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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 345093, 20 pages
Research Article

A Trend-Switching Financial Time Series Model with Level-Duration Dependence

1School of Mathematics and Statistics, Yunnan University, Kunming 650091, China
2School of Finance, Jiangxi University of Finance and Economics, Nanchang 330013, China
3The Postdoctoral Research Station, Credit Reference Center, The People’s Bank of China, Beijing 100031, China
4Academy of Mathematics and Systems Science, CAS, Beijing 100190, China

Received 25 August 2012; Revised 28 November 2012; Accepted 28 November 2012

Academic Editor: Wei-Chiang Hong

Copyright © 2012 Qingsheng Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The financial time series model that can capture the nonlinearity and asymmetry of stochastic process has been paid close attention for a long time. However, it is still open to completely overcome the difficult problem that motivates our researches in this paper. An asymmetric and nonlinear model with the change of local trend depending on local high-low turning point process is first proposed in this paper. As the point process can be decomposed into the two different processes, a high-low level process and an up-down duration process, we then establish the so-called trend-switching model which depends on both level and duration (Trend-LD). The proposed model can predict efficiently the direction and magnitude of the local trend of a time series by incorporating the local high-low turning point information. The numerical results on six indices in world stock markets show that the proposed Trend-LD model is suitable for fitting the market data and able to outperform the traditional random walk model.