Testing for a Random Walk Structure in the Frequency Evolution of a Tone in Noise

TL;DR

This paper develops a statistical test to verify if the frequency of sinusoidal signals in noisy data follows a random walk pattern, combining methods from economics and signal processing to assess model validity.

Contribution

It introduces a novel hypothesis testing framework for detecting random walk structures in the frequency evolution of signals in noise, bridging economics and signal analysis.

Findings

Test effectively detects random walk behavior in frequency data

Combines joint inference with frequency domain analysis

Applicable to complex sinusoidal signals in Gaussian noise

Abstract

Inference and hypothesis testing are typically constructed on the basis that a specific model holds for the data. To determine the veracity of conclusions drawn from such data analyses, one must be able to identify the presence of the assumed structure within the data. In this paper, a model verification test is developed for the presence of a random walk-like structure in the variations in the frequency of complex-valued sinusoidal signals measured in additive Gaussian noise. This test evaluates the joint inference of the random walk hypothesis tests found in economics literature that seek random walk behaviours in time series data, with an additional test to account for how the random walk behaves in frequency space.