EMA and SMMA Match When Their Periods Follow a Fixed Relation

Summary

The document explains that the exponential moving average (EMA) and smoothed moving average (SMMA) use recurrent formulas that become identical when their periods satisfy a particular relation: the EMA period is twice the SMMA period minus one. This offers a useful way to recognize that two differently named moving averages may represent the same ongoing calculation when configured accordingly.

It distinguishes that formula identity from differences during early values, which it attributes to initialization choices. An example compares a long-period EMA with an SMMA whose period follows the stated relation, and the accompanying figure is intended to show the initial discrepancy fading as calculations continue. The note gives no trading test or evidence that either average produces profitable signals. It explicitly frames the script as an illustration of the mathematical relationship, not as a trading tool.

Key ideas

• EMA and SMMA recurrent calculations match when the EMA period is twice the SMMA period minus one.
• Early differences can arise from how each average is initialized.
• The example illustrates that the initial gap diminishes as more values are calculated.
• The document presents an indicator equivalence, not a tested trading strategy.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.