| int __stdcall NDK_ARCHTEST | ( | double * | X, |
| size_t | N, | ||
| size_t | K, | ||
| double | alpha, | ||
| WORD | method, | ||
| WORD | retType, | ||
| double * | retVal | ||
| ) |
Calculates the p-value of the ARCH effect test (i.e. the white-noise test for the squared time series).
- 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
-
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. NaN) at either end.
- The lag order (k) must be less than the time series size, or an error value (#VALUE!) is returned.
- The test hypothesis for the population autocorrelation:
\[H_{o}: \rho_{k}=\rho_o\] \[H_{1}: \rho_{k}\neq a\] Where:- \(H_{o}\) is the null hypothesis.
- \(H_{1}\) is the alternate hypothesis.
- \(\hat \rho_o\) is the assumed population autocorrelation function for lag k.
- \(k\) is the lag order.
- Assuming a normal distributed population, the sample autocorrelation has a normal distribution: \[\hat \rho_k \sim N(\rho_k,\sigma_{\rho_k}^2)\] Where:
- \(\hat \rho_k \) is the sample autocorrelation for lag k.
- \(\rho_k \) is the population autocorrelation for lag k.
- \(\sigma_{\rho_k}\) is the standard deviation of the sample autocorrelation function for lag k.
- The variance of the sample autocorrelation is computed as: \[ \sigma_{\rho_k}^2 = \frac{1+\sum_{j=1}^{k-1}\hat\rho_j^2}{T} \] Where:
- \(\sigma_{\rho_k}\) is the standard error of the sample autocorrelation for lag k.
- \(T\) is the sample data size.
- \(\hat\rho_j\) is the sample autocorrelation function for lag j.
- \(k\) is the lag order.
- This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level (\(\alpha/2\)).
- Requirements
-
Header SFSDK.H Library SFSDK.LIB DLL SFSDK.DLL
- Examples
-
| Namespace: | NumXLAPI |
| Class: | SFSDK |
| Scope: | Public |
| Lifetime: | Static |
| int NDK_ARCHTEST | ( | double[] | pData, |
| UInPtr | nSize, | ||
| int | nLag, | ||
| double | alpha, | ||
| UInt16 | argMethod, | ||
| UInt16 | retType, | ||
| out double | retVal | ||
| ) |
Calculates the p-value of the ARCH effect test (i.e. the white-noise test for the squared time series).
- 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
-
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. NaN) at either end.
- The lag order (k) must be less than the time series size, or an error value (#VALUE!) is returned.
- The test hypothesis for the population autocorrelation:
\[H_{o}: \rho_{k}=\rho_o\] \[H_{1}: \rho_{k}\neq a\] Where:- \(H_{o}\) is the null hypothesis.
- \(H_{1}\) is the alternate hypothesis.
- \(\hat \rho_o\) is the assumed population autocorrelation function for lag k.
- \(k\) is the lag order.
- Assuming a normal distributed population, the sample autocorrelation has a normal distribution: \[\hat \rho_k \sim N(\rho_k,\sigma_{\rho_k}^2)\] Where:
- \(\hat \rho_k \) is the sample autocorrelation for lag k.
- \(\rho_k \) is the population autocorrelation for lag k.
- \(\sigma_{\rho_k}\) is the standard deviation of the sample autocorrelation function for lag k.
- The variance of the sample autocorrelation is computed as: \[ \sigma_{\rho_k}^2 = \frac{1+\sum_{j=1}^{k-1}\hat\rho_j^2}{T} \] Where:
- \(\sigma_{\rho_k}\) is the standard error of the sample autocorrelation for lag k.
- \(T\) is the sample data size.
- \(\hat\rho_j\) is the sample autocorrelation function for lag j.
- \(k\) is the lag order.
- This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level (\(\alpha/2\)).
- 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
