A0699
Title: Generalized multivariate threshold autoregressive models with linearly partitioned threshold space
Authors: Gan Yuan - Columbia University (United States) [presenting]
Abstract: A $k$-dimensional multiple-regime vector threshold autoregressive model is considered, in which the regime-switching mechanism is governed by another bivariate observable time series, known as threshold variables. Specifically, the regimes are induced by a partition of the threshold space by an unknown number of threshold lines. The process is governed by a specific vector autoregressive (VAR) model within each regime. The model selection and parameter estimation are formulated into a minimization problem based on the Minimum Description Length (MDL) principle, and the number of threshold lines, parametric forms of threshold lines and VAR model parameters in each regime simultaneously are estimated. Theoretically, it is shown that the MDL estimators of threshold lines are $n$-consistent, and their weak convergence is characterized. The main novelty in the proof is introducing a new functional space $\mathbb{G}$ for the local MDL difference functions, as opposed to earlier works, in which the weak convergence was established in the classical $\mathbb{D}$ space. Finally, some empirical studies are conducted with simulated datasets and real data analysis on US interest rates is performed.
