Hector Web Service

A program for the analysis of geophysical time-series


Hector is a software package that can be used to estimate the linear trend in time-series with temporal correlated noise.

Trend estimation is a common task in geophysical research where one is interested in phenomena such as the increase in temperature, sea level and position over time. It is well known that in most geophysical time series the noise is correlated in time and this has a significant influence on the accuracy by which the linear trend can be estimated.

Therefore, the use of a computer program such as HECTOR is advisable.

HECTOR assumes that the user knows what type of temporal correlated noise exists in the observations and estimates both the linear trend and the parameters of the chosen noise model using the Maximum Likelihood Estimation (MLE) method.

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Main features

Correctly deals with missing data. No interpolation or zero padding of the data nor an approximation of the co-variance matrix is required (as long the noise is, or has been made, stationary).

Allows yearly, half-yearly and other periodic signals to be included in the estimation process of the linear trend.

Allows the option to estimate offsets at given time epochs.

Includes power-law noise, ARFIMA, generalized Gauss-Markov and white noise models. Any combination of these models can be made.

Allows taking the first difference of the data if power-law noise model is chosen (including combination of white, flicker and random walk).

Comes with programs to remove outliers and to make power spectral density plots.

Requirements and Download

The hector software package is mainly intended to be run on computers with Unix-like operating systems. If you don’t want to use the static executable you can compile the source code. In this case one should also install the ATLAS, FFTW3 and the GSL libraries.

To download the latest version (1.9) of the statically compiled executables (for 32 and 64 bit operating Linux operating systems), the source code, the example, or the manual, click on the following links:












For previous versions, click here.

How to cite HECTOR

If you find the Hector program useful, please cite it in your work as:

Bos, M.S., Fernandes, R.M.S., Williams, S.D.P., and Bastos, L. (2013). Fast Error Analysis of Continuous GNSS Observations with Missing Data. J. Geod., Vol 87(4), 351-360, doi:10.1007/s00190-012-0605-0.

License and Copyright

Hector is Copyright © 2012-2016 Machiel Bos, Rui Fernandes and Luisa Bastos.

Hector is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

Contact information

This page was last updated on 04 May 2021. For comments or questions, email machiel@segal.ubi.pt.