| 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
- The underlying model is described here.
- 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. \(\eta=\frac{\sqrt{\nu-2}\times\Gamma(\frac{\nu-1}{2})}{\sqrt{\pi}\times\Gamma(\frac{\nu}{2})}\)
- The time series is homogeneous or equally spaced.
- The number of gamma-coefficients must match the number of alpha-coefficients.
- The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
- The number of parameters in the input argument - beta - determines the order of the GARCH component model.
- 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] 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
- The underlying model is described here.
- 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. \(\eta=\frac{\sqrt{\nu-2}\times\Gamma(\frac{\nu-1}{2})}{\sqrt{\pi}\times\Gamma(\frac{\nu}{2})}\)
- The time series is homogeneous or equally spaced.
- The number of gamma-coefficients must match the number of alpha-coefficients.
- The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
- The number of parameters in the input argument - beta - determines the order of the GARCH component model.
- 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
