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↔️ Donchian Channels

Donchian Channels draw the simplest possible volatility envelope: the highest high and lowest low over the last \(N\) periods, with no averaging or weighting at all — pure extrema.

💡 Financial Meaning

This is the indicator behind the legendary "Turtle Trading" breakout system: buy when price closes above the upper channel (a new \(N\)-period high), sell/short when it closes below the lower channel. The width of the channel also doubles as a volatility gauge — a wide channel means the market has ranged broadly over the window, a narrow one means it has been unusually contained.

🔢 Mathematical Formulas

  1. Upper Channel — the rolling maximum of the high over the window:

    \[ Upper_t = \max_{0 \le i < N} H_{t-i} \]

  2. Lower Channel — the rolling minimum of the low over the window:

    \[ Lower_t = \min_{0 \le i < N} L_{t-i} \]

  3. Middle Line — the simple midpoint of the two:

    \[ Middle_t = \frac{Upper_t + Lower_t}{2} \]

⚙️ Parameters

Parameter Key Default Description
Period (\(N\)) period 20 Lookback window for the rolling max/min, in sessions.

Drawn across closed days

The channels have a value on sessions only, while the chart's date axis runs through every calendar day. Over a weekend or a holiday, the shaded channel is drawn in a straight line from the last session before to the first one after, as the middle line is, so it does not break: the bridged stretch only shapes the fill and carries no value of its own.

🎛️ Signal Processing Equivalent — Sliding-Window Max/Min (Morphological Filter)

Donchian's channel construction is a max filter and a min filter applied over a sliding window — exactly the dilation and erosion operators from mathematical morphology, applied here in one dimension. Unlike every averaging filter in this catalogue, a max/min filter is not linear: it cannot be described by a convolution or a transfer function \(H(z)\), and it responds instantaneously to a new extreme rather than blending it in gradually.

flowchart LR
    H["📈 High"] --> UP["🔼 Rolling max over N bars"]
    L["📉 Low"] --> DN["🔽 Rolling min over N bars"]
    UP --> UPPER["↗️ Upper channel"]
    DN --> LOWER["↘️ Lower channel"]
    UPPER --> MID["➗ Middle = (Upper+Lower)/2"]
    LOWER --> MID

Step-function behaviour

Because the channel only updates when a new extreme appears, both bands move in discrete steps rather than smoothly — a sharp contrast with Bollinger Bands, whose \(\pm k\sigma\) envelope reacts gradually to every new observation.

Donchian channel on Wikipedia