Keltner Channel Breakout

1. Compute a 20-bar EMA midline and the average bar range (a 20-bar EMA of the true range); the upper channel sits 2 average ranges above the midline.
2. Buy when the close breaks above the upper channel — price has escaped its normal envelope with unusual force.
3. Sell when the close falls back below the midline — the thrust has faded back to average.

Worked example. The 20-bar EMA is 100 and the average bar range is 1.5, putting the upper channel at 103. A strong close at 103.6 breaks above it — buy. The trade rides the move until a close at 104.8 slips under the midline, which has by then risen to 105.

Everything runs on closing prices of the traded timeframe: P is a close, P_t today's close, and N counts bars — one bar is one candle of that timeframe, so 20 bars on a 1h chart is 20 hours.

Exponential Moving Average (EMA)

A running average that blends each new close into yesterday's value, so old prices fade away gradually instead of dropping out all at once. The blend factor α is larger for shorter periods, which makes short EMAs faster to react.

EMA_t = α · P_t + (1 - α) · EMA_t-1,     α = 2 / (N + 1)

Example: With N = 19, α = 2 / 20 = 0.1. If yesterday's EMA was 100 and today's close is 110, the new EMA is 0.1·110 + 0.9·100 = 101 — it moves toward the new price but keeps most of its history.

Average Range (ATR)

How much price typically moves per bar. Each bar's true range is its own high-to-low span, widened if the market gapped from the previous close — so an overnight jump counts as movement even when the bar itself is small. The ATR averages the last N of them. It sizes stops: a stop placed k ATRs away automatically adapts to how volatile the market currently is.

TR_t = max(H_t - L_t, |H_t - P_t-1|, |L_t - P_t-1|),     ATR_N = (1 / N)Σ_i=1^N TR_t-i+1

Example: A bar running from a low of 99 to a high of 102 after a previous close of 100 has a true range of 3 — the high-low span, since neither gap measure beats it. If the last three true ranges were 3, 1 and 2, the 3-bar ATR is 2, so a stop 2 ATRs below an entry at 100 sits at 96.