Dear Sir, greetings from Paris.

Your problem is quite complex in this context and you will need considerably more elaborate methods. I am not a specialist in spatial econometrics but I did some long ago. I advise you to check spatial econometrics models at the center for spatial data analysis of UChicago.

I think you could check the GeoDASpace spatial econometrics software here:

https://geodacenter.github.io/GeoDaSpace/

There are many possibilities for your question, some easy, some quite complex.

The easiest would be a LSDV model with region and time dummies, but this would not be the most accurate or consistent estimator but a start.

You could use panel specifications too or full spatio-temporal models which are covered in the courses and manuals in GEODA resources center on the indicated webpage.

Another possibility is to check for Singular Spectrum Analysis in R, a really completely different method.

I would also advise you to check for factomineR package for different multivariate data analysis methods. I use those for my own research in similar contexts but without the econometrics machinery. In this context, time and location dummies could indicate some interesting answers. I have many papers but they are in french...

Finally I found some spatiotemporal modelling tools in Rfrom natural sciences :

https://spacetimewithr.org/Spatio-Temporal%20Statistics%20with%20R.pdf

https://cran.r-project.org/web/views/SpatioTemporal.html

A RG member wrote a package:

Article sp Timer: Spatio-Temporal Bayesian Modeling Using R

Hope this helps. All the best.

Franck.

Greetings,

Have you considered applying Independent Component Analysis (ICA)? From the objective of your hypothesis if your meaning of statistically different is analogous to statistical independence then this may be worth looking into. The only underlying assumption for ICA is that the source signals are non-Gaussian which is most likely the case with your real-world data. If you were to perform ICA on the data matrix then project in the directions of maximal statistical independence you may observe a number of separate clusters similar to the number of your regions, this could very well support the hypothesis. For a conceptual check if this approach will have utility, check out the classical cocktail party problem and blind source separation.

I suggest using FastICA with Hyvärinen's fast fixed-point algorithm, http://bsp.teithe.gr/members/downloads/FastICA.html. There are also variants of ICA that find nonlinear subcomponents, if the underlying pattern you are seeking is not known it would be useful to try both.

I hope this suggestion is useful

Tyler J Grear

Some more details about these data would be helpful. Understanding the structure of your data is important for recommending the 'best' approach.

-Are these 20 years of data one observation / data point per year or is this daily data spanning 20 years?

-Are these observation spatially explicit (e.g. from a carbon flux tower at a fixed latitude and longitude) or are these data not spatially explicit (e.g. a value assigned to an administrative boundary that could have been collected anywhere within that boundary)?

-The two previous questions then lead to this: Have you plotted the data and assessed 1) Do there appear to be distinct differences? 2) Are there features that you will need complex statistics/modeling approaches for (trends or annual, monthly, daily seasonality?).

-Most importantly, what question are you trying to answer? "Are there differences in the long-term average?" or "Are there trends in the long-term dataset?" or "Are there changes in some other aspect of the data over time?"

After you assess what is in your data you can decide what the appropriate analysis is. A complex analysis is not better if it is not the most appropriate analysis for your data.