Determining the number of factors in a large-dimensional generalised factor model

Abstract: This paper proposes new estimators of the number of factors for a generalised factor model with more relaxed assumptions than the strict factor model. Under the framework of large cross-sections $N$ and large time dimensions $T$, we first derive the bias-corrected estimator $\hat \sigma^2_*$ of the noise variance in a generalised factor model by random matrix theory. Then we construct three information criteria based on $\hat \sigma^2_*$, further propose the consistent estimators of the number of factors. Finally, simulations and real data analysis illustrate that our proposed estimations are more accurate and avoid the overestimation in some existing works.