# NDK_WNTEST

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

Computes the p-value of the statistical portmanteau test (i.e. whether any of a group of autocorrelations of a time series are different from zero).

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 univariate time series data (a one dimensional array).
[in] N is the number of observations in X.
[in] K is the lag order (e.g. k=0 (no lag), k=1 (1st lag), etc.).
[in] alpha is the statistical significance level. If missing, a default of 5% is assumed.
[in] method is the statistical test to perform (1=Ljung-Box).
[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 time series is homogeneous or equally spaced.
2. The time series may include missing values (NaN) at either end.
3. The test hypothesis for white-noise: $H_{o}: \rho_{1}=\rho_{2}=...=\rho_{m}=0$ $H_{1}: \exists \rho_{k}\neq 0$ $1\leq k \leq m$ Where:
• $$H_{o}$$ is the null hypothesis.
• $$H_{1}$$ is the alternate hypothesis.
• $$\rho_k$$ is the population autocorrelation function for lag k
• $$m$$ is the maximum number of lags included in the white-noise test.
4. The Ljung Box test  modified $$Q^*(m)$$ statistic is computed as: $Q^* =T(T+2)\sum_{j=1}^{m}\frac{\hat\rho_{j}^2}{T-l}$ Where:
• $$m$$ is the maximum number of lags included in the test.
• $$\hat\rho_j$$ is the sample autocorrelation at lag j.
• $$T$$ is the number of non-missing values in the data sample.
5. The Ljung Box test  modified $$Q^*$$ statistic has an asymptotic chi-square distribution with $$m$$ degrees of freedom and can be used to test the null hypothesis that the time series is not serially correlated. $Q^*(m) \sim \chi_{\nu=m}^2()$ Where:
• $$\chi_{\nu}^2()$$ is the Chi-square probability distribution function.
• $$\nu$$ is the degrees of freedom for the Chi-square distribution.
6. The Ljung Box test  is a suitable test for all sample sizes including small ones.
7. This is one-side (i.e. one-tail) test, so the computed p-value should be compared with the whole significance level ($\alpha$).
8. In practice, the selection of $$m$$ may affect the performance of the $$Q(m)$$ statistic. Several values of m are often used. Simulation studies suggest that the choice of $$m\approx \ln(T)$$ provides better power performance.
Requirements
Examples



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

Computes the p-value of the statistical portmanteau test (i.e. whether any of a group of autocorrelations of a time series are different from zero).

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 univariate time series data (a one dimensional array).
[in] nSize is the number of observations in pData.
[in] nLag is the lag order (e.g. k=0 (no lag), k=1 (1st lag), etc.).
[in] alpha is the statistical significance level. If missing, a default of 5% is assumed.
[in] argMethod is the statistical test to perform (1=Ljung-Box).
[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 time series is homogeneous or equally spaced.
2. The time series may include missing values (NaN) at either end.
3. The test hypothesis for white-noise: $H_{o}: \rho_{1}=\rho_{2}=...=\rho_{m}=0$ $H_{1}: \exists \rho_{k}\neq 0$ $1\leq k \leq m$ Where:
• $$H_{o}$$ is the null hypothesis.
• $$H_{1}$$ is the alternate hypothesis.
• $$\rho_k$$ is the population autocorrelation function for lag k
• $$m$$ is the maximum number of lags included in the white-noise test.
4. The Ljung Box test  modified $$Q^*(m)$$ statistic is computed as: $Q^* =T(T+2)\sum_{j=1}^{m}\frac{\hat\rho_{j}^2}{T-l}$ Where:
• $$m$$ is the maximum number of lags included in the test.
• $$\hat\rho_j$$ is the sample autocorrelation at lag j.
• $$T$$ is the number of non-missing values in the data sample.
5. The Ljung Box test  modified $$Q^*$$ statistic has an asymptotic chi-square distribution with $$m$$ degrees of freedom and can be used to test the null hypothesis that the time series is not serially correlated. $Q^*(m) \sim \chi_{\nu=m}^2()$ Where:
• $$\chi_{\nu}^2()$$ is the Chi-square probability distribution function.
• $$\nu$$ is the degrees of freedom for the Chi-square distribution.
6. The Ljung Box test  is a suitable test for all sample sizes including small ones.
7. This is one-side (i.e. one-tail) test, so the computed p-value should be compared with the whole significance level ($\alpha$).
8. In practice, the selection of $$m$$ may affect the performance of the $$Q(m)$$ statistic. Several values of m are often used. Simulation studies suggest that the choice of $$m\approx \ln(T)$$ provides better power performance.
6. Special cases: By definition, $$\hat{\rho}(0) \equiv 1.0$$
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI SFSDK Public Static 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