Discussing the article: "Neural Networks Made Easy (Part 91): Frequency Domain Forecasting (FreDF)"
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Check out the new article: Neural Networks Made Easy (Part 91): Frequency Domain Forecasting (FreDF).
We continue to explore the analysis and forecasting of time series in the frequency domain. In this article, we will get acquainted with a new method to forecast data in the frequency domain, which can be added to many of the algorithms we have studied previously.
Among the models gaining popularity are those based on the Transformer architecture that use Self-Attention mechanisms for dynamic autocorrelation estimation. Also, we see an increasing interest in the use of frequency analysis in forecasting models. The representation of the sequence of input data in the frequency domain helps avoid the complexity of describing autocorrelation and improves the efficiency of various models.
Another important aspect is the autocorrelation in the sequence of predicted values. Obviously, the predicted values are part of a larger time series, which includes the analyzed and predicted sequences. Therefore, the predicted values preserve the correlation of the analyzed data. But this phenomenon is often ignored in modern forecasting methods. In particular, modern methods predominantly use the Direct Forecast (DF) paradigm, which generates multi-stage forecasts simultaneously. This implicitly assumes the independence of the steps in the sequence of predicted values. This mismatch between model assumptions and data features results in suboptimal forecast quality.
One of the solutions to this problem was proposed in the paper "FreDF: Learning to Forecast in Frequency Domain". The authors of the paper proposed a direct forecast method with frequency gain (FreDF). It clarifies the DF paradigm by aligning the predicted values and the sequence of labels in the frequency domain. When moving to the frequency domain, where the bases are orthogonal and independent, the influence of autocorrelation is effectively reduced. Thus, FreDF combats the inconsistency between the assumption about DF and the existence of autocorrelation of labels, while maintaining the advantages of DF.
The authors of the method tested its effectiveness in a series of experiments, which demonstrated the significant superiority of the proposed approach over modern methods.
Author: Dmitriy Gizlyk