Definition. The Moving Average Convergence/Divergence indicator measures the spread between a fast and a slow exponential moving average of price. This chart applies the standard 12/26/9 parameterisation to the natural logarithm of the Bitcoin price: the MACD line is the 12-day log-price EMA minus the 26-day log-price EMA, the signal line is the 9-day EMA of the MACD line, and the histogram is the MACD line minus its signal, split into positive and negative columns.

Technical. All series are computed on hourly closes with EMA spans of 288, 624 and 216 bars, equal to 12, 26 and 9 days. Because the averages are taken on log price, the MACD line expresses a ratio rather than a dollar spread: a value of x means the fast average sits exp(x) - 1 above the slow one, so 0.05 corresponds to a 5.1% gap. This makes the indicator scale-invariant - multiplying price by any constant shifts both log averages equally and leaves every series unchanged - so a reading means the same thing at $100 as at $100,000. A conventional MACD built on raw price lacks this property: the standard deviation of its histogram rises from about $13 in 2013 to several hundred dollars in recent years, tracking the price level itself and making readings from different eras incomparable. On log price the histogram's amplitude instead tracks realised volatility and has stayed within a narrow band across the whole history.

Interpretation. A MACD line above zero indicates the 12-day average sits above the 26-day average, with short-term momentum running ahead of the intermediate trend; below zero the relationship is inverted. Crossings between the MACD line and its signal mark turns in the rate at which that spread is widening or narrowing, and appear as the histogram changing sign. Because magnitude scales with the proportional gap rather than the price level, histogram extremes are directly comparable across cycles, and a positive reading and its negative counterpart represent moves of equal proportional size.

Notes. Hourly bars are a finer sampling of the same estimator rather than a different one: sampled at daily closes the hourly and daily constructions correlate at 0.998 and agree on the histogram's sign on roughly 97% of days. Price is shown on a logarithmic axis for reference. See also Relative Strength Index (RSI-14) and Stochastic Oscillator.