Robust factor models for high-dimensional time series and their forecasting

This paper deals with the factor modeling and forecasting for high-dimensional time series with additive outliers. Under the assumption that the sample size n and the dimension of time series p tend to infinity together, the asymptotic properties of several robust estimators are established, including estimation errors and forecast errors. We also propose a detailed algorithm of constructing bootstrap prediction intervals for the high-dimensional time series. We show the superiority of the approach by both simulation studies and an application to the daily air quality index for the main cities in the Yangtze River Delta region of China.