QuanTAlib/lib/trends/sma/Sma.md

SMA: Simple Moving Average

"The vanilla ice cream of technical analysis. Boring, ubiquitous, and the only thing your grandfather and your high-frequency trading bot agree on."

The Simple Moving Average (SMA) is the unweighted arithmetic mean of the last N data points. It acts as a low-pass filter, smoothing out high-frequency noise to reveal the underlying trend. While conceptually simple, efficient implementation on modern hardware requires careful attention to memory access patterns and vectorization.

Historical Context

The concept of a moving average dates back to 1901 (R.H. Hooker) for smoothing weather data, but it became a staple of financial analysis in the mid-20th century. It is the baseline against which all other averages are compared.

Architecture & Physics

The naive implementation of SMA sums N numbers at every step, resulting in O(N) complexity. QuanTAlib uses an optimized O(1) approach.

O(1) Running Sum

A running Sum and a RingBuffer of history are maintained.

Sum_{new} = Sum_{old} - Value_{oldest} + Value_{new} SMA = \frac{Sum_{new}}{N}

This ensures that calculating an SMA(200) takes the exact same time as an SMA(10).

Drift Correction

Floating-point addition is not associative. Repeatedly adding and subtracting values from a running sum introduces cumulative error (drift) over millions of ticks. QuanTAlib implements a periodic Resync mechanism (every 1000 ticks) that recalculates the sum from scratch to ensure precision remains within 1e-9 of the true mean.

SIMD Optimization

For batch processing of large datasets, Sma.Batch utilizes System.Runtime.Intrinsics (AVX2/AVX-512) to process multiple data points in parallel, significantly outperforming scalar loops.

Mathematical Foundation

1. The Mean

SMA_t = \frac{1}{N} \sum_{i=0}^{N-1} P_{t-i}

Performance Profile

Metric	Score	Notes
Throughput	10	SIMD-optimized; processes millions of bars/sec.
Allocations	0	Zero-allocation in hot paths.
Complexity	O(1)	Constant time regardless of period N.
Accuracy	10	Exact arithmetic mean.
Timeliness	3	Significant lag (\approx N/2).
Overshoot	0	Never overshoots the input data range.
Smoothness	5	Smooth, but susceptible to "drop-off" jumps.

Validation

Library	Status	Notes
TA-Lib	✅	Matches TA_SMA exactly.
Skender	✅	Matches GetSma exactly.
Tulip	✅	Matches sma exactly.
Ooples	✅	Matches CalculateSimpleMovingAverage.

Common Pitfalls

1. Lag: SMA has the most lag of all moving averages (Lag \approx N/2).
2. Drop-off Effect: An old, large outlier dropping out of the window causes the SMA to jump, even if the current price is flat. This "Barker effect" is why EMAs are often preferred.
3. NaN Handling: A single NaN in the history window corrupts the entire SMA. QuanTAlib handles this by substituting the last valid value.