Jarque-Bera hypothesis test of normality

Function JBTest(ReturnVector, SignificanceLevel)

Jarque-Bera hypothesis

test of normality:


' Andreas Steiner, March 2006
' http://www.andreassteiner.net/performanceanalysis

n = WorksheetFunction.Max(ReturnVector.Columns.Count, ReturnVector.Rows.Count)

ReturnVectorMean = WorksheetFunction.Average(ReturnVector)
ReturnVectorStDev = WorksheetFunction.StDev(ReturnVector)

' Normalize returns
ReDim NormalizedReturns(1 To n)
For i = 1 To n
NormalizedReturns(i) = (ReturnVector(i) - ReturnVectorMean) / ReturnVectorStDev
Next i

' Calculate 3rd and 4th moments (skewness and kurtosis)
S = 0
K = 0
For i = 1 To n
S = S + NormalizedReturns(i) ^ 3
K = K + NormalizedReturns(i) ^ 4
Next i
S = S / n
K = K / n - 3

JB = n * ((S ^ 2) / 6 + (K ^ 2) / 24)
pValue = WorksheetFunction.ChiDist(JB, 2)

JBTest = (SignificanceLevel < pValue)

End Function
Function JBCriticalValue(ReturnVector, SignificanceLevel)
' Jarque-Bera hypothesis test of normality.
'
' Andreas Steiner, March 2006
' http://www.andreassteiner.net/performanceanalysis

JBCriticalValue = WorksheetFunction.ChiInv(SignificanceLevel, 2)

End Function
Function JBpValue(ReturnVector, SignificanceLevel)
' Jarque-Bera hypothesis test of normality.
'
' Andreas Steiner, March 2006
' http://www.andreassteiner.net/performanceanalysis

n = WorksheetFunction.Max(ReturnVector.Columns.Count, ReturnVector.Rows.Count)

ReturnVectorMean = WorksheetFunction.Average(ReturnVector)
ReturnVectorStDev = WorksheetFunction.StDev(ReturnVector)

' Normalize returns
ReDim NormalizedReturns(1 To n)
For i = 1 To n
NormalizedReturns(i) = (ReturnVector(i) - ReturnVectorMean) / ReturnVectorStDev
Next i

' Calculate 3rd and 4th moments (skewness and kurtosis)
S = 0
K = 0
For i = 1 To n
S = S + NormalizedReturns(i) ^ 3
K = K + NormalizedReturns(i) ^ 4
Next i
S = S / n
K = K / n - 3

JB = n * ((S ^ 2) / 6 + (K ^ 2) / 24)
JBpValue = WorksheetFunction.ChiDist(JB, 2)

End Function
Function JBStat(ReturnVector, SignificanceLevel)
' Jarque-Bera hypothesis test of normality.
'
' Andreas Steiner, March 2006
' http://www.andreassteiner.net/performanceanalysis

n = WorksheetFunction.Max(ReturnVector.Columns.Count, ReturnVector.Rows.Count)

ReturnVectorMean = WorksheetFunction.Average(ReturnVector)
ReturnVectorStDev = WorksheetFunction.StDev(ReturnVector)

' Normalize returns
ReDim NormalizedReturns(1 To n)
For i = 1 To n
NormalizedReturns(i) = (ReturnVector(i) - ReturnVectorMean) / ReturnVectorStDev
Next i

' Calculate 3rd and 4th moments (skewness and kurtosis)
S = 0
K = 0
For i = 1 To n
S = S + NormalizedReturns(i) ^ 3
K = K + NormalizedReturns(i) ^ 4
Next i
S = S / n
K = K / n - 3

JBStat = n * ((S ^ 2) / 6 + (K ^ 2) / 24)

End Function
EXCEL FUNCTION