Multifractal Guide - Mandelbrot's Incredible Toolbox

Excellent work - from the thinking to using Python to tap into MT5. May not be tradeable yet but every discovery starts with a strong base like this.
The challenge is extracting applicable order. Have you tried deseasonalising the data to start with? Mon/Fridays often have higher vol than tue/wed/thu across FX so it may help or hinder. If this is the most basic thing you've heard all week, do ignore it, I'm new to everything stochastic.
Secondly, it'd be interesting to see if you discover any hard mathematical boundaries (maximum ratio for any factors between one day and the next) for any of the variables? I use a series of constants in a semi-deterministic model but I'd be surprised if they don't start aligning with stochastic ones as they get more refined.
Thirdly, have you looked at this more granularly? My experience at least has been the best way to discover order is to break it down to the smallest parts and build upwards rather than look at the whole and distil. In theory this'd mean tick data, in practice minute data.
Finally, is the aim to improve or replace existing vol models? I'm curious only as I've just constructed a HAR while I'll publish in next day or two. It was supposed to be a benchmark, but I'm surprised at how good and easily tradeable it is. Plus, you only need one marked improvement on what's out there and they'll be kicking down your door.

Thank you triphop for you kind and motivating words. Regarding your questions:

1. No, I have never deseasonalized data. It's the first time I am even hearing this term. However, don't really know what the benefit of this would be in terms of resasearch. In terms of practical applications, I guess strategies that depend on breakouts could favor from this but no I have not tried it.

2. Yes, it would not only be interesting but extremely profitable if I were to discover mathematical constants for the tools Mandelbrot offers. But, again, this can only be done after devising a strategy. The main issue is the link between academia and practical trading implications. The gap between this is immense.

3. You are extremely correct with the granularity. Markets are multi-fractal. Which basically means same things are happening at different scales with different levels of roughness. So, in theory, it's basically meaningless to use 30 minute or daily data. The best approach is tick data or M1 data as it represents true structure in terms of volatility, transactions etc. In other words, a lot of information is available. But so is noise. And noise is where it get's extremely complicated.

4. No, the aim is not to replace vol (volume or volatility) models. The aim is only to explore and find potential implications. I can't say that it will replace volatility, volume, mean-reversion or breakout models. Because I am yet uncertain to what the trading implications will be.

My final words. The main challenge right now is the linkage between academia and practical trading models/strategy construction. To me so far, it seems that Mandelbrot's work can act as an extremely well meta-layer, instead of main signal generation. This is due to the nature of output we get from his tools. Nothing is directly tradeable. But has information that can be taken advantage of in the sense of risk-management, entry/exit filters, position size rules etc. But, it's not directly tradeable, in the sense of signal generation.

I will try to explain this more clearly with some upcoming models I made and the results will make it clear what the trading implications can be. Thank you all for your interest in this thread. I greatly appreciate any discussion and contribution done on this thread for the intent of helping others.

Really interesting topic. Mandelbrot’s work doesn’t predict price direction, but it does help us understand the structure of market volatility. The main takeaway for traders is that markets aren’t smooth or “normal”—they’re clustered, jagged, and prone to extreme moves far more often than classic models assume.
So in practice, his ideas help with things like:
Risk management (expecting bigger, sharper swings)
Position sizing (respecting fat-tail events)
Timing volatility rather than trying to predict price direction
Recognizing when markets shift into more turbulent regimes
It’s less about forecasting and more about seeing the market’s texture—how chaos forms patterns and how those patterns repeat on different scales. That alone can change how you approach risk and survival in the markets.

In actual real-world trading beyond theory... The market is only "sometimes" fractal. It depends upon market conditions. For very long periods of time, markets generally stay in a stable trending normal distribution. Especially stocks.

You need to predict the market conditions, and figure out a trading model which works in those market conditions. Also recognize what is creating/created those conditions, and when they will fade away or change.

Fractal/wave patterns tend to be very "fragile". Especially in short term trading. It's very easy to collapse a pattern with large orders or cause a change in behavior.

1) I agree with you - it depends if you think seasonality (time-recurring changes in volatility) is noise or part of the signal. I go for the latter too but throwing it out there
2) Ah, I was thinking about constants within the values you're already calculating (max/mins). Boundaries define structure so that'd be my own starting point at least
3) totally
4 and others - well given Mandlebrot preceded black-scholes, he couldn't be aware of the volatility markets to come. You're in this space whether intentionally or not because he focuses on volatility rather than direction. So it may not be a case of generating signal for the underlying, it maybe a case of looking at what of his thinking has not been successfully implemented yet and where it leads you, on improving what's out there rather than replacing.

A reliable 1 bps improvement in forecast directly improves bottom line for MMs and corporate, which makes it very lucrative. With your skillset, that's where I'd be laser-focused

We are on the same page.

I thoroughly understand that Mandelbrot is more focused on volatility and his toolbox does not offer "buy" or "sell" signals. Hence, it can never be used for CFD/Spot in the way general traders expect it to be. However, things like risk-management, entry filters, position-sizing and a whole lot more can be done with this information that nothing else can provide such accurately and reliably.

Hence, I would take your advice and focus on improving what's already out there.

Let's take a popular example. GARCH and HAR are models, commonly used in econometrics to forecast volatility. These are published everyday in academic papers and be praised for its accuracy and sustainability. However, let's challenge those assumptions via Mandelbrot's toolbox. Even though, it's more complex, it should be on par, if not better. None of these statements are empirical, but will be on my next post.

This is what I'll do:

Build a GARCH model to set a baseline. Then, compare it with a model built via Mandelbrot's tools. Focusing on volatility forecasting purely. I have already tried doing this, but failed to make a model because of the complexity and time it takes. But, this post gives a huge burst of motivation and confidence to push further.

Discussing the implications or rather "advertising" them to a normal trader is as foolish as describing the significance of risk-management to a newbie trader, he just wants to see 100% returns. Hence, I will go in depth to the model's results to better suit the needs of the people who do understand the significance of this feat (if it were to happen).

Both models will be given equal chance to showcase their abilities. No bias. As we are seeking for empirical results. See you in the next post

Top work, look forward to it.
I can't vouch for accuracy but I came across this Garch in mt5 a few weeks back, plus I just published a HAR open source so either may save you benchmark time
https://www.mql5.com/en/market/produ...al#description
Good hunting!

Yes, it's been a while.

The thing is, dealing with Mandelbrot's work is no piece of cake. The main hurdle is the complexity and calibration it takes to correctly use his concepts.

However, I have been working on this for nearly 2 weeks and I believe I am getting closer to what Mandelbrot wanted to achieve with his work.

I still have not finished it. There are some crucial parts left still. But, it's coming together very methodically.

I haven't seen any activity since I left, so I will tell you the details of what I am doing in order to keep others up to date. It's not like this thread is popular anyways, but I hope there are people like triphop who are invested in seeing the end results

Firstly, let's make it clear what we're trying to do (as of currently):

My main objective as of now, is to see which model from the two, GARCH or MMAR, performs well for volatility forecasting.

The answer to this question is not straightforward, but let me not get ahead of myself.

Let's start from the beginning.

I needed a place to start from. I did not know how to construct MMAR (Multifractal Model of Asset Returns) which is the signature model of Benoit. It's not just that MMAR is a model, it's a whole process. In other words, like some models where you can just throw some data and expect a forecast, it does not work the same way for MMAR, and this is an extremely important point people need to understand if they are going to use MMAR.


MMAR IS NOT YOUR TYPICAL FORECASTING MODEL!

Hopefully, that makes it even more clearer. And to further delve on the point, let me show you where I started/learned to build MMAR.

The paper is: Volatility Forecasting with the Multifractal Model of Asset Returns - Yidong (Terrence) Zhang
DOI:10.2139/ssrn.2945672

Now, Zhang's paper is incredible. Not because of the bias (he also shows that MMAR outperforms GARCH), but because of his construction on MMAR Model.

He uses a 7 step process. I will explain each step in a digestible way. Hence, I will not go in depth to the technical/mathematics as this will only scare people.

Step 1: Does Fractality Exist?: This is a very important first step. You have to first ask, does fractality even exist on the timeframe, lookback or market you are trying to forecast for.
Why This Matters
If the market isn't fractal, MMAR doesn't work. Period. You'd be building a fractal model for non-fractal data. You're basically comparing apples to oranges. So, you can't proceed to step 2 if step 1 fails.

Step 2: How Fractal Is It?: Okay, now you know fractality exists. Good, but, how much?
Why This Matters
GARCH and MMAR are models that are share the same goal of forecasting volatility, but fundamentally different. GARCH will almost always outperform MMAR if little to no fractality exists. If it exists by a good margin, MMAR will almost certainly outperform GARCH. This is an extremely important point. There's no one-size fits all answer. The choice for GARCH and MMAR depends on the market, lookback period and timeframe.

Step 3: What Type of Fractal Is It?: This is where it gets a bit weird. You've confirmed the market is fractal (Step 1). You measured its fractal fingerprint (Step 2). But here's the thing: There are many types of fractals. Let's use an analogy to explain this:

Imagine you found a footprint in the forest:

1. Step 1: "Yes, it's definitely an animal footprint" ✓
2. Step 2: "It's 6 inches long, 4 inches wide" (measurements) ✓
3. Step 3: "Is it a bear, wolf, deer, or mountain lion?" ← This step

And the type of fractal has 4 types of possibilities. This is where some math comes in. But, I won't mention it.
Why this matters
This matters because before continuing to step 4, you need to know the type of fractal to generate artificial trading time that matches the real market. Stay with me.

Step 4: Generate Artificial "Trading Time": The core idea is: Markets don't run on clock time - they run on event time. Think about it:

1. - Some days, EUR/USD barely moves for hours (slow event time)
2. - Other days, central bank announces something and it moves 100 pips in 5 minutes (fast event time)

MMAR says: If I can model this "uneven flow of time," I can capture volatility clustering and fat tails.

Step 5-6: Create Fake Price Paths:
Now You Have Two Things:

1. FBM (Fractional Brownian Motion): A random walk with Hurst exponent H
   1. This gives you the long-memory property (trends)

2. Trading Time θ(t): The uneven time flow you just created
   1. This gives you the volatility clustering and fat tails

In step 5-6, you just Combine Them.
What this does:

1. When trading time is moving fast (volatile periods), you're jumping through the FBM quickly
2. When trading time is moving slow (calm periods), you're crawling through the FBM

The result: A price path that has both trends (from FBM) AND volatility bursts (from trading time)

Step 7: Do It 10,000 Times: This is where Monte Carlo simulation is done.
Why?
Because Steps 4-6 involve random sampling:

1. The cascade uses random multipliers
2. The FBM uses random walks

Every time you run it, you get a different price path. This is your MMAR volatility forecast.

Now you can understand why this is taking me time.

It took me a few days to just even wrap my head around the 7 steps I am mentioned above. And then to actually construct this was really a challenge. But in a fun way.

My current progress is almost finished. I will finish this by the end of this week (hopefully). Then, I will create a public Github repo where people can clone the project and use it for their own projects and perhaps contribute to the codebase aswell. Hopefully.

This is no small feat for a developer like me. To even construct this was extremely difficult, but I am almost done. And it feels like a relief.

I hope that people now understand why you can't blindly use models. There are pre-requisites that are necessary. You can't expect MMAR to work well in a non-fractal market. And I hope my previous post has made it even more clear.

See you all soon!

Brilliant stuff, I can see why this isn't straightforward. The modelling of time is really interesting. The monte carlo sims boggle my head however; the idea of deliberately introducing randomness into prediction makes me need a lie down.


Question - which markets exhibit fractal properties? I'm taking it you're expecting FX to do so right? And what properties of markets make it one that fractalizes vs one that doesn't? This may well be something you have answers to do once you're finished, but getting it in early.

I had a quick look - the expectation is MMAR can beat GARCH but not HAR-RV (for fx at least). That's the expectation but let's see. Can you generate MdAPE and RMSE stats on daily RV forecasts once you're done and we'll compare? I've remodelled mine to expose stats better so it'll be a good test.

As for popularity, it's always a very good inverse barometer of what's valuable round here. This is bloody good work.

Thank you triphop, your words of encouragement are exactly what I need to finish this.

Let me answer your question:

In the original paper, the author tested the MMAR model on stocks. But, I will be doing this for forex, so I expect forex markets to exhibit the same properties.
However, it's worth mentioning, that a few tests I performed, I found out that you have to do some calibration to find fractal properties. For instance:
EURUSD market is NOT fractal on the 1 minute timeframe. But it IS fractal on the 10 minute timeframe. Something interesting to note about.

The answer to the question of how to figure out if the market is fractal or not is a bit technical. If you calculate the average absolute return over 1 minute, 5 minutes, 15 minutes, etc., a truly fractal market will show a power law relationship. Non-fractal markets won't. You have to plot these returns. If the plots aren't linear, MMAR doesn't apply to this data. The main metric here is: R² (R-Squared). If it is above 0.6, then you have a fractal market.

I am not aware of HAR-RV, but there are many variants of GARCH itself, like MRS-GARCH, which is a much better, improved version of GARCH.

The main takeaway I see is that, if someone is building MMAR model, they better have a bloody good reason to do so, because this is no easy work. Even if I am able to construct this, the practicality of this is extremely limited. If you are going to be trading on small timeframes where speed is of the essence, MMAR is too slow. It will take 15 minutes at-least to get the 10k simulations. And we are not even talking about the previous steps! GARCH and other models are popular for a good reason. You can throw them at any market, at any timeframe, and they will generally be consistent with how they perform. MMAR just takes time.

It's also the expectation that GARCH is better at short-term predictions, while MMAR model is better at longer horizons.

Yes of course, in the end, I will extract a bunch of metrics so MMAR's performance can be compared to other models. Furthermore, you will have the choice to run the model yourself. I am putting a lot of effort in making it easier to run the model for people who are interested in fine-tuning the model to their own markets. So, it'll be fairly straightforward for other people to run and get the results.

The fractal proof sounds quite sane and beats brute forcing a market that won't receive a model well.

I suspect it might not be the case. An example - HAR-RV uses lagged averages of high frequency returns of daily RV. It spits out day/week/month forecasts. Anything shorter than a day, the model collapses. But take the daily forecast, add event weighting it gets more accurate. convert to a range. Then apply a pattern of intraday seasonality, and you've then got high probability reversal windows every hour. It works because FX has incredibly high seasonality factors; the quietness of Asia, picks up frankfurt, highest in London and the crossover with US. It's a completely different approach to the underlying model of course but the point is, what may appear to be only abstractly useful can be applied with some fairly well known steps.

All that's stats overlay but based on the hard yards of getting a good forecast. The bit you're wrestling with!

Best of luck with the next steps.

Huh, that is really interesting and insightful. I researched a little bit about HAR-RV aswell and it seems that it also shares a few properties with MMAR like being multiframe etc.

I think this is very well worth discussing in the future after the model has been created. I am interested in knowing the techniques people use (like seasonality you mentioned) to cascade longer timeframe information to higher timeframes.

Anyways, I will definitely remind you to continue this discussion. I'll get back to the construction and update the thread in a few days

THE GITHUB REPO IS NOW LIVE !

https://github.com/AyanDot/MMAR-vs-GARCH

I invite everyone to visit the project and test it out.

The project is finished, but improvements/features can always be made. By the request of the public, I will try to add them (if they're sensible requests), but overall, you can start using it and see if MMAR model is what you needed for your strategy.

My one wish from this project is that someone benefits from it. Be it through motivation, money, or getting new ideas, I jut hope my hard-work was not wasted.

In the post below, I will explain how to use the model. The README.md on the repo already states instructions, but I will be using screenshots alongside commentary to explain each step as I execute them.

If you are having trouble using github, the scripts etc, my post below probably contain the solutions.

Let's start with the tutorial.

Every step I do will be labeled, so if anyone has a problem during their setup, they can callout the specific STEP number so I can figure out potential solutions.

THIS TUTORIAL IS EXCLUSIVELY FOR WINDOWS OS (I am using windows 11 pro) if you are on another operating system then please refrain from following this tutorial as commands can be different.

PREREQUISITES:
1. Firstly, make sure you have Windows Powershell v7.x.x. In other words, the latest Powershell.

You can check the version of your Powershell by entering this command:


For me I have version 7.5.4. As long as you have version 7, we are good to go.

If you don't have Powershell 7, then open default powershell and copy+paste this command: this will automatically install the latest version of powershell.

(Context: Windows usually have a default powershell pre-installed, this has a version of 5.x.x, and can't be upgraded, you need the upgradeable one)

NOTE: If you don't have winget, this command will fail. It's better that you install it by going through this website: https://learn.microsoft.com/en-us/wi...anager/winget/
Otherwise, you can go to Microsoft Store, or Google for your installation. However, it's recommended to have Winget installed, as other steps require them and make it convenient to get packages/applications easily.

2. Secondly, make sure you have Python and Git installed globally on your system.

You can install python by going to this website: https://www.python.org/downloads/
The installer will guide you with everything (make sure to select default options in installer, otherwise I hope you know what you are doing)

You can install git by going to your Powershell7 and copy+paste this command: Or by going here: https://git-scm.com/install/windows

3. Obviously, have MetaTrader5 installed.

END OF PREREQUISITES


Next, I will continue with the actual usage of our model.

Let's start:

Step 1: Cloning The Repository

You will need to clone the repository in order to work with scripts. The cleanest way of doing this is by the following:

1. Open Powershell7
2. Paste this command:



That's literally it.

The "mmar" at the end of our command tells git to clone the repository inside mmar. It will create a new folder, and the repo would be inside it.

Now, you need to be inside the "mmar" directory you can do this by:
1. Then, see what is inside mmar:
2.


That's it! You have successfully cloned the repo and now you are inside it.
Let's move on.

Step 2: Creating Python Virtual Environment

It sounds scary, but it's extremely simple to do and is the recommended way to use python when dealing with lots of packages.

Firstly, make sure you are inside the mmar directory (or whatever directory/folder you cloned the repo).

Then, execute the following commands:
This will create the virtual environment in a folder called "venv":
1.
This will activate the venv:
2.
If above command gives an error inside powershell7, run this:
2.1.
This will install all libraries/dependencies needed to run the scripts:
3.
That's it! You have created the Python venv and have Activated it too.

Hint: Once you have activated the virtual environment, you should see (venv) at the most left-side of your prompt.

Great!

So far, we have dealt with the prerequisites and also applied step 1 and 2.

This is where the fun begins. We'll run the actual model, and you will be surprised as to how simple everything is. You are just running literal one-line commands.

Make sure you have some background in MMAR to understand how to use it, you can read it here: https://www.forexfactory.com/thread/...7#post15489237

I will also talk about how to configure the script in order to change the timeframe, market and periods. For now, I will be doing the tutorial on the defaults so people can understand the usage, then experiment with their own changes.

Step 3: Using MMAR

Make sure you have:
1. Activated The Python Virtual Environment & Installed ALL Packages
2. Are in the directory "mmar" or whatever you cloned the repo in
3. MT5 is opened

Once these checkboxes are complete, we can now move on.

Enter the following command in your terminal/Powershell7:

1.
This is telling python to run the "run_step1.py" script.
Once you run the script, you have successfully ran step1 from the total 7 steps process.

This will tell you if your market, timeframe and period is multifractal or not.



(I am hiding the addresses of my paths, as this can reveal sensitive info)

As you can see, the script is smart enough to tell you that the data is infact multi-fractal and encourages you to run step2.

Also, the output of each script is long and detailed for transparency purposes, so you know what the script is doing at each moment. I encourage people who are using this to read the full output of these scripts to better understand the usage and results they are getting. You will find plots and data inside the "plots" directory. Open it and see those charts!

Now, let's run step 2!

2.
This step tells you how much multifractality exists in your data.



As you can see, the current config is extremely multifractal. This is good, which means MMAR has a chance to outperform GARCH.

Now, I will skip running each step, but you will need to run all steps 1-7. The final step is the monte carlo simulation which will take some time depending on your hardware.

Step 4: Comparing with GARCH

I am now assuming you have run all steps. Now, you can actually compare the results of your forecast with GARCH to see which one is better.

Run the following command:
1.
This will train and test GARCH and its variants vs MMAR.



As you can see, MMAR performed better, as we got evidence of multifractality in our data, MMAR outperform GARCH and its variants by a huge margin!

However, this is important to note: You have only validated the forecast in one window. Meaning, there's no statistical significance. In other words, you might have been lucky. It's better, that you are to perform this test on multiple windows to confirm MMAR outperformance as significant and not luck.

Step 5: Changing the Config File

Now, you are an expert at running MMAR model and comparing it to GARCH variants. It's time that you actually get some usage out of this. So, for that, you need an IDE or some program to change the config file to train and test the models on your favorite markets/timeframe.





It is recommended that you ONLY change the "Data Parameters" section as shown in the above image to your liking. Other sections contains sensitive parameters that can alter the behavior of MMAR model. You can change other sections, but know that this is risky, can break the model, and not following the paper's guidance. However, you are free to do whatever you want, as long you understand the risks.

#####

In the paper, it's recommended to use 50 day lookback period, however, you cna increase and decrease that by changing the following constants:

#####

Also, you need to understand what both models are forecasting.
They are forecasting the standard deviation of volatility for the next 25 days. It's not per bar, or per hour, it's 25 days.

You may wish to change the number of days by changing the following constant:

FINAL NOTES:

I recommend everyone to double, triple check their results with a professional before risking real-capital on your research/model. As this was made by one single developer (me) I can't say if the results are mathematically accurate. However, I have done my best to do so.

If you want to use the MMAR model, make sure to test multiple windows of data. Make sure to take a second opinion on the results and make sure to validate that the results are not caused by luck, bugs or lapse of judgement.

Otherwise, have fun playing around with the model. I would love some feedback if people do try it out.

Good Luck !

Congratulations squire!
I'll be honest - it'll take me a week or two to get round to doing this and then I'll report back. And you'll be underwhelmed by the responses around here too - don't worry about that either. I know the effort this kind of thing takes and I admire your perseverance.
Back laters

Thank you triphop, this project was not meant for everybody so I can see why nobody was interested enough to try. But that's fine, I wouldn't had liked to give this in the hands of wrong people anyway

In the coming few days, I'll post case studies. This is a powerful project that has potential to grow a lot more. And now that it's available on github, I can slowly add features I am working on to make the script more "fun" to use and informative.

My own strategy would benefit from this if MMAR is successful for the markets I trade in.

Either way, this can be extremely useful in turning mediocre strategies to genuinely profitable ones. For instance, any strategy relying on basic indicators is regime dependent. Volatility is a measure for regimes. So, it can be particularly useful for classifying breakout vs mean-reverting vs choppy periods. Take an example of an extremely basic strategy, RSI for example, works perfectly in ranging markets, but completely breaks-down when markets are trending. Can volatility help classify this behavior? Yes. It solves one piece of the puzzle.

The road ahead is exciting so I'll keep the forum posted