Zero-Lag Exponential Moving Average (ZLEMA)

Summary

Zero-Lag Exponential Moving Average: an EMA applied not to price but to a de-lagged series that extrapolates price forward by the EMA's own lag, cancelling that lag to first order. It tracks a trend far more closely than an EMA of the same length, at the cost of overshooting sharp reversals — the extrapolation keeps pushing in the old direction for a bar or two. Read it as an EMA that turns sooner: crossings of price and average, and changes in its slope, arrive earlier than the equivalent EMA signal, and its overshoot after a spike is a property of the filter rather than a move in the market.

ZLEMA is also selectable as a moving-average type (TA_MAType_ZLEMA) wherever an optInMAType parameter is accepted (MA, BBANDS, STOCH, MACDEXT, ...).

Formula

lag = Integer( (n - 1) / 2 ) d = 2 * Price - Price[lag bars ago] ZLEMA(n) = EMA( d, n )

The inner average is the standard TA-Lib EMA: smoothing factor 2 / (n + 1), seeded with the simple average of the first n de-lagged values.

Notes

The paper this indicator is usually credited to describes a different filter. Ehlers and Way's Zero Lag (Well, Almost) specifies an error-correcting EMA with a per-bar gain search; neither the de-lagged series nor the (n-1)/2 lag appears anywhere in it. What TA-Lib ships here is the de-lagged-EMA construction published under the "zero lag" name by Tulip Indicators, pandas-ta, TradingView Pine and others, for which no primary source is traceable.
lag truncates: Integer((n-1)/2). For an even period that is one bar shorter than the round-to-nearest convention some descriptions use, which moves the whole line, not just its warm-up. Tulip Indicators, pandas-ta and Pine all truncate.
The de-lag is computed as 2 * Price - Price[lag] in one rounding, rather than the algebraically equal Price + (Price - Price[lag]) that Tulip Indicators, TradingView Pine and the Wikipedia statement use. The second form's extra rounding is one unit in the last place of the larger price — negligible against the de-lagged value, except where that value nearly cancels. When price is near double its value lag bars ago the two forms differ by about 5e-12 relative, so expect that much disagreement against those implementations on a strongly trending series, and do not attribute it to the seed or the smoothing factor.
Implementations disagree on how the inner EMA is seeded — TA-Lib uses its own EMA convention (the simple average of the first n de-lagged values), where Tulip Indicators seeds from a single raw price and so emits its first value earlier and converges to these values only after many bars.
ZLEMA inherits EMA's unstable period rather than owning one: TA_SetUnstablePeriod(TA_FUNC_UNST_EMA, ...) moves ZLEMA's first output too.
A period of 1 performs no smoothing: the output is a copy of the input.

Inputs

inReal — Source price series, close by convention

Outputs

outReal — Zero-lag exponential moving average of the input

Parameters

Parameter	Type	Default	Accepted values	Description
`optInTimePeriod`	integer	30	1–100000	Number of bars in the exponential average; the de-lag distance derives from it

Properties

Numerical Stability: Initial Unstable Period — Inherited from EMA, which ZLEMA computes internally; tunable via EMA's unstable period.


✅ Overlap Input i
☐ Independent Y-Axis
☐ Candlestick
☐ Can Output NaN or ±Inf
✅ Identity at Period 1 i

Implementation

TA-Lib Definition: zlema.c · zlema.yaml

Native	File
C	`ta_ZLEMA.c`
Rust	`zlema.rs`
Java	`Core_ZLEMA.java`

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

Zero Lag Exponential Moving Average, Zero-Lag EMA, ZLMA

References

John Ehlers and Ric Way, Zero Lag (Well, Almost), Technical Analysis of Stocks & Commodities, November 2010 — the paper the name comes from, describing a different, error-correcting filter: mesasoftware.com/papers/ZeroLag.pdf
Tulip Indicators, zlema — an independent implementation of the de-lagged form, differing in its seeding: tulipindicators.org/zlema