3.0 KiB
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
We maintain a running Sum and a RingBuffer of history.
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
The implementation is optimized for both streaming (latency) and batch (throughput) scenarios.
Zero-Allocation Design
The RingBuffer is pre-allocated at initialization. All updates are performed in-place using scalar operations or SIMD intrinsics, ensuring no heap allocations occur during the hot path.
| Metric | Score | Notes |
|---|---|---|
| Throughput | High | Optimized running sum |
| Complexity | O(1) | Constant time update |
| Accuracy | 5/10 | Baseline accuracy, unweighted |
| Timeliness | 4/10 | Significant lag (N/2) |
| Overshoot | 8/10 | Generally stable, no projection |
| Smoothness | 6/10 | Susceptible to "drop-off" effect |
Validation
Validated against TA-Lib (TA_SMA) and Skender.Stock.Indicators.
Common Pitfalls
- Lag: SMA has the most lag of all moving averages (Lag
\approx N/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.
- NaN Handling: A single
NaNin the history window corrupts the entire SMA. QuanTAlib handles this by substituting the last valid value.