Distribution-Free Probability Density Forecast Through Deep Neural Networks.

Area of Science:

• Machine Learning
• Statistical Forecasting
• Computational Intelligence

Background:

• Traditional probabilistic forecasting models like prediction intervals and quantile forecasts offer limited flexibility.
• Existing density forecast models often impose constraints on distributions, hindering accurate approximation of real-world scenarios and potentially leading to suboptimal results.

Purpose of the Study:

• To propose a novel distribution-free density forecast model using deep learning.
• To overcome the limitations of existing constrained density forecast models.
• To enhance the accuracy and flexibility of probabilistic forecasting.

Main Methods:

• A deep neural network (NN) with positive weights is employed to approximate cumulative density functions (CDFs) of forecasting targets.
• The model leverages the universal approximation capability of NNs to forecast distributions without prior constraints.
• The proposed model's forecasted distribution range is proven to encompass all distributions with continuous CDFs.

Main Results:

• The distribution-free deep learning model demonstrated superior performance compared to state-of-the-art methods.
• Evaluations across diverse scenarios, including wind power, wind speed, and electricity price forecasting, confirmed the model's effectiveness.
• The model's ability to approximate real distributions without constraints led to improved forecasting accuracy.

Conclusions:

• The proposed distribution-free deep learning density forecast model offers enhanced flexibility and accuracy.
• This approach surpasses existing methods by avoiding distribution constraints and providing a wider range of potential forecasts.
• The model shows significant promise for various time-series forecasting applications.