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Operators on Inhomogeneous Time Series

Olsen & Associates Working Paper No. 324

33 Pages Posted: 21 Mar 2000  

Gilles O. Zumbach


Ulrich A. Müller

Olsen & Associates

Multiple version iconThere are 2 versions of this paper

Date Written: February 1, 2000


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 in macroscopic operators (that have a limit value when the sampling frequency goes to infinity) and 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 ...

JEL Classification: C14, C52, C63, C80, G10

Suggested Citation

Zumbach, Gilles O. and Müller, Ulrich A., Operators on Inhomogeneous Time Series (February 1, 2000). Olsen & Associates Working Paper No. 324. Available at SSRN: or

Gilles Zumbach

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Ulrich A. Müller (Contact Author)

Olsen & Associates ( email )

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+41 (1) 422 22 82 (Fax)

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