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Range bar charts are Normal charts!

  • #21
  • Apr 29, 2014 2:44am Apr 29, 2014 2:44am
This is a recurring pattern in FF. Statistics must lead to an indi. An indi must lead to a set of trading rules. A set of trading rules must lead to an EA. Which in turn must lead to a trade explorer.... sad.

Well if it is the only thing you're interested in... have a look at the chart and spot the bullish reversal patterns where the background is green and the price is in the second or third lowest sub-band. Same story for the bearish patterns where the background is red and the price is in the second or third highest sub-band. Think in term of R:R.
No greed. No fear. Just maths.
  • #22
  • Edited 4:36am Apr 29, 2014 4:20am | Edited 4:36am
Quoting PipMeUp
{quote} 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.
Thanks for that. So I think you mentioned earlier that one of the nice properties of the Kalman filter is that it tends to split the time series equally (above/below) the filter. I take from your description above that this KF is based on the price and not the non-causal FIR filter, so it should split the price equally above and below.

And on second thought, isn't it the price returns that are normally distributed rather than the underlying price series? So is your KF based on price returns? Price retains its fat tails regardless of which sampling method is used. Or am I missing something?

Quote
This is a recurring pattern in FF. Statistics must lead to an indi. An indi must lead to a set of trading rules. A set of trading rules must lead to an EA. Which in turn must lead to a trade explorer.... sad.

Well, that didn't take long.
  • #23
  • Apr 29, 2014 4:32am Apr 29, 2014 4:32am
Quoting grin
{quote} I do not see how this can be true.
There are lots of ways to sample a time series. The obvious and most common way is to sample based on equal time periods. In this case time is a linear function, but price or range is obviously not.

You can also sample based on range in which case you end up with something like a range bar or a renko, which both have different and interesting properties where price ranges are emphasized, but time is eliminated from the equation.

You can sample by ticks or volume so you get linear ticks or volume respectively with price characteristics similar to that of a time-based chart.

You can move the series from the time domain to the frequency domain and back again.

There is no right or wrong answer here but there are generally tradeoffs for each type of analysis. When you sample something anywhere above 1 tick, you give up some information and hope to gain other information that can be used to benefit for analysis.
  • #24
  • Apr 29, 2014 5:16am Apr 29, 2014 5:16am
Quoting moomooforex
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.
It can be worked out by using a binary tree as you did above where 1 pip is the minimum move and the tree stops when the max range is hit. Then just by counting up the ending frequencies based on how many ways there are to reach a certain path. If you have a 20 pip range bar then it is prohibitive to work out the tree by hand.

Quote
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?

Nice job! Basically you have worked out the "ideal" probabilities of hitting each bar change amount given a strict 50/50 proposition. Actual market probabilities can be slightly higher or slightly lower than the ideal probabilities and this can also vary over time. The question is whether those divergences from 50/50 persist or not or provide any opportunity. Based on past analysis of an other bar type I would guess that the divergences are transitory and that while they persist they represent a market inefficiency but may not be stable enough to base a strategy solely on this data.
  • #25
  • Apr 29, 2014 7:24am Apr 29, 2014 7:24am
Quick correction: For this implementation the purple line is an IIR filter to get "only" 40 bars lag.
Quoting FXEZ
Price retains its fat tails regardless of which sampling method is used. Or am I missing something?
Quote
And on second thought, isn't it the price returns that are normally distributed rather than the underlying price series?
That's all the point of the thread. In RBC the price is NOT fat tail and cherry on the cake the 7-bar and more returns are normally distributed as well as the trend (slope of a filter). The prices returns for 1 bar are distributed as the M-shaped (bimodal) distribution.
Quote
So I think you mentioned earlier that one of the nice properties of the Kalman filter is that it tends to split the time series equally (above/below) the filter.
I don't remember I said this. I don't know in fact. But it is true for the lowpass filter. A lowpass removes the frequencies above the cutoff frequency. The complement are the residuals. They are
detrended and therefore will oscillate around 0. Because on top of that they are normally distributed they will be, in average, as many above and below the zero line.
Quote
I take from your description above that this KF is based on the price and not the non-causal FIR filter
The lowpass filter is based on the prices anyway ;-)
The FK is:
Attached Image

What is great is that n1, n2 and n3 are all normal noises (unfortunately not white). But what are their means and variances? You need this information to build the covariance matrix of the KF.
From the histograms you can see that all the three have zero mean.
For the variances, you use the filter over the historical data and where the filter is defined
For n1 the variance of the signed distance between the filter and the price (don't forget to backshift the index: dist = price[t-40] - filter[t] because of the lag)
For n2 the variance of the slope of the filter
For n3 the variane of the curvature of the filter
=> the KF tries to estimates the values of the filter where it isn't defined yet from the observation of the price in the last 40 bars. Or in trader's word: what is the current mean and the current trend?
When you start a KF you need an initial state. This state is
mean0 = the last value of the filter 40 bars ago
trend0 = slope of the filter at this last value
curvature0 = curvature of the filter at the last value
=> you run a new KF for each new bar. I update the estimate of the variances every week.
No greed. No fear. Just maths.
  • #26
  • Apr 29, 2014 7:27am Apr 29, 2014 7:27am
Quoting FXEZ
{quote}Therefore, someone much more math inclined than I am could probably calculate the probability of each using some formula I'm not aware of.{/quote} It can be worked out by using a binary tree as you did above where 1 pip is the minimum move and the tree stops when the max range is hit. Then just by counting up the ending frequencies based on how many ways there are to reach a certain path. If you have a 20 pip range bar then it is prohibitive to work out the tree by hand.
This is where the iterated convolution comes.
No greed. No fear. Just maths.
  • #27
  • Apr 29, 2014 8:44am Apr 29, 2014 8:44am
How wrong is the result of the KF? I ran the filter over my historical database for E/U.
On the x-axis is the error on the position. On the y-axis is the error on the slope. 76.4% of the time the sign of the trend is correct.
There is room for improvement...
Attached Image (click to enlarge)
Click to Enlarge Name: KF_error.png Size: 114 KB
No greed. No fear. Just maths.
  • #28
  • Apr 29, 2014 9:47am Apr 29, 2014 9:47am
Quoting PipMeUp
This is a recurring pattern in FF. Statistics must lead to an indi. An indi must lead to a set of trading rules. A set of trading rules must lead to an EA. Which in turn must lead to a trade explorer.... sad. Well if it is the only thing you're interested in... have a look at the chart and spot the bullish reversal patterns where the background is green and the price is in the second or third lowest sub-band. Same story for the bearish patterns where the background is red and the price is in the second or third highest sub-band. Think in term of...
charting is an applied science :nerd:
  • #29
  • Apr 29, 2014 11:06am Apr 29, 2014 11:06am
Quoting PipMeUp
That's all the point of the thread. In RBC the price is NOT fat tail and cherry on the cake the 7-bar and more returns are normally distributed as well as the trend (slope of a filter). The prices returns for 1 bar are distributed as the M-shaped (bimodal) distribution.
Ok then I'm not sure if I agree with the assertion that range bar prices are normally distributed. Perhaps the sample of prices that you studied appears to be normal. This sample of prices doesn't seem normally distributed. For instance:

Inserted Code
hist(Close,breaks=40,prob=T)
curve(dnorm(x, mean=mean(Close), sd=sd(Close)), add=TRUE, col='red')
 
qqnorm(Close)
qqline(Close,col='red')
 
dc = diff(Close)
hist(dc,breaks=40,prob=T)
curve(dnorm(x, mean=mean(dc), sd=sd(dc)), add=TRUE, col='red')
The upper plot is the distribution of close prices of a 20 pip range bar on EU. It appears to be skewed right and with higher kurtosis than the normal line (red). It doesn't appear to be a normal distribution to me, but perhaps it is closer to normal than the 60 minute chart. The qqplot shows the presence of fat tails. The lower pane shows the price differences and has a bimodal distribution.
Attached Image (click to enlarge)
Click to Enlarge Name: RBC_distribution_3.png Size: 7 KB

The hourly chart prices almost appear bimodal in the upper pane, with higher kurtosis and a fat tail showing on the right where they look skewed. The upper chart appears to be less normal than the upper range chart. The qqplot shows more deviation from the normal line than the range chart's qqplot and also the presence of fat tails. With my eye, the qqplot of the hourly chart doesn't look that different from the qqplot from the range bar chart, but the hourly has clearly fatter tails and deviates more from normality. The bottom plot of hourly price changes has a very high kurtosis with fat tails.
Attached Image (click to enlarge)
Click to Enlarge Name: EU_H1_distribution_3.png Size: 7 KB
  • #30
  • Apr 29, 2014 11:27am Apr 29, 2014 11:27am
I said 7-bar momentum.
Inserted Code
if (dev.cur() == 1) x11()
layout(c(1:2, 3:4))
 
path <- paste0(BASE_DIR, "EURUSD-RG20.csv")
data <- read.csv(path, sep=";")
 
oneBarMomentum <- diff(data$Close, lag=1)
hist(oneBarMomentum, breaks=300, probability=TRUE)
fitN <- fitdistr(oneBarMomentum, "normal")
curve(dnorm(x, mean=fitN$estimate["mean"], sd=fitN$estimate["sd"]), col="red", lw=2, add=TRUE)
qqnorm(oneBarMomentum)
qqline(oneBarMomentum,col='red')
 
sevenBarMomentum <- diff(data$Close, lag=7)
hist(sevenBarMomentum, breaks=300, probability=TRUE)
fitN <- fitdistr(sevenBarMomentum, "normal")
curve(dnorm(x, mean=fitN$estimate["mean"], sd=fitN$estimate["sd"]), col="red", lw=2, add=TRUE)
qqnorm(sevenBarMomentum)
qqline(sevenBarMomentum, col='red')
Attached Image (click to enlarge)
Click to Enlarge Name: qqplot.png Size: 12 KB


EDIT: Add the range data
Attached File(s)
File Type: csv EURUSD-RG20.csv   2.1 MB | 573 downloads
No greed. No fear. Just maths.
  • #31
  • Apr 29, 2014 11:32am Apr 29, 2014 11:32am
H1 for comparison
Attached Image (click to enlarge)
Click to Enlarge Name: qqplot-H1.png Size: 10 KB
No greed. No fear. Just maths.
  • #32
  • Edited 12:10pm Apr 29, 2014 11:57am | Edited 12:10pm
Hmm. I don't know how I missed that subtle but important point! I must be tired These plots are interesting. They all show thin tails. But it looks like on the range charts that it may be due to gaps in the data rather than the underlying distribution. The 7 bar momentum qqplot for the range chart looks very flat and so I can see what you mean regarding normality.
  • #33
  • Apr 30, 2014 4:13pm Apr 30, 2014 4:13pm
Quoting FXEZ
{quote}Nice job! Basically you have worked out the "ideal" probabilities of hitting each bar change amount given a strict 50/50 proposition. Actual market probabilities can be slightly higher or slightly lower than the ideal probabilities and this can also vary over time. The question is whether those divergences from 50/50 persist or not or provide any opportunity. Based on past analysis of an other bar type I would guess that the divergences are transitory and that while they persist they represent a market inefficiency but may not be stable enough...
Thanks for the reply FXEZ. I understand what you have said, but unfortunately the rest of this thread is now well beyond my current capacity. Perhaps in a few more months I can come back to it and it will make more sense.

Cheers
  • #34
  • May 2, 2014 4:37am May 2, 2014 4:37am
Quoting moomooforex
{quote} Thanks for the reply FXEZ. I understand what you have said, but unfortunately the rest of this thread is now well beyond my current capacity. Perhaps in a few more months I can come back to it and it will make more sense. Cheers
It takes some time to work through some of these concepts, such as what is a probability density function (PDF) and how to interpret a distribution (histogram) plot. I'm still learning and have had some new ideas because of this thread - thx PipMeUp! Yes, I'm playing in R with distributions again.

If someone is looking for a way to apply the concepts as related to trading, there is an interesting paper written by John Ehlers called Inferring Trading Strategies From Probability Distribution Functions that talks about one way to go about this type of analysis. While I don't agree with all of the methodology or conclusions in that paper (for instance that the Fisher transform makes your data nearly Gaussian: page 7 paragraph 2 - it should be more Gaussian), I think it presents ideas that can be used to extract useful trading information from a PDF.

By the way, here is a Q-Q-Plot Tutorial if you or anyone reading this wants to learn how to interpret that flat(ish) line in the charts posted above. As it was used in the plots above, the q-q plot can be used to visually determine if a given distribution is normal, or if it deviates from normal, in what way it does so. But more generally, it does the following:

Quote
The quantile-quantile (q-q) plot is a graphical technique for determining if two data sets come from populations with a common distribution. A q-q plot is a plot of the quantiles of the first data set against the quantiles of the second data set. By a quantile, we mean the fraction (or percent) of points below the given value. That is, the 0.3 (or 30%) quantile is the point at which 30% percent of the data fall below and 70% fall above that value.
  • #35
  • Dec 18, 2016 2:58am Dec 18, 2016 2:58am
Quoting PipMeUp
H1 for comparison {image}
I might be stupid.... but what's the point of above text,charts,magic,Kalman filters.... Any practical output??? Or usable conclusion? 
Gauss, tails fat or not, do they predict the market?

 
 
Beware of robber banks (RB), bad advisors.
  • #36
  • Dec 18, 2016 8:38am Dec 18, 2016 8:38am
Quoting Not-KPMG
{quote} I might be stupid.... but what's the point of above text,charts,magic,Kalman filters.... Any practical output??? Or usable conclusion? Gauss, tails fat or not, do they predict the market?  ÂÂ
They are called statistics. It has little to do with the market prediction, however it shows how the chart behaves from the perspective of probability.
  • #37
  • Last Post: Feb 22, 2017 3:41pm Feb 22, 2017 3:41pm
I feel like a 747 jet flew over my head.

To deep for me at this point.
Solutions ONLY!!!
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