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Statistical mean of the market [quant corner]

  • #21
  • Edited 6:59pm Sep 16, 2014 6:46pm | Edited 6:59pm
Quoting Adal
{quote} Really? The moving averages (filters) in the first two pictures are clearly drawn by hand in Paint. You can see the pixels overlap, or the missing pixels where you weren't careful enough. But if you insist that they are real, congrats, you'll be a billionaire very very soon. Just buy when the price is 15 pips below the average and sell when it's 15 pips above.
Lol drawn by hand in paint

You should see my prev posts where i drawn stuff in paint, you can see that i dont have the talent to draw this nice.It's not drawn in paint, it is a real indicator, and also it does not repaint and laggs only 1 bar in the slope form, in its real form it has 0 bar lagg.

Anyway it looks that way because is has a width of 5, here i reduced the width so you can see it better.

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It has a gap of 1 bar between the color change because it laggs 1 bar, so this slope MA is not the true, MA which is used its only a derivative of it so it laggs 1 bar, but the real indicator i wont show.Anyway its only for education purpose, i try to figure out the mean reversion precisely
"There's a sucker born every minute" - P.T. Barnum
  • #22
  • Sep 17, 2014 7:00am Sep 17, 2014 7:00am
Quoting Adal
But if you insist that they are real, congrats, you'll be a billionaire very very soon. Just buy when the price is 15 pips below the average and sell when it's 15 pips above.
Not even thats true,that was the first thing i tested, its "signal providing capacity"

I ran trough all possible parameters and all its combinations to find the best signal treshold with my GA, and this is the backtest result with the optimal parameters:

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Not very satisfying, anyhow thats not the point of it, the goal is to find a suitable mean upon from which i can plot good SD and have a very tiny tail so that i can put the stoploss outside it and have a very small chance of being hit.
"There's a sucker born every minute" - P.T. Barnum
  • #23
  • Sep 17, 2014 7:23am Sep 17, 2014 7:23am
Also here is how the variance changes around the moving average, as i set the parameters,it can be seen that if the BETA parameter is small then the variance around the MA is small aswell, and it increases as i increase my treshold.

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The BETA represents the treshold of trigger, of the MA to "change color", the bigger the MA treshold is the bigger the variance around it.

So i optimized the MA to have the smallest variance around it, yet, also to have a high winrate if i put trades around it.

As you can see from the backtest report it has a 63% winrate which is the optimal combination with the smallest variance possible, yet its not enough to be profitable by only trading the "color change"
"There's a sucker born every minute" - P.T. Barnum
  • #24
  • Sep 17, 2014 9:48am Sep 17, 2014 9:48am
Hi Proximus,

Have you ever tried to use your equity curve as input and repeat your strategy using it?
  • #25
  • Sep 17, 2014 10:34am Sep 17, 2014 10:34am
Quoting Proximus
{quote} Lol drawn by hand in paint You should see my prev posts where i drawn stuff in paint, you can see that i dont have the talent to draw this nice.It's not drawn in paint, it is a real indicator, and also it does not repaint and laggs only 1 bar in the slope form, in its real form it has 0 bar lagg. Anyway it looks that way because is has a width of 5, here i reduced the width so you can see it better. {image} {image} {image} It has a gap of 1 bar between the color change because it laggs 1 bar, so this slope MA is not the true,...
This filter is awesome. How do you do this? Can you post a screenshot of this filter on a range bar chart?
No greed. No fear. Just maths.
  • #26
  • Sep 18, 2014 7:00am Sep 18, 2014 7:00am
Quoting PipMeUp
{quote} This filter is awesome. How do you do this? Can you post a screenshot of this filter on a range bar chart?
I dont know why you think its awesome, since the strategy tester results clearly speak for themselves, but so be it.

Here is it applied on a 10 pip Range Bar Chart, although the filter was optimized for H4 timeframe, perhaps it needs to be adjusted and optimized if its used on CRB.

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"There's a sucker born every minute" - P.T. Barnum
  • #27
  • Sep 18, 2014 7:02am Sep 18, 2014 7:02am
Quoting Wanderer272
Hi Proximus, Have you ever tried to use your equity curve as input and repeat your strategy using it?
What do you mean by equity curve, i dont have such options

Attached Image
"There's a sucker born every minute" - P.T. Barnum
  • #28
  • Sep 18, 2014 8:39am Sep 18, 2014 8:39am
Quoting Proximus
{quote} I dont know why you think its awesome, since the strategy tester results clearly speak for themselves, but so be it. Here is it applied on a 10 pip Range Bar Chart, although the filter was optimized for H4 timeframe, perhaps it needs to be adjusted and optimized if its used on CRB. {image} {image} {image} {image} {image}
How do you make 10 pip Range Bar Chart ?
Can you give me some instructions please?
  • #29
  • Sep 18, 2014 8:43am Sep 18, 2014 8:43am
Quoting Proximus
{quote} What do you mean by equity curve, i dont have such options {image}

Your equity curve is the output your strategy gives in terms of balance. You will have write it to a file or something similar in order to use it. If you had a 63% win rate first time around, you can increase the overall performance by taking only long posisions on your equity curve or running the exact same strategy. You can repeat this multiple times, although it will not necessarily always work. It is a good way of optimizing a strategy, if it gives you an edge to start with. I hope this makes sense..
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  • #30
  • Sep 18, 2014 8:54am Sep 18, 2014 8:54am
Quoting Flaviu1981
{quote} How do you make 10 pip Range Bar Chart ? Can you give me some instructions please?
I used this indicator to construct the chart, its explained there how to use it

http://www.forexfactory.com/showthre...86#post4891386

Quoting Wanderer272
{quote} Your equity curve is the output your strategy gives in terms of balance. You will have write it to a file or something similar in order to use it. If you had a 63% win rate first time around, you can increase the overall performance by taking only long posisions on your equity curve or running the exact same strategy. You can repeat this multiple times, although it will not necessarily always work. It is a good way of optimizing a strategy, if it gives you an edge to start with. I hope this makes sense.. {image}
The MT4 strategy tester is already set to optimize the balance, i dont know what else you can do about it.Also long/short trends doesnt matter, a good filter needs to give accurate signals in all types of market shapes.

The 63% winrate is good but the RR is distorted because of this, the edge is present but when the market doesnt adapt to my filter's parameters then its out of control.

The only solution would be to always constantly optimize the parameters, but then if the sample size is too big the parameters dont represent then new price, if its too small then it may cause fakouts.

Its very hard to optimize it, that is why i use my hand made GA, which optimizes it for me the best possible way i found out so far.It still doesnt give an edge but atleast it resembles the market shape as close as possible so far.

I tend to use the "middle way" type of optimization method where i try to fit all parameters to the most optimum way, without distorting any of them too much, and be in a reliable balance for a longer time period.
"There's a sucker born every minute" - P.T. Barnum
  • #31
  • Sep 18, 2014 10:08am Sep 18, 2014 10:08am
Quoting Proximus
{quote} I dont know why you think its awesome, since the strategy tester results clearly speak for themselves, but so be it. Here is it applied on a 10 pip Range Bar Chart, although the filter was optimized for H4 timeframe, perhaps it needs to be adjusted and optimized if its used on CRB. {image} {image} {image} {image} {image}
These charts look like renko not CRB. Anyway. I'm still interested in the algorithm you used to generate the filter. I don't care the result of the trading backtest. I don't want to generate trading signals with it anyway.
No greed. No fear. Just maths.
  • #32
  • Sep 18, 2014 12:01pm Sep 18, 2014 12:01pm
Quoting PipMeUp
{quote} These charts look like renko not CRB. Anyway. I'm still interested in the algorithm you used to generate the filter. I don't care the result of the trading backtest. I don't want to generate trading signals with it anyway.
Yes indeed, its renko chart, although i dont know whats the difference because a 10 pip price chart is a 10 pip price chart.If its the lagg, then anyway its plotted on historical data, i would not really use price chart on live data.

I think the winrate is pretty much illustrating the filter's accuracy, but anyway.

I wont discuss the details here, i will send you a PM instead.
"There's a sucker born every minute" - P.T. Barnum
  • #33
  • Sep 18, 2014 4:32pm Sep 18, 2014 4:32pm
On my bands research, i specially modified the parameters to reconstruct a good mean for a "band type" of strategy, so that i can put the SL outside the bands, in this case outside the 2nd standard dev. and have a very small chance of being hit, but also not be too far, because the the RISK is too big.

I succeded finding the most optimal parameter setting, where everything lines up, here is it (purple bands =my band, teal bands=Bollinger bands)

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As you can see there is a 0.2260% change that the price is outside 2 SD, where on a normal distribution is 4.5500%, so its considerably better, as you can see from the previous post the tails are almost nonexistent, probably this distribution has a negative kurtosis.

Anyway, its may seem like a Holy Grail..... but not really.

The problem with it is that although at Bar[0+1] the probability is 0.2260%, but as the price goes on and on, the probability increases as the mean moves around and around, so much that inside 20 bars there is a 70% probability that the SL will be hit

So unless i scalp only 1 H4 bar, this is really useless, and then the trade will be random, as there is no useful way to predict any price bar-by-bar.

So the solution i thought about was to offset the deviation to have that outside probability for the next Bar[0+Y] bars implicitly, so i modified the indicator to look like this:

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But then the model is skrewed up, the red horizontal lines, represent the error, when the price is outside the deviations, and the nice 0.2260% probability turns into 53.08%, which is unacceptable, and doesnt carry any edge with it.

So definitely the price has a very hard time to adjust to my filter, and its hard to find a filter which adjusts the price.

The conclusion:

My current filter is not good enough, yet.
"There's a sucker born every minute" - P.T. Barnum
  • #34
  • Sep 18, 2014 4:42pm Sep 18, 2014 4:42pm
Quoting Proximus
I would like to dedicate this thread to the following questions:
Does the market have a constant mean ? If yes how to approximate it ?
If the mean is not constant, its variable as the market changes structure, how to approximate it given out sample size ?
What do you mean (no pun etc) exactly?

Of course the market, whatever it is, has a mean. But in no way is it constant. At all. on any timeframe.

Tho, in the modern FX markets, GBPUSD mean has varied between 1.75 and 1.80. More chance than anything tho, two similar economies with similar inflation/interest rates. No need for the pair to move large amounts to affect the mean.
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  • #35
  • Sep 18, 2014 5:12pm Sep 18, 2014 5:12pm
Quoting Aws1962
{quote} What do you mean (no pun etc) exactly? Of course the market, whatever it is, has a mean. But in no way is it constant. At all. on any timeframe. Tho, in the modern FX markets, GBPUSD mean has varied between 1.75 and 1.80. More chance than anything tho, two similar economies with similar inflation/interest rates. No need for the pair to move large amounts to affect the mean. {image}
Hehe i think you confuse the statistical mean with the statistical median, i`m looking for a mean here not the median.

The median is (HIGH+LOW) /2, while the mean is the middle price of the price's probability distribution.The mean changes too, because the market`s distribution changes too, its a heteroscedastic market.

Although in the large perspective the median is the mean, but in that case i need to hold trades for 10-15 years, which i`m not really up to.

I`m looking for a 1 day to 1 week window, as i specified on my first post, because the volatility distribution is swinging the most on these timeframes.
"There's a sucker born every minute" - P.T. Barnum
  • #36
  • Sep 18, 2014 5:48pm Sep 18, 2014 5:48pm
What are your thoughts on the Adaptive Moving Average??

This is mql5 but I am sure you could find a MT4 version.

http://www.mql5.com/en/code/10
What's it all about? It's all about money.
  • #37
  • Sep 18, 2014 6:00pm Sep 18, 2014 6:00pm
Quoting Innate
What are your thoughts on the Adaptive Moving Average?? This is mql5 but I am sure you could find a MT4 version. http://www.mql5.com/en/code/10
There are more variants to the moving averages than there are grains of sands in the desert, just look here how many MA's are there

http://en.wikipedia.org/wiki/Moving_average

I didnt had time to check all of them.

However just by looking at it with my eyes, i can see that its has small lagg, but its not that smooth as an EMA.I dont think its any better than a general ARMA model, but maybe i`m wrong, anyway when i`ll have time i shall test it.
"There's a sucker born every minute" - P.T. Barnum
  • #38
  • Sep 18, 2014 7:16pm Sep 18, 2014 7:16pm
Ok i here is the 2ND generation of my filter.

I had no other way of quantifying the precision, than to take trades off them and measure the expected profit.

The FIRST generation had an EP of 0.21 which was lame, and almost random, not really an edge.

My data comprises 11+ years on H4 bars, but i only looked at close price for now, because i looked for longer term periods.The spread was set to 20 pipettes, for E/U since thats a reasonable on backtest to prepare for the worst case scenario.

This one has an expected profit of 1.65, which is much better than 0.21

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Although not a holy grail, yet, but we are getting there eventually

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"There's a sucker born every minute" - P.T. Barnum
  • #39
  • Sep 18, 2014 8:54pm Sep 18, 2014 8:54pm
What is the win rate for above back test?
Holy grail, pls pm
  • #40
  • Sep 19, 2014 5:27am Sep 19, 2014 5:27am
Quoting Proximus
{quote} Hehe i think you confuse the statistical mean with the statistical median, i`m looking for a mean here not the median. The median is (HIGH+LOW) /2, while the mean is the middle price of the price's probability distribution.The mean changes too, because the market`s distribution changes too, its a heteroscedastic market. Although in the large perspective the median is the mean, but in...
No, I really am not confusing mean and median. Every 6 year old in the country knows the difference and what I showed was the mean.

Also, the median is high+low/2, so I really don't know what the hell you are talking about.

I can show you a chart of the mean for any currency over any time frame if you want, but there is no value to be gained from doing so.
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