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validation and profiles

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Miha Kralj
2026-02-26 22:02:52 -08:00
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lib/statistics/granger/Granger.md
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@@ -68,6 +68,21 @@ where $q = 1$ (one restriction: $d_2 = 0$) and $k = 3$ (unrestricted model param
## Performance Profile
### Operation Count (Streaming Mode)
Granger causality fits two rolling OLS regressions (restricted and unrestricted) per bar using sliding-window normal equations.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Ring buffer add/evict (2 series) | 2 | 3 cy | ~6 cy |
| Restricted OLS (AR of Y) | L ops | 8 cy | ~8L cy |
| Unrestricted OLS (AR of Y + lags of X) | 2L ops | 8 cy | ~16L cy |
| RSS computation (2 models) | 2N | 2 cy | ~4N cy |
| F-statistic calculation | 1 | 5 cy | ~5 cy |
| **Total (L=2, N=30)** | **O(L*N)** | — | **~189 cy** |
O(L·N) per update where L = number of lags, N = period. Heavy enough that batch mode (pre-computing all bars at once) is preferred for historical analysis.
| Metric | Value |
| :--- | :--- |
| Update complexity | O(1) amortized, O(N) for SSR2 loop |