A time-varying latent factor model with GARCH noise for high-dimensional covariance matrix estimation

In this paper, we established a time-varying latent factor model with GARCH (generalized autoregressive conditional heteroskedasticity) noise to study volatilities (conditional covariance matrix) under the high-dimensional framework, when factors are unobservable, factor loadings are time-varying, and the idiosyncratic error term shows heteroskedasticity. A projection method was proposed for more-precise estimation of the conditional covariance matrix. We demonstrated that our model is robust when the dimensionality and sample size are large. Asymptotic theories were developed for the proposed estimation. A simulation study was conducted to evaluate the performance of the proposed model, and a real example was provided to illustrate this approach.