Properties of a simple bilinear stochastic model: Estimation and predictability

PHYSICA D-NONLINEAR PHENOMENA

卷:237

Article

Sornette, D.¹  Pisarenko, V. F.² 

[1] Swiss Fed Inst Technol, Dept Management Technol & Econ, CH-8032 Zurich, Switzerland

[2] Russian Acad Sci, Int Inst Earthquake Predict Theory & Math Geophys, Moscow 113556, Russia

关键词: bilinear;    multiplicative noise;    estimation;    prediction;    nonlinear dependence;    fat-tail distributions;    sensitive dependence on initial conditions;    volterra discrete series;   

DOI  :  10.1016/j.physd.2007.08.020

来源: Elsevier

【 摘 要 】

We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and Multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear predictability (non-zero three-point correlation). It can thus be considered as a paradigm for testing the existence of a possible nonlinear predictability in a given time series. We present a rather exhaustive study of the process, including its ability to produce fat-tailed distributions from Gaussian innovations, the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super-exponential sensitivity of the inversion of the innovations in the presence of a large impulse. Our study emphasizes the conditions under which a degree of predictability call be achieved and describe a number of different attempts, which overall illuminates the properties of the process. In conclusion, notwithstanding its remarkable simplicity, the bilinear stochastic process exhibits remarkably rich and complex behavior, which makes it a serious candidate for the modeling of financial time series among others. (c) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free