If what you say was true, the price would be rising. Which it's not.
> then crashes to roughly 2x where it started,
I consider it to have started in the beginning of 2017, around $1k.
Can you point me to a chart and time frame during which the behavior described was occurring? It looked like it did something sort of like that (but not at the magnitudes described) a couple of times in the runup to $19k in late 2017, and I see a big spike in late 2013, but I don't see any sort of real pattern of any type, other than the fairly consistent small price spike after a big drop that comes from people buying at bargain prices.
https://99bitcoins.com/price-chart-history/
And click on 'all' and select 'logarithmic scale' (beneath the chart), you can see it fairly clearly.
https://www.reddit.com/r/CryptoCurrency/comments/9zvoe2/the_...