fintech-algorithms
/
Using a coding agent? Give it the skill: npx skills add IslamBaraka90/Fintech-Algorithms-Library What it does →

Zero-Lag Exponential Moving Average (ZLEMA)

Install and import#

bash
npm install fintech-algorithms
ts
import { zeroLagExponentialMovingAverageZlema } from "fintech-algorithms/technical-indicators/trend-smoothing/zero-lag-exponential-moving-average-zlema";

Signature#

zeroLagExponentialMovingAverageZlema(input)

Removes most of the EMA's lag by first de-lagging close into 2 * close[t] - close[t - lag], where lag is floor((period - 1) / 2), and then running an ordinary EMA of period over that adjusted series.

Parameters#

NameTypeNotes
inputTopicInputbars is a non-empty array of OHLCV records with strictly increasing timestamp, finite open, high, low, close and non-negative volume, all sharing one adjustment basis. From parameters this topic reads only period, an integer of at least 2, default 14, which sets both the de-lag distance and the EMA smoothing constant.

Returns#

TopicResult

series and latest carry a single key, value. The warm-up stacks the de-lag offset on top of the EMA seed, so with the default period ready_at is 19, not 13.

Warm-up#

The first floor((period - 1) / 2) + period - 1 bars (19 at the default period of 14) positions are null. The de-lagged series is null for its first floor((period - 1) / 2) bars, and the EMA then needs a further period non-null values to seed from their mean. ready_at is the index of the first non-null value.

Errors#

  • When parameters.period is not an integer of at least 2 — throws Error
  • When bars is empty, or a bar has a non-finite price, a negative volume, or a timestamp that does not increase — throws Error

Complexity: time O(n), space O(n).

Worked example#

executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

Input#

input
{
  "bars": [
    {
      "timestamp": "2024-01-02",
      "basis": "synthetic-unadjusted",
      "open": 100,
      "high": 101.45,
      "low": 98.695,
      "close": 100,
      "volume": 750000,
      "benchmark": 200
    },
    {
      "timestamp": "2024-01-03",
      "basis": "synthetic-unadjusted",
      "open": 101.49111452,
      "high": 103.38381693,
      "low": 100.05480022,
      "close": 101.78791214,
      "volume": 795117,
      "benchmark": 200.56326135
    },
    {
      "timestamp": "2024-01-04",
      "basis": "synthetic-unadjusted",
      "open": 102.45519048,
      "high": 104.6701838,
      "low": 100.91147007,
      "close": 102.9549389,
      "volume": 840234,
      "benchmark": 201.11020913
    }
  ],
  "parameters": {}
}

Call#

zeroLagExponentialMovingAverageZlema(input)

Returns#

object with 9 fields: topic_id, title, state, ready, ready_at, series, latest, parameters, …

{
  "topic_id": "D07-F01-A15",
  "title": "Zero-Lag Exponential Moving Average (ZLEMA)",
  "state": "calculated",
  "ready": true,
  "ready_at": 19,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 101.8372551421456
  },
  "parameters": {},
  "diagnostics": {
    "causal": true,
    "input_count": 96
  }
}

Diagrams#

Zero-Lag Exponential Moving Average (ZLEMA) — article hero
Zero-Lag Exponential Moving Average (ZLEMA) — concept map
Zero-Lag Exponential Moving Average (ZLEMA) — decision comparison
Zero-Lag Exponential Moving Average (ZLEMA) — worked example

Calculation flow#

Zero-Lag Exponential Moving Average (ZLEMA) calculation flow 
flowchart LR
    A["an oldest-to-newest finite price series, declared price so"] --> B["Validate order, basis, and finite values"]
    B --> C["Apply the selected Zero-Lag Exponential Moving Average (ZLEMA) convention"]
    C --> D["Emit value, readiness, and diagnostics"]
    D --> E["Interpret descriptively; test outcomes separately"]
    B -->|invalid or insufficient| X["Withhold output with a reason"]
Zero-Lag Exponential Moving Average (ZLEMA) readiness and evidence states 
stateDiagram-v2
    [*] --> Waiting
    Waiting --> Ready: enough valid causal observations
    Waiting --> Rejected: malformed or unsupported input
    Ready --> Calculated: selected formula applied
    Calculated --> Interpreted: diagnostic and limitation retained
    Interpreted --> Ready: next observation arrives
    Rejected --> Waiting: corrected input and deterministic reset

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

  • TA-Lib function groups — see linked primary or authoritative record
  • TA-Lib C/C++ API — see linked primary or authoritative record
  • TA-Lib maintained source — see linked primary or authoritative record
  • Evidence decision
  • Level 1 evidence map

The rest of the Trend Smoothing family#