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Instantaneous Trendline (Ehlers)

The Instantaneous Trendline is an adaptive trend-following tool that automatically adjusts to the current dominant cycle period of the market. It provides a "zero-lag" trend estimate by removing the cyclical component identified via Hilbert Transform phasors.

Formula

The Trendline is a complex multi-stage calculation: 1. Hilbert Transform: Identifies the market's instantaneous period (\(DCPeriod\)). 2. SMA Smoothing: A Simple Moving Average with a dynamic period equal to \(DCPeriod\). 3. WMA Smoothing: A 4-bar Weighted Moving Average applied to the output.

\[\text{Trendline} = \text{WMA}(\text{SMA}(Price, DCPeriod), 4)\]

Parameters

This indicator is fully adaptive and typically requires no user-defined lookback parameters, as it self-tunes to the market's internal rhythm.

Polars Usage

import polars as pl
import quantwave as qw

df = pl.read_csv("data.csv")
df = df.with_columns([
    pl.col("close").ta.instantaneous_trendline().alias("itrend")
])

Performance Note

The Instantaneous Trendline is one of the most computationally expensive indicators in the suite, involving trigonometric functions and dynamic windowing. While a Python implementation would struggle to maintain real-time performance on large datasets, QuantWave processes 1 million rows in ~74ms.

See also: Indicator Gallery