Thread: Statistical mean of the market [quant corner]

I Want to dedie this thread into the following questions:Does the market have a mean? If yes to approximate it? If the mean is not constant, its variable as the market changes structure to approximate it given out sample dimensions? My research to come up with the ideal version that models the expression.
From the expression I mean the http://en.wikipedia.org/wiki/Mean,not the median, that's the separator half of the distribution in case of the price the half line of the full market which for example aproximately the (alltime highest highs alltime lowest lows) /two

So because the market is ever changing, I fixed the sample size to 1440 M1 pubs which will be 1 day of data, because its likely a plausible separator between samples since the volatility distribution can also be separated by the minimal liquidity nights when the London SE and NY SE is closed.
So I chooses 1440 to be out sample size, possibly it could have been 7200 aswell that's 1 week, since there is a volatility gap between Friday afternoon and Monday morning aswell.

That I've analyzed various moving averages to locate the mean but the majority of them werent receptive to the price.Here are the classical moving averages, I always used Median Price,dont confuse it with market median, which can be (High[position] Low[position]) /2 since it reflects the market better than Close price.

These averages have PERIOD 1440, M1 pubs, MEDIAN PRICE,SHIFT 0
And by colour are the following: Yellow=Smoothed Straightforward,Blue =Simple(Arithmetic),Purple=Exponential Weighted, Red=Linear Weighted



since you can see the linear weighted is the most reactive, and not as lagging, and the smoothed is your worst,and the simple moving average is pretty far from a mean.

And I noticed these classical moving averages are as far away from a statistical mean as the sky is from the floor, so I took my abilities and coded my own moving average, and I've been experimenting with it.Set also to PERIOD 1440, and its own orange coloured, while another MA's are the same colour but set them dashed so it becomes more visible:






since you can see its much more responsive to the price, and not as much lagging.Also I'm quantifying the variance of the price around my moving average to try and gauge from the dispersion of price around it.
I assume the the variance is, the more accurately my MA measures the mean, the problem is that if I increase the size of my MA's filter then the variance declines almost to 0, and also my MA becomes identical with a PERIOD 1 moving average.

So its almost like a period 1 moving average is the mean of this market, that is, that each tick is the current mean.However this is absurd because the MA doesnt tell anything about the trend or the prejudice in the price.

So that I would need a perfect equilibrium between LAGG AND ACCURACY or Put simply the mean which the price will hover around the maximum, which is not itself (maybe not the previous price).

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LATEST MODEL: https://www.nigeriaforextrading.com/...ervations.htmlMY RESEARCH GOAL: 5,000% GROWTH (BASED ON BACKTEST)

”I have not failed. I've just found 10,000 ways that won't work”
#8213; http://www.goodreads.com/author/show...homas_A_Edison

”I have not failed. I've just found 10,000 ways that won't work”
#8213; http://www.goodreads.com/author/show...homas_A_Edison

Originally Posted by ;

”I haven't failed. I've just found 10,000 ways that will not work.” #8213; http://www.goodreads.com/author/show...homas_A_Edison

Haha thanks un inspirational.

Anyway if it might have workedthen I might have conquered 6 of the top 10 people currently in the FF 2014 yearly Leaderboard, which is quite a saying, of course these are live accounts and mine isn't even a demo test just a backtest, but still it might have been like I counted at the spread.

Since my typical yearly gain would have been: 9.48%,without lot scaling, which isn't realistic because the lot has to be climbed as the account grows, and my risk policy could have been to have a steady % of account based risk, so my expansion could have been much larger. However, concerning pips its accurate, my very best filter could have gave me 7,672.7 pips at total or 948.03 yearly pips, wheareas just: Breza,doktorforex,kdxrider3 and julius3419 had outperformed my study.

Which is funny because although it's only a fictional if scenario, yet these 4 men have very high succes in FX trading in live accounts, while probably the majority of the other traders are struggling to get breakeven or even 1-2%/month if lucky which is interesting as there's surely a difference between succes in FX trading, there is no middle a here you will find either constant losers/breakeven men OR immensely succesful traders, there's just no middleground.

So this pushes be because there's an advantage there, estimating these numbers, as those men who found it are instantly becoming very succesful, while the rest are just forever fighting.

Originally Posted by ;

”I haven't failed. I've just found 10,000 ways that will not work.” #8213; http://www.goodreads.com/author/show...homas_A_Edison

Haha thanks un inspirational.

Anyway if it might have workedthen I might have conquered 6 of the top 10 people currently in the FF 2014 yearly Leaderboard, which is quite a saying, of course these are live accounts and mine isn't even a demo test just a backtest, but still it might have been like I counted at the spread.

Since my typical yearly gain would have been: 9.48%,without lot scaling, which isn't realistic because the lot has to be climbed as the account grows, and my risk policy could have been to have a steady % of account based risk, so my expansion could have been much larger. However, concerning pips its accurate, my very best filter could have gave me 7,672.7 pips at total or 948.03 yearly pips, wheareas just: Breza,doktorforex,kdxrider3 and julius3419 had outperformed my study.

Which is funny because although it's only a fictional if scenario, yet these 4 men have very high succes in FX trading in live accounts, while probably the majority of the other traders are struggling to get breakeven or even 1-2%/month if lucky which is interesting as there's surely a difference between succes in FX trading, there is no middle a here you will find either constant losers/breakeven men OR immensely succesful traders, there's just no middleground.

So this pushes be because there's an advantage there, estimating these numbers, as those men who found it are instantly becoming very succesful, while the rest are just forever fighting.

1 Attachment(s) You seem depressed now prox'. I think that the collapse of your experimentation is a result of the fact that you try to predict the market. And that you overfit your information...

Unlike you, I do not believe the distribution of the market is changing from one distribution to another. I also don't think it's predictible. I'd ask one question to these 4 traders: Can you predict the market or do you follow the market? .

A Bernouilli distribution has one parameter: the probability of the favorable result. A Gaussian distribution has two parameters: the mean and the variance. A Cauchy: style and scale. A Beta: alpha and beta, etc.. . I think that these parameters are changing. I believe they are changing randomly and constantly. Your optimal EMA 25 is the mean EMA over your dataset. Envision a Gaussian that variance and mean change over time each driven by a separate random walk. A random walk is weak at seeing it is state space: it means it will stay more frequently than not close to where it's currently. This means the Gaussian will look exactly the same. A tendency remains in place for some times. A range does as well.

You state the market could be seen as the sum of two distributions, one for the ranges and one for the tendencies. Let's call them T and R. You searched for (R T) as one distribution. Now let's rewrite it w*R (1-w)*T. When w is close to 0 market is trending. When w is close to 1 market is ranging. Now let's say w it pushed by a random factor (bound between 0 and 1). What I've been attempting to do thus far would be to estimate all those hyper-parameters. For the trend I satistied. What my filter finds in time is close to what a human finds in hindsight. However, it fails at the ranging phases.

The film clearly shows this in the period from March to April. Where has attracted a flat line my filter locates a double shirt. I really don't think that it could be made better without knowning the future.

At first I thought that a range was no more than a flat trend. I think that it is something else. If you place w=0.5 above you obtain a volatile trend. Also it appears to exist two kinds of ranges: choppy (seems like nothing) and steady (resembles a sine wave). Each with its own distribution (stable =Arcsine and Altered =Gaussian). Or a mix of both. Or merely a Beta(a,b), that can approximate a Gaussian pretty well and is your Arcsine for alpha=beta=1/2.

1 Attachment(s) You seem depressed now prox'. I think that the collapse of your experimentation is a result of the fact that you try to predict the market. And that you overfit your information...

Unlike you, I do not believe the distribution of the market is changing from one distribution to another. I also don't think it's predictible. I'd ask one question to these 4 traders: Can you predict the market or do you follow the market? .

A Bernouilli distribution has one parameter: the probability of the favorable result. A Gaussian distribution has two parameters: the mean and the variance. A Cauchy: style and scale. A Beta: alpha and beta, etc.. . I think that these parameters are changing. I believe they are changing randomly and constantly. Your optimal EMA 25 is the mean EMA over your dataset. Envision a Gaussian that variance and mean change over time each driven by a separate random walk. A random walk is weak at seeing it is state space: it means it will stay more frequently than not close to where it's currently. This means the Gaussian will look exactly the same. A tendency remains in place for some times. A range does as well.

You state the market could be seen as the sum of two distributions, one for the ranges and one for the tendencies. Let's call them T and R. You searched for (R T) as one distribution. Now let's rewrite it w*R (1-w)*T. When w is close to 0 market is trending. When w is close to 1 market is ranging. Now let's say w it pushed by a random factor (bound between 0 and 1). What I've been attempting to do thus far would be to estimate all those hyper-parameters. For the trend I satistied. What my filter finds in time is close to what a human finds in hindsight. However, it fails at the ranging phases.

The film clearly shows this in the period from March to April. Where has attracted a flat line my filter locates a double shirt. I really don't think that it could be made better without knowning the future.

At first I thought that a range was no more than a flat trend. I think that it is something else. If you place w=0.5 above you obtain a volatile trend. Also it appears to exist two kinds of ranges: choppy (seems like nothing) and steady (resembles a sine wave). Each with its own distribution (stable =Arcsine and Altered =Gaussian). Or a mix of both. Or merely a Beta(a,b), that can approximate a Gaussian pretty well and is your Arcsine for alpha=beta=1/2.

Originally Posted by ;

You sound depressed today prox'. I believe the collapse of your experimentation is due to the fact that you attempt to forecast the market. And that you overfit your information... Unlike you, I don't think the supply of the market is changing from 1 supply to another. I don't think it's predictible. I would ask 1 question to these top 4 traders: Can you call the market or do you comply with the market? . Even a Bernouilli distribution has one parameter: the probability of the result that is favorable. A Gaussian distribution has two parameters: the...

Well it sucks if 3 weeks of work is worth nothing. One thing I did found out and that's that the market is really.

I dont even think that this strategy will work, because as you said the parameters will change randomly.

What I did is that I've measured the distribution of the chance itself, of switching between up and down candles from near close, and initially glance there is a small amount of benefit in shorting, precisely a 0.2057031732155% greater probability of red than green candles, although maybe not so quickly, because although theere are red candles (of EUR/USD I'm talking ) the dimensions of these candles is greater for UP candles.

What I did is that I slowed the likelihood of each candle with its average size, so that's:
50.2057031732155 % *16.281656862502 pipettes / 100 = 8.17432031606921 of DOWNSIDE MOVEMENT
49.7942968267845 % * 16.4255877374142 pipettes /100 = 8.17900591351193 of UPSIDE MOVEMENT

Which if you substract ought to be 0, that isn't, there is an offset of 0.00468559744272 in favor of up, which imply that the EUR/USD needs to proceed down that amount till it becomes 0 to strike the ideal equilibrium state. This could be used as a currency flow indior:
The probability of direction * the size of the movement in that path = The cash flow in that path

And when its at times, or the offset is large then the market should balance itself and undo.

This pretty much demonstrates that the market is really a zero sum game, no new cash is entered directly in the market (or atleast not right, because although the market capitalization rises, it's not increased by the amount of new players brand new funds but rather by the increase of the money supply of that particular currency). So that is an economic happenings compared to a mathematical one.

The possession of the money really can change, of course the big banks rock at this, but the market itself doesnt increase this way. And its logical, the more I thought about it, as for every BUY commerce you need a SELL transaction, so no matter how much cash I have in EUR, there has to be an equivalent amount (relative to the exchange rate) in USD for me to be able to execute the transaction.

So if I put 10.000 #8364; at the market, the market's size doesnt increase, because the mere fact that I got the EUR currently in my pocket, is currently a player in the market, not an energetic one, however a passive because you already use it for shopping or . While if I decide to change this 10.000#8364; into 12,436.85$ afterward I shrunk the #8364; market, but I've increased the USD market, yet the joint EUR/USD market remained the exact same size. It is logical.

Though the EUR/USD combined market is still the exact same regardless of what, the only way it can increase it through inflation, or the looseing of the currency supply, because the buying power may vary relative to the GDP, after a CB decides to adjust the money supply to the GDP subsequently the market rises. It is just economics if I think about it.

If both currencies are inflated at precisely the exact same rate then the exchange rate doesnt alter, but the market capitalization increases. If they are not the market still grows, however in the favor of 1 currency vs another. Since the FED printed a lot of dollars and devaluated the USD to pay off the debt, another CB's have had to devaluate it to keep the market in balance, so this is most likely the most important reason why the FX market has growth to 8 trillion, and not because Joe the normal trader found FX trading out of Google Ads...

So probably later on I'll be looking deeper into the economic mechanism supporting the market, because it makes more sense compared to guess the probabilities.

Originally Posted by ;

You sound depressed today prox'. I believe the collapse of your experimentation is due to the fact that you attempt to forecast the market. And that you overfit your information... Unlike you, I don't think the supply of the market is changing from 1 supply to another. I don't think it's predictible. I would ask 1 question to these top 4 traders: Can you call the market or do you comply with the market? . Even a Bernouilli distribution has one parameter: the probability of the result that is favorable. A Gaussian distribution has two parameters: the...

Well it sucks if 3 weeks of work is worth nothing. One thing I did found out and that's that the market is really.

I dont even think that this strategy will work, because as you said the parameters will change randomly.

What I did is that I've measured the distribution of the chance itself, of switching between up and down candles from near close, and initially glance there is a small amount of benefit in shorting, precisely a 0.2057031732155% greater probability of red than green candles, although maybe not so quickly, because although theere are red candles (of EUR/USD I'm talking ) the dimensions of these candles is greater for UP candles.

What I did is that I slowed the likelihood of each candle with its average size, so that's:
50.2057031732155 % *16.281656862502 pipettes / 100 = 8.17432031606921 of DOWNSIDE MOVEMENT
49.7942968267845 % * 16.4255877374142 pipettes /100 = 8.17900591351193 of UPSIDE MOVEMENT

Which if you substract ought to be 0, that isn't, there is an offset of 0.00468559744272 in favor of up, which imply that the EUR/USD needs to proceed down that amount till it becomes 0 to strike the ideal equilibrium state. This could be used as a currency flow indior:
The probability of direction * the size of the movement in that path = The cash flow in that path

And when its at times, or the offset is large then the market should balance itself and undo.

This pretty much demonstrates that the market is really a zero sum game, no new cash is entered directly in the market (or atleast not right, because although the market capitalization rises, it's not increased by the amount of new players brand new funds but rather by the increase of the money supply of that particular currency). So that is an economic happenings compared to a mathematical one.

The possession of the money really can change, of course the big banks rock at this, but the market itself doesnt increase this way. And its logical, the more I thought about it, as for every BUY commerce you need a SELL transaction, so no matter how much cash I have in EUR, there has to be an equivalent amount (relative to the exchange rate) in USD for me to be able to execute the transaction.

So if I put 10.000 #8364; at the market, the market's size doesnt increase, because the mere fact that I got the EUR currently in my pocket, is currently a player in the market, not an energetic one, however a passive because you already use it for shopping or . While if I decide to change this 10.000#8364; into 12,436.85$ afterward I shrunk the #8364; market, but I've increased the USD market, yet the joint EUR/USD market remained the exact same size. It is logical.

Though the EUR/USD combined market is still the exact same regardless of what, the only way it can increase it through inflation, or the looseing of the currency supply, because the buying power may vary relative to the GDP, after a CB decides to adjust the money supply to the GDP subsequently the market rises. It is just economics if I think about it.

If both currencies are inflated at precisely the exact same rate then the exchange rate doesnt alter, but the market capitalization increases. If they are not the market still grows, however in the favor of 1 currency vs another. Since the FED printed a lot of dollars and devaluated the USD to pay off the debt, another CB's have had to devaluate it to keep the market in balance, so this is most likely the most important reason why the FX market has growth to 8 trillion, and not because Joe the normal trader found FX trading out of Google Ads...

So probably later on I'll be looking deeper into the economic mechanism supporting the market, because it makes more sense compared to guess the probabilities.

I have followed this thread as among my ea's pivots (pun intended) on the MA so I was very curious about your results. Thank you.
I have previously studied the'finest' MA for my machine and came into the similar conclusions as you have. Ie the mean of the market keeps shifting, which makes it ridiculously difficult to pin the tail on the donkey.

I can't declare to have figured something out about the MA, but if I was planning to take additional study into MA's I'd focus on interrelationships.

Not sure where you want to take things, but I dont think you have failed in any way. Its not that easy. You were comparing your results with the top actors, I bet they would use a confluence of sign (unless they are nude traders) and your research into the MA is just 1 part of the confluence signal.

Anyhow back into interrelationships. I had mentioned it to you in the thread with regard.
Here:
Statistical mean of the market [quant corner] - Page 5 @ forum (just throwing ideas around, cant say they'll be effective )

This is only 1 appliion of local interrelationships (only MA's), no matter how the interrelationship I have been studying is between the MA and the ATR. There was a week in Dec 2008 on EURUSD my ea would struggle with in analyzing. Its an outlier (intense ) event that throws the data collection (you cited 2008 in your post above too ). One day I discovered this week was actually the week of the EURUSD's highest ever weekly ATR (something similar to 650 pips from memory) and I wondered if there was a link. You have to try out some thing right, although I'm aware that correlation does not imply causation.
It makes a bit of sense they are linked. If the ATR is high which means the delta's between each bars near (if you are studying the near or median etc it will be the same concept) will be bigger than'regular' market conditions. If I'm not mistaken it is these intense daily ranges which are skewing the data.

I have not got to the base of locating the link, I keep getting distracted looking at the rest of the pretty colours in the rainbow rainbow.
Initial research gives me the hunch that the interrelationship is polynomial. I want to do a lot more testing. I think the only way I will get a response is through a genetic algo.

Anyhow mate, I've got faith in you. Keep it up. The knowledge you have gained here will help you.