Robust Forecasting of Multiple Time Series with One-Sided Dynamic Principal Components

Given a high-dimensional vector of time series, we define a class of robust forecasting procedures based on robust one-sided dynamic principal components. Peña et al. (J Am Stat Assoc 114(528):1683–1694, 2019) defined one-sided dynamic principal components as linear combinations of the present and past values of the series with optimal reconstruction properties. In order to make the estimation of these components robust to outliers, we propose here to compute the principal components by minimizing the sum of squares of the M-scales of the reconstruction errors of all the variables. The resulting robust components are called scale one-sided dynamic principal components (S-ODPC), and an alternating weighted least squares algorithm to compute them is presented. We prove that when both the number of series and the sample size tend to infinity, if the data follow a dynamic factor model, the mean of the squares of the M-scales of the reconstruction errors of the S-ODPC converges to the mean of the squares of the M-scales of the idiosyncratic terms, with rate m 1 ∕ 2 $$m^{1/2}$$ , where m is the number of dimensions. A Monte Carlo study shows that the S-ODPC introduced in this chapter can be successfully used for forecasting high-dimensional multiple time series, even in the presence of outlier observations.