Portfolio optimization using a covariance structure based on dynamic time warping

Traditional covariance structures fail to capture non-linear relationships between assets and are distorted by time lags. We propose a covariance structure using the Dynamic Time Warping (DTW) algorithm for portfolio optimization. Two methods are presented: Transformed DTW, which transforms the DTW distance, and Covariance DTW, which uses a spatial covariance function to parametrically estimate the covariance. Using data from the U.S. stock market, we examine our approach to the Maximum Diversification, Equally Weighted Risk Contribution, and Hierarchical Risk Parity portfolios. The empirical analysis shows improved performance over traditional covariance structures, with lower weight changes during rebalancing.