Aug 2026· Annals of Statistics· Vol 54, pp. 2005-2030· 0 citations· 23 references
Abstract
We consider a k-dimensional multiple-regime vector threshold autoregressive model, in which the regime-switching mechanism is governed by a bivariate threshold variable. 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. We formulate the model selection and parameter estimation into a minimization problem based on the Minimum Description Length (MDL) principle and estimate the number of threshold lines, parametric forms of threshold lines and VAR model parameters in each regime simultaneously. Theoretically, we show that the MDL estimators of threshold lines are n-consistent and characterize their limiting distribution. This requires novel proving techniques of introducing a new functional space G for the local MDL difference functions and establishing weak convergence results therein. Finally, we conduct some empirical studies with simulated datasets and perform real data analyses on U.S. interest rates and U.S. GNP Data.
Threshold and change-plane models provide a useful framework for capturing regime-dependent dynamics, but most existing approaches typically rely on scalar thresholds or linear splitting boundaries. We propose a scalable semiparametric change-plane regression framework that allows the regime boundary to depend nonlinea...
We develop a general framework for model specification testing in stationary functional time series. The approach is based on an autoregressive approximation that represents a broad class of stationary functional processes through coefficient kernels whose dimension and autoregressive order may increase with the sample...
We develop a framework for simultaneous change-point inference of high-dimensional functional time series. The observations are modeled as temporally dependent vectors whose coordinates take values in possibly different separable Hilbert spaces, thereby covering a broad class of functional data. Heterogeneous mean chan...
Bounded response variables, such as rates, proportions, and indices, frequently arise in the applied sciences and require regression models that respect the unit interval support, rather than relying on Gaussian regression. In this work, we propose a new regression model for continuous bounded data based on the unit Gu...
O. Alqasem, A. Gemeay, D. Alnagar et al.· Boundary Value Problems· 0 citations
We study estimation and inference for a semiparametric class of time series models that specify only the conditional expectation, which is a known link function applied to a linear combination of past observations and covariates. The class covers count, binary, bounded and conditionally heteroskedastic responses within...
Z. Debaly, A. Zotsa-Ngoufack· 0 citations
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