- Zelen-Severo CDF aproximation

- p-value for varianceRatioTest

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/VarianceRatioTest.kt

@@ -9,10 +9,11 @@ import space.kscience.kmath.operations.DoubleField.pow
 import space.kscience.kmath.operations.algebra
 import space.kscience.kmath.operations.bufferAlgebra
 import space.kscience.kmath.operations.fold
+import kotlin.math.absoluteValue
 
 
 // TODO: add p-value with formula: 2*(1 - cdf(|zScore|))
-public data class VarianceRatioTestResult(val varianceRatio: Double=1.0, val zScore: Double=0.0)
+public data class VarianceRatioTestResult(val varianceRatio: Double=1.0, val zScore: Double=0.0, val pValue: Double=0.5)
     /**
      * Container class for Variance Ratio Test result:
      * ratio itself, corresponding Z-score, also it's p-value
@@ -23,6 +24,7 @@ public fun varianceRatioTest(series: Series<Double>, shift: Int, homoscedastic:
     /**
      * Calculates the Z-statistic and the p-value for the Lo and MacKinlay's Variance Ratio test (1987)
      * under Homoscedastic or Heteroscedstic assumptions
+     * with two-sided p-value test
      * 	https://ssrn.com/abstract=346975
      * **/
 
@@ -63,6 +65,11 @@ public fun varianceRatioTest(series: Series<Double>, shift: Int, homoscedastic:
         }
 
         val zScore = (varianceRatio - 1) / phi.pow(0.5)
-        return VarianceRatioTestResult(varianceRatio, zScore)
+        val pValue = 2*(1 - zSNormalCDF(zScore.absoluteValue))
+        return VarianceRatioTestResult(varianceRatio, zScore, pValue)
     }
 }
+
+
+
+

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/zSNormalCdf.kt

@@ -0,0 +1,24 @@
+/*
+ * Copyright 2018-2023 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.series
+
+import space.kscience.kmath.operations.DoubleField.pow
+import kotlin.math.PI
+import kotlin.math.absoluteValue
+import kotlin.math.exp
+
+public fun zSNormalCDF(x: Double): Double {
+
+    /**
+     * Zelen & Severo approximation for the standard normal CDF.
+     * The error is bounded by 7.5 * 10e-8.
+     * */
+
+    val t = 1 / (1 + 0.2316419 * x.absoluteValue)
+    val summ = 0.319381530*t - 0.356563782*t.pow(2) + 1.781477937*t.pow(3) - 1.821255978*t.pow(4) + 1.330274429*t.pow(5)
+    val temp = summ * exp(-x.absoluteValue.pow(2) / 2) / (2 * PI).pow(0.5)
+    return if (x >= 0)  1 - temp else temp
+}

kmath-stat/src/commonTest/kotlin/space/kscience/kmath/series/TestVarianceRatioTest.kt

@@ -21,9 +21,11 @@ class TestVarianceRatioTest {
             assertEquals(1.818181, resultHomo.varianceRatio, 1e-6)
             // homoscedastic zScore
             assertEquals(2.587318, resultHomo.zScore, 1e-6)
+            assertEquals(.0096, resultHomo.pValue, 1e-4)
             val resultHetero = varianceRatioTest(monotonicData, 2, homoscedastic = false)
             // heteroscedastic zScore
             assertEquals(0.819424, resultHetero.zScore, 1e-6)
+            assertEquals(.4125, resultHetero.pValue, 1e-4)
         }
     }
 
@@ -35,9 +37,11 @@ class TestVarianceRatioTest {
             assertEquals(0.0, resultHomo.varianceRatio, 1e-6)
             // homoscedastic zScore
             assertEquals(-3.162277, resultHomo.zScore, 1e-6)
+            assertEquals(.0015, resultHomo.pValue, 1e-4)
             val resultHetero = varianceRatioTest(volatileData, 2, homoscedastic = false)
             // heteroscedastic zScore
             assertEquals(-1.0540925, resultHetero.zScore, 1e-6)
+            assertEquals(.2918, resultHetero.pValue, 1e-4)
         }
     }
 
@@ -62,6 +66,7 @@ class TestVarianceRatioTest {
             val result = varianceRatioTest(zeroVolData, 4)
             assertEquals(1.0, result.varianceRatio, 1e-6)
             assertEquals(0.0, result.zScore, 1e-6)
+            assertEquals(0.5, result.pValue, 1e-4)
         }
     }
 }