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Open AccessArticle

Complexity-Regularized Regression for Serially-Correlated Residuals with Applications to Stock Market Data

by David Darmon 1,2,* and Michelle Girvan 2,3,4
1
Department of Mathematics, University of Maryland, College Park, MD 20742, USA
2
Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
3
Department of Physics, University of Maryland, College Park, MD 20742, USA
4
Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA
*
Author to whom correspondence should be addressed.
Entropy 2015, 17(1), 1-27; https://doi.org/10.3390/e17010001
Received: 18 September 2014 / Accepted: 17 December 2014 / Published: 23 December 2014
(This article belongs to the Section Complexity)
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 “look random”. 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. View Full-Text
Keywords: non-parametric regression; smoothing; time series; epsilon-machine non-parametric regression; smoothing; time series; epsilon-machine
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Darmon, D.; Girvan, M. Complexity-Regularized Regression for Serially-Correlated Residuals with Applications to Stock Market Data. Entropy 2015, 17, 1-27.

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