Conformal Predictions for Time Series Probabilistic Forecasting

Real-world applications and planning require probabilistic forecasts rather than a point estimate. Probabilistic forecasts, also called prediction intervals or prediction uncertainty, can give planners a sense of uncertainty. However, the typical machine learning models such as linear regressions, random forecasts, or gradient boosting machines, are designed to produce mean estimation rather than a range of possible values. Developing from a point estimate to prediction intervals is what this book is interested in and the modern time series modeling techniques are concerned about. In the series of probabilistic forecasting, we introduced the Monte Carlo simulation techniques in “Monte Carlo Simulation for Time Series Probabilistic Forecasting” and the quantile regression technique in “Quantile Regression for Time Series Probabilistic Forecasting”. In this chapter, we will introduce another popular method — the Conformal Prediction (CP).

Let’s explain CP from the basic prediction context. We know the goal of a predictive model is to deliver unbiased estimates for the conditional mean. The gap between an estimate and an actual value in the sample is called the error. What are the errors? They are the uncertainty that the model is not sure about. So how do we quantify uncertainty? The answer to the question is just in the question itself. Since the errors between estimates and actual values represent the uncertainty, we can analyze the errors to quantify the uncertainty. We then add and subtract the quantified uncertainty to an estimate to render the prediction intervals. CP uses past data to determine precise levels of confidence in new predictions. CP produces the required confidence (such as 95%) that the new prediction will be within the prediction range. Notice that we do not mention any specific model, thus CP is model-agnostic.

The construction of CP goes like this:

• Errors are the absolute values between actual values and predictions. We will line up the errors between estimates and actual values from small to large. We will use a histogram to show the percentage of the error values.
• Most of the time, say, 95% of the time, the errors will be under a threshold. This threshold can be considered as our tolerance value for prediction errors…