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]muis the GARCH model conditional mean (i.e. mu).
[in]Alphasare the parameters of the ARCH(p) component model (starting with the lowest lag).
[in]pis the number of elements in Alphas array
[in,out]Gammasare the leverage parameters (starting with the lowest lag).
[in]gis the number of elements in Gammas. Must be equal to (p-1).
[in]Betasare the parameters of the GARCH(q) component model (starting with the lowest lag).
[in]qis the number of elements in Betas array
[in]nInnovationTypeis 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]nuis the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[out]retValis 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
Header SFSDK.H
Library SFSDK.LIB
DLL SFSDK.DLL
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]muis the GARCH model conditional mean (i.e. mu).
[in]Alphasare the parameters of the ARCH(p) component model (starting with the lowest lag).
[in]pis the number of elements in Alphas array
[in,out]Gammasare the leverage parameters (starting with the lowest lag).
[in]Betasare the parameters of the GARCH(q) component model (starting with the lowest lag).
[in]qis the number of elements in Betas array
[in]nInnovationTypeis 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]nuis the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[out]retValis 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
Class SFSDK
Scope Public
Lifetime Static
Package 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