A0511
Title: Generalized multivariate threshold autoregressive models with linearly partitioned threshold space
Authors: Gan Yuan - City University of Hong Kong (Hong Kong) [presenting]
Chun Yip Yau - Chinese University of Hong Kong (Hong Kong)
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. Within each regime, the process follows a specific vector autoregressive (VAR) model. 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 are estimated in each regime simultaneously. Theoretically, it is shown that the MDL estimators of threshold lines are $n$-consistent, and their limiting distribution is characterized. The main novelty in the proof is the introduction of 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 with simulated datasets are conducted, and real data analyses are performed on U.S. interest rates and U.S. GNP Data.
