The Laguerre RSI attempts to improve the responsiveness of the regular RSI, whilst keeping whipsaw trades to a minimum.

Let’s see how well it detects short-term pullbacks for a trend following strategy!

The complete strategy can be downloaded in the Free Strategies section.

If you’ve ever used a technical indicator, you’ll understand the perennial conflict between lag and reliability.

You want your indicator to respond quickly to prices, while minimizing the number of false signals.

In his book *Cybernetic Analysis for Stocks and Futures*, John Ehlers developed the Laguerre RSI as a way to minimize both the noise and lag of the regular RSI.

# Laguerre RSI in a Nutshell

The Laguerre RSI is similar to a 4-period regular RSI, except that a Laguerre transform has been applied for price smoothing.

The Laguerre transform is a mathematical technique that allows smooth indicators to be built using small amounts of data. It is well beyond the scope of this blog; check out Ehlers’ paper for a full explanation.

This smoothing minimizes the choppiness that a regular 4-period RSI would otherwise have.

The Laguerre RSI is much smoother, but still does a good job at capturing the bigger price moves. Also notice that it varies from 0 to 1, unlike 0 to 100 for the regular RSI.

In this way, the Laguerre transform gives you a fast-reacting RSI without sacrificing reliability.

There is only one input parameter: gamma. The gamma is a damping factor that determines the amount of price smoothing.

The larger the gamma, the smoother (but more laggy) the Laguerre RSI becomes. The comparison below illustrates the huge difference between a 0.5 and 0.8 gamma.

The 0.5 gamma is way too choppy for my liking. I’ll use a gamma of 0.8 from here on out.

# Trading the Laguerre RSI

Like the regular RSI, the Laguerre version can be used for both trend following and countertrend strategies.

I’ll try trend following in this case.

I’ve rarely found success when using the RSI in isolation. It’s usually more effective when paired with trend detection indicators such as moving averages.

One way to achieve this is to trade in the direction of the longer-term trend, but use the RSI for pullback detection.

## Trend Detection

I’ll keep it simple and use a 50-period EMA.

Longs will only be taken when the close is above the EMA, while shorts require the close to be below the EMA.

## Pullback Detection

With the regular RSI, the 30/70 levels are usually the thresholds for oversold and overbought conditions, respectively.

The Laguerre RSI is more responsive and often reaches the 0 and 1 levels. I will instead use 0.15 and 0.85 for the oversold and overbought thresholds, respectively.

Longs will be taken when the Laguerre RSI *crosses above* 0.15, indicating that the market is exiting a short-term oversold condition and is continuing the longer-term trend.

Conversely, shorts will be taken when the Laguerre RSI *crosses below* 0.85.

Here’s a long example.

Let’s try this strategy concept on the hourly AUDUSD!

# Programming the Laguerre RSI Strategy

The trading conditions were programmed using AlgoWizard:

For trade management, I threw in a simple 120-pip stop loss.

I consider the AUDUSD a ‘middle ground’ market, meaning it doesn’t trend or range particularly well.

Therefore I don’t expect to see many long trends. For this reason, I’ll add a 60-bar time stop, which translates to 2.5 trading days.

Finally, I added an intraday time filter so the strategy only trades from the London open to New York’s midday.

The high trading volume during this period should improve the likelihood of riding a good trend.

# Backtesting the Laguerre RSI Strategy

Here’s the 10-year backtest.

There is a two-year stagnation in the middle, but this isn’t uncommon for higher timeframe trend following strategies.

# Laguerre vs. Regular RSI

I like to keep my strategies as simple as possible.

The Laguerre RSI is much more complex than the regular RSI. Can the performance improvements justify the increased complexity?

To find out, I decided to use a regular 4-period RSI in place of the Laguerre version, with all other strategy elements remaining constant.

What parameters should I use for the regular RSI?

It is difficult to establish any sort of equivalency between the Laguerre and regular RSI.

Both RSIs use a 4-period lookback in this case, but how can I adjust for the Laguerre transform? And what overbought/oversold threshold values should I use for the regular RSI?

To circumvent these questions, I decided to simply optimize the following regular RSI parameters:

- Low (oversold) threshold: 10-49, in steps of 1
- High (overbought) threshold: 51-90, in steps of 1

I plotted an optimization profile of these 1600 backtest runs and the results are below.

Wow! That was a disaster. 96.5% of the 1600 runs are losing and the average profit is negative 2500 pips.

The 3D optimization profile plot is just as depressing, with broad areas of losing parameters.

Of course, this is just a cursory test.

The only way to comprehensively answer the Laguerre vs. regular RSI question is to compare both indicators over a broad range of parameters, strategies and markets.

But the results above may make me focus more on the Laguerre version in future.

# Wrapping Up

The Laguerre RSI uses a clever mathematical technique to improve both the responsiveness and reliability of the regular RSI.

Like the regular RSI, it is great at detecting overbought/oversold conditions and can be used as a pullback filter for trend following strategies.

It shows promising results compared to the regular RSI and probably deserves your attention.

The complete trend following strategy tested above can be downloaded in the Free Strategies section.

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