doc headers

lib/statistics/acf/Acf.Validation.Tests.cs

@@ -114,11 +114,11 @@ public class AcfValidationTests
         // For white noise, ACF at any lag > 0 should be close to zero
         var acf = new Acf(100, 5);
 
-        // Generate pseudo-random values with zero mean
-        var random = new Random(42);
+        // Generate pseudo-random values with zero mean via GBM log-returns
+        var random = new GBM(startPrice: 100.0, sigma: 1.0, seed: 42);
         for (int i = 0; i < 500; i++)
         {
-            double val = random.NextDouble() * 2 - 1; // Uniform [-1, 1]
+            double val = Math.Log(random.Next().Close / 100.0); // ~N(0, vol²*dt) centered near 0
             acf.Update(new TValue(DateTime.UtcNow.AddSeconds(i), val));
         }
 
@@ -215,12 +215,12 @@ public class AcfValidationTests
 
         double[] ar1Data = new double[n];
         ar1Data[0] = 0;
-        var random = new Random(42);
+        var random = new GBM(startPrice: 100.0, sigma: 1.0, seed: 42);
 
         // Generate AR(1) process
         for (int i = 1; i < n; i++)
         {
-            double epsilon = (random.NextDouble() * 2 - 1) * 0.1; // Small noise
+            double epsilon = Math.Log(random.Next().Close / 100.0) * 0.1; // Small noise
             ar1Data[i] = phi * ar1Data[i - 1] + epsilon;
         }
 

lib/statistics/acf/Acf.md

@@ -1,5 +1,22 @@
 # ACF: Autocorrelation Function
 
+| Property         | Value                            |
+| ---------------- | -------------------------------- |
+| **Category**     | Statistic                        |
+| **Inputs**       | Source (close)                          |
+| **Parameters**   | `period`, `lag` (default 1)                      |
+| **Outputs**      | Single series (Acf)                       |
+| **Output range** | Varies (see docs)                     |
+| **Warmup**       | `period` bars                          |
+
+### TL;DR
+
+- The Autocorrelation Function (ACF) measures the correlation of a time series with a lagged copy of itself.
+- Parameterized by `period`, `lag` (default 1).
+- Output range: Varies (see docs).
+- Requires `period` bars of warmup before first valid output (IsHot = true).
+- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
+
 > "The past doesn't predict the future, but it whispers patterns to those who listen."
 
 The Autocorrelation Function (ACF) measures the correlation of a time series with a lagged copy of itself. It is fundamental for identifying repeating patterns, seasonal effects, and determining the order of time series models like ARMA/ARIMA.
@@ -159,4 +176,4 @@ A random walk should have ACF ≈ 0 at all lags. Significant ACF values indicate
 
 - Box, G.E.P., Jenkins, G.M. (1970). *Time Series Analysis: Forecasting and Control*. Holden-Day.
 - Hamilton, J.D. (1994). *Time Series Analysis*. Princeton University Press.
-- Yule, G.U. (1927). "On a Method of Investigating Periodicities in Disturbed Series." *Philosophical Transactions of the Royal Society*.
+- Yule, G.U. (1927). "On a Method of Investigating Periodicities in Disturbed Series." *Philosophical Transactions of the Royal Society*.