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-- refactoring

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This commit is contained in:
mrFendel 2023-05-05 18:45:54 +03:00
parent 1e27af9cf5
commit 16385b5f4e
3 changed files with 51 additions and 52 deletions
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12
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/zSNormalCdf.kt → kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/zSNormalCdf.kt
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@ -3,19 +3,19 @@
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. * 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 package space.kscience.kmath.distributions
import space.kscience.kmath.operations.DoubleField.pow import space.kscience.kmath.operations.DoubleField.pow
import kotlin.math.PI import kotlin.math.PI
import kotlin.math.absoluteValue import kotlin.math.absoluteValue
import kotlin.math.exp import kotlin.math.exp
public fun zSNormalCDF(x: Double): Double {
/** /**
* Zelen & Severo approximation for the standard normal CDF. * Zelen & Severo approximation for the standard normal CDF.
* The error is bounded by 7.5 * 10e-8. * The error is bounded by 7.5 * 10e-8.
* */ * */
public fun zSNormalCDF(x: Double): Double {
val t = 1 / (1 + 0.2316419 * x.absoluteValue) 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 summ = 0.319381530*t - 0.356563782*t.pow(2) + 1.781477937*t.pow(3) - 1.821255978*t.pow(4) + 1.330274429*t.pow(5)

2
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/SeriesAlgebra.kt
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@ -216,7 +216,7 @@ public open class SeriesAlgebra<T, out A : Ring<T>, out BA : BufferAlgebra<T, A>
override fun multiply(left: Buffer<T>, right: Buffer<T>): Buffer<T> = left.zip(right) { l, r -> l * r } override fun multiply(left: Buffer<T>, right: Buffer<T>): Buffer<T> = left.zip(right) { l, r -> l * r }
public fun Buffer<T>.diff(shift: Int=1): Buffer<T> = this.zipWithShift(shift) {l, r -> r - l} public fun Buffer<T>.difference(shift: Int=1): Buffer<T> = this.zipWithShift(shift) {l, r -> r - l}
public companion object public companion object
} }

89
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/VarianceRatioTest.kt
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@ -5,6 +5,7 @@
package space.kscience.kmath.series package space.kscience.kmath.series
import space.kscience.kmath.distributions.zSNormalCDF
import space.kscience.kmath.operations.DoubleField.pow import space.kscience.kmath.operations.DoubleField.pow
import space.kscience.kmath.operations.algebra import space.kscience.kmath.operations.algebra
import space.kscience.kmath.operations.bufferAlgebra import space.kscience.kmath.operations.bufferAlgebra
@ -12,62 +13,60 @@ import space.kscience.kmath.operations.fold
import kotlin.math.absoluteValue import kotlin.math.absoluteValue
// TODO: add p-value with formula: 2*(1 - cdf(|zScore|)) /**
* Container class for Variance Ratio Test result:
* ratio itself, corresponding Z-score, also it's p-value
* **/
public data class VarianceRatioTestResult(val varianceRatio: Double=1.0, val zScore: Double=0.0, val pValue: Double=0.5) 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
* **/
public fun varianceRatioTest(series: Series<Double>, shift: Int, homoscedastic: Boolean=true): VarianceRatioTestResult {
/** /**
* Calculates the Z-statistic and the p-value for the Lo and MacKinlay's Variance Ratio test (1987) * Calculates the Z-statistic and the p-value for the Lo and MacKinlay's Variance Ratio test (1987)
* under Homoscedastic or Heteroscedstic assumptions * under Homoscedastic or Heteroscedstic assumptions
* with two-sided p-value test * with two-sided p-value test
* https://ssrn.com/abstract=346975 * https://ssrn.com/abstract=346975
* **/ * **/
public fun SeriesAlgebra<Double, *, *, *>.varianceRatioTest(series: Series<Double>, shift: Int, homoscedastic: Boolean=true): VarianceRatioTestResult {
require(shift > 1) {"Shift must be greater than one"} require(shift > 1) {"Shift must be greater than one"}
require(shift < series.size) {"Shift must be smaller than sample size"} require(shift < series.size) {"Shift must be smaller than sample size"}
val sum = { x: Double, y: Double -> x + y } val sum = { x: Double, y: Double -> x + y }
with(Double.algebra.bufferAlgebra.seriesAlgebra()) {
val mean = series.fold(0.0, sum) / series.size val mean = series.fold(0.0, sum) / series.size
val demeanedSquares = series.map { power(it - mean, 2) } val demeanedSquares = series.map { (it - mean).pow(2) }
val variance = demeanedSquares.fold(0.0, sum) val variance = demeanedSquares.fold(0.0, sum)
if (variance == 0.0) return VarianceRatioTestResult() if (variance == 0.0) return VarianceRatioTestResult()
var seriesAgg = series var seriesAgg = series
for (i in 1..<shift) { for (i in 1..<shift) {
seriesAgg = seriesAgg.zip(series.moveTo(i)) { v1, v2 -> v1 + v2 } seriesAgg = seriesAgg.zip(series.moveTo(i)) { v1, v2 -> v1 + v2 }
}
val demeanedSquaresAgg = seriesAgg.map { power(it - shift * mean, 2) }
val varianceAgg = demeanedSquaresAgg.fold(0.0, sum)
val varianceRatio =
varianceAgg * (series.size.toDouble() - 1) / variance / (series.size.toDouble() - shift.toDouble() + 1) / (1 - shift.toDouble()/series.size.toDouble()) / shift.toDouble()
// calculating asymptotic variance
val phi = if (homoscedastic) { // under homoscedastic null hypothesis
2 * (2 * shift - 1.0) * (shift - 1.0) / (3 * shift * series.size)
} else { // under heteroscedastic null hypothesis
var accumulator = 0.0
for (j in 1..<shift) {
val temp = demeanedSquares
val delta = series.size * temp.zipWithShift(j) { v1, v2 -> v1 * v2 }.fold(0.0, sum) / variance.pow(2)
accumulator += delta * 4 * (shift - j).toDouble().pow(2) / shift.toDouble().pow(2)
}
accumulator
}
val zScore = (varianceRatio - 1) / phi.pow(0.5)
val pValue = 2*(1 - zSNormalCDF(zScore.absoluteValue))
return VarianceRatioTestResult(varianceRatio, zScore, pValue)
} }
val demeanedSquaresAgg = seriesAgg.map { (it - shift * mean).pow(2) }
val varianceAgg = demeanedSquaresAgg.fold(0.0, sum)
val varianceRatio =
varianceAgg * (series.size.toDouble() - 1) / variance / (series.size.toDouble() - shift.toDouble() + 1) / (1 - shift.toDouble()/series.size.toDouble()) / shift.toDouble()
// calculating asymptotic variance
val phi = if (homoscedastic) { // under homoscedastic null hypothesis
2 * (2 * shift - 1.0) * (shift - 1.0) / (3 * shift * series.size)
} else { // under heteroscedastic null hypothesis
var accumulator = 0.0
for (j in 1..<shift) {
val temp = demeanedSquares
val delta = series.size * temp.zipWithShift(j) { v1, v2 -> v1 * v2 }.fold(0.0, sum) / variance.pow(2)
accumulator += delta * 4 * (shift - j).toDouble().pow(2) / shift.toDouble().pow(2)
}
accumulator
}
val zScore = (varianceRatio - 1) / phi.pow(0.5)
val pValue = 2*(1 - zSNormalCDF(zScore.absoluteValue))
return VarianceRatioTestResult(varianceRatio, zScore, pValue)
} }