| 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
