Time-changed self-similar processes : an application to high frequency financial data
Time-changed self-similar processes : an application to high frequency financial data
We consider processes of the form X(t) = X̄;(θ(t)) where X̄; 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 propose three new methods for estimation the activity and review an existing estimator for it. We present some experimental studies of the estimators performances. We finish with an application to high frequency financial data such as foreign exchange rates and FTSE100 futures contract.
University of Southampton
Arroum, Wahib
42409093-e444-4600-98bd-33941a3deb4c
2007
Arroum, Wahib
42409093-e444-4600-98bd-33941a3deb4c
Arroum, Wahib
(2007)
Time-changed self-similar processes : an application to high frequency financial data.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
We consider processes of the form X(t) = X̄;(θ(t)) where X̄; 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 propose three new methods for estimation the activity and review an existing estimator for it. We present some experimental studies of the estimators performances. We finish with an application to high frequency financial data such as foreign exchange rates and FTSE100 futures contract.
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Published date: 2007
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Local EPrints ID: 466518
URI: http://eprints.soton.ac.uk/id/eprint/466518
PURE UUID: fea88d13-390f-4b0d-9029-1fa06d3d07d7
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Date deposited: 05 Jul 2022 05:34
Last modified: 16 Mar 2024 20:45
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Author:
Wahib Arroum
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