Abstract

Lieberman and Phillips (Journal of Time Series Analysis) proposed a stochastic unit root model in which the source of the variation of the autoregressive coefficient is driven by a stationary process. More recently, Lieberman and Phillips (Journal of Econometrics) generalized this model to the multivariate case and a hybrid case. Their studies revealed that these stochastic unit root models lead to a generalization of the Black-Scholes formula for derivative pricing. Inspired by their studies, in this paper, we propose a new stochastic unit root model, in which the source of the variation of the autoregressive coefficient is driven by a (nearly) non-stationary process. The asymptotic theory for this model is established. Our study reveals some new findings which are different from those established by Lieberman and Phillips. Results of Monte Carlo simulations are given to illustrate the finite-sample performance of estimators in the model. Moreover, a comparison between the stochastic unit root model proposed by Lieberman and Phillips and that proposed in this paper is conducted via an empirical study.

摘要

Lieberman 和 Phillips（Journal of Time Series Analysis）提出了一个随机单位根模型，其中自回归系数的变化源由平稳过程驱动。最近，Lieberman 和 Phillips ( Journal of Econometrics) 将此模型推广到多变量情况和混合情况。他们的研究表明，这些随机单位根模型导致了 Black-Scholes 公式对衍生品定价的推广。受他们研究的启发，在本文中，我们提出了一种新的随机单位根模型，其中自回归系数的变化源由（几乎）非平稳过程驱动。建立了该模型的渐近理论。我们的研究揭示了一些与 Lieberman 和 Phillips 建立的不同的新发现。给出了蒙特卡罗模拟的结果来说明模型中估计器的有限样本性能。此外，通过实证研究对利伯曼和菲利普斯提出的随机单位根模型与本文提出的随机单位根模型进行了比较。