QuanTAlib/lib/channels/kc/kc.md

KC: Keltner Channel

Keltner wraps an EMA in ATR-scaled bands — a volatility envelope that responds to both trend and range.

Property	Value
Category	Channel
Inputs	OHLCV bar (TBar)
Parameters	period (default 20), multiplier (default 2.0)
Outputs	Multiple series (Upper, Lower)
Output range	Tracks input
Warmup	period * 2 bars
PineScript	kc.pine

• Keltner Channel constructs a volatility-adaptive envelope by projecting Average True Range above and below an Exponential Moving Average center line.
• Similar: BBands, APZ | Complementary: Bollinger Band squeeze (BBands inside KC signals compression); MACD for trend direction | Trading note: ATR-based width adapts to true volatility including gaps; Chester Keltner's 1960 original used typical price and average range.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

Keltner Channel constructs a volatility-adaptive envelope by projecting Average True Range above and below an Exponential Moving Average center line. The channel differs from ATR Bands solely in the center line: Keltner uses EMA (faster, more responsive) while ATR Bands use SMA (more stable, more lag). The EMA center combined with ATR width creates a channel that both tracks trend and adapts to volatility, making it one of the most widely used channel indicators for trend-following and mean-reversion strategies. The implementation uses EMA with warmup compensation for accurate early values and Wilder's smoothing (RMA) for ATR.

Historical Context

Chester Keltner introduced the original "Ten-Day Moving Average Trading Rule" in his 1960 book How to Make Money in Commodities. Keltner's original channel used a 10-day SMA of the "typical price" (HLC/3) as the center, with the band width based on the 10-day SMA of the daily range (High - Low, without gap adjustment).

Linda Bradford Raschke modernized the indicator in the 1990s by replacing the SMA center with an EMA and the simple range with Average True Range. This modern version became widely known as "Keltner Channels" and is the standard implementation in most platforms. The switch to EMA reduces lag in the center line, and the switch to ATR ensures that gaps contribute to band width — critical for futures and stocks that gap regularly. The ATR component uses Wilder's smoothing (\alpha = 1/n), providing infinite memory that makes the channel particularly stable after sufficient warmup.

Architecture & Physics

1. Center Line (EMA with Warmup Compensation)

\alpha = \frac{2}{n + 1} \text{raw}_t = \alpha \cdot x_t + (1 - \alpha) \cdot \text{raw}_{t-1} w_t = \alpha + (1 - \alpha) \cdot w_{t-1} \text{EMA}_t = \frac{\text{raw}_t}{w_t}

The weight accumulator w compensates for EMA initialization bias, producing accurate values from bar 1.

2. True Range

TR_t = \max(H_t - L_t,\; |H_t - C_{t-1}|,\; |L_t - C_{t-1}|)

3. Average True Range (Wilder's Smoothing / RMA)

\alpha_{\text{atr}} = \frac{1}{n} \text{raw\_rma}_t = \frac{\text{raw\_rma}_{t-1} \cdot (n-1) + TR_t}{n} e_t = (1 - \alpha_{\text{atr}}) \cdot e_{t-1} ATR_t = \frac{\text{raw\_rma}_t}{1 - e_t} \text{ (during warmup)}

4. Band Construction

\text{Upper}_t = \text{EMA}_t + k \cdot ATR_t \text{Lower}_t = \text{EMA}_t - k \cdot ATR_t

5. Complexity

O(1) per bar: one EMA update, one True Range computation, one RMA update, and two band calculations. No buffers required.

Mathematical Foundation

Parameters

Parameter	Description	Default	Constraint
period	Lookback for EMA and ATR smoothing (n)	20	> 0
multiplier	ATR scale factor (k)	2.0	> 0
source	Input series for EMA center	close

Keltner vs. ATR Bands vs. Bollinger

Feature	Keltner	ATR Bands	Bollinger
Center	EMA	SMA	SMA
Width	ATR	ATR	StdDev
Gap sensitivity	Yes (via TR)	Yes (via TR)	No
Distribution assumption	None	None	Gaussian

Output Interpretation

Output	Description
middle	EMA center line (trend direction)
upper	EMA + scaled ATR (dynamic resistance)
lower	EMA - scaled ATR (dynamic support)

Performance Profile

Operation Count (Streaming Mode)

KC combines an EMA with warmup compensation (center), True Range computation, and Wilder's RMA with warmup compensation (ATR):

Operation	Count	Cost (cycles)	Subtotal
FMA (EMA: α×source + (1-α)×prev)	1	4	4
FMA (weight accumulator update)	1	4	4
DIV (raw / weight for EMA)	1	15	15
SUB (H - L)	1	1	1
SUB + ABS (H - prevC, L - prevC)	2	2	4
CMP (max of 3 for TR)	2	1	2
FMA (RMA: prev×(n-1)/n + TR/n)	1	4	4
MUL (multiplier × ATR)	1	3	3
ADD/SUB (EMA ± width)	2	1	2
Total (hot)	12	—	~39 cycles

During warmup (RMA compensator active):

Operation	Count	Cost (cycles)	Subtotal
MUL (e × (1 - α))	1	3	3
SUB (1 - e)	1	1	1
DIV (raw_rma / (1 - e))	1	15	15
CMP (e > ε)	1	1	1
Warmup overhead	4	—	~20 cycles

Total during warmup: ~59 cycles/bar; Post-warmup: ~39 cycles/bar.

Batch Mode (SIMD Analysis)

All IIR recursions (EMA, RMA) are state-dependent, preventing SIMD parallelization across bars:

Optimization	Benefit
FMA instructions	3 hardware FMAs per bar
True Range computation	Vectorizable in a batch pre-pass
Band arithmetic	Vectorizable in a post-pass
No buffers	Zero allocation; all state fits in registers

Resources

• Keltner, C. How to Make Money in Commodities. 1960. (Original channel concept)
• Raschke, L.B. & Connors, L. Street Smarts. M. Gordon Publishing, 1995. (Modern EMA + ATR version)
• Wilder, J.W. New Concepts in Technical Trading Systems. Trend Research, 1978. (ATR and Wilder's Smoothing)