Operators on Inhomogeneous Time Series

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