EMA (Exponential Moving Average)

Exponential moving average of an upstream series. Edge-first and chainable, with a symbol-fetch fallback when unconnected. Wired to more than one Price Factor, it fans out to per-ticker by_symbol results.

What (One-liner)

EWM recursive smoothing (α = 2/(span+1), adjust=False) — reacts faster than SMA, and feeds MACD / Bollinger / momentum chains.

Inputs

• span (number, optional) — EMA span, default 20.
• symbol (string, optional) — fallback ticker used only when there is no upstream series.

Outputs

• series — EMA series aligned to the input.
• current — latest EMA value.
• by_symbol — per-ticker map when fed by multiple Price Factors.

How to use

1. Connect an upstream series.
2. Set span (default 20; 12 / 26 for MACD components).
3. Output series chains downstream.

Core formulas

α = 2 / (span + 1)
EMA_0 = P_0
EMA_t = α·P_t + (1-α)·EMA_{t-1}

# pandas equivalent
series.ewm(span=span, adjust=False).mean()

Assumptions & applicability

Assumptions: TradingView / MT4 convention α = 2/(span+1) + recursive (adjust=False) + first-value init.

Applicability: MACD components, Bollinger middle band, momentum strategies; any asset class, any frequency.

Out of scope: Wilder α = 1/n (that is RSI), triangular / WMA weighting, short series.

Known limitations

1. More responsive than SMA, but more prone to whipsaw on noisy input.
2. Early values reflect a short effective lookback before the span fills in (recursive init bias).
3. α = 2/(span+1) and adjust=False are hardcoded conventions.

References

Murphy (1999), Technical Analysis of the Financial Markets; Roberts (1959), EWM statistical origin.

Golden Test

tests/golden/fixtures/tier1/compute_ema/ — tolerance 1e-12 absolute, benchmarked against pandas.Series.ewm(span=span, adjust=False).mean(), last verified 2026-05-25, status passing.

Changelog

• 1.0.0 (2026-05-25) — Activated as canonical Layer-1 transform; merged governance fields from the superseded Layer-0 compute_ema card.