First approach to LSTM with multiple univariate time series

Question

First of all, thank you for any help or comments you can make. I have been reading related posts since it is a quite discussed topic but I have not found anything that helps me.

I present my problem:

• Imagine that you know the variation in the average price of housing sales, monthly, in the last 10 years, in all the municipalities of 5 cities in your country. If we consider 100 municipalities per city, it will lead to 500 univariate time series.

• Given this situation, I want to develop a neural network model that uses the municipalities of three of those cities, 300 time series. The objective is to see how he then generalizes it to the other two cities that he does not know.

I am absolutely at a loss on how a model can be trained on such a large number of time series at once.

Answer 1

Since there are spatial temporal issues I don't think a vanilla LSTM will work well for these purposes. You could potentially use graph neural networks (GNNs) they are good at learning spatial temporal dependencies. Essentially here you could treat this as a multivariate time series forecasting problem like the authors of STEMGNN

In order to emphasize the relationships among multiple time-series, we formulate the problem of multivariate time-series forecasting based on a data structure called multivariate temporal graph, which can be denoted as G = (X,W). X = {xit} ∈ RN×T stands for the multivariate time-series input, where N is the number of time-series (nodes), and T is the number of timestamps. We denote NN×N the observed values at timestamp t as Xt ∈ R. W ∈ R is the adjacency matrix, where wij > 0 indicates that there is an edge connecting nodes i and j, and wij indicates the strength of this edge.

There are implementations publicly available. I recommend that you check out the PyTorch Geometric Library.