Timing correlations
There seems to be a set cyclical pattern on the timing of bull markets. The definition of a bull market in this thread is an uptrend lasting over a month and moving the price up a lot. The following bull markets have occured:

• #1) June 2011 bull market going from $0.8 to $32
• #2) January 2012 bull market going from $2 to $7
• #3) August 2012 bull market going from $5 to $15
• #4) April 2013 bull market going from $13 to $260
• #5) November 2013 bull market going from $125 to $1175
• #6) June 2014 bull market going from $425 to $675
• #7) March 2015 bull market going from $166 to $300?
• #8) November 2015 bull market going from $230 to $500
• #9) June 2016 bull market going from $450 to $780
• #10) Late 2016/early 2017 bull market, which made an unexpected change; it lasted more than twice as long as previous ones, going from $600 to $2800 approx

There is an obvious cyclical correlation. Each bull market is 7-9 months apart. During these bull market occurs the only lasting bull markets. The rest of the time, BTCUSD is constantly in a bear market. The bull markets which reach a new ATH are henceforth called high magnitude bull markets. They occur approximately half of all the times and they are the ones we are interested in analyzing.



Analysis of increase ratio between high magnitude bull markets
Bull market  Peak                   Increase ratio from previous bull market     Increase ratio of increase ratio      
#1              32                    
#4              260                     8.125          
#5              1150                   4.4231                                            0.5443786
#10            2800                   2.43                                                0.55
 
The increase ratio of the increase ratio (the second derivative) seems to be approximately one half. This means that the increase ratio of bull market #x will be approximately 0.5*((#x-2)/(#x-1)). I'd make a graph but its easy to visualize what is going on here.



Price increase factor analysis
Bull market  Start   Peak      Price increase factor    Increase ratio of price increase factor        
#1              0.8      32         40          
#4              13.5    260        19.25925926              0.4815
#5              125     1150       9.2                          0.4777
#10            600     2800      4.67                         0.51
 
The increase ratio of the start and the peak of a bull market seems to follow a pattern too.



Metrics correlated with high magnitude bull markets
Metrics correlated with successful bull markets are:

• Google trends http://www.google.com/trends/explore#q=bitcoin
• Number of transactions https://blockchain.info/en/charts/n-transactions?showDataPoints=false×pan=all&show_header=true&daysAverageString=1&scale=0&address=

These metrics show that high magnitude bull markets correlate with increased usage of bitcoin and a sharp increase in media mentions. The downside with these metrics is that they lag behind usually, or at best follow the price.
[/quote]