I can't believe people fall into the Technical Analysis pseudo-science-ish analysis of the markets. It's like forecasting from chicken bones or tarot cards. It's non scientific and it's just a way to keep people away from profits. It's basically a scam, whoever invented it. It's like substituting science for mysticism.
So let's use science instead of mysticism, I will analyze the BTC_USD market scientifically in this article, with real scientific tools, and not quackery.
QUANTITATIVE ANALYSIS OF THE BTC/USD MARKET
First of all we determine what the market is, statistically. The BTC_USD market is a heteroskedastic joint probability distribution, where the current price is the random variable that is confined to this statistical distribution. The market is also a continuous time series, since it's a function of time as well.
Now let's analyze the properties of it. I have gathered daily price data from Blockchain.info, from the first datapoints available up to Dec 4th. In total we have a sample of 2302 points, and we will analyze this data.
Since it's heteroskedastic, we can't estimate the true characteristics because it is changing, however we calculate the aggregate properties of this sample.
| Sample Property (T=2302) | Value |
|---|---|
| Mean | 239.40 |
| Median | 143.56 |
| Minimum | 0.060900 |
| Maximum | 1151.0 |
| Standard Deviation | 251.40 |
| Coefficient of Variation | 1.0501 |
| Skewness | 0.75597 |
| Ex. Kurtosis | -0.53753 |
| 5% Percentile | 0.28030 |
| 95% Percentile | 697.55 |
| Interquartile Range | 420.94 |
So far so good, we see that it's not a normal distribution. It has a positive skew meaning that higher prices happened less times, and the bulk of the price was at lower or closer to the mean. It has negative excess kurtosis or it's Platykurtic, meaning that it has thin tails, the price stayed less time around higher levels. 95% of the price was below 697.55$ price level.
Let's plot a frequency chart (with 2301 bins) to estimate and view the sample distribution:
Obviously not a normal distribution, let's compare it to a normal distribution bell curve:
It's barely visible, that central spike is too big, so here it is with less bins:
Perhaps a density plot shows the distribution better:
Normality Tests:
Doornik-Hansen test = 810.393, with p-value 1.06027e-176
Shapiro-Wilk W = 0.856609, with p-value 1.37073e-41
Lilliefors test = 0.197649, with p-value ~= 0
Jarque-Bera test = 246.977, with p-value 2.34266e-54
All of them reject the null hypothesis, for normality, the heteroskedasticity is confirmed.
Spectrum Analysis
A spectral density graph reveals a lot about the concentration of signal into different frequencies or periods. Here is a top 10 breakdown of them, good to set moving averages around those numbers for example.
| Ω | scaled frequency | period | log spectral density |
|---|---|---|---|
| 0.00273 | 1 | 2302 | 15.459 |
| 0.00819 | 3 | 767.33 | 14.772 |
| 0.00546 | 2 | 1151 | 14.04 |
| 0.01365 | 5 | 460.4 | 13.218 |
| 0.02457 | 9 | 255.78 | 12.742 |
| 0.01911 | 7 | 328.86 | 12.734 |
| 0.03002 | 11 | 209.27 | 11.983 |
| 0.03548 | 13 | 177.08 | 11.893 |
| 0.02729 | 10 | 230.2 | 11.277 |
Auto-Correlation
For Autocorrelation tests we perform an ACF and PACF test.
The test shows us that the strongest correlation is at lag 1 level. Which means that the price is mostly defined by it's previous value, rather than older ones.
The Box-Jenkins method also tells us that:
Decay, starting after a few lags = Mixed autoregressive and moving average (ARMA) model.
It is minimum an ARMA(1,1) model with p=1, q=1. Since the first lag levels are the strongest.
I did a KPSS test for BTC_USD (including trend and seasonals):
| Variable | Value |
|---|---|
| T | 2302 |
| LAG | 502 |
| AIC | 30017.7 |
| Test | 0.0670265 |
| P-value > .10 (null hypothesis rejected) |
ADF test with constant and trend plus seasonal dummies:
- asymptotic p-value 0.1802 (null hypothesis rejected)
So d=1, and we also have seasonality. It's technically a SARIMA(1,1,1) model , a Seasonal ARIMA and it can be further estimated with "secret regressors", but I am not going deep into this, read my other analysis here, if you are interested in forecasting/modeling with regressors:
Volatility / Local Variance
The volatility of the price can be easily seen if we calculate the natural logarithmic difference:
As you can see, the volatility is going down as Bitcoin gets more mature and liquidity increases. The volume at LocalBitcoins is astonishing, so it probability has to do with it.
https://coin.dance/volume
The logarithmic difference function has the following properties:
| Sample Property (T=2301) | Value |
|---|---|
| Mean | 0.0040004 |
| Median | 0.0000 |
| Minimum | -1.0393 |
| Maximum | 1.0043 |
| Standard Deviation | 0.066946 |
| Coefficient of Variation | 16.735 |
| Skewness | 1.0119 |
| Ex. Kurtosis | 60.941 |
| 5% Percentile | -0.066603 |
| 95% Percentile | 0.090217 |
| Interquartile Range | 0.029708 |
| Missing Values | 1 |
QQ Plot
Here is a QQ plot of the BTC_USD against it's sample mean:
Gini coefficient
The Gini coefficient is used to measure statistical dispersion. It is widely used in economics to measure income inequality, but here it measures the inequality of the price distribution, or the smoothness.
Sample Gini coefficient = 0.572432
Estimate of population value = 0.572681
Range Mean Statistics
Since BTC_USD is heteroskedastic, it means that it's made up of different probability distributions joined together. We estimate the boundaries between the local distributions:
We determined that the price is best segmented in 49 segments, of the size of 47 observations, or days.
| date | range | mean |
|---|---|---|
| 2010-08-17 - 2010-10-02 | 0.1141 | 0.066584 |
| 2010-10-03 - 2010-11-18 | 0.438599 | 0.184284 |
| 2010-11-19 - 2011-01-04 | 0.097 | 0.264088 |
| 2011-01-05 - 2011-02-20 | 0.801002 | 0.642306 |
| 2011-02-21 - 2011-04-08 | 0.29 | 0.873304 |
| 2011-04-09 - 2011-05-25 | 8.1411 | 3.91267 |
| 2011-05-26 - 2011-07-11 | 26.5008 | 17.3969 |
| 2011-07-12 - 2011-08-27 | 6.0099 | 12.4839 |
| 2011-08-28 - 2011-10-13 | 5.34109 | 6.2073 |
| 2011-10-14 - 2011-11-29 | 1.82455 | 3.00614 |
| 2011-11-30 - 2012-01-15 | 4.29 | 4.52837 |
| 2012-01-16 - 2012-03-02 | 2.85555 | 5.63988 |
| 2012-03-03 - 2012-04-18 | 0.76706 | 4.9961 |
| 2012-04-19 - 2012-06-04 | 0.48112 | 5.15025 |
| 2012-06-05 - 2012-07-21 | 4.23 | 6.87492 |
| 2012-07-22 - 2012-09-06 | 6.63002 | 10.8339 |
| 2012-09-07 - 2012-10-23 | 1.9629 | 12.1282 |
| 2012-10-24 - 2012-12-09 | 3.08783 | 11.8449 |
| 2012-12-10 - 2013-01-25 | 5.79109 | 14.3668 |
| 2013-01-26 - 2013-03-13 | 30.1204 | 29.6119 |
| 2013-03-14 - 2013-04-29 | 190.88 | 107.013 |
| 2013-04-30 - 2013-06-15 | 45.959 | 118.065 |
| 2013-06-16 - 2013-08-01 | 44.1116 | 94.7816 |
| 2013-08-02 - 2013-09-17 | 34.47 | 114.173 |
| 2013-09-18 - 2013-11-03 | 102.38 | 148.598 |
| 2013-11-04 - 2013-12-20 | 925.9 | 691.525 |
| 2013-12-21 - 2014-02-05 | 321.71 | 788.192 |
| 2014-02-06 - 2014-03-24 | 250 | 626.464 |
| 2014-03-25 - 2014-05-10 | 184.7 | 465.133 |
| 2014-05-11 - 2014-06-26 | 239.98 | 567.415 |
| 2014-06-27 - 2014-08-12 | 84.91 | 609.379 |
| 2014-08-13 - 2014-09-28 | 170.14 | 472.612 |
| 2014-09-29 - 2014-11-14 | 136.4 | 362.776 |
| 2014-11-15 - 2014-12-31 | 70.91 | 353.331 |
| 2015-01-01 - 2015-02-16 | 139.65 | 241.836 |
| 2015-02-17 - 2015-04-04 | 62.52 | 260.029 |
| 2015-04-05 - 2015-05-21 | 41.03 | 234.565 |
| 2015-05-22 - 2015-07-07 | 50.97 | 240.798 |
| 2015-07-08 - 2015-08-23 | 83.26 | 273.705 |
| 2015-08-24 - 2015-10-09 | 33.43 | 234.084 |
| 2015-10-10 - 2015-11-25 | 191.26 | 313.518 |
| 2015-11-26 - 2016-01-11 | 113.16 | 419.466 |
| 2016-01-12 - 2016-02-27 | 78.28 | 398.062 |
| 2016-02-28 - 2016-04-14 | 35.18 | 417.9 |
| 2016-04-15 - 2016-05-31 | 105.44 | 455.634 |
| 2016-06-01 - 2016-07-17 | 222.96 | 648.909 |
| 2016-07-18 - 2016-09-02 | 158.144 | 602.686 |
| 2016-09-03 - 2016-10-19 | 44.0025 | 615.703 |
| 2016-10-20 - 2016-12-04 | 142.21 | 713.458 |
The range is just like the variance measurement except it's not squared, it's just the absolute value the price moved in that segment.
Filters
Finally, we will plot a few filters to see the smooth price.
Simple Moving Average 126 (because I found autocorrelation + high spectral density in this zone):
A 15th order polynomial trend:
And more advanced filter like a HP Filter with 8000 order of smoothness:
It can be used to play around with it, measure seasonality, cycles and whatnot.
THE END
Thanks for reading through, this has to be my longest article. Now you can see how to actually analyze the price with real statistical tools not with mysticism and quackery.
Upvote, ReSteem & 
