Tree-based XGB, LightGBM, and CatBoost Models for Multi-period Time Series Probabilistic Forecasting

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The chapter title covers three essential concepts: “probabilistic forecasting”, “multi-period”, and “tree-based”. First is “probabilistic forecasting”. Many real-world applications request prediction intervals for resource planning or anomaly detection, as mentioned in Chapter 1: Introduction. Quantile regression is one of the four solutions mentioned in Part 2 of this book. Quantile predictions can inform users of the likelihood of a predicted value, whether it is very likely in the 50th percentile, or very unlikely in the upper 90th percentile as shown in Figure (A).

Figure (A): Quantile predictions (image by author)

The second concept in the title is the multi-period predictions. We often need forecasts for multiple periods rather than just a point estimate. When we plan for a week-long vacation, we need the 5-day weather forecasts rather than 1-day forecast. However, a linear regression or a tree-based algorithm typically provides a point estimate. How do we design the forecasting process to provide multiple periods? Intuitively, if we get the prediction for the next period, maybe we can include it as the input for the same model to get the prediction for the next next period? This solution is popular and is called the recursive forecasting strategy as shown in Figure (B). The recursive forecasting strategy uses the model’s forecasts as inputs for subsequent predictions. The strategy starts with the past values yt to yt-k for the model to predict the one-step-ahead yt+1. Then it incorporates yt+1 and updates other inputs to forecast yt+2. It repeats the process to predict all the subsequent time steps. In the Darts library, you can assign this strategy as well.