Trajectory estimation is what is at stake when studying rising temperatures, sea level rise linked to climate change, or position shifts caused by the vertical movement of the earth and tectonic plates. These are slow phenomena, measured over years, in which the trend is precisely what matters. And this is where correlated noise becomes dangerous, because it significantly impacts the accuracy of the linear trend estimation. Ignoring it does not solve the problem, it merely hides it inside a line that looks steadier than it should.

Hector exists to correct this. It is a geophysical time series analysis software package that estimates the linear trend and the noise model at the same time, not in separate steps. It uses the maximum likelihood method to determine, in a single process, the slope of the trend and the parameters of the noise that accompanies it. The result is not just a number, it is a number with its uncertainty quantified alongside it.

The tool starts from an honest assumption: the user knows, from the outset, the type of correlated noise present in their observations. From there, Hector allows annual, semi-annual and other periodic signals to be included in the process, and offsets to be estimated at specific epochs. Everything that distorts the reading in a real series becomes part of the model, instead of staying hidden in the margin of error.

Estimating trends has always been the work of science. What changes with a tool like Hector is the honesty of the result. In an age when so much research rests on long, imperfect series, telling the real signal apart from the noise that distorts it is no longer a technical detail. It is the difference between a defensible conclusion and a statistical illusion.

Hector was designed to need none of them. As long as the noise is, or has been produced, stationary, the tool handles missing data directly, without interpolation, without zero-padding and without approximations to the covariance matrix. The incomplete series goes in as it is, and the estimate comes out without the bias the shortcuts used to introduce.

From here, Hector opens up a range of control that few tools offer. It allows annual, semi-annual and other periodic signals to be included in the trend estimation process. It allows offsets to be estimated at specific epochs, those abrupt jumps that mark a series and that, ignored, distort the slope. And it allows the noise model to be chosen among power-law, ARFIMA, generalised Gauss-Markov and white noise, or any combination of these, fitting the analysis to the real nature of the observations.

The care for data quality extends to the rest of the work. Hector includes programs to remove outliers and to generate power spectral density plots, which help reveal the structure of the noise before modelling. It also includes a program with a script to detect offsets automatically, saving the work of hunting them down one by one. And when the power-law model is selected, with combinations of white, flicker and random walk noise, it allows the first difference of the data to be obtained.

For the researcher, this translates into something concrete. Less time patching series and justifying shortcuts, more time interpreting results that can be trusted. The integrity of the estimate no longer depends on the luck of having complete data. It depends on the right tool.

Hector is an open-source academic software package, made available to the research community. Researchers can use, study and build upon it, and that is not merely a licensing detail, it is a stance. The rigorous analysis of geophysical time series is a common good of science, and tools of this kind gain value when they circulate among those who need them.

Alongside this academic version, TeroMovigo provides commercial solutions based on Hector, including professional support, integration, and a maintained Python implementation designed to run on Windows and macOS.

Behind Hector is TeroMovigo, the main author of the software, responsible for its development and its maintenance. The aim is to provide continuous support to both the academic community and professional users. It is not a product that is handed over and abandoned; it is a tool that is maintained over time, as the science and its applications evolve.

That seriousness shows in the rigour with which Hector positions itself in its field. The methodology behind it is documented in the book Geodetic Time Series Analysis in Earth Sciences, and the software engages openly with existing alternatives. There are other programs for similar tasks, such as CATS and est_noise, and comparisons between Hector and est_noise have shown consistent results between the two. Users of Hector in scientific publications are invited to cite the reference by Bos, Fernandes, Williams and Bastos (2013) on the fast error analysis of continuous GNSS observations with missing data.

It is from this DNA that TeroMovigo makes its signature: serious science, placed in practical hands, maintained responsibly and shared with the community. Hector is not just a computation tool. It shows that advanced geoscientific knowledge can be both rigorous and openly available, while supporting professional use where reliability, support and integration are essential.