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Krzysztof Podgorski: From negative binomial process to functional autoregressive gamma processes and a Wright process

Tid: On 2017-04-26 kl 15.15 - 16.15

Plats: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University

Medverkande: Krzysztof Podgorski (Lund University)

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Abstract: In engineering and financial applications, one frequently encounters data that have a certain within a time unit (day, hour, etc) variability and some autoregressive functional dependence between the time units.
A typical example in finance is the within a day stochastic volatility driving high frequency returns vs. between trading days dependence of the stock values. Various at hoc data driven approaches have been applied to address this situation. Here we propose a model in which a sequence of gamma motions (think about daily high frequency stochastic volatilities) has its terms related through functional autoregressive dependence. The relation is defined through a new stochastic process that we call the Wright process as it involves distributions known in the literature as the Wright distributions. Several functional results on the mathematical structure of the model are derived. An estimation methods  for both model and distributional parameters is developed and used to fit high frequency financial data. It can be extended to generalized asymmetric Laplace models that are Gaussian conditionally on gamma distributed variance. The model is suitable for the engineering and environmental data in which variable variance in the Gaussian components is desirable. For illustration we present an mechanical engineering example based on the road profile data.

The work is jointly with Nima Shariati, Igor Rychlik and Tomasz J. Kozubowski.