# NDK_EGARCH_LRVAR

 int __stdcall NDK_EGARCH_LRVAR ( double mu, const double * Alphas, size_t p, const double * Gammas, size_t g, const double * Betas, size_t q, WORD nInnovationType, double nu, double * retVal )

Calculates the long-run average volatility for a given E-GARCH model.

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Parameters
 [in] mu is the GARCH 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,out] 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. [out] retVal is the calculated Long run volatility.
Remarks
1. The underlying model is described here.
2. The EGARCH long-run average log variance is defined as: $$\ln V_L=\frac{\alpha_o+\eta \times \sum_{i=1}^p\alpha_i}{1-\sum_{j=1}^q\beta_j}$$ Where:
• Gaussian distributed innovations/shocks: $$\eta=\sqrt{\frac{\pi}{2}}$$
• GED distributed innovations/shocks. $$\eta=\frac{\Gamma(2/\nu )}{\sqrt{\Gamma(1/\nu)\times\Gamma(3/\nu)}}$$
• Student's t-Distributed innovations/shocks. $$\eta=\frac{\sqrt{\nu-2}\times\Gamma(\frac{\nu-1}{2})}{\sqrt{\pi}\times\Gamma(\frac{\nu}{2})}$$
3. The time series is homogeneous or equally spaced.
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. EGARCH_CHECK examines the model's coefficients for:
• Coefficients are all positive
Requirements
 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static

 int NDK_EGARCH_LRVAR ( double mu, double[] Alphas, UIntPtr p, double[] Gammas, double[] Betas, UIntPtr q, short nInnovationType, double nu, ref double retVal )

Calculates the long-run average volatility for a given E-GARCH model.

Return Value

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

 NDK_SUCCESS operation successful Error Error Code
Parameters
 [in] mu is the GARCH 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,out] Gammas are the leverage parameters (starting with the lowest lag). [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. [out] retVal is the calculated Long run volatility.
Remarks
1. The underlying model is described here.
2. The EGARCH long-run average log variance is defined as: $$\ln V_L=\frac{\alpha_o+\eta \times \sum_{i=1}^p\alpha_i}{1-\sum_{j=1}^q\beta_j}$$ Where:
• Gaussian distributed innovations/shocks: $$\eta=\sqrt{\frac{\pi}{2}}$$
• GED distributed innovations/shocks. $$\eta=\frac{\Gamma(2/\nu )}{\sqrt{\Gamma(1/\nu)\times\Gamma(3/\nu)}}$$
• Student's t-Distributed innovations/shocks. $$\eta=\frac{\sqrt{\nu-2}\times\Gamma(\frac{\nu-1}{2})}{\sqrt{\pi}\times\Gamma(\frac{\nu}{2})}$$
3. The time series is homogeneous or equally spaced.
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. EGARCH_CHECK examines the model's coefficients for:
• Coefficients are all positive
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