<CENTER>[![BTC.png](https://s11.postimg.org/4hz11cxcz/BTC.png)](https://postimg.org/image/rjfm73x0f/)</CENTER>


Have you ever wondered what influences the Bitcoin price? In this article I will reveal to you the relationship between different data and Bitcoin and how it affects the Bitcoin price. Keep in mind that correlation =/= causation, but nontheless, it can be used to model the price more accurately, and eventually do more accurate forecasts with it.

Well the price could be correlated with itself, with it's lagged self, otherwise it would be hard to forecast it accurately. If the price is correlated with it's lagged self, that implies [seasonality](https://en.wikipedia.org/wiki/Seasonality), and a repeating pattern in the price, so forecasting could work this way.

However we are out of luck, the BTC_USD price is not seasonal, and it is only correlated with it's 1st lag, therefore any prediction we make on the price alone, won't reveal any information to us, and won't give us an edge over the market.

<center>[![PRICE CORR.png](https://s10.postimg.org/nmijbp5cp/PRICE_CORR.png)](https://postimg.org/image/7o9tlkb4l/)</center>

The ACF and PACF, according to the [Box-Jenkins protocol](https://en.wikipedia.org/wiki/Box%E2%80%93Jenkins), suggests us a:

>Decay, starting after a few lags: 	Mixed autoregressive and moving average (ARMA) model.

So we know that the price will be an ARIMA model, so far so good. But first let's talk about correlation with other data.

----------------------------

<BR/>
<center><h1>Correlation</h1></center>

Now that we know that the price is only correlated with it's first lag, we know it's model, however this won't tell us anything useful, or anything that would give us an edge over the others at predicting the price.  So I went around looking for data related to Bitcoin.

I have found many statistics at: [Blockchain](https://blockchain.info/charts) and at [Bitcointalk](https://bitcointalk.org/index.php?action=stats).

These statistics are related very much to the price of Bitcoin, for example the `Total Number Bitcoin's` is effectively the Bitcoin supply, so it's obvious that it will correlate with the price. But I looked at the `Number of transactions`, the `Exchange Trading Volume` and even at the statistics on Bitcointalk, like: `New Topics/Day`, `New Posts/Day`, you name it.

It should be straight forward that the number of activity on the forum, and the statistics on Blockchain.info, should relate to the price, influence it, or even predict it.

So I have done a correlation matrix between these values:


Price      |      TotalBitcoins    |     Difficulty      |      Avgblocksize      |     Hashrate  
---------|-------------------------|-------------------|-------------------------|--------------
1.0000    |      0.7274                |      0.5556          |      0.6481                       |  0.5559    | Price  |
     x               |      1.0000             |      0.6649            |      0.8491                    |      0.6650    | TotalBitcoins  |
      x             |              x                  |     1.0000             |      0.8963                     |    0.9940    | Difficulty  |
     x                |               x                |          x                      |    1.0000                        |    0.8860    | Avgblocksize  |
	x	    |		       x                 |		x                |	            x                                |    1.0000    | Hashrate  |

-------------------------------

## And more....  

Price   |  TotBTC   |   Wallet Users   |    NewTopics  |   NewPosts   |  NewMembers  |  Online  |  Pageviews
------------|---------------------|---------------------------|----------------|---------------|-----------|--------------|-------------------
          1.0000     |     0.6587            |     0.5276     |     0.6533  |     0.6073            |           0.6063     |        0.6751              |      0.5763         |    Price
               x           |    1.0000               |      0.7900     |     0.9026 |      0.8713           |              0.8686  |        0.9569         |        0.8393           | TotBTC
                 x        |          x                     |   1.0000      |    0.9628  |        0.9750           |            0.9859   |         0.6233              |      0.9886          | Wallet Users
                x         |          x                          |          x   |    1.0000  |           0.9960           |     0.9913           |           0.7847            |     0.9882          |   NewTopics
               x          |         x                      |           x      |         x          |               1.0000            |      0.9926     |          0.7357               |       0.9962       |      NewPosts
            x          |          x                    |            x      |                 x  |            x                             |    1.0000        |        0.7287             |      0.9932         |    NewMembers
         x       |             x                |                  x     |               x       |               x                      |      x                   |        1.0000            |      0.6920           |    Online
           x       |      x               |                    x         |              x         |              x               |           x              |                x              |          1.0000              |      Pageviews

----------------------------------

And much more... I won't put them all here because it takes a while to format tables with Markdown, sigh... :(  .... But you can now see the relationships between different data, how they affect the Bitcoin price. Now let's model the price based on these dependent variables.

----------------------

<br/>
<center><h1>[ARIMAX](http://robjhyndman.com/hyndsight/arimax/)</h1></center>

It is `Auto Regressive Integrated Moving Average with Exogeneous Input`, it's based on [ARIMA](https://en.wikipedia.org/wiki/ARIMA) but this model can handle multiple inputs instead of one. It is essential if we want to model the BTC_USD price with the other variables as regressors.

I am using the Blockchain.info price data obviously, on BTC_USD, with the data up until 22nd of October. Then the [Correlogram](https://en.wikipedia.org/wiki/Correlogram) shown earlier tells us that the maximum lag is 1. So we will have alternating ARIMA/ARMA models for each comparison. I have gone through all combinations, and will only show here the best ones.

Let's start forecasting the best datasets, by my usual methodology, forecasting 20% of the data from the rest of the 80%, in this case starting from the 2000th up until the latest.

<CENTER><h1>Naked ARIMA ( 1 1 1 )</h1></CENTER>

<center>[![ARIMA 1 1 1 - NUDE (142.34).png](https://s22.postimg.org/j679l6na9/ARIMA_1_1_1_NUDE_142_34.png)](https://postimg.org/image/4a8qdlbvh/)</center>

This is the naked ARIMA model for the price, without adding any additional inputs. It has an error of `142.34`, therefore we expect, a better accuracy and smaller error from the regressed models. Moving on.

<CENTER><h1>ARIMAX ( 1 1 1 ){ Bitcointalk Online People } </h1></CENTER>

<CENTER>[![ARIMA 1 1 1 ONLINE 172.43.png](https://s17.postimg.org/x0x0hq83z/ARIMA_1_1_1_ONLINE_172_43.png)](https://postimg.org/image/y37709qx7/)</CENTER>

We can see that the number of people online on Bitcointalk, doesn't really help us predict the price, in fact it's even worse than our naked prediction with an error of `172.43`. It is missing a lot of data therefore this variable is not that accurate.

<CENTER><h1>ARIMAX ( 1 0 1 ){ Bitcointalk Pageviews } </h1></CENTER>

<CENTER>[![ARIMA 1 0 1 PAGEVIEW 146.95.png](https://s9.postimg.org/4aote8rzj/ARIMA_1_0_1_PAGEVIEW_146_95.png)](https://postimg.org/image/ekr8dhhuz/)</CENTER>

The pageview statistics is slightly better, but not that much. An error of `146.95`. I guess there are many bots visiting the forum and people reloading pages, so it is not that accurate of a predictor for the price.

<CENTER><h1>ARIMAX ( 1 1 1 ){ Total Bitcoins } </h1></CENTER>

<CENTER>[![ARIMA 1 1 1 -TOT BTC (119.79).png](https://s15.postimg.org/m72g1gt7f/ARIMA_1_1_1_TOT_BTC_119_79.png)](https://postimg.org/image/gvnjgr74n/)</CENTER>

This is interesting. Despite the supply of Bitcoin having a correlation >70% with the price, it barely predicts it with an error of `119.79`. I guess the market has priced it in. Although it's still a better predictor than the other variables above.

<CENTER><h1>ARIMAX ( 1 0 1 ){ Bitcointalk Posts } </h1></CENTER>

<CENTER>[![ARIMA 1 0 1 POSTS 111.4.png](https://s18.postimg.org/g7e5a1zcp/ARIMA_1_0_1_POSTS_111_4.png)](https://postimg.org/image/j1hani1it/)</CENTER>

It is getting better, the number of posts on the Bitcointalk forum, reflects the price much better, the error is only `111.4`, so we are getting there! The number of posts actually reflects the number of users/buyers/sellers more, than the other statistics.

<CENTER><h1>ARIMAX ( 1 0 1 ){ Bitcointalk New Members } </h1></CENTER>

<CENTER>[![ARIMA 1 0 1 MEMBERS 101.66.png](https://s12.postimg.org/fgtmsxfm5/ARIMA_1_0_1_MEMBERS_101_66.png)](https://postimg.org/image/qt68apoax/)</CENTER>

Much better, the number of new members on the Bitcointalk forum has a predictive error of only `101.66`, so we are very close to finding a variable that helps us predict the price. Looks like from fake bots visiting the forum, from forum spammers, to new accounts (still people could create many accounts), represents the number of bitcoin activity more and more accurately.

---------------------------------

So by going through all variables, we are finding better and better predictors, and in the next article, I will reveal to you the best data that I have found!

<CENTER><H1>TO BE CONTINUED ...</H1></CENTER>

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***Disclaimer: The information provided on this page might be incorrect. I am not responsible if you lose money using the information on this page! This is not an investment advice, just my opinion and analysis for educational purposes.***


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