Range bar charts are Normal charts! | Forex Factory

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Range bar charts are Normal charts!

  • #1
  • First Post: Apr 28, 2014 7:37am Apr 28, 2014 7:37am
Here is a little finding of mine about range bar charts (RBC). For those of you who don't know what a range bar chart is:
http://www.investopedia.com/articles...erent-view.asp

Side note: I know a lot of you are using MT4. Unfortunately MT4 is unable to correctly build RBC. RBC must be build tick-by-tick. MT4 uses 1 min candles and interpolates the result. RBC are approximate on MT4. I built my RBC from tick historical data (source FXCM).

The only problem with the RBC is that one bar may take hours to appear or a bunch of them can pop up in no time. This is why they are perhaps better suited for automated systems. But this isn't what I want to show today.

I will show a comparison between RBC and usual time charts from the probabilistic point of view.

I'm sure all of you heard about the fat-tailed distribution of the markets. In finance, fat-tailed distribution (FTD) is associated with risk because extreme events occur "too often". In some FTD, like the Cauchy distribution, the probability of extreme events fades so slowly to zero that the risk is almost unbounded. Markets aren't Cauchy but near of.

Let's start by having a look at the distribution of the market movement from bar close to bar close (return). I use E/U H1 as a reference time chart. I use a range of 20 pips on E/U for the RBC.

Over the historical data, for each bar, let's count how many time a given move (X pips) occurred. The result is shown as a histogram. A Gaussian (normal) distribution is fitted to the charts. The time chart (left) shows the fat tails: it is where the histogram is above the normal distribution when it is almost zero on the left and on the right sides. The range chart (right) is more surprising with a bimodal distribution (two bumps). Also the time chart have the highest probability of a zero move (a doji), while the RBC has a probability of zero of having no move for the bar (per construction). The most probable move in a RBC is a full range move. This is explained because the big temporal moves are broken down into full range bars.
Attached Image (click to enlarge)
Click to Enlarge Name: range20vsH1.png Size: 7 KB
No greed. No fear. Just maths.
  • #2
  • Apr 28, 2014 7:39am Apr 28, 2014 7:39am
Quick reminder on moving averages
This is off-topic but it will be used shortly later. To compute a simple moving average (SMA) you sum up the N previous prices and divide by N. It can also be realized by multiplying the N previous prices by 1/N and sum up the results. The values 1/N are called weights. You can change the weights. For instance you can multiply the last price by 4/10, the previous price by 3/10, the one before by 2/10 and the fourth price by 1/10 and then sum the values. Here you have a Linearly Weight Moving Average (LWMA) of length 4. Note that the sum of the weights is one.

In the histograms, let's divide the count in each bar by the total number of bars. We get the probability of the returns. Now the histograms approximate the probability distribution function (PDF) of the movement of the price over one bar.

What is the probability of the movement of the price over two bars? Over N bars?
From the histogram one can build another histogram which answers these questions. The operation on the histogram is called a discrete convolution. To make it very simple, a discrete convolution is a moving average of a function with another function used as the weights. To get the distribution of a 2-bar move you perform a moving average of the histogram using the histogram itself as the weights. To get the 3-bar momentum histogram you run the same convolution over the result. And so on for the N-bar momentum. You always use the original histogram for the weights over the previous result. This is called an iterated convolution or power convolution.

Note that gaps make the range chart histogram go over the edges of the defined range of 20 pips. Yet this effect is very limited. The distribution of the RBC is quickly zero everywhere beyond the defined range. This is a so-called "compactly supported function". Central Limit Theorem says that any bumpy compactly supported function convolved with another such function several times will converge to the normal distribution.

On the picture below the first column is an idealized version of the RBC histogram and its 6 first iterated convolutions. The second and third columns are the real histograms built from the measurement of the N bars momentum of the historical data for E/U. The second column is the RBC 1, 2, 3, ... and 7 bar momentum. The third column is the same for a hourly chart. As predicted by the theory after 7 bars the distribution of the RB momentum becomes normal. The hourly N-bar momentum is never even near of a bell curve. It keeps its typical shape of a power distribution.

Attached Image (click to enlarge)
Click to Enlarge Name: n_bar_histogram.png Size: 24 KB
No greed. No fear. Just maths.
  • #3
  • Apr 28, 2014 7:42am Apr 28, 2014 7:42am
The trend
Since we are investigating historical data we can use non-causal filters. They are the filters which use data in the future. Let's use a very long period moving average. The moving average isn't a SMA. It is a finite impulse filter which approximates an ideal low pass filter. This is a good approximation of the trend. The coefficients are in the text file and are plotted below.
Attached Image (click to enlarge)
Click to Enlarge Name: filter_weights.png Size: 4 KB
[]

Let's see what it looks like on a H1 chart (left) and on a RBC (right). Both the charts show the same period of time (more or less).
Attached Image (click to enlarge)
Click to Enlarge Name: EURUSD-trend-H1.png Size: 32 KB
Attached Image (click to enlarge)
Click to Enlarge Name: EURUSD-trend-RG20.png Size: 28 KB


Let's do some stats. What is the distance between the price and the moving average trend? As you can see on the RBC the prices are normally distributed around the trend. It's not the case on the time chart.
Attached Image (click to enlarge)
Click to Enlarge Name: price_scattering_around_trend.png Size: 5 KB
[]

Because the moving average is very smooth we can use the first finite difference (MA[n] - MA[n-1]) as the slope of the MA. This is the histogram of the slope. Here again, for the RBC, the slope (i.e. the strength of the trend) is normally distributed and it's not the case of a time chart.
Attached Image (click to enlarge)
Click to Enlarge Name: slope_of_the_trend.png Size: 6 KB


What about the acceleration (how quickly does the trend change)? We get used to the result, aren't we!
Attached Image (click to enlarge)
Click to Enlarge Name: acceleration_of_the_trend.png Size: 5 KB
Attached File(s)
File Type: txt filter_coefficients.txt   5 KB | 658 downloads
No greed. No fear. Just maths.
  • #4
  • Apr 28, 2014 7:43am Apr 28, 2014 7:43am
The variance (volatility)
Markets returns exhibit volatility clustering. They are said heteroskedastic. The graph below is a running variance of 500 samples over ~50000 bars. In red you can see the variance of the time based returns. In blue you can see the variance of RBC is almost constant. Range bar charts are almost homoskedastic: they don't have volatility clustering. On a RBC a Bollinger band has a constant width.
Attached Image (click to enlarge)
Click to Enlarge Name: variance_of_returns.png Size: 8 KB
No greed. No fear. Just maths.
  • #5
  • Apr 28, 2014 9:36am Apr 28, 2014 9:36am
Ssssshh now they all know!
  • #6
  • Apr 28, 2014 12:48pm Apr 28, 2014 12:48pm
Quoting 9047
Ssssshh now they all know!
Yes, but now they also know that you know! But not all is lost, it no doubt flew over the head of 99.7% of the FF elite. I'm just waiting for the first MT4 indicator request.
  • #7
  • Apr 28, 2014 1:45pm Apr 28, 2014 1:45pm
so this test suggests that MA cross system shall perform better using a range-bar chart? sorry for my dumbness.

a very enlightening read, though i might have misread it, lol

Quoting PipMeUp
The trend Since we are investigating historical data we can use non-causal filters. They are the filters which use data in the future. Let's use a very long period moving average.
  • #8
  • Apr 28, 2014 1:48pm Apr 28, 2014 1:48pm
let's say, there's a certain price action trader, profitable trading price actions, you know, higher higher, lower low, 1,2,3 pattern, you name it......

assuming this profitable trader are profitable in both charts, this variance test might suggests that he will very likely suffer from much lower DD on range-bar than normal candle chart, right?

Quoting PipMeUp
The variance (volatility) Markets returns exhibit volatility clustering.
  • #9
  • Apr 28, 2014 4:43pm Apr 28, 2014 4:43pm
Quoting charvo
so this test suggests that MA cross system shall perform better using a range-bar chart?
It suggests that a volatility breakout trader will never find any opportunity because the volatility is almost constant. But a mean reversion trader using Bollinger bands has a good reason to try his system on a range bar chart.

Quoting charvo
let's say, there's a certain price action trader, profitable trading price actions, you know, higher higher, lower low, 1,2,3 pattern, you name it...... assuming this profitable trader are profitable in both charts, this variance test might suggests that he will very likely suffer from much lower DD on range-bar than normal candle chart, right? {quote}
He will avoid the huge bars against his positions at least.
No greed. No fear. Just maths.
  • #10
  • Apr 28, 2014 4:53pm Apr 28, 2014 4:53pm
Quoting FXEZ
{quote} Yes, but now they also know that you know! But not all is lost, it no doubt flew over the head of 99.7% of the FF elite. I'm just waiting for the first MT4 indicator request.
I can't code in MQL. Count me out for the mq4 file
For now I have this. The purple channel is the trend defined by an IIR filter. Its lag is 40 bars. It is shifted backward in time. The green and red indi is an estimator of where the channel will be when it reaches the current bar (it doesn't repaint).
Attached Image (click to enlarge)
Click to Enlarge Name: EURUSD-RG20-trend.png Size: 59 KB
No greed. No fear. Just maths.
  • #11
  • Edited 8:17pm Apr 28, 2014 7:19pm | Edited 8:17pm
Quoting PipMeUp
{quote} I can't code in MQL. Count me out for the mq4 file For now I have this. The purple channel is the trend defined by an IIR filter. Its lag is 40 bars. It is shifted backward in time. The green and red indi is an estimator of where the channel will be when it reaches the current bar (it doesn't repaint). {image}
How does your red and green line do in terms of this? (below)

Quote
As you can see on the RBC the prices are normally distributed around the trend.

Some info on the Central Limit theorem and how it applies to all types of distributions:
http://www.youtube.com/watch?v=EXKUN...otation_229192
www.youtube.com/watch?v=JNm3M9cqWyc
http://www.youtube.com/watch?v=FXZ2O...28115D3D8A2566
  • #12
  • Apr 29, 2014 12:11am Apr 29, 2014 12:11am
Quoting PipMeUp
The range chart (right) is more surprising with a bimodal distribution (two bumps). Also the time chart have the highest probability of a zero move (a doji), while the RBC has a probability of zero of having no move for the bar (per construction). The most probable move in a RBC is a full range move. This is explained because the big temporal moves are broken down into full range bars. {image}
PipMeUp, your maths is much better than mine and you kind of lost me in this thread, but isn't the above kind of obvious?

After all, Range Bar Charts don't care about the noise so all we interested in are where the price can be after n-pips move So, let's say we have a 3-pip range bar chart, assuming the price of a bar opens at 0, and moves one pip up/down at a time (smallest unit is a whole pip)... that means the there are only a finite list of possibilities for where the price could be at close of the bar. You could draw it out on a nice tree to see all the possibilities.

Ultimately the price could end up at +3, +2, +1, -1, -2, -3. Zero is not possible.

Therefore, someone much more math inclined than I am could probably calculate the probability of each using some formula I'm not aware of. I simply wrote a generator to generate all the possibilities and I came up with something like.

3: 25% (3/12)
2: 16.66% (1/6)
1: 0.0833% (1/12)
-1: 0.0833% (1/12)
-2: 16.66% (1/6)
-3: 25% (3/12)

I'm sure you could then use these probabilities over multiple iterations to calculate where the price will be n-multiples from now.

All we have done is grouped together the probabilities when iterating the 50/50 odds of the price going up or down 1 pip ... no?
  • #13
  • Apr 29, 2014 12:41am Apr 29, 2014 12:41am
Quoting moomooforex
{quote}After all, Range Bar Charts don't care about the noise so all we interested in are where the price can be after n-pips move So, let's say we have a 3-pip range bar chart, assuming the price of a bar opens at 0, and moves one pip up/down at a time (smallest unit is a whole pip)...
I would not call time as "noise". Range chart distorts impact of time.
  • #14
  • Apr 29, 2014 12:59am Apr 29, 2014 12:59am
Quoting grin
{quote} I would not call time as "noise". Range chart distorts impact of time.
By this same logic you could say that time charts distort the impact of range.
  • #15
  • Apr 29, 2014 1:03am Apr 29, 2014 1:03am
Quoting FXEZ
{quote} By this same logic you could say that time charts distort the impact of range.
I do not see how this can be true.
  • #16
  • Apr 29, 2014 2:48am Apr 29, 2014 2:48am
Quoting grin
{quote} I do not see how this can be true.
In this screenshot the range of the H1 bars is more or less 10-15 pips. But a single bar can be 6 times bigger. This can be seen as a distortion of the impact of the range. I hate this kind of bar especially when I'm long... I know the price won't come back (only dumb money buys that; it's not enough to push the price up). The fat tailed distribution of the time charts tells me that I will get those quite often.
Attached Image (click to enlarge)
Click to Enlarge Name: AUDUSD-H1.png Size: 9 KB
No greed. No fear. Just maths.
  • #17
  • Apr 29, 2014 2:57am Apr 29, 2014 2:57am
Quoting FXEZ
{quote} How does your red and green line do in terms of this? (below)
The line and its colors are the result of a Kalman filter. Because everything is normal everywhere I can use a plain good old simple KF; not an extended or unscented KF. The purple line (the lagging filter) is used to extract the (co)variance information using the past data. It is from this data collection I produced the various histograms. I also use it to "seed" the initial state of the KF.
No greed. No fear. Just maths.
  • #18
  • Apr 29, 2014 3:01am Apr 29, 2014 3:01am
Quoting PipMeUp
{quote} In this screenshot the range of the H1 bars is more or less 10-15 pips. But a single bar can be 6 times bigger. This can be seen as a distortion of the impact of the range. I hate this kind of bar especially when I'm long... I know the price won't come back (only dumb money buys that; it's not enough to push the price up). The fat tailed distribution of the time charts tells me that I will get those quite often. {image}
Multiplicity (6x) of your arbitrarily sized chunk of price move can be easily determined from a time based chart. Visual split is lost, but that is merely a visual preference. There is no range impact distortion.
  • #19
  • Apr 29, 2014 3:38am Apr 29, 2014 3:38am
Quoting grin
{quote} Multiplicity (6x) of your arbitrarily sized chunk of price move can be easily determined from a time based chart. Visual split is lost, but that is merely a visual preference. There is no range impact distortion.
The size of the chuck is perhaps arbitrary but the candle in the middle of the screenshot is objectively much bigger than all the other ones.

Visual split is lost = distortion of the impact of the range
=> maybe just a matter of wording.

Yet I agree that filtering out the time removes valuable information. How to re-introduce the time? An idea is to choose the range based on the "usual" time based volatility of the asset. What is the best range for E/U? I'm certain it's not the same as for E/G or G/J.
No greed. No fear. Just maths.
  • #20
  • Apr 29, 2014 4:05am Apr 29, 2014 4:05am
Certainly, it all can be fit such way. Would it provide any edge though?
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