test: setup common stability and robustness properties tracking

lib/statistics/pacf/Pacf.Quantower.Tests.cs

@@ -325,4 +325,4 @@ public class PacfIndicatorTests
 
         Assert.Equal(acfValue, pacfValue, 6); // Allow for minor floating-point differences
     }
-}
+}

lib/statistics/pacf/Pacf.Tests.cs

@@ -575,4 +575,4 @@ public class PacfTests
     }
 
     #endregion
-}
+}

lib/statistics/pacf/Pacf.Validation.Tests.cs

@@ -105,13 +105,16 @@ public class PacfValidationTests
         // For AR(1) process: x_t = φ*x_{t-1} + ε_t
         // PACF should be significant at lag 1 and cut off (near zero) after
         double phi = 0.7; // AR(1) coefficient
-        var random = new GBM(startPrice: 100.0, sigma: 1.0, seed: 42);
-        var arProcess = new List<double> { 100.0 };
 
-        // Generate AR(1) process
+        // Use incremental bar-to-bar log-returns as i.i.d. noise: log(close_i / close_{i-1})
+        var gbm = new GBM(startPrice: 100.0, sigma: 0.2, seed: 42);
+        var bars = gbm.Fetch(501, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
+        var arProcess = new List<double> { 0.0 };
+
+        // Generate AR(1) process using incremental log-returns as white noise ε
         for (int i = 1; i < 500; i++)
         {
-            double noise = Math.Log(random.Next().Close / 100.0); // ~N(0, vol²*dt) noise
+            double noise = Math.Log(bars[i].Close / bars[i - 1].Close); // i.i.d. incremental return
             double newValue = phi * arProcess[^1] + noise;
             arProcess.Add(newValue);
         }
@@ -345,4 +348,4 @@ public class PacfValidationTests
     }
 
     #endregion
-}
+}

lib/statistics/pacf/Pacf.cs

@@ -294,9 +294,10 @@ public sealed class Pacf : AbstractBase
 
     public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
     {
+        Reset();
         foreach (double value in source)
         {
-            Update(new TValue(DateTime.UtcNow, value));
+            Update(new TValue(DateTime.MinValue, value));
         }
     }
 

lib/statistics/pacf/Pacf.md

@@ -15,7 +15,7 @@
 - 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.
+- Validated against mathematical properties and Durbin-Levinson recursion expectations.
 
 > "Strip away the intermediaries, and you'll see the true direct relationship."