Forecasting Simultaneously High-Dimensional Time Series: A Robust Model-Based Clustering Approach

This paper considers the problem of forecasting high-dimensional time series. It employs a robust clustering approach to perform classification of the component series. Each series within a cluster is assumed to follow the same model and the data are then pooled for estimation. The classification is model-based and robust to outlier contamination. The robustness is achieved by using the intrinsic mode functions of the Hilbert-Huang transform at lower frequencies. These functions are found to be robust to outlier contamination. The paper also compares out-of-sample forecast performance of the proposed method with several methods available in the literature. The other forecasting methods considered include vector autoregressive models with ∕ without LASSO, group LASSO, principal component regression, and partial least squares. The proposed method is found to perform well in out-of-sample forecasting of the monthly unemployment rates of 50 US states.