Z-Score Kit

October 5, 2014: New 00sd Looping Bands.mq4. It will go into the SD kit, but can be downloaded separately below for now.

August 28, 2014:
The entire set of Basic Indicators has been updated and re-worked. Ready for 600+
It is necessary to download and install all new versions from foot of this post.
Documentation and thread outlay will follow.

SD-Kit has been added as a second Zip and can be downloaded below.
New in there is Average Joe.mq4

+++++++++

Documentation and MT4 software relating to the Standardized Z Score and Standard Deviation as encountered in Trading.

One will find things of practical interest concerning the former in the Z-Score Kit, but no detail on theory of the SD.

On Wikipedia several excellent articles address the subject, among them:

http://en.wikipedia.org/wiki/Normal_distribution
http://en.wikipedia.org/wiki/Standard_score

Where one can also find this perfect visual reference
http://en.wikipedia.org/wiki/File:No...and_scales.gif

Knowing the z score on a price value for example, allows one to situate it under a Bell Curve on the horizontal axis, while obtaining information on associated probabilities. Very theoretical?

Not really. If one turns an image of a Bell Curve 90° to the left, the view is as in the market. Price going up and down and passing the SD scale markers as its z score "tag" changes. Crossing the SMA, hitting a BB? What's up after crossing that BB into the wild blue yonder?

The z score will tell you.

A new thread was started recently concerning the z-score: Gramps' Greedy Indicator @ Forex Factory
It should be read more or less in parallel with this one, as both threads have a common source of interest.
Also, posts there have additional details on the z-score that should have been better posted here.

//+----------------------------Downloads----------------------------------+
October 5, 2014 - New:
Please find a description in post #52.

August 28, 2014
A new Zip has been added. An SD-Kit to collect follow-up material on the original Z-score subject: Average Joe.mq4 is also new and found along with Mu.mq4 and the Bell demo previously seen in post #24.
If not yet done, also please download the updated code for the basic z-score indicators below, and read up on use of Customizer.mq4

All new versions of the Basic Indicators can be found in this zip: It has all current files and is needed to replace all versions in use.
Check the ReadMe please. Old chart-outlays will be invalid mostly, as graphical elements may have been renamed.
A simple tpl has been included to quickly load most indicators.

The old documentation is still useful until updated. Please find copies below: "Intro and Basic Indicators.doc" along with "Essential Information.doc" are sort of required reading to start using the Basic Indicators.

For a quick start, try "At Price.mq4" on any pair: It needs a BB and setting of the corresponding SMA Period from the Input Box.
Give it some room on the right for display.

All *.mq4 go to MQL4\Indicators and any *.tpl to \templates.

A ways back innovation brought about machines that could capture the interaction of sound waves and the air or any other medium.
Truly, ‘t were a wondrous thing and the talk of the day.



The greatest Diva of them all hit the highest C, and a master flutist gave his best for these rare recordings.



Obviously not.
Just a bunch of BBs and another one at 314 sigma.

But one can carry the analogy over to computers and Standard Deviation and turn it from an abstract mathematical field into just another medium, which can be visualized and inspected.

Lessee, more BBs and colors, higher sigma …

Oops, my spouse is calling! “Quit playing with your terminal already and go do the chores”.
Same old, same old.

Thanks for opening this thread, good to see you again !

Hi Mr. Apip short from Switzerland.

This is Brian Twomey, author of Wiley/ Bloomberg Press "Inside the Currency Market". btwomey.com to prove I'm real and factual.

I've followed older posts here regarding the Z Score and found many interesting yet not totally factual. I would know respectfully since my new E-book coming shortly is all about how to properly trade currency pairs using Z Scores with standard deviations.

When we talk about Z Score Slopes, we only address the Beta Coefficients. For non mathematical persons, since a Z Score is a standard deviation all we are doing is calculating a correlation so a correlation then gives us the slopes. Therefore we will see the usual EUR/USD vs USD/CHF with a correlation in the 0.91 range almost on a constant historical basis. its a Zx X Zy / N concept. Without a Z Score, we would need to calculate the Beta Coefficient first then calculate the correlation in a two step process.

Using critical value Z Scores on short term averages 5--20 SMA's is a 50/50 win loss rate, a loser for trends and questionable for range trading days. So the early 2001 Stocks and Commodities article written by the girl whose name escapes me was a nice try to trade BB's against critical values but wholly questionable in its true profit potential. Better maybe to try frequencies against critical values since both are pure mathematical values.

What I do respectfully is use the true Z Score/Standard Deviation in its most purest form because I find the accuracy perfect and because I don't have to rely on an indicator of any sort that gives me questionable price action readings.

Therefore who needs a chart to determine prices, nobody. Who uses the word volatility anymore, nobody since volatility is long seen way in advance of any price move. I define volatility as information priced in the markets since my Z Score readings tell me something is coming and when.

I'll stop here with hope to engage in other discussions as you post. Take care a pip short, your friend Brian Twomey

Hello Brian,

Thank you for taking the time to post your #1 here and I’m certainly looking forward to studying your coming E-book. I found nothing much freely available on accessing the z-score with indicators, and even less on its application in trade, except as in “the” BB system view.

The article by Veronique Valcu was the only one that stood out, a bit like a tree in the desert actually. No doubt the subject has been thoroughly researched by professionals, but the applications are proprietary and the theoretical treatment mostly inaccessible without the fundamentals (duh).

When you say “not totally factual”, you are being very kind. I was not happy with the way the second part of the thread was developed, and in the end left unsubstantiated. This has led me to separate the seemingly conventional from the more “iffy”, and keep the option of editing open.

I would be interested to hear if you find that the basic indicators in the kit address the Z-Score in its pure form, such as you put it to use. That has been a primary purpose at least within the context of use on MT4.

Beyond that, I took a stab at inference, which amounts to building statistical cargo-cult code models. I shall take care to be very clear on that point when applicable.

In that respect; sorry for stealing the Z Slope. I am handing it right back, hopefully none the worse for wear. It was coined as a variable name and got carried over into the presentation.

I shall much appreciate if you care to comment on things as you see them, and try to incorporate any other factual corrections or pointers to a more adequate treatment of the subject.

apipshort

Hello A PipShort,

Much to say. I don't think you will ever find the Z Score used in conjunction with another indicator because it would take much time to test. I would like to do it myself once the final details are completed with my e-book but I don't hold out much hope personally.

And the reason for this is the Z Score/Standard Deviation is a matrix that must be used together, one can't work without the other. Its a pure price system trade of averages so in this instance, why would we even want to trade it against another indicator since its an all encompassing trade system on its own. Its mouth dropping accurate if one knows what they are doing. Yet its simple.

I'm in the US but my friend in London is looking at your Z kit and sending me charts and information. My fallacy is computer illiteracy so my friend is helping so we will have an answer how it works and how its doing. I want to know myself.

I was merely explaining the Z Slope as it relates exactly to statistics and correlations. The 2 pi aspect must be viewed in the context of the Standard Normal Curve as 1 / Square root of 2 pi --e minus power of ( z squared / 2). What we want here is the height of y so we can draw our bell curve accurately in relation to our x values, which is our standard deviations and Z Scores.

I could go on and on about this topic but one aspect is relevant that you addressed and that is the calculation of time in relation to the Z Score. The question must be how do you want to look at time. Do you want to view it as a risk measure or viewed in relation to time in your trade.

As a risk measure, you may want to look at Spot price ( in Logs) X e (2.718) X Z X SD X square root of time. Time has two factors, square rooted or as a stand alone. How its employed is a matter of choice. What is surmised here is the question, is the Z Score stetched in relation to the standard deviation and when.

This stuff may look like rocket science on its face but I assure you, its not only quite simple but highly rewarding.

Take care, I'll be back, Brian Twomey

Hi A Pip,

I respectfully hope you will continue to post. I'm here to work with you not against you my friend. Brian Twomey

That is a given from your contributions, which are much appreciated.

I've printed out your last post, and am off in pursuit of missing y dimension ;-)

Participants here on Platform Tech are actually all unflappable characters with the best of dispositions. Can't go wrong.

apipshort

A note to readers:
Some material has been added to the "Experimental Folder", and the zip updated.

Hi A Pip,

Glad to see you back. I'm just now viewing literally my averages with your Z Kit and I find the results not bad at all. I will delve deeper though and report back.

I assume the Y dimensions must be the probabilities. That's good, helpful and important regarding Z Scores because you shape the overarching Bell.

I'll be back as you post, take care Brian Twomey

Am now looking forward to the guidenotes on probability,
typically I avoid reading manuals until all parts are dismantled
and beyond reassembly, thankfully, I read, well skimmed,
the nodding donkey manual, fabulous, easy on the eye too,
and it answers the time lord issues where I've been adding multiplying
trying to get Z scores and SMAs relevant in different timeframes,
( I cant get things to work when I type in 32,134 into the parameter boxes )
So apip thanks for the additions to the experimental bit -
Brian, will there be an explanation on beta coefficients and Y axis ?
Good posts and stuff

Hello aminpip,

Glad you find useful things here.

I shall put back a program that shows these and more data at the same time. There is a bit of math there that needs checking first though.

Can you tell me in what indicator you have this problem? Maybe try 32.134 with a dot.

apipshort

I respectfully take Mr. A Pip's Z Score methodology a step further. And all this information is fully outlined by example and charts in my upcoming E-book called Using Z Scores to Trade Foreign Exchange and other Financial Instruments.

First, trading by using Z Scores is a pure price system approach by targeting the Standard Deviation by use of the Z Score as the trade signal. Now this Z Score can be viewed from many angles. Let's take the question of probabilities.

Imagine a Bell Curve cut down the middle and we address prices on the right side of the middle cut line. Now suppose we find a Z Score of say 0.4750. What do we have? First we have a 1.96 Z Score or 1.96 Standard Deviations with an area of 47.50 %. But that addresses only the right side of the cut line in Z Score, Standard Deviations and the percentages of the area on the right side. We want to know what this means for the whole area.

So 4750 X 2 = 0.9750 in probability terms. Those prices factored for the right of the cut line is actually at a 97.50 percentage context if we look at the entire area under the full Bell. This says prices are completely stretched at the 97.50 confidence interval and must come back so we implement a trade back to somewhere near the cut line. If the Trade was the EUR/USD and we went short, then we also want to go long USD/CHF.

A probability is the Y axis that comprises the overall Bell of the Z Score/Standard Deviation X Axis. Probabilities can be viewed as percentages or areas under the curve or calculated as exact heights so the bell can be drawn exactly. Every X and Y expands and contracts as prices move up and down so therefore does the bell expand and contract.

A Beta Coefficient is a fancy word to mean correlations (Pearson's r) or better said a comparison of Standard Deviations. But since we are dealing with Z Scores, the terms change. With both we want to know the slope of the regression line or the change in X to the change in Y. Let's say we want to compare EUR/USD against USD/CHF in Z Score terms.

Since a Z Score is a Standard Deviation, we don't have to factor correlations. We just need the slope. The formula is Zx X Zy / N. Zx = the EUR/USD and Zy= USD/CHF. N= number of periods or number of moving averages. This formula could easily say SDx X SDy / N.

Let's say we have 7 moving averages for each pair calculated to Z Scores. Z Score X price at each average and record for each pair. Add then divide by 7 for each. Then divide the EUR and USD/CHF numbers together. Now we have a beta coefficient factored against each average or your b slope. What you will find is the correlation or beta coefficient between the EUR/USD and USD/CHF to be around 0.90, 0.91. That says both are almost 100 % opposite each other. So a long Euro is a short USD/CHF. But you also know this will occur across all averages.

I'm Brian Twomey also author of Inside the Currency Market: Mechanics, Valuation and Strategies. At btwomey.com

I'll be back

I shall put back a program that shows these and more data at the same time. (There is a bit of math there that needs checking first though.

Can you tell me in what indicator you have this problem? Maybe try 32.134 with a dot.)

Hi, when I was messing around in lower TFs 1 min to 15 min I thought it would be useful to have the median from higher TFs on the chart. In the SMA indicator I would type in the numbers like 7200. I recognise these numbers from the table you placed at the end of nod donkey guidance notes. Quite often the MA would sulk and put back in a number like 14. So I would try 3600 or something similar and experience the same difficulty. Sometimes the MA would accept larger numbers. In the end I just put a fat arrow on the (1 to 15 ) minute based TFs based on the Z score and median from the daily, weekly charts, depending which direction I guessed the price was moving in. The nodding donkey thing kind of resolves this, so thanks.

Hello Brian,

Assuming that the z-score is nailed down, within the context of mt4, at least to where a coder can easily work it into the program logic and display it adequately, we would have met a first requirement for modeling what you have just outlined.

However, that is also where I come to a full stop, conceptually. No idea what one is supposed to do with the darn critter.

Now you lay out a complete blueprint for integrating it into a high caliber statistical setup.

That is wicked! I suppose you envision this setup live on a trade screen and not in a math program or spreadsheet. Sorry if I’m off, but I did think of trying live bell curves, say they are on a hard-to-do list.

Also, I never viewed things on a multi-pair basis. You mentioning correlation however, made me think of a screenshot of just those two pairs:

EUR/USD and USD/CHF, H4, Jul 13 2012


Nodding Donkey at bottom.
In the chart a hypothetical average SMA, with its equally hypothetical sigma structure, at price scale. The “real” mean TF z-score, as found in donkey appears at the right, visualized as muZ. (sorry, a lousy shot, never meant to show it.)

This is a view of the Average Joe setup, which you may or may not have seen before it was removed.
It is in want of a proper review, I should PM you about that later if I may.

So please discount anything in the chart window as unsubstantiated.

What stands out first is the mirror image impression, but when one runs down the numbers it can be mind boggling. And this would just go on and on. Even the value of (here incorrectly named) Z Slope clicks.

apipshort

PS. Do you think we already have the building blocks to whip up your beta coefficient ;-) or does it require averages of z-scores over N periods?
When you say 7 averages, you presumably mean from 7 TFs?

Newest: Nodding Donkey Indicator and Doc in Experimental Folder.

I suppose you envision this setup live on a trade screen and not in a math program or spreadsheet

gets my vote !

The numbers in that table are not meant as input for a program, sorry for any confusion there.
They represent, in minutes, how long a particular TF lasts.

Please tell me the name of the indicator and in what option you tried to use these numbers. I will off course try to set you right.

Regards, apipshort

Hello, a while back not related to this thread or the original gramps, I was trying to put moving averages for a year say in a low one minute 5 minute or 15 min time frame. I was trying to achieve that by placing say 7200 in the parameter and the moving average just wouldnt play. It may be that there weren't 7200 periods for it to collect, so I lowered the numbers till it accepted it. Your work on nodding donkey has solved this for me. Plus your explanation on time I found helpful.

Is the new nodding donkey modified, because it seems slightly different to the older version. Thanks apipshort for all your help.

Ok, got that first part, likely as you say a problem with bar count. If you hover the mouse, bottom of screen over the name tab of your chart, it will show how many bars in the TF. One can load more.

Yes Donkey was modified, slightly.

Z Slope is now named Z Spread, it is not a formal statistical element. Just made up in the code as an internal yardstick.
I moved a lot of graphics blocks into function calls.

It is best to do away, with what you have from before. Keep copies if you are not sure. I have added a last edit date to all mq4, so one can tell if anything is newer.

That's it, I hope ;-)

Hi A Pip,

Your system is almost exactly where it needs to be to achieve the most reliable system out there.

To nail down the true Z Score for every pair I think is doable for coding purposes. Yet know I speak not with proper knowledge of computers and programs. If you've achieved the point in your coding where you are presently then you've got this thing covered.

Once you know the Z Score, you have to target a Standard deviation. But which one? That's why you need a set of averages, short, intermediate and long so you can see the full market to factor which average you want as your target.

You may see one day's market where the 5 day average may be your trade of the day therefore implemented for the short term. The next day may see a 100 or 253 day as your target therefore a trade targeted for the longer term. Trends are the best because its easy calculated yet range days offer the same profit potential with a slight more work. What you see with the Z Score/Standard deviation is your full market context.

What Z Scores, Standard deviations, Correlations, Beta Coefficients and probabilities are is straight statistics.

How about this for correlations. If the EUR/USD goes up and the USD/CHF goes down, is the market buying Euros and selling US Dollars and how would you know. Well EUR/CHF answers that question since it should rise along with the EUR/USD. If it doesn't, its a false EUR/USD move so that high can be sold.

The Beta Coefficients can easily be added to your system. its a matter of doing it one time then its permanently done because correlations hardly change or change little. What's the difference between a .88 and .91 correlation between the EUR/USD and USD/CHF, nothing really, a few pips. Not enough to make a giant difference.

My last two cents respectfully. The perfect system I think must have a full market view to satisfy traders of all sorts. Too many of these small retail traders are trading on the 1 and 5 minute charts. What that says to me is they don't have understanding of their pairs or this market so they know not what they do. Ask yourself who is your target market.

A true system must attract not only these retail guys but longer term and more professional traders since they are the guys trading and spending on a regular basis. If these guys can be shown a system where all that is required is hit a button with reliability, then you are a big winner.
Check out my friends at futurestruth.com for examples to what I'm saying here.

I'll be back, Brian

Speechless, to be sure.

Won't be ready before next week.
Clients waiting on perpetual motion, anti-gravity ...
Well, they'll just have to manage, I suppose ;-)

apipshort