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On Singularity of Fisher Information Matrix for Stochastic Processes Under High Frequency Sampling

In: Numerical Mathematics and Advanced Applications 2011

Author

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  • R. Kawai

    (University of Sydney, School of Mathematics and Statistics)

Abstract

We discuss the singularity of the Fisher information arising from statistical inference for continuous-time stochastic processes of practical interest, such as asset price dynamics in finance and individual animal movement in biology, under high frequency discrete sampling schemes. Singularity seems to be caused by the scale parameter and the selfsimilarity index, while there exists a different type of singularity resulting from some redundancy of parameters in the short time framework. We derive the speed of convergence of the Fisher information to singularity for some instances and show that the convergence to singularity may be delayed through a wise expansion of the total observation window.

Suggested Citation

  • R. Kawai, 2013. "On Singularity of Fisher Information Matrix for Stochastic Processes Under High Frequency Sampling," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 841-849, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_87
    DOI: 10.1007/978-3-642-33134-3_87
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