{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:27:26Z","timestamp":1760243246781,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2014,12,23]],"date-time":"2014-12-23T00:00:00Z","timestamp":1419292800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A popular approach in the investigation of the short-term behavior of a non-stationary time series is to assume that the time series decomposes additively into a long-term trend and short-term fluctuations. A first step towards investigating the short-term behavior requires estimation of the trend, typically via smoothing in the time domain. We propose a method for time-domain smoothing, called complexity-regularized regression (CRR). This method extends recent work, which infers a regression function that makes residuals from a model \u201clook random\u201d. Our approach operationalizes non-randomness in the residuals by applying ideas from computational mechanics, in particular the statistical complexity of the residual process. The method is compared to generalized cross-validation (GCV), a standard approach for inferring regression functions, and shown to outperform GCV when the error terms are serially correlated. Regression under serially-correlated residuals has applications to time series analysis, where the residuals may represent short timescale activity. We apply CRR to a time series drawn from the Dow Jones Industrial Average and examine how both the long-term and short-term behavior of the market have changed over time.<\/jats:p>","DOI":"10.3390\/e17010001","type":"journal-article","created":{"date-parts":[[2014,12,23]],"date-time":"2014-12-23T15:33:56Z","timestamp":1419348836000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Complexity-Regularized Regression for Serially-Correlated Residuals with Applications to Stock Market Data"],"prefix":"10.3390","volume":"17","author":[{"given":"David","family":"Darmon","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Maryland, College Park, MD 20742, USA"},{"name":"Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michelle","family":"Girvan","sequence":"additional","affiliation":[{"name":"Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA"},{"name":"Department of Physics, University of Maryland, College Park, MD 20742, USA"},{"name":"Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,12,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Fan, J., and Yao, Q. 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