QuanTAlib/lib/channels/starchannel/starchannel.md

STARCHANNEL: Stoller Average Range Channel

Stoller channels use ATR to build a corridor around the average — a volatility-aware boundary for range traders.

Property	Value
Category	Channel
Inputs	OHLCV bar (TBar)
Parameters	period (default 20), multiplier (default 2.0), atrPeriod (default 0)
Outputs	Multiple series (Upper, Lower)
Output range	Tracks input
Warmup	Math.Max(period, effectiveAtrPeriod) bars
PineScript	starchannel.pine

• Stoller Average Range Channel creates a volatility-adaptive price envelope using Average True Range (ATR) to determine band width around a simple m...
• Similar: KC, ATRBands | Complementary: ADX for trend confirmation | Trading note: Stoller Average Range Channel; ATR-based bands around a moving average.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

Stoller Average Range Channel creates a volatility-adaptive price envelope using Average True Range (ATR) to determine band width around a simple moving average centerline. The bands automatically expand during volatile periods and contract during calmer markets. The implementation uses a circular buffer for the SMA running sum and Wilder's RMA with a warmup compensator for ATR, achieving O(1) streaming updates per bar.

Historical Context

Manning Stoller developed STARC Bands in the early 1980s as a volatility-adaptive alternative to fixed percentage envelopes. His insight was straightforward: channels should widen during high volatility and contract during low volatility, reflecting actual market conditions rather than arbitrary percentages.

The indicator combines two established building blocks: the simple moving average (for trend direction) and Average True Range (for volatility measurement). J. Welles Wilder had already introduced ATR in his 1978 book New Concepts in Technical Trading Systems. Stoller's contribution was recognizing that ATR-based bands would naturally adapt to each security's volatility characteristics without requiring manual adjustment across different instruments or timeframes.

STARC Bands gained popularity among futures traders in the 1980s and influenced many subsequent volatility-adaptive channel indicators. The structure is similar to Keltner Channels (EMA center + ATR width) but uses an SMA centerline, which gives equal weight to all bars in the window rather than exponentially decaying emphasis on recent prices.

Architecture & Physics

1. Simple Moving Average (Middle Band)

The centerline is a standard SMA of the source price using a circular buffer with running sum:

\text{Middle}_t = \frac{1}{n} \sum_{i=0}^{n-1} C_{t-i}

where C is the source price (typically close) and n is the period.

2. True Range

True Range captures the full extent of price movement including gaps:

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

3. Average True Range (RMA with Warmup Compensation)

ATR uses Wilder's smoothing (RMA) with a warmup compensator to eliminate cold-start bias:

\text{raw\_rma}_t = \frac{\text{raw\_rma}_{t-1} \cdot (n - 1) + TR_t}{n}

e_t = (1 - \alpha) \cdot e_{t-1}, \quad \alpha = \frac{1}{n}

ATR_t = \begin{cases} \text{raw\_rma}_t \;/\; (1 - e_t) & \text{if } e_t > \epsilon \\ \text{raw\_rma}_t & \text{otherwise} \end{cases}

The compensator e_t converges to zero as bars accumulate, removing the initialization bias that would otherwise undercount early ATR values.

4. Band Construction

U_t = \text{Middle}_t + k \cdot ATR_t

L_t = \text{Middle}_t - k \cdot ATR_t

where k is the multiplier (default 2.0).

5. Complexity

Streaming: O(1) per bar. The SMA uses a running sum with circular buffer (add new, subtract oldest). The RMA is a single-pole IIR filter. Memory: one circular buffer of n floats for SMA, plus scalar state for RMA/compensator.

Mathematical Foundation

Parameters

Symbol	Name	Default	Constraint	Description
n	period	20	> 0	SMA and ATR lookback period
k	multiplier	2.0	> 0	ATR multiplier for band width
n_{\text{atr}}	atr_length	0	\geq 0	Separate ATR period (0 = same as SMA period)

Output Interpretation

Output	Interpretation
Band width expanding	ATR rising; volatility increasing
Band width contracting	ATR falling; volatility decreasing
Price at upper band	Overextended above SMA by ATR measure
Price at lower band	Overextended below SMA by ATR measure
Middle band slope positive	SMA trending upward

Performance Profile

Operation Count (Streaming Mode)

STARCHANNEL combines an SMA running sum (center), True Range, and Wilder's RMA with warmup compensation — identical cost to ATRBANDS:

Operation	Count	Cost (cycles)	Subtotal
SUB (oldest from SMA sum)	1	1	1
ADD (new to SMA sum)	1	1	1
DIV (SMA = sum / count)	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 (middle ± width)	2	1	2
Total (hot)	12	—	~33 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: ~53 cycles/bar; Post-warmup: ~33 cycles/bar.

Batch Mode (SIMD Analysis)

The SMA running sum and RMA recursion are sequential. True Range computation is independent per bar:

Optimization	Benefit
True Range (3-way max)	Vectorizable with Vector.Max and Vector.Abs
RMA recursion	Sequential (IIR dependency)
SMA running sum	Sequential
Band arithmetic	Vectorizable in a post-pass

Resources

• Stoller, M. (1980s). Development of the Stoller Average Range Channel.
• Wilder, J. W. (1978). New Concepts in Technical Trading Systems. Trend Research.
• Kaufman, P. (2013). Trading Systems and Methods, 5th ed. Wiley.