Return Autocorrelation and Moving-Average Trend Following
Summary
The document asks what properties of a stochastic process could allow a simple moving-average timing rule to outperform buy-and-hold. The proposed rule switches between buying and selling when price crosses its moving average, and the question sets aside transaction costs to focus on underlying return behavior. The goal is to identify empirically testable conditions that may explain when such strategies work.
The answer connects moving-average timing to trend following and suggests that positive return autocorrelation, or a Hurst exponent above 0.5, may favor these strategies. It also points to research arguing that timing success depends on characteristics of the underlying price process, rather than market efficiency alone. The material offers a hypothesis and a reference rather than a general proof or a tested result across specified markets. It does not establish that autocorrelation or the Hurst exponent is sufficient, nor does it address estimation uncertainty, trading costs, or implementation choices.
Key ideas
- Simple moving-average rules can be studied as trend-following strategies that switch exposure when price crosses an average.
- Positive return autocorrelation is proposed as a process feature that may support moving-average timing.
- A Hurst exponent above 0.5 is also suggested as a potentially favorable condition.
- The cited research frames timing success as dependent on underlying price characteristics.
- The document presents candidate explanations, not proof that these properties guarantee outperformance.
Tags
Full text
# Statistical properties of stochastic processes for moving average trading to work # Statistical properties of stochastic processes for moving average trading to work Common wisdom holds it that a moving average approach is more successful than buy-and-hold. There is quantitative evidence for that across different asset classes (see e.g. this book, or this paper from the same author Mebane Faber). My question takes a different turn: I am trying to generalize these empirical findings to a general class of stochastic processes. My question: What properties must a stochastic process have for moving average trading to outperform naive buy-and-hold. At the moment I am only talking about simple moving average strategies like when the process crosses the average from above/below sell/buy. There could also be simplifying assumptions like no trading costs etc. The plan behind this is to find general properties which are empirically testable on their own. In a way I want to find the building blocks for moving average strategies to work. Do you have some ideas, papers, references...? Thank you! ## Answer by onlyvix.blogspot.com (score 11, accepted) https://quant.stackexchange.com/a/356 These moving strategies are also known as trend-following. If returns have positive autocorrelation, hurst exponent > 0.5 that would be good for these strategies. ## Answer by vonjd (score 4) https://quant.stackexchange.com/a/1729 In fact there is an exhaustive paper on this issue available now: "The Trend is not Your Friend! Why Empirical Timing Success is Determined by the Underlying’s Price Characteristics and Market Efficiency is Irrelevant" by Peter Scholz and Ursula Walther, Frankfurt School Working Paper, CPQF No. 29, 2011 Fascinating read - highly recommended!
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.