{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:01:31Z","timestamp":1760230891861,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T00:00:00Z","timestamp":1660521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Australian Commonwealth Government","award":["CE170100004","DP170103625"],"award-info":[{"award-number":["CE170100004","DP170103625"]}]},{"name":"University of Melbourne","award":["CE170100004","DP170103625"],"award-info":[{"award-number":["CE170100004","DP170103625"]}]},{"name":"Australian Government Research Training Program","award":["CE170100004","DP170103625"],"award-info":[{"award-number":["CE170100004","DP170103625"]}]},{"name":"Australian Research Council (ARC) Centre of Excellence for Gravitational Wave Discovery","award":["CE170100004","DP170103625"],"award-info":[{"award-number":["CE170100004","DP170103625"]}]},{"name":"ARC Discovery project","award":["CE170100004","DP170103625"],"award-info":[{"award-number":["CE170100004","DP170103625"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/s22166103","type":"journal-article","created":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T23:44:03Z","timestamp":1660607043000},"page":"6103","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Testing for a Random Walk Structure in the Frequency Evolution of a Tone in Noise"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9923-9043","authenticated-orcid":false,"given":"Scarlett","family":"Abramson","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3010, Australia"}]},{"given":"William","family":"Moran","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3010, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7988-3189","authenticated-orcid":false,"given":"Robin","family":"Evans","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3010, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4642-141X","authenticated-orcid":false,"given":"Andrew","family":"Melatos","sequence":"additional","affiliation":[{"name":"School of Physics, University of Melbourne, Parkville, VIC 3010, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.dsp.2015.06.012","article-title":"Bayesian evidence and model selection","volume":"47","author":"Knuth","year":"2015","journal-title":"Digit. 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