Spectral Analysis of Irregularly Sampled Data with Time Series Models

Piet M.T. Broersen*
Department of Multi Scale Physics, Delft University of Technology, The Netherlands

© 2008 Piet M.T. Broersen.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Multi Scale Physics, Delft University of Technology, The Netherlands; Tel: +31 15 2786419; E-mail:


Slotted resampling transforms an irregularly sampled process into an equidistant missing-data problem. Equidistant resampling inevitably causes bias, due to aliasing and the shift of the irregular observation times to an equidistant grid. Taking a slot width smaller than the resampling time can diminish the shift bias. A dedicated estimator for time series models of multiple slotted data sets with missing observations has been developed for the estimation of the power spectral density and of the autocorrelation function. The algorithm estimates time series models and selects the order and type from a number of candidates. It is tested with benchmark data. Spectra can be estimated until frequencies higher than 100 times the mean data rate.