# NDK_EGARCH_RESID

 int __stdcall NDK_EGARCH_RESID ( double * pData, size_t nSize, double mu, const double * Alphas, size_t p, const double * Gammas, size_t g, const double * Betas, size_t q, WORD nInnovationType, double nu, WORD retType )

Returns an array of cells for the standardized residuals of a given GARCH model.

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Deprecated:
this function is being replaced by NDK_EGARCH_FITTED()
NDK_GARCH_VALIDATE()
Parameters
 [in] pData is the univariate time series data (a one dimensional array). [in] nSize is the number of observations in pData. [in] mu is the EGARCH model conditional mean (i.e. mu). [in] Alphas are the parameters of the ARCH(p) component model (starting with the lowest lag). [in] p is the number of elements in Alphas array [in] Gammas are the leverage parameters (starting with the lowest lag). [in] g is the number of elements in Gammas. Must be equal to (p-1). [in] Betas are the parameters of the GARCH(q) component model (starting with the lowest lag). [in] q is the number of elements in Betas array [in] nInnovationType is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) INNOVATION_GAUSSIAN Gaussian Distribution (default) INNOVATION_TDIST Student's T-Distribution, INNOVATION_GED Generalized Error Distribution (GED) [in] nu is the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function. [in] retType is a switch to select a residuals-type:raw or standardized. see RESID_RETVAL_FUNC
Remarks
1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The time series may include missing values (e.g. #N/A) at either end.
4. The number of gamma-coefficients must match the number of alpha-coefficients.
5. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
6. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
7. The standardized residuals have a mean of zero and a variance of one (1).
8. The E-GARCH model's standardized residuals is defined as:$\epsilon_t = \frac{a_t}{\sigma_t}$ $a_t = x_t - \mu$ Where:
• $$epsilon$$ is the E-GARCH model's standardized residual at time t.
• $$a_t$$ is the E-GARCH model's residual at time t.
• $$x_t$$ is the value of the time series at time t.
• $$\mu$$ is the E-GARCH mean.
• $$\sigma_t$$ is E-GARCH conditional volatility at time t.
Requirements
 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static
 int NDK_EGARCH_RESID ( double[] pData, UIntPtr nSize, double mu, double[] Alphas, UIntPtr p, double[] Gammas, double[] Betas, UIntPtr q, short nInnovationType, double nu, short retType )

Returns an array of cells for the standardized residuals of a given GARCH model.

Return Value

a value from NDK_RETCODE enumeration for the status of the call.

 NDK_SUCCESS operation successful Error Error Code
Deprecated:
this function is being replaced by NDK_EGARCH_FITTED()
NDK_GARCH_VALIDATE()
Parameters
 [in] pData is the univariate time series data (a one dimensional array). [in] nSize is the number of observations in pData. [in] mu is the EGARCH model conditional mean (i.e. mu). [in] Alphas are the parameters of the ARCH(p) component model (starting with the lowest lag). [in] p is the number of elements in Alphas array [in] Gammas are the leverage parameters (starting with the lowest lag). [in] g is the number of elements in Gammas. Must be equal to (p-1). [in] Betas are the parameters of the GARCH(q) component model (starting with the lowest lag). [in] q is the number of elements in Betas array [in] nInnovationType is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) INNOVATION_GAUSSIAN Gaussian Distribution (default) INNOVATION_TDIST Student's T-Distribution, INNOVATION_GED Generalized Error Distribution (GED) [in] nu is the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function. [in] retType is a switch to select a residuals-type:raw or standardized. see RESID_RETVAL_FUNC
Remarks
1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The time series may include missing values (e.g. #N/A) at either end.
4. The number of gamma-coefficients must match the number of alpha-coefficients.
5. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
6. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
7. The standardized residuals have a mean of zero and a variance of one (1).
8. The E-GARCH model's standardized residuals is defined as:$\epsilon_t = \frac{a_t}{\sigma_t}$ $a_t = x_t - \mu$ Where:
• $$epsilon$$ is the E-GARCH model's standardized residual at time t.
• $$a_t$$ is the E-GARCH model's residual at time t.
• $$x_t$$ is the value of the time series at time t.
• $$\mu$$ is the E-GARCH mean.
• $$\sigma_t$$ is E-GARCH conditional volatility at time t.
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI SFSDK Public Static NumXLAPI.DLL
Examples

References
* 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