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Operators On Inhomogeneous Time Series

Author

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  • GILLES ZUMBACH

    (Olsen & Associates, Research Institute for Applied Economics, Seefeldstrasse 233, 8008 Zürich, Switzerland)

  • ULRICH MÜLLER

    (Olsen & Associates, Research Institute for Applied Economics, Seefeldstrasse 233, 8008 Zürich, Switzerland)

Abstract

We present a toolbox to compute and extract information from inhomogeneous (i.e. unequally spaced) time series. The toolbox contains a large set of operators, mapping from the space of inhomogeneous time series to itself. These operators are computationally efficient (time and memory-wise) and suitable for stochastic processes. This makes them attractive for processing high-frequency data in finance and other fields. Using a basic set of operators, we easily construct more powerful combined operators which cover a wide set of typical applications.The operators are classified as either macroscopic operators (that have a limit value when the sampling frequency goes to infinity) or microscopic operators (that strongly depend on the actual sampling). For inhomogeneous data, macroscopic operators are more robust and more important. Examples of macroscopic operators are (exponential) moving averages, differentials, derivatives, moving volatilities, etc.…

Suggested Citation

  • Gilles Zumbach & Ulrich Müller, 2001. "Operators On Inhomogeneous Time Series," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 147-177.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:01:n:s0219024901000900
    DOI: 10.1142/S0219024901000900
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    Cited by:

    1. Gilles Zumbach & Paul Lynch, 2001. "Heterogeneous volatility cascade in financial markets," Papers cond-mat/0105162, arXiv.org.
    2. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.

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