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Introduction¶

A time series is a succession of chronologically ordered data spaced at equal or unequal intervals. The forecasting process consists of predicting the future value of a time series, either by modeling the series solely based on its past behavior (autoregressive) or by using other external variables.

This guide explores the use of scikit-learn regression models for time series forecasting. Specifically, it introduces skforecast, an intuitive library equipped with essential classes and functions to customize any Scikit-learn regression model to effectively address forecasting challenges.

Machine learning for forecasting¶

In order to apply machine learning models to forecasting problems, the time series has to be transformed into a matrix in which each value is related to the time window (lags) that precedes it.

In a time series context, a lag with respect to a time step $t$ is defined as the values of the series at previous time steps. For example, lag 1 is the value at time step $t − 1$ and lag $m$ is the value at time step $t − m$.

This type of transformation also allows to include additional variables.

Once data have been rearranged into the new shape, any regression model can be trained to predict the next value (step) of the series. During model training, every row is considered a separate data instance, where values at lags 1, 2, ... $p$ are considered predictors for the target quantity of the time series at time step $t + 1$.

Multi-Step Time Series Forecasting¶

When working with time series, it is seldom needed to predict only the next element in the series ($t_{+1}$). Instead, the most common goal is to predict a whole future interval (($t_{+1}$), ..., ($t_{+n}$)) or a far point in time ($t_{+n}$). Several strategies allow generating this type of prediction.

Recursive multi-step forecasting¶

Since the value $t_{n-1}$ is required to predict $t_{n}$, and $t_{n-1}$ is unknown, a recursive process is applied in which, each new prediction, is based on the previous one. This process is known as recursive forecasting or recursive multi-step forecasting and can be easily generated with the ForecasterRecursive class.

Direct multi-step forecasting¶

Direct multi-step forecasting consists of training a different model for each step of the forecast horizon. For example, to predict the next 5 values of a time series, 5 different models are trained, one for each step. As a result, the predictions are independent of each other.

The main complexity of this approach is to generate the correct training matrices for each model. The ForecasterDirect class of the skforecast library automates this process. It is also important to bear in mind that this strategy has a higher computational cost since it requires the train of multiple models. The following diagram shows the process for a case in which the response variable and two exogenous variables are available.

Forecasting multi-output¶

Some machine learning models, such as long short-term memory (LSTM) neural networks, can predict multiple values of a sequence simultaneously (one-shot). This strategy implemented in the ForecasterRnn class of the skforecast library