Impact of missing data on the prediction of random fields

Area of Science:

• Statistics
• Time Series Analysis
• Random Fields

Background:

• Stationary random fields are widely used in various scientific domains.
• Missing observations pose significant challenges in prediction tasks.
• Quantifying the impact of missing data is crucial for reliable forecasting.

Purpose of the Study:

• To address prediction problems in stationary random fields with missing past observations.
• To quantify the influence of missing values on prediction error variance.
• To identify conditions under which missing data does not affect prediction accuracy.

Main Methods:

• Developing simple bounds for prediction error variance.
• Analyzing the theoretical impact of missing observations.
• Conducting simulation experiments to validate findings.
• Applying the methodology to a real-world dataset.

Main Results:

• Established bounds for prediction error variance in the presence of missing data.
• Characterized specific types of stationary random fields where missing observations have no impact on predictions.
• Demonstrated the effectiveness of the bounds through simulations.
• Validated the approach with a practical data application.

Conclusions:

• The derived bounds provide a method to assess the influence of missing data on predictions.
• Identified random field properties that mitigate the effect of missing observations.
• The study offers practical tools for handling missing data in time series prediction.