Estimation for time-changed self-similar stochastic processes

W. Arroum; O.D. Jones

doi:10.1117/12.638404

16 January 2006 Estimation for time-changed self-similar stochastic processes

W. Arroum, O.D. Jones

Proceedings Volume 6039, Complex Systems; 60390F (2006) https://doi.org/10.1117/12.638404
Event: Microelectronics, MEMS, and Nanotechnology, 2005, Brisbane, Australia

Abstract

We consider processes of the form X(t) = X^~(θ(t)) where X^~ is a self-similar process with stationary increments and θ is a deterministic subordinator with a periodic activity function a = θ'> 0. Such processes have been proposed as models for high-frequency financial data, such as currency exchange rates, where there are known to be daily and weekly periodic fluctuations in the volatility, captured here by the periodic activity function. We review an existing estimator for the activity function then propose three new methods for estimating it and present some experimental studies of their performance. We finish with an application to some foreign exchange and FTSE100 futures data.

Citation Download Citation

W. Arroum and O.D. Jones "Estimation for time-changed self-similar stochastic processes", Proc. SPIE 6039, Complex Systems, 60390F (16 January 2006); https://doi.org/10.1117/12.638404

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