Time-Varying Efficiency and Economic Shocks: A Rolling DFA Test in Western European Stock Markets

This paper investigates the time-varying efficiency of Western European stock markets and examines how macroeconomic events defined as endogenous and exogenous shocks influence the degree of efficiency by either long-range dependence or mean reverting. We apply a rolling-window detrended fluctuation analysis (DFA) with two window sizes, complemented by the Efficiency Index to synthetize multiple measures of market efficiency. The results confirm that efficiency evolves dynamically in response to macroeconomic disruptions. Specifically, endogenous shocks tend to generate anti-persistent behavior, while exogenous shocks are associated with long-memory effect. These shifts in efficiency are also reflected in rolling Kurtosis estimates, suggesting that only the most severe shocks produce spikes in Kurtosis, fat-tailed returns distributions, and structural inefficiencies. This dual approach allows us to classify shocks as major or minor based on their joint impact on both market efficiency and tail behavior. Overall, our findings support the adaptive market hypothesis and extend its implications through the fractal market hypothesis by underlining the role of heterogenous investment horizons during periods of turmoil. The combined use of dynamic DFA and Kurtosis offer a framework to assess how financial markets adapt to different types of macroeconomic shocks.