Dynamic Semiparametric Factor Model with Structural Breaks

For the change-point analysis of a high-dimensional time series, we consider a semiparametric model with dynamic structural break factors. With our model, the observations are described by a few low-dimensional factors with time-invariant loading functions of the covariates. Regarding the structural break, the factors are assumed to be nonstationary and follow a vector autoregression (VAR) process with a change in the parameter values. In addition, to account for the known spatial discrepancies, we introduce discrete loading functions. We study the theoretical properties of the estimates of the loading functions and the factors. Moreover, we provide both the consistency and the asymptotic normality for making an inference on the estimated breakpoint. {Importantly, our results hold for both large and small breaks in the factor dependency structure.} The estimation precision is further illustrated via a simulation study. Finally, we present two empirical applications in modeling the dynamics of the minimum wage policy in China and analyzing a limit order book dataset.