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This paper considers a structural-factor approach to modelinghigh-dimensional time series and space-time data by decomposing individualseries into trend, seasonal, and irregular components. For ease in analyzingmany time series, we employ a time polynomial for the trend, a linearcombination of trigonometric series for the seasonal component, and a newfactor model for the irregular components. The new factor model can simplifythe modeling process and achieve parsimony in parameterization. We propose aBayesian Information Criterion (BIC) to consistently determine the order of thepolynomial trend and the number of trigonometric functions. A test statistic isused to determine the number of common factors. The convergence rates for theestimators of the trend and seasonal components and the limiting distributionof the test statistic are established under the setting that the number of timeseries tends to infinity with the sample size, but at a slower rate. We usesimulation to study the performance of the proposed analysis in finite samplesand apply the proposed approach to two real examples. The first exampleconsiders modeling weekly PM$_{2.5}$ data of 15 monitoring stations in thesouthern region of Taiwan and the second example consists of monthlyvalue-weighted returns of 12 industrial portfolios.

A Structural-Factor Approach to Modeling High-Dimensional Time Series and Space-Time Data