Statistical properties of Multiscale Regression Analysis: Simulation and application to human postural control

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.