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Data-Driven Time-Series Prediction

September 14, 2025

Dima Bykhovsky Link to PDF version of this file.

This work is licensed under a Creative Commons “Attribution-NonCommercial-ShareAlike 4.0 International” license.

Preface

In recent years, the convergence of machine learning (ML) and signal processing (SP) has gathered growing attention in engineering education. Students are often introduced to ML principles at an early stage, yet many advanced SP topics, ranging from linear systems and time-frequency analysis to probabilistic modeling, traditionally require multiple specialized courses [4]. Although these SP methods yield comprehensive performance insights and rigorous conclusions, teaching them can be both time-consuming and demanding.

A key bridge between basic ML concepts and advanced SP techniques is the least squares (LS) method. LS is grounded in a simple and intuitive idea: minimizing the sum of squared errors. While direct LS computations may be $\mathcal {O}(N^3)$, and thus less efficient than typical SP methods ($\mathcal {O}(N \log N)$ to $\mathcal {O}(N^2)$), the LS perspective fosters a simpler, data-driven understanding of fundamental SP tasks. For example, the estimation of sinusoidal signal parameters in noise can be introduced by viewing it purely as a regression problem, bypassing the need for more involved probabilistic analyses. Likewise, the discrete Fourier transform (DFT) can be reframed as an extension of sinusoidal parameter estimation, illustrating SP principles with real arithmetic alone.

An LS-centric viewpoint aligns well with the foundational prerequisites of many ML courses and can be integrated at an early stage of engineering or data science programs. It offers an accessible path for teaching core SP ideas to engineering students who might lack extensive mathematical or probabilistic training. Although the underlying techniques are not new, this data-driven, regression-based interpretation may be more intuitive for those already familiar with basic ML concepts, enabling them to explore SP topics with minimal additional theoretical overhead.

Data-Driven Time-Series Prediction

Contents

Preface