Statistics in Technical Analysis

Beginner Questions
1

I am starting this thread to offer a place for people to discuss with reference to evidence the statistical value or edge offered by the multitude of tools available in technical analysis.

There are a lot of tools available and a lot of rules that we are told rule the markets. It’s my hope here for us to test and experiment with those rules and laws to see if we can see any worth in them ourselves. I am sure some of the more seasoned people here will have tested these tools themselves before I however have not and figured it would be fun to share my thoughts and results here.

I encourage everyone and anyone to post in this thread. In the course of this thread I hope we as developing traders will all learn something of worth and maybe highlight some excellent tools and debunk some others. A lot of technical analysis is down to the observers perspective but I still feel that seeing some of the numbers behind the tools being applied and tested will be interesting.

[B]Posting Rules:
[/B]

  • All arguments made must be supported with none anecdotal evidence. The claims should all be testable by anyone else.
    This is a relaxed forum after all so don’t worry about going over board with evidence and spreadsheets but if you make a claim back it up with some proof that others can check themselves.

  • No cherry picking results.
    Systematically test ideas and don’t just pick highlights of tools working.

  • Results sample sizes must be large enough to offer value as a rough outline your sample size should be over 50.

  • Always be polite to one another keeping emotions in check.

Feel free to discuss the analysis I or anyone else presents, but remember in this thread the focus is on evidence and results. If someone asks you why you think something the answer should be based on facts and figures not emotions and beliefs.

It’s not about the money you make or the money you loose it’s about the theories we all see discussed and used here and everywhere.

2

There is a common belief in technical analysis that higher highs bring more higher highs, and that lower lows indicate future lower lows.

I will now look at the idea that when price makes a higher high another higher high will follow. I have drawn out on an hourly chart price swings as I see them on an hourly chart for the EURUSD pair.


If the following price move makes a higher high it scores 1. If the previous low is taken out then it scores -1. If there is a range between the the high and the low then the eventual break out will be counted.

100 price swings that broke higher highs have been counted between the 15th of August and Today.

The results from my tests show:
There were 58 higher highs following a previous break higher and 42 lower lows following a previous break higher.

So my conclusions from this are that there is a 58% chance that there will be another higher high following a previous break higher.

Next thing to look at is the idea that when price makes a lower low another lower low will follow. Again the same tally system is used to investigate this theory.

Looking at 100 examples on the EURUSD chart where price broke the previous low downwards there were 62 lower lows and 48 higher highs. Suggesting that there is a 62% chance of seeing lower lows following a lower low.

Having said this however this was just a look at what price did following a higher high or lower low. It did not in anyway look at entries or exits. That is to say simply trading a buy when price breaks a higher high will not lead to a system with a 58% win rate. That is a whole different thing to look at.

Other things I wish to look at:
Does the wave count matter? Does the initial upward breakout after a string of lower lows offer a larger probability of another higher high than when a higher high occurs after a string of them?

I don’t know but something I’ll look at soon I hope.

3

I have plotted a 200 simple moving average on the EURUSD 1H chart applied to closing price. I am going to count out 64 instances where price has come into contact with this average and then note if it acted as a support or resistance or if price broke through. The data taken from June up until today.


I’m sure someone could easily back test this with an EA but i’ll do it manually for now.

So if price reacts to the 200 SMA as support or resistance it gets a 1. If it breaks through it gets a -1. What counts as a reaction? If price bounces off the line within 2 candle sticks I count it as a reaction. If price crosses by with two closed candle sticks it’s a breakthrough.

Price bounced 24 times and crossed for more than 2 candles 40 times.

That’s telling me that in this test there is a 62% chance that price will break through the 200 SMA on the hourly chart. That is to say that the 200 SMA is not acting as a support and resistance.

I’ll do some more evaluations later on when I get some time. When doing this like everything else a lot of “What if’s” come to mind. I’ll probably have a play about with them too later.

4

Great thread woolo!

I understand the time taken to do this manually, but it would be interesting to compare these results over different time frames.

I have not tested it myself, but my hunch would be that a 200 week SMA would have greater ‘strength’ than a 200 minute one

5

Edit: Most the stuff that follows is incorrect but i’ll leave it here anyway.

[B]Probability and it’s importance in trading.
[/B]

There is frequentist probability and subjective probability. The probabilities we are dealing with are a mixture of the two.

Frequentist probability is what people generally think of when they are told about probability, it the percentage value that an outcome will happen if you repeat something many many times.

Subjective probability is a probability derived from someones personal judgement. They are not based on formal calculations and reflect the persons opinions. In trading this would come about through anticipating news impact on a market. For example buying apple shares prior to a keynote speech where you anticipate a new iGadget to be released.

Primarily in this thread the things being looked at will be from the first type of probabilities. Measurable qualities but with a bit of subjectivity when dealing with price patterns.

Anyway in all theories of probability:

P(True) + P(False) = 100% or 1.

An example of a probability is rolling a die. You have a 1/6 probability of getting a six, or 16.6%.

But what are the probabilities of getting two sixes? This is what is called a successive event.

[B]Successive events:
[/B]
To find the probability of successive events you multiply the probabilities together.

So in your die example we wish to know the probability of rolling two sixes in a row. One six after the other.

So we take the probability of the first dice getting a six. 16.6% and we multiply that by the probability of the second die getting a six, also 16.6%.

P(0.166) x P(0.166) = P(0.0275)

So we see that the probability of scoring a double six is 2.75%.

You could apply this reasoning to certain market events. Although the market is not ruled solely by probability it’s worth being aware that things like group psychology and human events influence the market.

Ignoring these influences for the time being with this understanding we can interpret the odds of something repeating itself within our analysis.

[B]Mutually Exclusive Events:
[/B]
You add the probabilities together.
What are mutually exclusive events? Two events are independent if the outcome of one event does not change the probability of the outcomes for the next event.

Using die as an analogy again when you roll the first die the outcome of that roll has no impact what so ever on the outcome of the roll of the next die.

So lets say you are rolling die and you want to find the probability of getting one six with two die. You would add the probabilities.

P(0.166)+P(0.166) = P(0.332)

That is to say there is a 33.2% probability of getting one six between the two throws.

[B]Why does this matter?[/B]

Well this is the rule that inspires traders to combine indicators, theories and or patterns. Lets say you have an indicator that when oversold gives a 20% probability of giving you an entry at the low of a move. Lets then say you have another indicator built off of completely different formulae that has a 33% probability of letting you buy the low. Independently those indicators would offer no statistical edge but combined you are given the 53% probability of entering on a low.

Probabilities are just one piece of the pie that make up a successful trading strategy. But in this thread I’ll continue to look at the probabilities of certain approaches and start to eventually combine them into tradable methods based purely on a probabilities alone.

Hopefully this is a little bit more insight into why i’m bothering with this thread.

6

I’ll give it a go. I can’t really do the weekly with a large sample just because of my data feed, I’ll give the daily chart a go though as that’s one where the 200 SMA has been mentioned many a time on investopedia etc.

7

very interesting thread! could you do the same test with h4 and daily? would be awesome!

8

Sorry for jumping in to your thread with this woolo, as it is not on topic with what you are discussing at the moment, but I thought I would add it as you are discussing statistics.

Shortly before the new year I looked at pivot points and the % of time price reached any given zone (ie. how many times did price use the zone between say R2 and R2/R3 midpoint as the high for the day, or the zone between S2 and S2/S3 midpoint as the low for the day)

This is what I found. Please keep in mind thought hat this was for the EUR/USD and I would be reluctant to use the same probabilities on any other pair without independently testing them first)

[I]Using a standard pivot indicator on the EUR/USD pair,–

Trading Days:

2011 - 260 days

2012 - 260 days

2011/2012 - 520 days

RESISTANCE

Days price hit and/or went above R2 but DID NOT reach R2/R3 mid-point:

2011 - 15.38%

2012 - 16.9%

2011/2012 - 16.15%

Days price hit and/or went higher than R2/R3 mid-point but DID NOT reach R3, (including days detailed above):

2011 - 5.77%

2012 - 6.9%

2011/2012 - 5.58%

Days price hit and/or went above R3, (including days detailed above):

2011 - 1.54%

2012 - 3.5%

2011/2012 - 2.5%

SUPPORT

Days price hit and/or went lower than S2 but DID NOT reach S2/S3 mid-point:

2011 - 16%

2012 - 18.1%

2011/2012 - 17.88%

Days price hit and/or went lower than S2/S3 midpoint but DID NOT reach S3 (including days detailed above):

2011 - 5.8%

2012 - 4.6%

2011/2012 - 5.58%

Days price hit and/or went below S3 (including days detailed above):

2011 - 3.5%

2012 - 1.54%

2011/2012 - 2.5%

So there you have the things that keep an international jet-setting playboy like myself busy when I’m not internationally jet-setting playboying.

But what do we take from such thrilling information? Well, since we are continually being reminded by those in the know, that forex trading is a business of probabilities, I suppose the probabilities are this:

On any given day, if price was to reach R2 or S2, probabilities are roughly a 6 to 1 chance in your favour that price will reverse before it reaches R2/R3 or S2/S3 mid-points for THAT day. So there is a good chance that somewhere between R2 and the next mid-point, or S2 and the next mid-point would be the High/Low for THAT day.

Incidentally, why do I keep high-lighting the word THAT? Well I’ll tell you why. The stats detailed above are only of use for THAT days trading since what is R3 or R2 or S2 or S3 or ANY pivot level for TODAY, can correspond to a totally different level tomorrow. Today’s R2 can be tomorrows Pivot point, so if you are mad enough to use any of the stats above as part of your thinking in taking a trade, REMEMBER the stats are only good for the SAME TRADING DAY you took the trade. Tomorrow you have to start again.

So, moving on, if price was to carry on through R2 or S2 and hit the mid-points between R2/R3 or S2/S3, there is roughly a 18 to 1 in your favour chance that price will reverse before it reaches R3 or S3 for THAT day. Chances are therefore very good that somewhere between the mid-points and R3 or S3 would be the high or low for THAT day.

Should price actually get to R3 or S3, there is roughly a 40 to 1 chance in your favour that price will reverse before it goes too much further. In the two years worth of data that i looked at I did not see price hit R3/R4 mid-point, or S3/S4 mid-point on one single occassion.

It did actually cross my mind as to whether it would be possible to predict what zone would be the high and low for the next day going from what zone price reached today. I fear I may be an old man before I cracked that particular little enigma code though LOL!![/I]

[B][U]I had posted this before and later these stats were updated by JohnLeonard to include this:[/U][/B]

[I]For the EUR/USD (the past 406 trading days with daily pivots calculated at the NY close)

If price opens above the pivot (but below R1):
Price will go beyond the R1 level 52.7% of the time.
Price will drop below S1 only 34.6% of the time.

If price opens below the pivot (but above S1):
Price will drop below the S1 level 57% of the time.
Price will go beyond R1 only 35.3% of the time.

How far and how often price will go beyond the R1/S1 levels was kindly provided by HoG.

*The 57% found for EUR/USD is a bit of an anomaly. For the GBP/USD, the percentages are a much more even 53.2 and 53.3, respectively. Other pairs seem to track much more closely with the GBP with only a slight variation here and there. Averaged, the EUR 57 and 52.7 percentages come to 54.8% which actually falls right in line with GBP and the rest.

So what does this tell us? Pivot points actually can be one of the few leading indicators out there (they are calculated at the close for the next trading day). By going long at the start of every day when price opens above the pivot is obviously not a trading system in and of itself but it does help overcome one very important hurdle – it beats the spread on most of the majors which is actually no small feat. Most “systems” are really nothing more than random entries and using pivots can help eliminate some of the randomness. More importantly, pivots can also keep the trader out of those trades which are stacked against him by 65% (shorting when price opens above the pivot and expecting it to reach the S1 level and vice versa). A 65% chance that price will NOT get to a certain level? Well… I find it useful.

Pivots can also act as predictive trend lines. If today’s pivot is above yesterday’s pivot and price opens above today’s pivot then the percentages are skewed even more. Instead of having to overcome that 65% obstacle the percentage increases to around 70%.

Only taking trades on the right side of the pivot, combined with some other trading method(s) such as supply and demand levels, price action, etc., should at least give novice traders a fighting chance at long term profits and possibly assist veteran traders that have just never really considered using them.

[/I]

Like I say woolo, sorry for barging in with this, thought it may be useful though.

9

No need to apologise, it’s this kind of thing thats awesome and fascinating really. I’ll give it a proper read through.

10

I would assume theoretically your answer and calculation is misrepresentative, because a trending market will have a higher percentage of (your first sentence), and that a ranging market will have a lower percentage of (your first sentence). So maybe you should split your back testing for both camps and compare the %'s to each other?

edit: can we give suggestions on things for you to test? I am very busy just doing my own trading and blogging, but I always got a bunch of ideas, and it wouldn’t hurt if you start crunching some numbers to verify my own strategies lol :slight_smile:

11

Hi, I will definetly join in here, its one subject Im also wery interrested in:)

12

Woolo,
This is a great idea for a thread. I look forward to any and all future contributions you and others make (and I hope to make several of my own) and also realize the time commitment that can be involved in undertaking such studies. I have only one suggestion for readers. If you have questions about the testing, methods, results, how the conclusions were reached, etc., then that is, IMO, worthy of discussion. If you just want someone else to test this, test that, try a different timeframe or pair (which are, in fact, legitimate queries) then please test them yourselves and report your findings back on the thread.

I am sure Woolo is looking for contributions and discussions much more than he is looking for an increased workload!

13

This is not true, you can’t add probabilities like that. The probability of getting one six between two throws is 1/65/6+5/61/6 = 0.277…

And probability of getting at least one six per two throws is 1/6+5/6*1/6 = 0.30555…

But the probability of getting either 6 or 5 in one throw is P(5)+P(6) = 0.332

This is again not true - you can’t add probabilities like that and get such a conclusion. If we denote: A - probability that 1st indicator has given successive entry and B - probability that 2nd indicator has given successive entry.

“completely different formula” does’t mean P(A or B) is zero.
For calculating probability of successive entry if both indicators are giving signal at the same time you should use one of these formulas:

P(A and B) = P(A) + P(B) - P(A or B)
or
P(A and B) = P(B)P(A|B) = P(A)P(B|A)

200SMA is one of those things that have become a self-fulfilling prophecy. I would rank it as number one price derived indicator, also I think it is by far more effective on daily chart than on any other timeframe.

Brokers differ as some have 6 trading days in a week and some have only 5 (not even mentioning that closing prices differ) Indicators become good if everyone is looking at the same picture, but if I expect that traders using some other brokers see different 200 day SMA readings it becomes hard to use it for things like support/resistance.

Also… some are looking at 40 week SMA which is same time period, but readings again differ.

14

I think this is the whole purpose of the thread. Is the 200SMA more effective on the daily? “I think,” though you could certainly support such an assertion with various arguments, doesn’t prove whether it is or isn’t. Is the 200SMA a self-fulfilling prophecy? Only if enough traders (retail or institutional) use it to make it so. If so, then the 200SMA will have some predictive value on various timeframes and across the various pairs. Otherwise, it will not.

It may very well be the number one price-derived indicator (other than candles or bars) but I don’t think any of us have any way of demonstrating this to be true.

If some are also using the 40 week SMA, even if readings/results differ, there should be a general correlation between the two.

I took statistics back in college. The only thing I vividly remember about the class was the instructor was totally hot. She was a young brunette in her mid 20’s with piercing blue eyes and had a penchant for wearing [very] mini-skirts. It was a very popular class [for guys, anyway] but I am sure that most of us had a hard time concentrating and thus, most of the formulas you posted didn’t leave the same lasting impressions on us the instructor did!

15

200 day SMA doesn’t get crossed all that often. If one defines what successful support/resistance means one can probably backtest that by hand pretty well.

But yeah, there are a lot of a lot of so called ‘‘price behaviours’’ that are hard to backtest. Human eye is well trained to mention confluences, patterns and similarities that are difficult to put in code.

Damn! Well, at least you were concentrating on what happens in front of auditory. From my experience I can say that it is also very hard to concentrate if instructor is boring, but auditory is full of peer girls that are as bored as you are.

16

This is the problem in fx with statistics ( what did Winston Churchill say about them - ’ I only believe in statistics that I doctored myself’ )

MA’s are that - they are average and moving, in fx every single retail trader in the world can react at the 200 and it would be meaningless - the only possible effect is that non retail know and take advantage of what retail may do at that level.

On jan 02 fibre was 3180 at close - on Jan 16 fibre was 3280 at close. Statistics told us that we had 86% chance that a winner was to short the euro on Jan 02 and exit Jan 16.

On Jan 23 fibre was 3300 close - on Feb 11 close was 3400. Statistics told us that we had 86% chance that a winner was to short the euro on Jan 23 and exit on Feb 11.

So I ask this simple question - when I post next that you have a 86% chance, based on statistics, that the the euro will rise - would you put live money on it? - or would you trust your own judgement?

Source:- Moore Research Inc.

17

Hi guys, I worked on finding out when during the day the High/Low was made, IF you knew if it was a down day or up day…(In other words, if your bias is its down, the high(where you should get in) happens at this time).
you can read all about it here:
http://forums.babypips.com/forextown/51170-testing-theories-about-price-statistical-processor-r-excel-etc.html

or you can just see the results:

This is GMT time, and the data comes from 15min Oanda datafeed, exported from MT4, 1999 to 1 week ago :slight_smile:
[EDIT] Forgot to mention, saturday/sunday candles have been removed before processing the data :slight_smile:

Here is the R code for testing/modification:
[C] When A high is made in a Low day/oppisit for up day - Pastebin.com
Just copy the code into R and pick your data(needs to be less than daily to work

I’ll try out the touch and reverse strategy on pivots/200SMA etc when I get a chance

[B][EDIT 2] Btw, forgot to add that this is EUR/USD :D, im running AUD/USD and GBP/USD and will post shortly[/B]

18

another thing I want to test, is when(during the day) we get the longest streak of bullish/bearish candles :slight_smile:

19

Check this out:

AUD/USD:
Pretty destinctive peak first thing GMT

GBP/USD:

2 peaks, 1. thing, and 2. peak around 11 :slight_smile:

I find it wery interesting how sharp the peaks are, there are noe ‘side peaks’, its just suddenly 11, and then its ON :slight_smile:

[EDIT] Sorry for the huge images, no idea how I can change that :confused:

20

I’ll edit the post shortly. My maths skill are not what they used to be as you can no doubt tell. Could you expand on calculating the probability for successive entries? In a sort of “Explain it like i’m 5” type of way?