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Dimension Reduction in Statistical Estimation of Partially Observed Multiscale Processes

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  • Andrew Papanicolaou
  • Konstantinos Spiliopoulos

Abstract

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced dimension. Then, this result is used to justify statistical estimation for the unknown parameters of interest based on the model of reduced dimension but using the original available data. This allows to learn the unknown parameters of interest while working in lower dimensions, as opposed to working with the original high dimensional system. Simulation studies support and illustrate the theoretical results.

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  • Andrew Papanicolaou & Konstantinos Spiliopoulos, 2016. "Dimension Reduction in Statistical Estimation of Partially Observed Multiscale Processes," Papers 1607.06158, arXiv.org, revised Nov 2017.
    • Handle: RePEc:arx:papers:1607.06158
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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
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