On buffered double autoregressive time series models

TL;DR

This paper introduces a buffered double autoregressive (BDAR) model that captures complex regime switching and buffering phenomena in time series, providing rigorous theoretical properties, estimation methods, and empirical validation.

Contribution

The paper proposes a novel BDAR model with a flexible regime switching mechanism and signal retrospection, extending classical models with new theoretical and estimation results.

Findings

BDAR model is strictly stationary and geometrically ergodic.

Threshold estimators are $n$-consistent and converge to a functional of a two-sided compound Poisson process.

Simulation studies confirm the effectiveness of QMLE and model selection criteria.

Abstract

A buffered double autoregressive (BDAR) time series model is proposed in this paper to depict the buffering phenomenon of conditional mean and conditional variance in time series. To build this model, a novel flexible regime switching mechanism is introduced to modify the classical threshold time series model by capturing the stickiness of signal. Besides, considering the inadequacy of traditional models under the lack of information, a signal retrospection is run in this model to provide a more accurate judgment. Moreover, formal proofs suggest strict stationarity and geometric ergodicity of BDAR model under several sufficient conditions. A Gaussian quasi-maximum likelihood estimation (QMLE) is employed and the asymptotic distributions of its estimators are derived. It has been demonstrated that the estimated thresholds of the BDAR model are $n$-consistent, each of which converges weakly to a functional of a two-sided compound Poisson process. The remaining parameters are $\sqrt{n}$-consistent and asymptotically normal. Furthermore, a model selection criteria and its asymptotic property have been established. Simulation studies are constructed to evaluate the finite sample performance of QMLE and model selection criteria. Finally, an empirical analysis of Hang Seng Index (HSI) using BDAR model reveals the asymmetry of investors' preference over losses and gains as well as the asymmetry of volatility structure.