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# Using Hurst Exponent in Forex Trading

You could have probably already read about the Hurst exponent (coefficient) in one of the previously published research papers on Recurrent Neural Networks. Even though it was only briefly mentioned there, it has probably caught your attention as a measure of market predictability that could be calculated using the commonly available chart data. It seems plausible that such a measure could be used as a handy indicator to back up other indicators and signals. But can it be really used in Forex trading?

## What is Hurst exponent?

In general, the Hurst exponent (usually denoted as H) describes the persistence or its lack in the timeseries (e.g., price) behavior. The value of this exponent can be between 0 and 1. If `0 < H < 0.5` for some timeseries, it means that these timeseries are anti-persistent — i.e., a movement in one direction is likely to be followed by a movement in the opposite direction. If `0.5 < H < 1`, the timeseries are persistent and the next movement's direction is likely to repeat the previous movement's direction. If `H = 0.5` or is very close to it, the timeseries will demonstrate a purely random (Brownian) motion. That is in the ideal world, of course.

Originally, the Hurst exponent was used by Harold Edwin Hurst to predict the Nile floods' levels (you can read more about it in a Wikipedia article.) For traders, the main interest of H is in its alleged ability to show persistence of trends.

In theory, knowing the current H for a given currency pair, we could buy after bullish candles and sell after bearish ones if H is significantly greater than 0.5. Of course, we could also buy after bearish candles and sell after bullish ones, hoping for a reversal, if H is significantly below 0.5. Seems plausible, doesn't it?

To follow this plan, we would have to go through the following steps:

1. Calculate the current Hurst exponent (H).
2. Compare it to 0.5.
3. Look at the previous candlestick's direction or measure the current trend with moving averages.
4. Trade in the appropriate direction depending on the values derived from the previous steps.

## Hurst exponent calculation

Unfortunately, we would fail at the first step, because Hurst exponent cannot be precisely calculated. You can only estimate this coefficient. One of the simple ways to do so is to use the rescaled range method. It won't be described here in detail because it is already described so well by Pietro Ponzo. You will find step-by-step explanations of the whole calculation process there. You can even download a working Excel spreadsheet for calculating Hurst exponent on stock market charts simply by entering a stock ticker in a cell.

We will just mention here that H estimation is a slope of a linear regression drawn over several dots (the more the better) derived from logarithms (any base) of R/S statistic and respective number of data points (N). R/S statistic is calculated as Range divided by standard deviation. Range is calculated as a difference between maximum and minimum of the sums of deviations of price from the mean price across all N data points.

It can be easily done in MetaTrader as the math is rather simple. Of course, the higher N is, the more CPU overhead will be required. Though it may sound like a lot of calculations, the process can be optimized to avoid recalculation of the known values and their parts. As of now, there are several paid versions of Hurst coefficient indicator for MetaTrader and some free ones. The latter include:

• Hurst Difference (for MT5) claims to calculate the difference of Hurst exponent compared to the previous bar, though, from looking at its source code, it isn't entirely clear if it really does that.
• Variation Index (for MT4) offers a substitute for Hurst exponent in the form of an index derived from fractal characteristics of a chart. It is unknown how close it is to the original Hurst exponent as the calculation process is totally different, but the author of the indicator claims that it is better because it uses fewer bars (thus fewer old bars) and shows more recent values. It is also available for MetaTrader 5.

A lot more explanation and code examples for the process of H estimation can be found at Ian Kaplan's website. However, the source code is available only in C++ language.

## Will it work?

That all sounds nice but will it work? Unfortunately, after some thought process and reading, and some more reading, it became evident that the concept is interesting but, at the same time, is nearly useless in Forex trading.

It requires a very large number of bars to work, with 1,000 usually mentioned as a necessary minimum. Estimating the Hurst exponent on the latest 1,000 bars would give us a value that may no longer be relevant at the time of analysis. The real value of the Hurst exponent is constantly shifting, getting its estimate over the last N bars gives us a good notion about how things were going within that period, but it has little information for the future bars. Too bad, we can only trade future bars and not the old ones.

One could object that H can be calculated on a lower timeframe (for example, hourly) and then used on a higher one (for example, weekly). It would solve the old/new bars problem but wouldn't help us at all as the Hurst exponent is completely different on different timeframes. For example, it can be estimated as below 0.3 on H1 chart and be higher than 0.8 on W1 chart at the same time.

Using it as a comparative factor when choosing a currency pair to trade for a particular strategy hits the same obstacle. Let us assume that you have a good long-term trend-following strategy. Ideally, you would want a currency pair with as high H as possible. You estimate Hurst exponent for 12 currency pairs over last 5 years and get some values. You find that NZD/USD has the highest H at 0.65 (for example). Unfortunately, it does not mean that using that strategy on NZD/USD during the next 5 years would bring better results than using it on other currency pairs, with smaller H.

## Is Hurst exponent completely useless?

Considering Hurst exponent's inability to produce a good forecasting tool, you might decide that it cannot be used at all. Actually, it isn't so. Hurst exponent estimation is a viable tool for analyzing the past. Looking at a correctly estimated H value can answer the following question: was the market persistent or was it anti-persistent? In its turn, that would help you analyze performance of your trading strategy or expert advisor during that particular period. For example, if you were using a trend reversal system for a month and it performed poorly but H estimated for that period turned out to be high above 0.5 level, you would know that it was a rather bad time for your strategy, not that the strategy itself is defective.

PS: Actually, this guide might not be too interesting to an average Forex trader, but it was written mostly for those traders who are interested in applying various math concepts to trading. Because when such traders stumble upon the concept of Hurst exponent, it surely captures their imagination making that ask themselves: "What if?" This guide now offers a starting point for such Forex traders.

If you have any questions or ideas about applying the Hurst exponent in currency trading, you can discuss it on our trading forum.