. To estimate the number of factors in this two-way factor model, we decompose the series into two parts: one being a non-weakly correlated series and the other being a weakly correlated noise. By comparing the difference between two series, we can construct white-noise based signal statistics to determine the number of factors in row loading matrix (column loading matrix). Furthermore, to mitigate the negative impact on the accuracy of the estimation, which is caused by the interaction between the row loading matrix and the column loading matrix, we propose a transformation so that the transformed model only contains the row loading matrix (column loading matrix). We define sequences of ratios of two test statistics as signal statistics to determine the number of factors and derive the consistence of the estimation. We implement the numerical studies to examine the performance of the new methods.