Statistical properties of Multiscale Regression Analysis

Simulation and application to human postural control

Aaron D. Likens, Polemnia Amazeen, Stephen West, Cameron T. Gibbons

Research output: Contribution to journalArticle

Abstract

Multiscale Regression Analysis (MRA) is a promising new tool for the analysis of bivariate time series that is based on Detrended Fluctuation Analysis (DFA) and Ordinary Least Squares (OLS) regression. The method was developed within the economics and environmental science literatures (Kristoufek, 2015, 2018; Kristoufek and Ferreira, 2018) and is beginning to be applied in other scientific domains. To date, however, no systematic studies have investigated the behavior of the estimator with respect to short time series. This paper fills that gap by assessing the performance of the MRA estimator using time series with varying length, distribution, and structure (e.g., autocorrelation, stationarity). Simulations show that MRA performs well under many circumstances with as few as 512 observations. Linear and quadratic time trends contribute considerable systematic bias; however, using a detrending polynomial of order ≥ 2 effectively attenuates time trend associated deviations from expected values. We apply MRA to a previously published dataset in order to explore the relationship that emerges between body segments during an act of quiet standing. Results suggest that the velocity of the hip asymptotically depends on velocity of the ankle. In contrast, ankle velocity was a much weaker predictor of shoulder velocity. We conclude by providing suggestions for best practice and future model development.

Original languageEnglish (US)
Article number121580
JournalPhysica A: Statistical Mechanics and its Applications
Volume532
DOIs
StatePublished - Oct 15 2019

Fingerprint

Multiscale Analysis
Regression Analysis
Statistical property
regression analysis
Time series
Simulation
simulation
estimators
Estimator
Order of a polynomial
Least Squares Regression
Ordinary Least Squares
Best Practice
Stationarity
trends
Expected Value
Autocorrelation
Predictors
shoulders
Deviation

Keywords

  • Detrended fluctuation analysis
  • Dynamics
  • Fractal regression
  • Multiscale regression analysis
  • Posture

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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title = "Statistical properties of Multiscale Regression Analysis: Simulation and application to human postural control",
abstract = "Multiscale Regression Analysis (MRA) is a promising new tool for the analysis of bivariate time series that is based on Detrended Fluctuation Analysis (DFA) and Ordinary Least Squares (OLS) regression. The method was developed within the economics and environmental science literatures (Kristoufek, 2015, 2018; Kristoufek and Ferreira, 2018) and is beginning to be applied in other scientific domains. To date, however, no systematic studies have investigated the behavior of the estimator with respect to short time series. This paper fills that gap by assessing the performance of the MRA estimator using time series with varying length, distribution, and structure (e.g., autocorrelation, stationarity). Simulations show that MRA performs well under many circumstances with as few as 512 observations. Linear and quadratic time trends contribute considerable systematic bias; however, using a detrending polynomial of order ≥ 2 effectively attenuates time trend associated deviations from expected values. We apply MRA to a previously published dataset in order to explore the relationship that emerges between body segments during an act of quiet standing. Results suggest that the velocity of the hip asymptotically depends on velocity of the ankle. In contrast, ankle velocity was a much weaker predictor of shoulder velocity. We conclude by providing suggestions for best practice and future model development.",
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AU - Likens, Aaron D.

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AU - Gibbons, Cameron T.

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