Gaussian Filter – Rules, Settings, Strategy, Returns
In the fast-paced world of financial trading, traders are always looking for better indicators to improve their analysis of the markets — one such indicator is the Gaussian Filter. What do you know about this indicator?
The Gaussian filter is a technical indicator that uses the Gaussian distribution model to reduce the random noise in price data so as to make trend changes and patterns more visible. Introduced by John F. Ehlers, the Gaussian Filter models a Gaussian distribution of the price data over a given period and uses a certain multiple of the standard deviation, the sigma (σ), to filter outliers that constitute market noise.
In this post, we will take a look at most of the questions you may have about this Gaussian Filter indicator: what it is, how it works, and how you can use it to improve your trading strategies. Let’s dive in!
Key Takeaways
- Definition and Purpose: The Gaussian Filter is a trading indicator that reduces noise in price data, making trend changes and patterns more visible.
- Origin: Introduced by John F. Ehlers in “Gaussian and Other Low Lag Filters.”
- Mechanism: Models a Gaussian distribution of price data over a period.
- Uses the standard deviation (sigma, σ) to filter high-probability data points while removing outliers.
- Weighting: Assigns weights to data based on the period length, sigma, and recency.
- Similar to EMAs, with more weight on recent data.
- Effect: Smooths short-term fluctuations and emphasizes longer-term trends.
- Provides a clearer view of market trends by highlighting higher-probability data.
- Advantages Over EMAs: Uniform response to price changes.
- Less sensitivity to sudden price spikes, reducing false signals.
- Highly customizable with Sigma and Poles options.
- We provide you with a backtested trading strategy that contains the Gaussian Filter.
- Please click here for a technical indicators list.
What is the Gaussian Filter in trading?
In trading, the Gaussian filter is a technical indicator that uses the Gaussian distribution model to reduce the random noise in price data so as to make trend changes and patterns more visible. Introduced by John F Ehlers.
Ehlers in his publication “Gaussian and Other Low Lag Filters”, the Gaussian Filter models a Gaussian distribution of the price data over a given period and uses a certain multiple of the standard deviation, the sigma (σ), to characterize the data such that those with higher probability are filtered in and outliers are filtered out.
The filtering process involves assigning the selected price data with weights based on the chosen length (the number of data points considered), the sigma, and the recency of the data. As with EMAs, more weights are given to more recent data points than those further away.
By selecting only higher-probability data points and filtering out the outliers, the Gaussian Filter smooths out short-term fluctuations and highlights longer-term movements, thereby providing a clearer view of market trends.
Traders often prefer the Gaussian Filter to EMAs in identifying market trends, as the former offers a more uniform response to price changes. The Gaussian Filter is less sensitive to sudden price changes, which can help reduce the occurrence of false signals during volatile market conditions. Moreover, it is more customizable with the Sigma and Poles options.
How does the Gaussian Filter indicator work?
The Gaussian Filter indicator works as a sort of data-smoothing algorithm that reduces the random market noise in the price data so that the market trends and price patterns can be seen more clearly. It uses a filtering process that involves modeling the price data over a chosen period using the Gaussian distribution and a chosen sigma value (number of standard deviations).
With this model, it selects the most probable data points and assigns weights to them based on the recency of the data and their probability. In other words, it assigns more weight to the most recent probable data points than those that are further away. This way, it filters out short-term price fluctuations that constitute market noise so that the longer-term trend can be clearly seen.
On the chart, the Gaussian Filter behaves like an EMA in that it assigns more weight to recent data, but it reacts more uniformly to price changes than the EMA. It is less reactive and provides a more uniform line over the course of the price trend.
Gaussian filter trading strategy – rules, settings, returns, and performance
Let’s backtest a trading strategy that uses the Gaussian Filter – complete with trading rules and settings.
We make the following trading rules:
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We backtested stocks (SPY), bonds (TLT), Bitcoin (BTC), and gold (GLD). GLD and BTC were the only good performers, perhaps expected for such an indicator.
Below is the equity curve for GLD since its inception until today:
Trading statistics, returns, and performance (including commissions and slippage) for gold (GLD):
- Number of trades: 328
- Average gain per trade: 0.55%
- Annual returns (CAGR): 8.5%
- Win rate: 40%
- Time spent in the market: 53%
- Risk-adjusted return: 15.8%
- Max drawdown: 20%
Despite a win rate of only 40%, the average gain is high at 0.55% per trade, including 0.03% slippage per trade. Can you trade such a strategy with a low win rate? Read here for why a high win rate in trading is important.
This is the code we used for the backtest (Amibroker):
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Why use the Gaussian Filter in trading strategies?
You use the Gaussian Filter in trading strategies because of the following reasons:
- It can filter out random price fluctuations, which constitute the market noise, so you can focus on the price movements that matter to your trading style.
- Through the direction of its slope, you can figure out the trend direction
- The indicator can also show when there is a market reversal.
- You can use it to generate trade signals when the price crosses in the direction of the trend after a pullback to the opposite side.
- You can use it to create standard deviation bands for identifying overbought and oversold market conditions.
How is the Gaussian Filter different from other filters?
The Gaussian Filter is different from other filters in that it uses the Gaussian distribution model to select only high-probability data points and filter out the outliers, while other indicators use some form of averaging technique to smooth out the entire data. As a result, the Gaussian Filter has less lag than those smoothening indicators, such as the SMA and EMA.
Also, the Gaussian Filter provides a more uniform reaction to price changes, as it is less sensitive to sudden increases in volatility. This helps reduce the incidence of false signals. Moreover, it offers options via the standard deviation and pole settings.
What are the key features of the Gaussian Filter?
The key features of the Gaussian Filter include:
- It is based on the Gaussian distribution model and uses standard deviations of the data points to identify outliers
- It chooses higher-probability data points and filters out the outliers
- It gives more recent data points
- It introduces less lag than most smoothening indicators that average every data point in the data set
- Its use of standard deviation and poles provides more customization options.
- It focuses on the more important data points, thereby reducing the effects of sudden outlier changes in price data.
How does the Gaussian Filter smooth price data?
The Gaussian Filter smooths price data by filtering out low-probability data points (aka, outliers) from the data set of a chosen cycle period. It does this by using a certain sigma value (number of standard deviations) to select only the highly probable data points from the data set.
Then, some weights are assigned to the selected data points based on the recency of the data, such that more recent data points are assigned more weight than the data points that are further away from the current data point. This smooths the data plot by ensuring that outliers are not allowed to skew the plot.
What does the Gaussian Filter reveal about market trends?
What the Gaussian Filter reveals about market trends will depend on what the trader is looking for. But it generally shows, in a clearer fashion, the direction of the longer-term trend by filtering out the minor price fluctuations that constitute the market noise so that the main market trend can be seen.
With that information, traders can decide how they approach the market. Some may choose to trade in the direction of the trend after a pullback, while others may choose to look for reversal signals and trade in the opposite direction.
How do you calculate the Gaussian Filter?
Calculating the Gaussian Filter is very complex. But here are the basic steps in the calculation:
- Obtaining the Gaussian distribution of the data over a period length
- Choosing the Sigma for the filtering process
- Using the Sigma to calculate the weights based on the formula: Weight = math.exp(-x*x / (2 * Sigma * Sigma))
- Applying the filter to get the selected data for your plot
Note that the trading platform automatically does the calculation and plots the indicator when you attach it to your chart. You don’t have to do the calculation yourself.
What are the main components of the Gaussian Filter?
The main components of the Gaussian Filter are as follows:
- The period length: This is the cycle period for selecting the data points to be considered. The longer the period, the more the data points.
- The sigma: This is the number of standard deviations used to select the more probable data points. It determines the width of the Gaussian bell curve, which impacts the smoothening.
- The poles: This refers to the number of passes in which the Gaussian Filter was applied to the data. Every pass makes the smoothing effect stronger, just like blurring a picture multiple times produces more effects.
How do you interpret Gaussian Filter signals?
To interpret Gaussian Filter signals, you have to understand how the indicator works. The Gaussian Filter smooths the price data by selecting highly probable data points from a data set and discarding the outliers. It then assigns weights to the selected data points based on recency.
This way, it shows the direction of the main market trend via the direction of its slope. If the indicator line is sloping upward, the trend is up. If it is sloping downward, the trend is to the downside.
In an uptrend, the price going below the indicator line and then crossing back above it gives a bullish continuation signal. In a downtrend, the price going above the indicator line and then crossing back below it gives a bearish continuation signal.
When should traders use the Gaussian Filter?
Traders can use the Gaussian Filter when they want to filter out the market noise so they can clearly see the direction of the price movements. It can help them identify the trend and trade in that direction if it is part of their trading strategy.
They can also use it to identify when the market has reversed. In this situation, the indicator’s slope must have changed direction and the price would have changed structure — from higher highs and lows to lower highs and lows or the other way around. Traders can also use the indicator to formulate entry and exit strategies.
Can the Gaussian Filter reduce trading noise?
Yes, the Gaussian Filter can reduce trading noise so that the main market trend can be seen more clearly. It does this by filtering out outlier price data points from the set of data used in calculating its plotted line. It uses the Gaussian distribution bell curve to select high-probability price data out of the data set, leaving out the outliers that could introduce market noise.
This way, the indicator line is not easily influenced by sudden and temporary price changes that cause trading noise.
What parameters should be used for the Gaussian Filter?
The parameters that should be used for the Gaussian Filter will depend on the trader’s trading strategy and backtesting results. Depending on the developer and the trading platform, there are often three or four adjustable parameters for the indicator — the cycle period, sigma, number of poles, and price source.
It is up to the trader to set the parameters that work for their strategies. To know that, they will have to backtest their strategies to find out what works.
How do you apply the Gaussian Filter to a trading chart?
To apply the Gaussian Filter to a trading chart, you go to the indicator section of your trading platform and search for it. If it is there, you double-click on it, and it will pop up on your chart. You then input your preferred settings on the settings box that popped up, as in the chart below:

However, the indicator may not be already preinstalled in your trading platform. In that case, you may have to get a programmer to code one for your platform.
What markets can the Gaussian Filter be used in?
The Gaussian Filter can be used in every financial market since it uses only the price data in its computation and every financial market post its price data. This is unlike volume-based indicators that cannot be used in markets that don’t have central exchanges that document valid volume data.
Since the Gaussian Filter is a purely price-based indicator, it can be used on any market as long as there is a platform with the data from that market.
How does the Gaussian Filter improve trading accuracy?
The Gaussian Filter improves trading accuracy by reducing market noise so that the overall trend direction can be seen. It uses a normal distribution bell curve to select the most probable data points from a set of data over a chosen period.
In order words, it discards the outliers that can skew the plots and introduce random market noise. Since the indicator makes the trend clearer, it enables traders to make better trading decisions, which improves their trading accuracy.
Can the Gaussian Filter help identify trend reversals?
Yes, the Gaussian Filter can help identify trend reversals by changing the direction of its slope and its relationship with the price action. If an up-trending market reverses to the downside, the indicator line would change the direction of its slope from up to down and the price would be trading below the indicator line.
On the other hand, when a down-trending market reverses to the upside, the slope of the indicator line would change from the downward to the upward direction and the price would be trading below the indicator line.
Is the Gaussian Filter suitable for day trading?
Yes, the Gaussian Filter can be suitable for day trading if it is used with the right trading strategy and applied on a suitable timeframe for day trading. Some of the common day trading timeframes include the hourly, 30-minute, 15-minute, and 5-minute timeframes.
If a reliable trading strategy that is based on the Gaussian Filter is proven to have an edge on any of the day trading timeframes, then the indicator is suitable for day trading.
What timeframes work best with the Gaussian Filter?
The timeframes that work best with the Gaussian Filter will depend on your trading style and backtesting results. If your trading style is day trading, you will have to backtest the indicator on various intraday timeframes for day trading, such as the hourly, 30-minute, 15-minute, and 5-minute timeframes to find out where it works the best.
A swing trader, on the other hand, will have to backtest their strategy on the daily, 8-hourly, and 4-hourly timeframes to know the one that works best for their trading style.
Can the Gaussian Filter be combined with other indicators?
Yes, the Gaussian Filter can be combined with other indicators to get the best out of it. Since the Gaussian Filter is a trend indicator, you can combine it with a momentum oscillator or volume indicator to find better trade setups.
A momentum oscillator, like the RSI, can show when a pullback is over so you can trade the next impulse swing in the trend direction. With a volume indicator, you can know when the market is accumulating or distributing before a major trending move.
How does the Gaussian Filter affect trading decisions?
The Gaussian Filter can affect trading decisions by providing a clear direction of the trend so traders can make well-informed decisions on how to tackle the market. If it shows that the market is in an uptrend, a trader may choose to wait for a pullback and then trade the continuation impulse swing after it, closing out before the next pullback. Another may choose to ride the trend for as long as it lasts.
What are the limitations of the Gaussian Filter?
The limitations of the Gaussian Filter include:
- Depending on the parameters used, there can be over-smoothing, which can hide significant price movements.
- As with all smoothing techniques, there is often a lag between the actual price movements and the indicator’s signal, which can cause a delay in decision-making.
- Even if you find a way to use it as a standalone trading strategy, it cannot tell you how to manage risk
How do you optimize the Gaussian Filter settings?
To optimize the Gaussian Filter settings, you must have a trading strategy that is based on the indicator.
Then, you will have to backtest the strategy, experimenting with different settings to find the one that offers the best performance. You then retest these settings on different historical data (out-of-sample data) or in a real-time market to be sure the new settings are robust enough to perform well with the new data. This helps to avoid curve fitting.
What trading strategies work well with the Gaussian Filter?
The trading strategies that work well with the Gaussian Filter are trend-following strategies, especially breakout and trend continuation impulse swing strategies. With a breakout strategy, you are looking to trade when the price breaks out in the trend direction, which the indicator has identified.
Continuation impulse swing trades simply wait for the end of a pullback to enter the next impulse swing in the trend direction.
Can beginners use the Gaussian Filter effectively?
Yes, beginners can use the Gaussian Filter effectively. What they need to do is to understand how the indicator works and formulate simple strategies with it.
Then, they open a demo account and practice their strategies until they get used to the indicator and how it responds to the markets.