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Miha Kralj
a7b7207801
- Updated mathematical foundations and performance profiles where necessary to maintain clarity and coherence.
50 lines
2.4 KiB
Markdown
50 lines
2.4 KiB
Markdown
# SMA: Simple Moving Average
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> "The vanilla ice cream of technical analysis. Boring, ubiquitous, and the only thing your grandfather and your high-frequency trading bot agree on."
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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.
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## Historical Context
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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.
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## Architecture & Physics
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The naive implementation of SMA sums $N$ numbers at every step, resulting in $O(N)$ complexity. QuanTAlib uses an optimized $O(1)$ approach.
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### O(1) Running Sum
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A running `Sum` and a `RingBuffer` of history are maintained.
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$$ Sum_{new} = Sum_{old} - Value_{oldest} + Value_{new} $$
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$$ SMA = \frac{Sum_{new}}{N} $$
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This ensures that calculating an SMA(200) takes the exact same time as an SMA(10).
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### Drift Correction
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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.
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### SIMD Optimization
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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.
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## Mathematical Foundation
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### 1. The Mean
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$$ SMA_t = \frac{1}{N} \sum_{i=0}^{N-1} P_{t-i} $$
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## Performance Profile
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The implementation is optimized for both streaming (latency) and batch (throughput) scenarios.
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## Validation
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Validated against TA-Lib (`TA_SMA`) and Skender.Stock.Indicators.
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### Common Pitfalls
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1. **Lag**: SMA has the most lag of all moving averages (Lag $\approx N/2$).
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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.
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3. **NaN Handling**: A single `NaN` in the history window corrupts the entire SMA. QuanTAlib handles this by substituting the last valid value.
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