Nonparametric Density Estimation for Energy Price Returns

  • Nigel Da Costa Lewis
Part of the Finance and Capital Markets Series book series (FCMS)


Sitting on the very tip of my chair, feigning interest in the mumbled string of motivational buzz words spouting out of the mouth of an unusually dull director of global risk, it occurred to me that if I looked hard enough, through the gray mist of the incoherent mutterings, there would emerge some shape, some form to their ideas, which as yet my colleagues and I could not perceive. I mused on this thought, toyed with the idea of developing a statistical algorithm that would filter out the noise, revealing the underlying structure. My jocose thoughts were shattered by what was supposed to be the motivational crescendo — we all rose to our feet and clapped our hands somewhat like well-fed seals at feeding time at the local zoo — that is, with not much enthusiasm. Unfortunately, for that individual, there was no form to his ideas, no shape to his plan. Needless to say the listless, MBA-clad, mumbo-jumbo speaking “hot shot” was not head of global risk for very long. However, the experience stuck in my mind and re-stimulated my interest in nonparametric statistical methods, a subset of which, non parametric density estimation, is the subject of this chapter. It introduces nonparametric density estimation as a complementary statistical mechanism for describing energy price returns. It begins by discussing, the simplest nonparametric density estimator — the histogram, how to construct it, and its properties and limitations.


Kernel Density Price Return Kernel Density Estimator Nonparametric Density Estimation Bandwidth Selector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Further Reading

  1. Härdle, W. (1991) Smoothing Techniques, With Implementations in S, Springer, New York.CrossRefGoogle Scholar
  2. Härdle, W. and Scott, D. (1992) Smoothing in by weighted averaging using rounded points, Computational Statistics, 7, 97–128.Google Scholar
  3. Marron, J. (1989) “Comments on a data based band width selector,” Computational Statistics & Data Analysis, 8, 155–70.CrossRefGoogle Scholar
  4. Marron, J. S. and Nolan, D. (1988) “Canonical kernels for density estimation,” Statistics & Probability Letters, 7(3), 195–9.CrossRefGoogle Scholar
  5. Park, B. U. and Turlach, B. A. (1992) Practical performance of several data driven bandwidth selectors, Computational Statistics, 7, 251–70.Google Scholar
  6. Scott, D. W. (1992) Multivariate Density Estimation: Theory, Practice, and Visualization, John Wiley & Sons, New York and Chichester.CrossRefGoogle Scholar
  7. Silverman, B. W. (1986) Density Estimation for Statistics and Data Analysis, Vol. 26 of Monographs on Statistics and Applied Probability, Chapman and Hall, London.CrossRefGoogle Scholar
  8. Turlach, B. A. (1993) Bandwidth Selection in Kernel Density Estimation: A Review, Discussion Paper 9307, Institut für Statistik und Ökonometrie, Humboldt-Universität zu Berlin.Google Scholar
  9. Wand, M. P and Jones, M. C. (1995) Kernel Smoothing, Vol. 60 of Monographs on Statistics and Applied Probability, Chapman and Hall, London.CrossRefGoogle Scholar

Copyright information

© Nigel Da Costa Lewis 2005

Authors and Affiliations

  • Nigel Da Costa Lewis

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