Conformal Prediction for Time Series and Forecasting

In this chapter, we will explore the exciting field of conformal prediction for time series and forecasting. Conformal prediction is a powerful tool for producing prediction intervals (PIs) for point forecasting models, and we will show you how to apply this technique to your data using open source libraries. This chapter will take you on a journey from understanding the fundamentals of uncertainty quantification (UQ) in time series to the intricate mechanisms behind conformal prediction in forecasting.

With this chapter, you will have a solid understanding of the various approaches to producing PIs, and you will be able to build your PIs using conformal prediction.

In this chapter, we’re going to cover the following main topics:

• UQ for time series and forecasting problems
• The concept of PIs in forecasting applications
• Various approaches to producing PIs
• Conformal prediction for time series and forecasting...

UQ for time series and forecasting problems

UQ is not just a sophisticated addition to time series forecasting; it is a fundamental aspect that provides invaluable insights into the nature of the predictions. Let’s look at why it’s important and a brief history of its development.

The importance of UQ

UQ is a critical component of time series forecasting. While a forecast model may provide accurate predictions on average, understanding the uncertainty around those predictions is equally essential. There are several key reasons why properly quantifying uncertainty is vital for practical time series forecasting:

• Risk assessment: In many domains, such as finance, healthcare, and environmental science, forecasting is closely linked with decision-making. Understanding the uncertainty in predictions aids in assessing potential risks, thus enabling informed decisions.
• Model confidence: UQ provides an understanding of the confidence in each model’s predictions...

The concept of PIs in forecasting applications

PIs are vital tools in forecasting, providing a range of plausible values within which a future observation is likely to occur. Unlike point forecasts, which give a single best estimate, PIs communicate the uncertainty surrounding that estimate.

This section explores the fundamental concepts behind PIs and their significance in various forecasting applications.

Definition and construction

PIs are constructed around a point forecast to represent the range within which future observations are expected to lie with a given confidence level. For example, a 95% PI implies that 95 of 100 future observations are expected to fall within the defined range.

PIs can take several forms, depending on the approach used to generate them. Two key distinguishing factors are as follows:

• Symmetric versus asymmetric intervals: PIs can be symmetric, where the bounds are equidistant from the point forecast, or asymmetric, reflecting differing...

Various approaches to producing PIs

PIs are an essential tool in forecasting, allowing practitioners to understand the range within which future observations are likely to fall. Various approaches have been developed to produce these intervals, each with advantages, applications, and challenges. This section will explore the most prominent techniques for creating PIs.

Parametric approaches

Parametric approaches make specific assumptions about the distribution of forecast errors to derive PIs. Some standard techniques in this category are as follows:

• Normal distribution assumptions: By assuming that the forecast errors follow a normal distribution, we can compute symmetric PIs based on standard errors and critical values from the normal distribution.
• Time series models: Models such as ARIMA and exponential smoothing can generate PIs by modeling the underlying stochastic process and using the estimated parameters to produce intervals.
• Generalized linear models ...

Conformal prediction for time series and forecasting

Creating reliable PIs for time series forecasting has been a longstanding, intricate challenge that remained unsolved for years until conformal prediction emerged.

This problem was underscored during the 2018 M4 Forecasting Competition, which necessitated participants to supply PIs and point estimates.

In the research paper titled Combining Prediction Intervals in the M4 Competition, (https://www.sciencedirect.com/science/article/abs/pii/S0169207019301141), Yael Grushka-Cockayne from the Darden School of Business and Victor Richmond R. Jose from Harvard Business School scrutinized 20 interval submissions. They assessed both the calibration and precision of the predictions and gauged their performances across different time horizons. Their analysis concluded that the submissions were ineffective in accurately estimating uncertainty.

Ensemble batch PIs (EnbPIs)

Conformal Prediction Intervals for Dynamic Time-Series (http...

Summary

This chapter taught you how to apply conformal prediction to time series forecasting. Conformal prediction is a powerful technique for crafting PIs for point forecasting models.

This chapter also offered insights into how to harness this method using open source platforms.

We began by exploring UQ in a time series, delving into the significance of PIs, and showcasing various strategies to generate them.

The concept of conformal prediction and its application in forecasting scenarios was central to this chapter. At this point, you are equipped with the knowledge to apply these methodologies in real-world settings, empowering your forecasting models with precise uncertainty bounds. Adding confidence measures to predictions ensures that the forecasts are accurate and reliable.

With a solid understanding of conformal prediction for time series, we will now focus on another critical application area – computer vision.