On Buffered Double Autoregressive Time Series Models

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 switch mechanism is introduced to modify the classical threshold AR 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 judgement. 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 to compute the estimators in this model. The strict proof reveals the asymptotic normality of the estimated coefficients of double AR models. More importantly, it has been demonstrated that the estimated threshold of the BDAR model weakly converges to a functional of a two-sided compound Poisson process. Furthermore, a model selection criteria and 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.