Persistence in Stock Returns: Robotics and AI ETFs Versus Other Assets

This paper examines the long-memory properties of the returns of exchange-traded funds (ETFs) that provide exposure to companies operating in the fields of artificial intelligence (AI) and robotics listed on the US market, along with other assets such as the WTI crude oil price (West Texas Intermediate), Bitcoin, the S&P 500 index, 10-year US Treasury bonds, and the VIX volatility index. The data frequency is daily and covers the period from 1 January 2023 to 23 June 2025. The adopted fractional integration framework is more general and flexible than those previously used in related studies and allows for a detailed assessment of the degree of persistence in returns. The results indicate that all return series exhibit a high degree of persistence, regardless of the error structure assumed, and that, in general, a linear model adequately captures their dynamics over time. These findings suggest that newly developed AI- and robotics-themed ETFs do not provide investors with additional hedging or diversification benefits compared to more traditional assets, nor do they create new challenges for policymakers concerned with financial stability.