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Memories of a market

We review yet another tool, borrowed from civil engineering (and used to predict flood levels of the Nile River over time), which could be helpful for the selection and tactical allocation of assets.

The Hurst exponent is used to estimate variability in the time series. In plain English, it allows us to test whether the asset has a (long-term) memory so that the recent gains or drops would be likely followed by the moves in a similar trajectory, i.e. it measures the autocorrelation of the series. You may want to challenge the possibility of such phenomena, referring to the Efficient Market Hypothesis (EMH, for short), but there are good reasons why one may observe some autocorrelation (at least for a short/medium period). The Hurst exponent, denoted by H, varies between 0 and 1. We subdivide it into three main states: mean-reverting, random and persistent which correspond to H being less than, equal or greater than a half, respectively.

The random state (H=0.5) is what one expects from the EMH, that being the price of an asset is reflected in the available information and one cannot foresee future trends. Therefore, past performance does not predict future results and we should not expect to 'beat' the market.

The persistent state (H>0.5) implies that the past performance is indicative of where the asset should move next: it is positively correlated. For example, if H=0.8, recent increases in the time series should be followed by increases in the future for the same period of reference. Some instances when this is the case is Europe Brent Spot Price FOB (H=0.6389) for the period between June 2017 - June 2021 (see Fig. 1). In an earlier publication, Alvarez-Ramirez et al showed that for the oil market from 1987 to 2007, such phenomena are momentary (i.e. observed only over a short period) and can be explained by the cyclic nature of the asset and long-term veers towards H=0.5. Similar investigations were recently performed with respect to cryptocurrencies (see Bariviera et al.), finding that until 2014, the time series of Bitcoin had a persistent behaviour, but after that, H tended towards 0.5.

Figure 1: Oil (Europe Brent Spot Price FOB)

Source: U.S. Energy Information Administration, as at 20/06/2020

Finally, if H<0.5, the time series is said to be mean-reverting, and the past performance is negatively correlated to the future. That is, if the asset was down last month, we would expect it to be up next month, and vice versa. Such markets are generally riskier to trade. Like with a persistent state, we cannot expect such a case to be sustained over a long period.

A recent working paper by Caporale et al, studied the long-term memories in the stock market, FOREX and commodities from 2004 to 2016. Interestingly, they found different levels of Hurst exponents, depending on the frequencies one uses. In particular, lower frequencies (monthly) had persistent states across almost all classes of assets considered, strongest for the stock markets. Say, for FTSE, they found H=0.47, 0.52 and 0.74 for daily, weekly and monthly data respectively.

In conclusion, the Hurst exponent should be considered as an auxiliary tool in analysing one's portfolio, performance attribution and for picking the right investment strategy. Speculatively, one would guess that as we are entering (in the midst of?) a new commodity supercycle, the Hurst exponent can play a prominent role in momentum investing strategies.


Aurelio F. Bariviera, María José Basgall, Waldo Hasperué, Marcelo Naiouf (2017) Some stylized facts of the Bitcoin market, Physica A: Statistical Mechanics and its Applications, Volume 484, 82--90,

Guglielmo Maria Caporale, Luis Gil-Alana & Alex Plastun (2019) Long memory and data frequency in financial markets, Journal of Statistical Computation and Simulation, 89:10, 1763--1779, DOI: 10.1080/00949655.2019.1599377

Jose Alvarez-Ramirez, Jesus Alvarez, Eduardo Rodriguez (2008) Short-term predictability of crude oil markets: A detrended fluctuation analysis approach, Energy Economics, Volume 30, Issue 5, 2645--2656,

N.B. This article does not constitute any professional investment advice or recommendations to buy, sell, or hold any investments or investment products of any kind, and should be treated as more of an illustrative piece for educational purposes.

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