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.
This work was carried out largely while the author was based at University of Leicester, UK
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Kawai, R. (2013). On Singularity of Fisher Information Matrix for Stochastic Processes Under High Frequency Sampling. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_87
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DOI: https://doi.org/10.1007/978-3-642-33134-3_87
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