Examining Nonlinear Changes of Coefficients in Time-Varying Dynamic Factor Models

To better investigate complex nonstationary multivariate time series, the current thesis aims to extend earlier work on using time-varying dynamic factor models to represent linear changes of coefficients to nonlinear cases. A method is proposed that uses the extended Kalman smoother (EKS) to track dynamics of both latent factors and time-varying coefficients, the Gaussian maximum likelihood (GML) for point and the bootstrap for standard error (SE) estimation of parameters. The performance of the proposed method was examined via Monte Carlo simulations. Results suggest that (i) the EKS recovered dynamics of latent factors and time-varying coefficients rather faithfully; (ii) the GML and the bootstrap worked well, expect for certain parameters in the dynamic model; (iii) the amplitude of changes of the time-varying coefficient played a crucial role in whether the coefficient can be assumed to be fixed and the accuracy of estimates. Explanations and implications for applied research were also provided.