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Cyber Cycle (Ehlers)

The Cyber Cycle is a high-resolution oscillator introduced by John Ehlers that isolates the cyclical component of market price movement while minimizing lag.

Formula

The calculation involves a symmetrical FIR filter followed by a recursive alpha-smoothing process:

  1. FIR Smoothing: $\(\text{Smooth}_t = \frac{X_t + 2X_{t-1} + 2X_{t-2} + X_{t-3}}{6}\)$
  2. Cycle Calculation: $\(CC_t = (1 - 0.5\alpha)^2 (\text{Smooth}_t - 2\text{Smooth}_{t-1} + \text{Smooth}_{t-2}) + 2(1 - \alpha)CC_{t-1} - (1 - \alpha)^2 CC_{t-2}\)$ where \(\alpha = \frac{2}{\text{Length} + 1}\).

Parameters

Parameter Default Description
length 14 The alpha smoothing length parameter.

Polars Usage

import polars as pl
import quantwave as qw

df = pl.read_csv("data.csv")
df = df.with_columns([
    pl.col("close").ta.cyber_cycle(length=14).alias("cc")
])

Performance Note

Due to the recursive nature of the Cyber Cycle (\(CC_t\) depends on \(CC_{t-1}\) and \(CC_{t-2}\)), this indicator is notoriously slow in Python (Pandas/NumPy). QuantWave's native Rust implementation executes this recursive logic at the hardware level, processing 1 million rows in ~5ms.

See also: Indicator Gallery