Constructing MACD from exponential average spreads and a signal line

Begin with the exponential moving average

An exponential moving average is a recursively updated average that gives more weight to the latest close than to older observations. The price oscillator is the spread between a shorter and a longer exponential average of closing prices. The signal line is a further exponential average of the oscillator, used as a slower comparison series.

Convert a smoothing weight into a lookback

An exponential moving average can be updated by combining a chosen percentage of the latest close with the complementary percentage of the prior average. That percentage converts to a period count with the relation time periods equals two divided by the percentage, minus one. After rounding to a whole period, a 9 percent smoothing weight is treated as a 21-period exponential moving average because two divided by 0.09 minus one equals 21.2.

Form the price oscillator and the signal line

In the usual construction, the oscillator is a 12-period exponential moving average minus a 26-period exponential moving average, and the signal line is a 9-period exponential moving average of that difference. The 12- and 26-period pair is only one conventional setting among series-specific alternatives.

Read the finished stack in three ways

The finished stack is read in three ways: oscillator-versus-signal intersections, distance from the zero line as an overextended stretch, and disagreement between price and the oscillator.

A zero oscillator reading means the two exponential averages are changing at the same rate. The zero line is the level at which the shorter and longer averages are changing at the same rate. The sign and size of the spread describe how much faster one average is moving relative to the other.

A crossover is an intersection between the oscillator and its signal line, used to mark a change in relative momentum. An intersection is labeled a downward-type signal when the oscillator crosses below the signal line and an upward-type signal when it crosses above. A separate pair of signals is defined by the oscillator crossing the zero line.

A stretch reading is a large oscillator value treated as a possible overextended price move rather than as a separate indicator. Distance from the zero line is that overextended stretch.

Divergence is a mismatch in which price and the oscillator fail to confirm each other's new extremes. A bearish-type mismatch is defined as the oscillator making a new low while price does not. A bullish-type mismatch is the oscillator making a new high while price does not. Those mismatches are treated as more meaningful near stretch extremes.

Display choices and cross-checks

The same stack can be drawn as two lines or as a histogram display, a bar plot of oscillator minus signal drawn above or below the zero level. Rapid price reversals can produce false intersections because the averages follow price history. The oscillator is meant to be checked against measures built on different properties.