Generalized dynamic semi‐parametric factor models for high‐dimensional non‐stationary time series

High‐dimensional non‐stationary time series, which reveal both complex trends and stochastic behaviour, occur in many scientific fields, e.g. macroeconomics, finance, neuroeconomics, etc. To model these, we propose a generalized dynamic semi‐parametric factor model with a two‐step estimation procedure. After choosing smoothed functional principal components as space functions (factor loadings), we extract various temporal trends by employing variable selection techniques for the time basis (common factors). Then, we establish this estimator's non‐asymptotic statistical properties under the dependent scenario (β‐mixing and m‐dependent) with the weakly cross‐correlated error term. At the second step, we obtain a detrended low‐dimensional stochastic process that exhibits the dynamics of the original high‐dimensional (stochastic) objects and we further justify statistical inference based on this. We present an analysis of temperature dynamics in China, which is crucial for pricing weather derivatives, in order to illustrate the performance of our method. We also present a simulation study designed to mimic it.