Fourier Analysis

Any experimental physicist would tell you that the number one tool for analyzing an electric signal is a Fast Fourier Transform (FFT). For those of you not familiar with the concept, an FFT can take a signal in the time domain, and break it apart into a frequency domain. Since electric signals are very much like price data (they oscillate and they're full of noise), I was wondering if anybody has ever tried to analyze price data using fourier Analysis.

On a seperate topic, there are also lots of noise reducing techniques in experimental physics, like dithering, and adding white noise to a signal (in this case, price movement). Has anybody tried either of these techniques?

The Fourier Transform analysis can only be applied to periodic functions.
A peridic function is defined as a function which repeats itself every certain period of time. This of course is not applicable to the price action of any known financial instrument, simply because the price action does not repeat equally during certain time periods.

So, from the theoritical point of view, the Fourier Transform can't be used to analyze the price action of currencies or any other financial instrument.

However, I believe that it can be managed to apply the fourier transform analysis but to portions of price actions. Let me explain this a little bit.

If the price action of a certain currency pair is considered, it must be cut down in which each piece must be confined within a certain known limit. For example, cutting the price action of the EUR/USD for 2 days based on the 1 hour chart provided that the price during these 2 days was oscillating between 1.1900 and 1.2000 for example.

Then applying a smoothing moving average for the extracted data, and then getting the time function of the moving average, and after all applying the Fourier Transform for the time function of the moving average.

The step of the moving average is important, as it will be very difficult to get the time function of the price data itself. It can be done by using curve fitting, but it's a very difficult and time consuming issue. I don't even know if there is any software out there that do curve fitting for inserted data or not.

When you apply the Fourier Transform, you will get another time function which consists of only Sines and/or Cosines. The function will contain an infinite number of terms. The first term is called the fundamental component, and the rest are called the harmonics. That's what the Fourier Transform function is called when analyzing the Alternating Electric Current or anyother waveform.

The Fundamental component is usually the most effective component, with the 3rd, 5th & the 7th components being taken into consideration. Usually, all the higher order harmonics are neglected due to their minimal effect. Of course, I don't know what will be the analysis of the price action of currencies will result in.

Now the real question is: How can this improve trading and speculation?

If you are analyzing the most recent data, this can be a very useful tool to project price targets as well as defining market trend. Simply insert the required future time in the Fourier time function, calculate the fundamental, 3rd, 5th and 7th components, and you get a price. This price relative to what the price is right now will give an idea about the market next move.

Why this won't work as expected?

1- I don't believe that this will work as expected, just because the pair doesn't move in completely identical cycles. This deviation will result in errors in the Fourier Transform projections.

2- The market is trending during 60-70% of the time. These trending periods can't be analyzed using the Fourier Transform Analysis.

3- The Fourier Transofrm was created to analyze the behavior of waves, electric signals and electric current. These phenomenas are completely natural and are moving without any kind of emotions. On the other hand, the currencies and any financial market is being affected by many things, and emotions drive the markets sometimes, so there can be no fixed formula for the market, that's why trading systems that used to work in the past do not work in the future, because people change, but waves and electricity do not change their attitude because they don't like the way of their life for example, or because of terrorist attacks.

Hope that I have been helpful

Nader.

Mark Jurik has brought a substantial signal processing background from his military career developing missile tracking algorithms and other noise filtering techniques to processing price/time data for the financial markets. He currently builds the best smoothing algorithms I've seen in the financial industry. Whereas most indicators lag the more you add smoothing characteristics Juriks don't suffer the same problems. Quite clever really and you don't have to spend a lot of your time reinventing the wheel. He also references some other notables such as Kauffman. Also Ehlers applied a great deal of sound processing techniques used in filtering sound in amplifiers to his work and uses a lot of sound processing jargon as metaphors for filtering market noise.

http://www.jurikres.com/about/company.htm#top

FT

Thanks Narafa for the extensive explanation of the FFT. That was a much more thorough explanation than I proveded. It actually insn't overly difficult to write an algorithm to do an FFT on a data set (I believe that's the whole point of the "fast" part of FFT). In fact, microsoft excel already has an FFT funtion built into it's analysis toolpack. And Mathematica and Matlab can do FFTs as well. So, the only time-intensive part of this would be entering data into a spreadsheet or textfile of some sort. In any case, you are probably right. Performing an FFT on price data may not yeild any strong harmonics. Price data probably isn't as repetative as I think it is. But, I still think I might try it to see if it does yeild anything interesting.

Narafa, your explanation was just great...

I understood from you some minor facts about Fourier Series, which I didn't understand from the mathematics professor in college last year...

This thread is quite old, but I think it's worth bringing back up. Specifically, I wondered if anybody had tried to do realtime spectral analysis on the markets. If you don't know what I mean, here's an image of a real-time FFT applied to sound:

http://www.steinberg.net/typo3temp/pics/7bf15c628e.jpg

The color (black->purple->blue->green->red) implies the strength of each frequency component during the given sample window. Anybody tried this? If not, it might be interesting to try on tick data... Perhaps the market whistles a certain note before it is likely to reverse .

You guys should check out this blog http://ai-quant.com/.
This guy is right into his transforms.

Wow, that blog is fascinating. Thanks for the link!

That's DSP lecture told,"send an impulse into a system and you can then tell the system"

i even wondered i could use this impulse signal to get the picture of "forex model" out! worth to flip the textbooks again.

Hello to you all,

I got very into fourier analysis and time cycle work. I pulled a fourier analysis out of the GBPUSD on the daily which indicates we are approaching a top position. I attach a screen shot, now if there are any programmers out there that would like to work on some ideas I would be greatfull and I think that we can use fourie in combination with price targets to nail entries to the nearest 20 pips or so.

I also had a good look at the gbpusd in terms of cyclical behaviour and found that it often moves in 3,4,7 month moves, which is again interesting as you have an additional cycle perspective. We are right on a 7 month cycle point and we hit a .786 of the previous move down a couple of days back which I shorted.

Anyone interested in working with me please drop me a PM with your email so we can get together and start building a robust analysis tool.

Kind regards


Mike Haran

Hi @ll (or whoever is still here)

Really interesting thread. I love to learn and get new ideas...

There are many points though that imho can be discussed. Let me just get started, I hope for a fruitful exchange of opinions.

Why opinions? Because in Forex as in real life we can only gain from opinions, hopes. Because if there was THE rule, things would not work. We have to mix analysis with stochastics. I know that in the past many economy Einsteins wrote countless theses. If there was THE rule, sorry for repeating, everyone would be rich. Which does not work neither. Remember: the money is not lost, someone else has it...

Who still attends this forum has not found the grail yet or at least came close to it. Otherwise you would not be reading this rather than enjoying your life on a beach. Okay, enough philosophy...

Quote:

Really? Isn't that exactly the situation where institutional, professional investors rely on periods? Wins can only be made on changes. So there must be an oscillation. Taking a look at the frequency of these (small) oscillations might give you an idea when the next highs/lows can be expected.

Quote:

No? Let's take a simple example from electrotechnics: filters. If electricity was so clean and stable, why would we need filters? Right, because we have spikes in reality. My spikes on an electric signal is the terrorist attack for the forex. Filter this out, the forex signal continues to follow waves.
I have made countless (graphical) analysis of signals. There are so many astonishing coincidences, that you cannot call them coincidences anymore. Call me an idiot, but if you knew better you would not be sitting here reading this...

Enough for now, the buffet is opened...

Just downloaded a fourier extrapolator (free via google search and it does look very promising at first site - effectively it attempts to predict the short term future price action as a nice smoothed curve. I have several reservations, however - the comments associated with those who have tried it suggest it can only be applied to 15M charts or less, which actually suits me but perhaps not others, and that high impact news events would be tricky to filter out, if at all..

One interesting observation: often the calculated (fourier) signal inverts. Meaning: high/low changes, but the frequency (!!!) remains.

Example? One picture explains more than thousands of words:

Trend changes, forecast flips vertically

Okay, you could say: coincidence! But believe me, I could fill the Vatican library with these coincidences. The question is, how can we use these coincidences to our advantage in practice? Especially in the fast moving forex world?

I've already tested a fourier approach.
of course it didn't work.

And that's why I should give up? Fourier sure not as stand-alone, in combination with one or two other indies (trend and fibo?). As well you could say: I have tried Bollinger Bands and of course it did not work... ;-)

Hi
it didn't work for me in any way.
if you believe in it, good luck to it.

It's too early to have results. Sure I believe in it, otherwise I would not try to find more evidence...
May I ask what you did and why do you think you failed? Which indicator did you use? What parameters? Stand alone or in combination with a trend indicator?

Thanks and have a great weekend!

Another example, why I think it is worth trying an approach. Look at the beauty of the waveforms (blue is actual, red is forecast). I put also a simple trend indicator that shows me when trend changed. Can you see what I see?

That's a valid algorithm. Market noise is present and most visible on lower times frames like M1, M2, M3.
I can't believe this thread was posted in 2005 and that it was revived after such a long time.

Here is a comparison of Extrapolator with mladen's Holt_double_exponential_smoothing_2.2 indicator.
The dotted red line is Holt's predicted next 15 bars.

Thanks 1000 times! Shows me that I was on the right track. Haha, most funny: I already had the indicator in my endless list ;-)