Identification of continuous-time linear filters when only discrete-time data is available

62 Pages Posted: 17 Mar 2022 Last revised: 27 Mar 2024

See all articles by Giuseppe Buccheri

Giuseppe Buccheri

University of Verona - Department of Economics

Date Written: March 24, 2024

Abstract

We study the inference of continuous-time linear filters from discrete-time observations of the underlying stochastic differential equation. This problem poses several identification issues related to the existence of infinite continuous-time specifications with different covariance structures having the same exact discrete-time representation. We derive a set of restrictions on the drift dynamics allowing to uniquely determine the drift linear projections and other relevant covariance structures of the stochastic differential equation. Our results are employed to identify, based on discrete-time data, the solution to an optimal stochastic control problem under partial information, thereby reconciling the continuous-time formulation of the problem with the statistical inference of the model parameters based on discrete-time information. The example of a partially informed investor maximizing the expected terminal utility is illustrated in detail.

Keywords: Kalman-Bucy filter, Linear stochastic differential equations, VARMA models, Partial information, Learning.

JEL Classification: C22, C51

Suggested Citation

Buccheri, Giuseppe, Identification of continuous-time linear filters when only discrete-time data is available (March 24, 2024). Available at SSRN: https://ssrn.com/abstract=4017696 or http://dx.doi.org/10.2139/ssrn.4017696

Giuseppe Buccheri (Contact Author)

University of Verona - Department of Economics ( email )

Via Cantarane, 24
37129 Verona
Italy
045 8028525 (Phone)

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