Linear Models for Multi-period Probabilistic Forecasting

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Linear regression models, not surprisingly, can do a point estimate for time series. Linear regression models are appealing because they are quick, interpretable, and easy to deploy. It still is a good choice in many organizations. The common type of linear regressions is the autoregressive model, as demonstrated in Chapter 9: Automatic ARIMA. However, many real-world use cases demand us to provide the following two: (1) probabilistic forecasts (or called prediction intervals or prediction uncertainty), and (2) multi-period predictions. How can we extend a linear regression to perform the above two outcomes?

The solution for (1) is to use quantile regression to provide the prediction uncertainty. Figure (A) shows the quantile forecasts. For any future time t, it returns the forecasting samples on the 10th, 50th, and 90th percentile. More quantile samples can be generated if needed. You can go to Chapter 6: “Quantile regression for prediction uncertainty” to learn it.