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89 lines
3.3 KiB
Markdown
89 lines
3.3 KiB
Markdown
# Covariance: Covariance
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Statistic |
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| **Inputs** | Source (close) |
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| **Parameters** | `period`, `isPopulation` (default false) |
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| **Outputs** | Single series (Cov) |
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| **Output range** | Varies (see docs) |
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| **Warmup** | `period` bars |
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### TL;DR
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- Covariance measures the joint variability of two random variables.
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- Parameterized by `period`, `ispopulation` (default false).
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- Output range: Varies (see docs).
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- Requires `period` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "Correlation is just covariance normalized by standard deviation. But sometimes you want the raw, unadulterated relationship."
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Covariance measures the joint variability of two random variables. It indicates the direction of the linear relationship between variables.
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## Architecture & Physics
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Covariance is calculated using a sliding window approach. It maintains running sums of $x$, $y$, and $xy$ to allow for $O(1)$ updates.
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* **Positive Covariance**: Indicates that the two variables tend to move in the same direction.
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* **Negative Covariance**: Indicates that the two variables tend to move in opposite directions.
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* **Zero Covariance**: Indicates that the two variables are uncorrelated.
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## Mathematical Foundation
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### 1. Population Covariance
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$$ Cov(X, Y) = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{n} $$
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### 2. Sample Covariance
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$$ Cov(X, Y) = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{n - 1} $$
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### 3. Computational Formula (Running Sums)
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$$ Cov(X, Y) = \frac{\sum xy - \frac{(\sum x)(\sum y)}{n}}{n} \quad \text{(or } n-1 \text{)} $$
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## Performance Profile
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### Operation Count (Streaming Mode)
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Covariance uses a dual-input sliding window with running cross-product sums for O(1) update.
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| Ring buffer add/evict (2 inputs) | 2 | 3 cy | ~6 cy |
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| Update 3 running sums (Sx, Sy, Sxy) | 3 | 2 cy | ~6 cy |
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| Compute covariance formula | 1 | 5 cy | ~5 cy |
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| NaN guard + state update | 1 | 2 cy | ~2 cy |
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| **Total** | **O(1)** | — | **~19 cy** |
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O(1) per update using online running sums. Periodic resync every 1000 bars prevents floating-point drift accumulation.
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| Metric | Score | Notes |
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| :--- | :--- | :--- |
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| **Throughput** | High | $O(1)$ updates using running sums. |
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| **Allocations** | 0 | No heap allocations in hot path. |
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| **Complexity** | $O(1)$ | Constant time update regardless of period. |
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| **Accuracy** | High | Uses `double` precision; periodic resync prevents drift. |
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## Validation
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| Library | Status | Notes |
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| :--- | :--- | :--- |
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| **Manual** | ✅ | Verified against manual calculation. |
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| **Excel** | ✅ | Matches `COVARIANCE.P` and `COVARIANCE.S`. |
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## Usage
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```csharp
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using QuanTAlib;
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// Create a Covariance indicator with period 20 (Sample Covariance by default)
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var cov = new Covariance(20);
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// Update with new values
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cov.Update(price1, price2);
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// Access the result
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double result = cov.Last.Value;
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