Computational Statistics

, Volume 32, Issue 4, pp 1583–1596 | Cite as

A test for a parametric form of the volatility in second-order diffusion models

  • Tianshun Yan
  • Changlin Mei
Original Paper


Second-order diffusion models have been found to be promising in analyzing financial market data. Based on nonparametric fitting, Nicolau (Stat Probabil Lett 78(16):2700–2704, 2008) suggested that the quadratic function may be an appropriate specification of the volatility when a second-order diffusion model is used to analyze some European and American financial market data sets, which motivates us to develop a formal statistical test for this finding. To achieve the task, a generalized likelihood ratio test is proposed in this paper and a residual-based bootstrap is suggested to compute the p value of the test. The analysis of many real-world financial market data sets demonstrates that the quadratic specification of the volatility function is in general reasonable.


Second-order diffusion models Generalized likelihood ratio test Local-linear fitting Bootstrap 



This work is supported by the National Natural Science Foundation of China (No. 11271296).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Statistics, School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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