Work

Least squares as random walks: The general case of arbitrary spacing

Year: 2026

Type: article

Abstract: Recently, we introduced the notion of a random walk based on a discrete sequence of data samples ( data walk ) and discovered a surprising link between ordinary least squares (OLS) fits to evenly sampled data and random walks. Here we generalize earlier results by showing that the slope of a linear fit to data which annuls the net area under a residual data walk equals that found by OLS for irregularly spaced data sequence. We also discover a deep connection with the orthogonality principle of estimation theory, leading to interpretation of suitably defined scalar products of data vectors as areas under data walks. The results are extended to weighted and generalized least squares (GLS). The new approach is illustrated on cosmic ray arrival time series.

Source: Physics Open

DOI: 10.1016/j.physo.2026.100378

Authors: Daniel Kestner, Alexander Kostinski

Institutions: University of Saint Francis, Michigan Technological University

Language: English

Topic: Statistical and numerical algorithms

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,700

Funder: National Science Foundation