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- Zelen-Severo CDF aproximation

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- p-value for varianceRatioTest
This commit is contained in:
mrFendel 2023-04-19 17:13:47 +03:00
parent 0193349f94
commit 1e27af9cf5
3 changed files with 38 additions and 2 deletions
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11
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/VarianceRatioTest.kt
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@ -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)
}
}

24
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/zSNormalCdf.kt Normal file
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@ -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
}

5
kmath-stat/src/commonTest/kotlin/space/kscience/kmath/series/TestVarianceRatioTest.kt
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@ -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)
}
}
}