Dependent multi-series forecasting (Multivariate forecasting)¶

In univariate time series forecasting, a single time series is modeled as a linear or nonlinear combination of its lags, where past values of the series are used to forecast its future. In multi-series forecasting, two or more time series are modeled together using a single model.

In dependent multi-series forecasting (multivariate time series), all series are modeled together in a single model, considering that each time series depends not only on its past values but also on the past values of the other series. The forecaster is expected not only to learn the information of each series separately but also to relate them. An example is the measurements made by all the sensors (flow, temperature, pressure...) installed on an industrial machine such as a compressor.

Time series transformation to train a forecaster with multiple dependent time series.

Since as many training matrices are created as there are series in the dataset, it must be decided on which level the forecasting will be performed. To predict the next n steps a model is trained for each step to be predicted, the selected level in the figure is Series 1. This strategy is of the type direct multi-step forecasting.

Diagram of direct forecasting with multiple dependent time series.

Using the ForecasterAutoregMultiVariate class, it is possible to easily build machine learning models for dependent multi-series forecasting.