NDK_XKURTTEST

int __stdcall NDK_XKURTTEST ( double *  X,
size_t  N,
double  alpha,
WORD  method,
WORD  retType,
double *  retVal 
)

Calculates the p-value of the statistical test for the population excess kurtosis (4th moment).

Returns
status code of the operation
Return values
NDK_SUCCESS  Operation successful
NDK_FAILED  Operation unsuccessful. See Macros for full list.
Parameters
[in] X is the sample data (a one dimensional array).
[in] N is the number of observations in X.
[in] alpha is the statistical significance level. If missing, a default of 5% is assumed.
[in] method is the statistical test to perform (1=parametric).
[in] retType is a switch to select the return output:
Method Value Description
TEST_PVALUE 1 P-Value
TEST_SCORE 2 Test statistics (aka score)
TEST_CRITICALVALUE 3 Critical value.
[out] retVal is the calculated test statistics.
Remarks
1. The data sample may include missing values (e.g. #N/A).
2. The test hypothesis for the population excess kurtosis:
\[H_{o}: K=0\]
\[H_{1}: K\neq 0\],
where:
  • \(H_{o}\) is the null hypothesis.
  • \(H_{1}\) is the alternate hypothesis.
3. For the case in which the underlying population distribution is normal, the sample excess kurtosis also has a normal sampling distribution: \(\hat K \sim N(0,\frac{24}{T})\), where: \(\hat k\) is the sample excess kurtosis (i.e. 4th moment). \(T\) is the number of non-missing values in the data sample. \(N(.)\) is the normal (i.e. gaussian) probability distribution function.
4. Using a given data sample, the sample excess kurtosis is calculated as:
\[\hat K (x)= \frac{\sum_{t=1}^T(x_t-\bar x)^4}{(T-1)\hat \sigma^4}-3\],
where:
  • \(\hat K(x)\) is the sample excess kurtosis.
  • \(x_i\) is the i-th non-missing value in the data sample.
  • \(T\) is the number of non-missing values in the data sample.
  • \(\hat \sigma\) is the sample standard deviation.
5. The underlying population distribution is assumed normal (gaussian)..
6. This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level \(\frac{\alpha}{2}\).
Requirements
Header SFSDK.H
Library SFSDK.LIB
DLL SFSDK.DLL
Examples


   
Namespace:  NumXLAPI
Class:  SFSDK
Scope:  Public
Lifetime:  Static
int NDK_XKURTTEST ( double[]  pData,
UIntPtr  nSize,
double  alpha,
UInt16  argMethod,
UInt16  retType,
out double  retVal 
)

Calculates the p-value of the statistical test for the population excess kurtosis (4th moment).

Returns
status code of the operation
Return values
NDK_SUCCESS  Operation successful
NDK_FAILED  Operation unsuccessful. See Macros for full list.
Parameters
[in] pData is the sample data (a one dimensional array).
[in] nSize is the number of observations in pData.
[in] alpha is the statistical significance level. If missing, a default of 5% is assumed.
[in] argMethod is the statistical test to perform (1=parametric).
[in] retType is a switch to select the return output:
Method Value Description
TEST_PVALUE 1 P-Value
TEST_SCORE 2 Test statistics (aka score)
TEST_CRITICALVALUE 3 Critical value.
[out] retVal is the calculated test statistics.
Remarks
1. The data sample may include missing values (e.g. #N/A).
2. The test hypothesis for the population excess kurtosis:
\[H_{o}: K=0\]
\[H_{1}: K\neq 0\],
where:
  • \(H_{o}\) is the null hypothesis.
  • \(H_{1}\) is the alternate hypothesis.
3. For the case in which the underlying population distribution is normal, the sample excess kurtosis also has a normal sampling distribution: \(\hat K \sim N(0,\frac{24}{T})\), where: \(\hat k\) is the sample excess kurtosis (i.e. 4th moment). \(T\) is the number of non-missing values in the data sample. \(N(.)\) is the normal (i.e. gaussian) probability distribution function.
4. Using a given data sample, the sample excess kurtosis is calculated as:
\[\hat K (x)= \frac{\sum_{t=1}^T(x_t-\bar x)^4}{(T-1)\hat \sigma^4}-3\],
where:
  • \(\hat K(x)\) is the sample excess kurtosis.
  • \(x_i\) is the i-th non-missing value in the data sample.
  • \(T\) is the number of non-missing values in the data sample.
  • \(\hat \sigma\) is the sample standard deviation.
5. The underlying population distribution is assumed normal (gaussian)..
6. This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level \(\frac{\alpha}{2}\).
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI
Class SFSDK
Scope Public
Lifetime Static
Package NumXLAPI.DLL
Examples

	
References
Hull, John C.; Options, Futures and Other DerivativesFinancial Times/ Prentice Hall (2011), ISBN 978-0132777421
Hans-Peter Deutsch; , Derivatives and Internal Models, Palgrave Macmillan (2002), ISBN 0333977068
John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay, Andrew Y. Lo; The Econometrics of Financial Markets; Princeton University Press; 2nd edition(Dec 09, 1996), ISBN: 691043019
* Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
* Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
* D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
* Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848