A singular value decomposition entropy approach for testing stock market efficiency

Abstract

This work proposed an approach to test the efficient market hypothesis (EMH) based on the singular value decomposition (SVD) entropy. The entropy is computed from the singular value distribution of a matrix formed by lagged returns up to a scale n. To decide whether a time series is predictable, the estimated SVD entropy was compared with a reference entropy obtained from uncorrelated (white noise) time series of the same size. The application of the method to the US stock markets (Dow Jones, Nasdaq and Standard & Poor-500) for the period 1980–2021 provided consistent results with previous reports. In this way, it was shown that the US stock markets in the scrutinized period have fulfilled the EMH most of the time, except for some periods that can be linked to important market events, like crises (e.g., 1987 Black Monday crash) and instabilities. In particular, the SVD entropy exhibited significant decreases in such events, which were interpreted as the formation of patterns with certain degree of predictability. Overall, the SVD entropy is a tool that can complement the existing nonlinear analysis methods to test the complexity of financial time series.