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Can statistical methods be used to create a trading strategy?

  • #21
  • Jun 14, 2014 4:02pm Jun 14, 2014 4:02pm
Quoting Adal
{quote} If you throw away high frequency data you are losing valuable information. There are techniques for working with non-equally spaced high frequency tick data. For example, the volatility computed this way is much more accurate than when you compute it starting from smoothed data. The timing between the ticks is also important (see ACD model and it's derivatives). This kind of data is again thrown away if you aggregate ticks into candles, since candles are regularly spaced and lose the timing information in the original data. Also of notice...
I agree with you, and I don't think we actually disagree. My comment was about a whole different kind of analysis than you are talking about. I don't think that tick data is worthless at all. I think it is worthless for people who are trading month-long trades. I likewise think that people who trade using tick data for their analysis don't care about trends lasting months.

My comment pertained entirely to standard analytic methods using equally-spaced samples. You are talking about non-equally spaced analyses. I am talking about mid-to-low frequency analysis. You are talking about high frequency analysis. For you, a highpass filter would make more sense than a lowpass filter

I would be very curious to hear more about these methods you have mentioned; they sound fascinating.
  • #22
  • Jun 14, 2014 4:37pm Jun 14, 2014 4:37pm
There is a constant stream of people talking about using DSP filters on this forum, and about the particular advantages/disadvantages of different kinds (IIR versus FIR, ...)

But what I never saw was a discussion what to do with the data after you've filtered it.

Trade it's momentum? Trade it's deviation from the mean? Extract it's frequencies (FFT, wavelets, Hilbert-Huang, ...) and trade it's cycle on a mean-reversion basis on it's own? BTW, the Oanda hedge-fund does something somewhat similar, but they use an agent based model, and they go one level deeper, looking for the trader actions generating the frequencies instead of just extracting the frequency.

Also, I get a strange feeling of the hammer problem (as in everything looks like a nail) - your suggestion to use a high-pass filter for example.

Don't take this the wrong way, I just see a lot of focus on the filters themselves, but little with the steps after that. Of course, secret sauce and all that are a factor also.
  • #23
  • Jun 14, 2014 4:43pm Jun 14, 2014 4:43pm
Quoting Fractalist
{quote} I would be very curious to hear more about these methods you have mentioned; they sound fascinating.
Here are some starting points, you can branch from that:
http://en.wikipedia.org/wiki/Autoreg...ional_duration
https://www.olseninvest.com/customer...7-emaOfEma.pdf
  • #24
  • Edited 6:53pm Jun 14, 2014 5:00pm | Edited 6:53pm
Let me throw up a major warning sign to some of you.

Statistical models are predominantly used for removing observer bias and attaching a probability to an event being significant. The more complex the statistical model, generally the less reliable that model is.

For example, I work in biology, we use statistical models to represent biological phenomenons - I can assure you a single cell is more complicated than a financial market. I admit most of the statistics I use are normal distribution models (not all), but generally if a model doesn't at first look good you can apply filters to make it look better. The strongest statistical test generally is the simplest, t-test or anova, calculated against data as close to raw as possible. However once you start transforming data you lose a lot of it's power, we generally are not big fans of data manipulation because it can become another method of curve fitting, in this case, finding a statistical model that will give you the answer you want.

Let me give you a real world example. Currently we are bombarded in the media about how eating too much of x/y and/or z will give you cancer. Anything these days gives you cancer it seems, but to those with an ounce of common sense you can see that at least some of these claims must be nonsense. For example, red meat apparently gives you cancer if you eat too much of it, however I would argue that it is the lifestyle choices of the person who eats lots of red meat that is most important, not if you eat more than 2 portions a week. Big red meat eaters, I can guarantee, are likely to have a lifestyle more conducive to producing cancer compared to a vegan.

Let me be clear, I personally believe that the markets are perfectly rational. I believe there are statistical trends that can be examined, but this would be a whole lot easier and more simple if people stopped ignoring the elephant in the room. Technicals are a bit like the media and cancer, but fundamentals and supply and demand are the real key, it is the real reason markets wax and wane. Stop ignoring it.
  • #25
  • Jun 14, 2014 5:24pm Jun 14, 2014 5:24pm
I believe some of you here will like the discussion in this old thread. These methods do work and are in use by people who understand them.

http://www.forexfactory.com/showthread.php?t=68181
Think : Trade : Live Life
  • #26
  • Edited 9:16pm Jun 14, 2014 5:31pm | Edited 9:16pm
Quoting Adal
There is a constant stream of people talking about using DSP filters on this forum, and about the particular advantages/disadvantages of different kinds (IIR versus FIR, ...) But what I never saw was a discussion what to do with the data after you've filtered it...
Good point. Here are some things that I am doing:

1) By just using a good filter on price data, and then drawing those smoothed lines on the price chart, it is possible to observe the location of dynamically-changing S/R levels that are related to Fibonacci frequencies. This is not possible with MAs because of the deficiencies I mentioned previously, and so most people tend to discount the significance of what I just said because they have tried some attempt at this idea before, using MAs, and the results were unimpressive. Also, there is a lot more depth to this subject than just tuning a bunch of lines to 8, 13, 21, 34, etc. A lot more. Most never get that far.

I believe in the Pilot Wave Theory of Quantum Mechanics, which states (among other things) that 'particles' tend to like to 'flow' along 'paths' which they have already travelled earlier in time. In markets, that 'particle' is the current price (the Price Particle) and it flows according to the various forces applied to it. These forces are a combination of outside pressures and internal natural intentions. That is, price will flow entirely according to its own internal 'natural' rules unless traders apply a lot of outside pressure, pushing the system past its natural flow barriers. Then, when that outside pressure wanes, the Price Particle will settle back into natural flows, but within the new natural environment to which it has been just displaced by the outside forces.

In addition to this, sometimes it is possible to see when and how that outside pressure will be applied, just by looking at the natural system. This is a dual-feedback system. The outside forces provide the energy that powers the system and causes intermittent discontinuous changes. The internal system dissipates that energy via a tuned array of dissipating dominant cycles, which can sometimes coalesce to 'nodes' of confluence, which causes traders to act similarly and en masse.

That 'natural system' can be seen by using properly-tuned lowpass filters. I have discovered 3 different ways of doing this so far.

2) A lot of traders know about differencing and how this can depict phase-advanced representations of the current cyclic situation. At least, that's the theory. You look at the velocity of prices and you see a phase-advanced picture; acceleration is even more advanced. But again, most traders who have tried this have made the mistake of using either raw prices or prices filtered thru MAs. It won't work that way. The noise gets exaggerated versus the signal way too much, and that happens because there is too much noise in the data being analyzed.

The way to fix this is lowpass filters. Use cleaner data and suddenly those velocity and acceleration studies start looking readable and usable, and predictive. Simple little oscillators based on LPFs work much better than standard ones based on MAs.

3) Linear prediction. Any kind of LP technique (tons of them out there), no matter how advanced, requires clean data to operate properly. Garbage In, Garbage Out. Please, nobody try to predict 1-step-ahead predictions just from raw price data. Futility. You have to predict filtered data. You have to be happy with a less specific prediction that is more accurate overall.

4) Artificial Neural Networks. Again, data clarity and cleanliness is essential to getting any decent output. People tend to assume that the ANN will just 'figure it all out' even with noise being present. The ANN isn't alive guys. It is a math equation. Math equations always work better when the input data more precisely depicts the input process. You have to use data that actually pertains to the question you want the ANN to answer. It needs to be clean.

There are more things going on...

In general, lots of analytic techniques that traders try and discard turn out to work much better when lowpass filtered data is used. This specific pre-processing technique is the key to success in a variety of methods that many traders have given up on.
  • #27
  • Jun 14, 2014 5:47pm Jun 14, 2014 5:47pm
Quoting MCRotter
Let me throw up a major warning sign to some of you. Statistical models are predominantly used for removing observer bias and attaching a probability to event being significant. The more complex the statistical model, generally the less reliable that model is. For example, I work in biology, we use statistical models to represent biological phenomenons - I can assure you a single cell is more complicated than a financial market. I admit most of the statistics I use are normal distribution models (not all), but generally if a model doesn't at first...
I would be inclined to believe your opinion more if I saw any evidence that you had done any actual experimentation with the techniques I have mentioned, or any others. I understand that you are repeating the bias you learned, and which applies to many real world situations. I would suggest that you at least experiment with some of these concepts you are discounting. What's more scientific that experimentation and observation?

What I have described cannot possibly cause curve fitting. That would render Nyquist-Shannon and all DSP as biased methods. I have read about this subject extensively and also have a degree (of sorts) in Audio Engineering. I would know if DSP had any such curve fitting biases because that would be audible in digital audio and would be an issue for Audio Engineers to address. Nobody in either the EE or AE communities ever mentions DSP as any kind of curve fitting, so your opinion is totally contrary to the people who actually work with these technologies.
  • #28
  • Edited 7:13pm Jun 14, 2014 6:08pm | Edited 7:13pm
Quoting Fractalist
{quote} I would be inclined to believe your opinion more if I saw any evidence that you had done any actual experimentation with the techniques I have mentioned, or any others. I understand that you are repeating the bias you learned, and which applies to many real world situations. I would suggest that you at least experiment with some of these concepts you are discounting. What's more scientific that experimentation and observation? What I have described cannot possibly cause curve fitting. That would render Nyquist-Shannon and all DSP...
Seriously, that bold worries me and it is not something a person would normally say.

I didn't say the methods you mentioned were curve fitted or that there is an inherent flaw with them, I know very little about them, nor am I discounting them.

I was saying however that the search to find a suitable statistical method is often a search to find something that confirms your already formed bias. Like I said, in my field, often if the results don't show promise some people start looking to manipulate the data - it always happens when money is on the line. Be that grant money, or forex. Note I'm not saying all data transformations are bad either.

Like I said, the simplest statistical tests are the most powerful. The raw data is the most true.
  • #29
  • Jun 14, 2014 6:11pm Jun 14, 2014 6:11pm
Presumably when you use a filter to smooth the data, you need to choose the filters parameters (order, cutoff, gain, q factor, ...). Tuning those parameter until you can use the filter to make financial predictions can be considered curve fitting.

There is good curve fitting (extract maximum profits while staying in a risk profile), and there is bad curve fitting (predict the past instead of the future).
  • #30
  • Jun 14, 2014 7:27pm Jun 14, 2014 7:27pm
Ok let me reply to both of you.

Your replies both show some confusion about basic DSP theory. According to the Nyquist-Shannon Sampling Theorem the final stage in the sampling process, essential to creating a neutral output, is a lowpass filter tuned to specific settings. The filter does not create any bias in the output - it corrects the stepped time domain response and aliased frequency domain response. It is a required, internal component within the overall algorithm used to digitize continuous data.

If this were not true, every professional digital recording system on the planet would exhibit a non-flat frequency response within the audio band. They don't. They are flat to within tiny fractions of a decibel. This tiny difference has been proven to be both inaudible and even statistically insignificant. If DSP were systemically biased in the manner you have alleged, the recording studios of the world would all have corrective frequency equalizer systems in place to compensate for the biased frequency response inherent to digital recordings, as was done for mastering phono records in past years. They don't have such systems, because DSP isn't biased in the manner you say.

DSP is capable of expressing the entire bandwidth that is contained within the data. There is no bias. Every frequency below the Nyquist Limit is represented equally. The Nyquist Limit is not any kind of bias, but a limit of basic physics.

"I was saying however that the search to find a suitable statistical method is often a search to find something that confirms your already formed bias"
There is no bias. The filter is the final step to create a non-biased outcome.

"Presumably when you use a filter to smooth the data, you need to choose the filters parameters "
This isn't smoothing. This is the reconstruction stage of DSP.

When I was discussing smoothing, I was pretty clear that I was using that to exhibit cycles which is obviously a biased implementation because the intention is biased. That is simply using an unbiased telescope to observe a specific (biased) star.

The argument you both have been making is that the basic tool, DSP method, must be inherently biased. It isn't. I use that unbiased tool to investigate biased intentions (hypotheses) and then observe the results of those experiments. That doesn't bias the tool.

Let me be really clear what I mean now. Using a lowpass filter, tuned to 2-bars (the Nyquist Limit) on raw price data is necessary to perform the final DSP reconstruction stage. Ignoring this means using data with an aliased frequency response. That means that any kind of indicator or tool which performs any numerical analysis on equally-spaced samples must, as its first stage, apply a 2-bar lowpass filter to the input data.

Smoothing is the application of a lowpass filter which is tuned to any setting below the Nyquist Limit. This creates a biased output, but biased in the manner which the user intends. It is like using a color filter on video data.
If smoothing is applied, the 2-bar filter for the DSP reconstruction isn't needed because that function will be accomplished by the LPF which is set lower than Nyquist.

Regarding the comment about fundamental analysis, that reflects an assumption that the fundamental data you receive is reliable. Price data is always reliable. The price really is the price, and it really is the only thing that matters in the end. Government-issued reports are often too late to be profitably actionable or are simply distortions of the facts intended to manipulate fundy traders like you into taking action in the markets in managed ways. You are sometimes a pawn they use to manage the economy. They feed a report out to you, indicating 'something', and you all jump in the market on command. They use your money to perform week-to-week housekeeping duties of managing the markets and the economy.

You might wish to reconsider the value of technical analysis.
  • #31
  • Edited 8:35pm Jun 14, 2014 8:21pm | Edited 8:35pm
Quoting Fractalist
Ok let me reply to both of you. Your replies both show some confusion about basic DSP theory. According to the Nyquist-Shannon Sampling Theorem the final stage in the sampling process, essential to creating a neutral output, is a lowpass filter tuned to specific settings. The filter does not create any bias in the output - it corrects the stepped time domain response and aliased frequency domain response. It is a required, internal component within the overall algorithm used to digitize continuous data. If this were not true, every professional...
Sorry, I don't meant to keep saying this, but I have no problems with the method of DSP - thanks for the run down btw, I know that took ages to write.

What I want to drill down to is why you are using this method? That is where I feel a bias could (note I didn't say had) come in. Why are you using this test over a chi-square test for example? Is it because you are automating your testing real time?

---------------------------------
Another example:

I manually back tested a strategy with 486 separate trades over 2.5 years with a 2:1 payoff. I want to know if it is statistically significant, one method I could use is to see if the observed frequency of winners from my strategy is statistically significant from my expected frequency of winners. The simplest test is the chi-square test which looks for differences in frequencies between two groups.

Specifically I want to know is my strategy better than just picking a price at random?

Randomized I would expect to have roughly a 33% win rate when using a 2:1 risk reward - therefore my expected result is about 33% win rate, my hope is my strategy would perform better than that. I went further though and choose a random number generator for 486 data points and calculated the win rate for that:

The expected randomized results were: 166 winners vs 320 losers = 486 total = 0.34 win ratio
The observed results for my strategy were: 201 winners vs 285 losers = 486 total = 0.41 win ratio

These are the results from the chi-square test
Attached Image


p value is 0.024 which means there is a less than 1 in 40 chance of my result being down to chance. That is not to say the system will work in the long run however.
----------------------------------------

So here is the question, why not just use a chi-squared test? Why is there a need for anything more, especially when I have just shown that it works decently well? Is it because the chi-squared tests says there is no statistical significance with your system? Or is there another reason?
  • #32
  • Jun 14, 2014 8:34pm Jun 14, 2014 8:34pm
Quoting MCRotter
{quote} Sorry, I don't meant to keep saying this, but I have no problems with the method of DSP - thanks for the run down btw, I know that took ages to write. What I want to drill down to is why you are using this method? That is where I feel a bias could (note I didn't say had) come in. ....So here is the question, why not just use a chi-squared test?
Why am I using this method...
Because the raw data we receive is DSP data, by default. It is a digital sample of a continuous process. It is, in its raw state, incompletely processed. It does not accurately reflect the continuous process it purports to represent. It has artifacts contained within it that must be removed. If I wish to see the digital representation of the continuous process clearly, I have to follow the final step of DSP and LPF @ Nyquist. Virtually nobody understands this, so I get your confusion.

The method is mandated by the form of the input data.

Why not just use chi-squared?
That isn't unbiased at all. It assumes a normal distribution (or one of its cousins) in the data. Market data is not normally distributed; the distribution has been shown to be more like the Pareto-Levy distribution.

Pleased to talk more about this, but I gotta run now...
  • #33
  • Edited Jun 15, 2014 10:16am Jun 14, 2014 8:47pm | Edited Jun 15, 2014 10:16am
Quoting Fractalist
{quote} Why am I using this method... Because the raw data we receive is DSP data, by default. It is a digital sample of a continuous process. It is, in its raw state, incompletely processed. It does not accurately reflect the continuous process it purports to represent. It has artifacts contained within it that must be removed. If I wish to see the digital representation of the continuous process clearly, I have to follow the final step of DSP and LPF @ Nyquist. Virtually nobody understands this, so I get your confusion. The method is mandated...
From what I can tell you are strategy hunting? If you take the market as a whole as a continuous process, you are probably right in that markets aren't normally distributed. Again I go back to fundamentals being king here and would suggest using that a your touch post.

But regarding technical entries, we are not interested in every bit of information the market has to offer, we are interested in only that which conforms to your particular strategy.

When you have a strategy, you are interested in a particular set up on a particular market and timeframe (reducing information), with a particular risk reward (creating expected variances), and which have only one of two outcomes (win or lose). By imposing these type of rules you drastically reduce information, you have a more 'normal distribution' and you therefore have something that can be analysed much easier. It is akin to a normalization of a constant stream of info.

My point is that you don't need any other statistics to analyse technicals, not when it broken up into a particular strategy.



I think I understand what you are doing (finally), I just can't really get my head around why you have felt the need to make it more complicated than what I personally feel it needs to be.

Anyway, you either make money or you don't, talk is cheap and I have done enough talking for one night.

Best of luck mate, will be reading some of your other posts to see what you are putting together.
  • #34
  • Jun 14, 2014 10:50pm Jun 14, 2014 10:50pm
Quoting Fractalist
Using a lowpass filter, tuned to 2-bars (the Nyquist Limit) on raw price data is necessary to perform the final DSP reconstruction stage. Ignoring this means using data with an aliased frequency response. That means that any kind of indicator or tool which performs any numerical analysis on equally-spaced samples must, as its first stage, apply a 2-bar lowpass filter to the input data. Smoothing is the application of a lowpass filter which is tuned to any setting below the Nyquist Limit.
As it happens in high-school I've written a simple FM synthezier with subtractive filtering so I do have a basic understanding of what you are talking about - https://dl.dropboxusercontent.com/u/...f/defiance.png

You say that you filter at Nyquist, and that is correct in a DSP ADC/DAC scenario, but I ask you this: what is the Nyquist freq of the market?

Is it 2 M1 bars? Or is it 2 microseconds?

An audio signal sampled at 11 kHz will sound muffled to us, because it's Nyquist is set too low, way in the middle of our perception region.

There are HFT algorithms which operate on a microsecond timeframe. I collect tick data from 5 sources, and on average I have 10 ticks per second on major pairs during the liquid periods of the day.

So that would suggest that I should set a Nyquist of at least 20 Hz, or else I would be analyzing a "muffled market". What some would consider noise (10 quotes per second), others consider signal.

So I am very curious - what is the Nyquist frequency that you are using?

Quote
Because the raw data we receive is DSP data, by default. It is a digital sample of a continuous process. It is, in its raw state, incompletely processed. It does not accurately reflect the continuous process it purports to represent. It has artifacts contained within it that must be removed.
You are making a very very big assumption here - that trading is a continuous process. The double auction market that your usual financial market is can as easily be considered a discrete time process, and a large number of people are doing just that, considering that, well, trading is in fact discrete (unlike an analog signal).

So the burden of prof is on you to prove that the market is the manifestation of a continuous time process.
  • #35
  • Edited Jun 15, 2014 12:03am Jun 14, 2014 11:52pm | Edited Jun 15, 2014 12:03am
Quoting Adal
{quote} As it happens in high-school I've written a simple FM synthezier with subtractive filtering so I do have a basic understanding of what you are talking about - https://dl.dropboxusercontent.com/u/...f/defiance.png You say that you filter at Nyquist, and that is correct in a DSP ADC/DAC scenario, but I ask you this: what is the Nyquist freq of the market? Is it 2 M1 bars? Or is it 2 microseconds? An audio signal sampled at 11 kHz will sound muffled to us, because it's Nyquist is set too low, way in the middle of our perception...
Ok excellent response.

The Nyquist Limit for all standard bar/candle charts is 2 bars. That is because it is related to the sample rate, which is the rate at which new bars appear. Nyquist is half the rate at which bars appear, therefore it is always 2 bars.

" You are making a very very big assumption here - that trading is a continuous process"
Excellent. Glad you saw the weakness there. I have no proof but a decent reason, I think.
I think the way I am looking at it is 'Functionally Continuous', if that makes any sense to you. I know that there is not a constant stream of unique new observations available at each moment in time. Prices change in discrete steps and the minimum magnitude of that change is limited by the tick value, which also makes the data more discontinuous, in another sense. So I completely see what you are talking about and you do have a big point.

Think about time itself. Imagine the smallest discernable quanta of time. There is recent research which suggests that time does not scale smaller and smaller to infinitely-smaller and smaller chunks. It has a finite minimum size or quantity. That means that everything, at its core, is discontinuous and the things we think are continuous are merely perceived to be that way because our minimum perception of time (human threshold of temporal observation) is much greater than Time's minimum size. So to us, all those accumulated discontinuous events become smoothed out to the extent that we perceive them to be smooth and continuous.

That means (if this is true) that Functional Continuity occurs when the Observer's 'maximum sample rate' for observations is much less than Time's 'maximum sample rate'. I am using a different metaphor here as a way of fleshing out what I meant before, not to contradict it. So many samples accumulate from the stream of Time within each Observer sample that the discontinuity becomes smooth.

So to apply this to the markets, I am presuming that although ticks come in erratically, they occur often enough within the time period of the bar duration such that the accumulated process can be thought of as Functionally Continuous. This hypothesis is more likely to be true at longer bar durations, of course. I do see some erratic outputs sometimes from M1 bars which have been processed, due likely to tick insufficiency.

So that's my best guess. Also, the fact that I can see the onset of problems occurring right in the manner where my theory expects, and the lack of observations of those problems at longer bars, tends to reinforce my theory.
  • #36
  • Jun 15, 2014 12:25am Jun 15, 2014 12:25am
Quoting Fractalist
{quote} Ok excellent response. The Nyquist Limit for all standard bar/candle charts is 2 bars. That is because it is related to the sample rate, which is the rate at which new bars appear. Nyquist is half the rate at which bars appear, therefore it is always 2 bars.
You need to remove frequencies above Nyquist to avoid aliasing before sampling. You cannot do this afterwards, since the aliasing is already embedded in the signal and can't be distinguished from the actual signal anymore:

http://www.manlab.vn/wp-content/uplo...gular-wave.png

So shouldn't you apply the filtering before converting to bars? It doesn't make any sense to apply an anti-aliasing filtering (brickwall LPF) after you have already sampled the signal since by definition the signal doesn't contain any more frequencies above Nyquist.

And what about the other point that I raised? That maybe your sampling frequency that you use is too low and you are discarding valid data.
  • #37
  • Jun 15, 2014 8:20am Jun 15, 2014 8:20am
Quoting Fractalist
{quote} All MAs are lowpass filters. Correct. They are extremely poor lowpass filters because they leak and their stopband attenuation is poor. If you look at the frequency response of a moving average and a 2-pole Butterworth IIR lowpass filter, you can see that the Butterworth shows increasing attenuation in the stopband as frequency increases. No part of that curve shows any frequencies in the stopband that 'leak'. The MAs have frequencies where the attenuation curve goes sharply upwards (weaker) allowing leakage. {image} {image} The effect of...
Reading your answer I fully agree with Adal who says that what is important is "what to do with the data after you've filtered it".

You seem to put a lot of importance on the attenuation. From what I read you need a very strong attenuation in the stop band. I'm satisfied with -20dB. You seem to care much less about the linearity of the phase which is critical to me. Also I need a flat 0dB gain in the pass band. You don't talk about it.

Clearly our needs differ. I need low lag. Butterworth have crappy lag on top of the non linear phase. I can't use the forward/backward trick. Especially with IIR that needs a lot of samples to stabilize. If I did so I would introduce fake low frequencies.

Let's compare a 1st order butterworth and a LWMA 9.
In the picture below the butterworth is in red and the LWMA is blue. The frequencies are normalized (0=DC 1=Nyquist)
The cutoff and the general attenuation are pretty much the same. You can see that the phase linearity of the LWMA is much better than the one of the butterworth in the pass band. This phase response is crucial for the delay to be constant over the frequencies. Look at the delay response of the butterworth it varies from 3 to 2 over the pass band it is almost constant for the LWMA. This is very important to me.
So for me the LWMA is preferable to a butterworth given the same lag and the same attenuation because of the better linear phase response.
Attached Image (click to enlarge)
Click to Enlarge Name: Butterworth_vs_LMWA.png Size: 11 KB


Your screenshots let me think that you are interested in the medium to high frequencies (0.2 - 0.6 Nyquist). I'm personally interested in the very low frequencies, the periods of 20 bars and more (<0.1 Nyquist). I have to tolerate frequencies in 0.1-0.2, because I've no choice. To reduce the cutoff with a butterworth I would need to increase the order but the lag becomes unacceptable (4 bars is already 20% of the cycle, way too much). I use chebyshev filters instead to keep the lag under control but the phase linearity is bad.

You suggested to use oversampling. Actually, I work with so low frequencies for the filters that I came to use downsampling instead. I filter the odd indexed samples and the even indexed samples separately. I average the result of the current filtered value with the last output of the other filter.
No greed. No fear. Just maths.
  • #38
  • Jun 15, 2014 8:22am Jun 15, 2014 8:22am
Quoting Ponzi Jr
Whilst at school, I covered 2 units of statistics. These included things like: - Normal, Poisson, Chi-squared, t, and binomial distributions - Confidence intervals - Hypothesis testing using a given significance level to determine whether a critical value lies within a critical region - Correlation and regression analysis - All the basics regarding numerical methods and such Does anyone implement any of these principals in their approach to trading? If you don't, but are familiar with these concepts, can you see any way in which they would be useful...
i was trying something similar but no one help
  • #39
  • Jun 15, 2014 8:50am Jun 15, 2014 8:50am
Quoting Ponzi Jr
Whilst at school, I covered 2 units of statistics. These included things like: - Normal, Poisson, Chi-squared, t, and binomial distributions - Confidence intervals - Hypothesis testing using a given significance level to determine whether a critical value lies within a critical region - Correlation and regression analysis - All the basics regarding numerical methods and such Does anyone implement any of these principals in their approach to trading? If you don't, but are familiar with these concepts, can you see any way in which they would be useful...
Quoting zelenko
{quote} i was trying something similar but no one help
I posted an example of Chi-squared test a couple of posts up the page... It is used for frequencies, so basically comparing win rates.
  • #40
  • Jun 15, 2014 8:37pm Jun 15, 2014 8:37pm
Quoting MCRotter
{quote} {quote} I posted an example of Chi-squared test a couple of posts up the page... It is used for frequencies, so basically comparing win rates.
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