QuanTAlib/lib/statistics/stddev/StdDev.md

STDDEV: Standard Deviation

Volatility is not risk, but it's the only thing we can measure.

Property	Value
Category	Statistic
Inputs	Source (close)
Parameters	period, isPopulation (default false)
Outputs	Single series (StdDev)
Output range	Varies (see docs)
Warmup	period bars
PineScript	stddev.pine

• Standard Deviation measures the amount of variation or dispersion of a set of values.
• Parameterized by period, ispopulation (default false).
• Output range: Varies (see docs).
• Requires period bars of warmup before first valid output (IsHot = true).
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

Standard Deviation measures the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Historical Context

The concept of standard deviation was introduced by Karl Pearson in 1893. It has since become the most common measure of statistical dispersion in finance, used to quantify volatility and risk.

Architecture & Physics

StdDev is implemented as a wrapper around the highly optimized Variance indicator. It leverages the O(1) streaming updates and SIMD-accelerated batch processing of Variance, applying a square root transformation to the result.

Zero-Allocation Design

The implementation ensures zero heap allocations during the Update cycle. The Batch method operates directly on Span<double> using SIMD instructions (AVX2, AVX512, Neon) where available, ensuring maximum throughput for large datasets.

Mathematical Foundation

Standard Deviation is the square root of Variance.

\sigma = \sqrt{\text{Variance}}

Where Variance is calculated as:

\text{Variance} = \frac{\sum_{i=1}^{N} (x_i - \mu)^2}{N}

(For Population Standard Deviation)

Or:

\text{Variance} = \frac{\sum_{i=1}^{N} (x_i - \mu)^2}{N-1}

(For Sample Standard Deviation)

Performance Profile

Operation Count (Streaming Mode)

Standard Deviation uses Welford-style running sums of x and x^2 for exact O(1) update.

Operation	Count	Cost (cycles)	Subtotal
Ring buffer add/evict	1	3 cy	~3 cy
Update sum_x and sum_x2	2	2 cy	~4 cy
Compute variance via shortcut formula	1	5 cy	~5 cy
sqrt (variance -> std dev)	1	14 cy	~14 cy
NaN guard + state update	1	2 cy	~2 cy
Total	O(1)	—	~28 cy

O(1) per update. sqrt() dominates at ~14 cy. Periodic resync prevents catastrophic cancellation in the shortcut variance formula for near-constant series.

Metric	Score	Notes
Throughput	1.5ns/bar	SIMD-accelerated batch processing.
Allocations	0	Zero-allocation hot path.
Complexity	O(1)	Constant time streaming updates.
Accuracy	10/10	Matches iterative calculation with high precision.

Validation

Validated against external libraries to ensure correctness.

Library	Status	Notes
Skender	✅	Matches GetStdDev (Population).
TA-Lib	✅	Matches STDDEV (Population).
Tulip	✅	Matches stddev (Population).

Usage

using QuanTAlib;

// Create a 20-period Standard Deviation (Sample)
var stdDev = new StdDev(20, isPopulation: false);

// Update with a new value
var result = stdDev.Update(new TValue(DateTime.UtcNow, 100.0));

// Get the last value
double value = stdDev.Last.Value;