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Entropy 2015, 17(1), 1-27; doi:10.3390/e17010001

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

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.
Received: 18 September 2014 / Accepted: 17 December 2014 / Published: 23 December 2014
(This article belongs to the Section Complexity)
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Abstract

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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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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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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