Predictable Bitcoin Momentum or Reversion?

Does bitcoin (BTC) price predictably exhibit momentum or reversion? To investigate, we try three tests:

1. Calculate autocorrelations (serial correlations) between daily, weekly and monthly (4-week) BTC returns and BTC returns for the next five respective intervals (for example, correlation of daily return with returns the next five days). Positive and negative correlations suggest momentum and reversion, respectively.
2. Calculate correlations between next-week BTC return and current BTC price relative to its high or low over the last 13 weeks. A positive correlation for closeness to the recent high (low) suggests momentum (reversion).
3. Calculate average next-week BTC returns by ranked fifth (quintile) of BTC price relative to its high or low over the last 13 weeks.

Using daily, weekly and monthly (4-week) BTC closing prices during September 14, 2014 (the earliest available from the source) through August 31, 2021, we find that:

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