GARCH-M Model

GARCH-in-mean (GARCH-M) model functions. More...

Functions
int __stdcall	NDK_GARCHM_GOF (double *pData, size_t nSize, double mu, double flambda, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, WORD retType, double *retVal)
	Computes the log-likelihood (LLF), Akaike Information Criterion (AIC) or other goodness of fit functions of the GARCH-M model.
int __stdcall	NDK_GARCHM_RESID (double *pData, size_t nSize, double mu, double flambda, const double *Alphas, size_t p, 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-M model.
int __stdcall	NDK_GARCHM_PARAM (double *pData, size_t nSize, double *mu, double *flambda, double *Alphas, size_t p, double *Betas, size_t q, WORD nInnovationType, double *nu, WORD retType, size_t maxIter)
	Returns the initial (non-optimal), optimal or standard errors of the model's parameters.
int __stdcall	NDK_GARCHM_SIM (double mu, double flambda, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, double *pData, size_t nSize, double *pSigmas, size_t nSigmaSize, UINT nSeed, double *retArray, size_t nSteps)
	Returns a simulated data series the underlying GARCH process.
int __stdcall	NDK_GARCHM_FORE (double *pData, size_t nSize, double *pVols, size_t nVolSize, double mu, double flambda, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, size_t nSteps, WORD retType, double alpha, double *retVal)
	Returns a simulated data series the underlying GARCH process.
int __stdcall	NDK_GARCHM_FITTED (double *pData, size_t nSize, double mu, double flambda, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, WORD retType)
	Returns an array of cells for the fitted values (i.e. mean, volatility and residuals).
int __stdcall	NDK_GARCHM_LRVAR (double mu, double lambda, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, double *retVal)
	Calculates the long-run average volatility for the given GARCH model.
int __stdcall	NDK_GARCHM_VALIDATE (double mu, double lambda, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu)
	Examines the model's parameters for stability constraints (e.g. stationary, etc.).

Detailed Description

In finance, the return of a security may depend on its volatility (risk). To model such phenomena, the GARCH-in-mean (GARCH-M) model adds a heteroskedasticity term into the mean equation. The GARCH-M (p, q) model is written as:

\[x_t = \mu + \lambda \sigma_t + a_t \]

\[\sigma_t^2 = \alpha_o + \sum_{i=1}^p {\alpha_i a_{t-i}^2}+\sum_{j=1}^q{\beta_j \sigma_{t-j}^2}\]

\[a_t = \sigma_t \times \epsilon_t \]

\[\epsilon_t \sim P_{\nu}(0,1)\]

Where:

• \(x_t\) is the time series value at time \(t\).
• \(\mu\) is the mean of the GARCH model.
• \(\lambda\) is the volatility coefficient for the mean.
• \(a_t\) is the model's residual at time \(t\).
• \(\sigma_t\) is the conditional standard deviation (i.e., volatility) at time \(t\).
• \(p\) is the order of the ARCH component model.
• \(\alpha_o,\alpha_1,\alpha_2,...,\alpha_p\) are the parameters of the ARCH component model.
• \(q\) is the order of the GARCH component model.
• \(\beta_1,\beta_2,...,\beta_q\) are the parameters of the GARCH component model.
• \(\left[\epsilon_t\right]\) are the standardized residuals:

  \[\left[\epsilon_t \right]\sim i.i.d\]

  \[E\left[\epsilon_t\right]=0\]

  \[\mathit{VAR}\left[\epsilon_t\right]=1\]

• \(P_{\nu}\) is the probability distribution function for \(\epsilon_t\). Currently, the following distributions are supported:
  1. Normal Distribution:

     \[P_{\nu} = N(0,1)\]

  2. Student's t-Distribution:

     \[P_{\nu} = t_{\nu}(0,1)\]

     \[\nu \gt 4\]

  3. Generalized Error Distribution (GED):

     \[P_{\nu} = \mathit{GED}_{\nu}(0,1)\]

     \[\nu \gt 1\]

     
     

Remarks

1. The time series is homogeneous or equally spaced.
2. The time series may include missing values (e.g. NaN) at either end.
3. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
4. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
5. GARCH-M (p, q) model with normal-distributed innovation has p+q+3 estimated parameters.
6. GARCH-M (p, q) model with GED or student's t-distributed innovation has p+q+4 estimated parameters.
7. A positive risk-premium (λ) indicates that the data series is positively related to its volatility.
8. Furthermore, the GARCH-M model implies that there are serial correlations in the data series itself which were introduced by those in the volatility \(\sigma_t^2\) process.
9. The mere existence of risk-premium is, therefore, another reason that some historical stock returns exhibit serial correlations.

Related Links

• Wikipedia: Autoregressive conditional heteroskedasticity

References

• James Douglas Hamilton; Time Series Analysis by James Douglas Hamilton, Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.

• Tsay, Ruey S.; Analysis of Financial Time Series by Ruey S. Tsay, John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.

Function Documentation

NDK_GARCHM_FITTED()

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

Returns an array of cells for the fitted values (i.e. mean, volatility and residuals).

Parameters

[in,out]	pData	(Required) The univariate time series data.
[in]	nSize	(Required) The number of observations in pData.
[in]	mu	(Optional) The GARCH model conditional mean (i.e. mu).
[in]	flambda	(Optional) The volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
[in]	Alphas	(Optional) The parameters of the ARCH(p) component model (starting with the lowest lag).
[in]	p	(Optional) The number of elements in Alphas array.
[in]	Betas	(Optional) The parameters of the GARCH(q) component model (starting with the lowest lag).
[in]	q	(Optional) The number of elements in Betas array.
[in]	nInnovationType	(Optional) is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) Value Distribution 1 Gaussian Distribution (default) 2 Student's T-Distribution 3 Generalized Error Distribution (GED)
[in]	nu	(Optional) the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[in]	retType	(Required) A switch to select the desired output type (see FIT_RETVAL_FUNC). Value Output Type 1 Fitted conditional mean 2 Fitted conditional volatility or standard deviation 3 Raw residuals (actual - fitted mean) 4 Standardized residuals - (actual - fitted mean)/fitted volatility.

Returns

status code of the function call: zero = success, positive = success with a warning, and negative = error occurred.

Return values

NDK_SUCCESS	success
NDK_INVALID_ARG	failed (see remarks)
NDK_LOW_LICENSE_ARG_LIMIT	failed (see remarks)
NDK_FAILED	failed

Remarks

1. The underlying model is described here.
2. The data sample may include one or more observation with missing values (i.e., NaN) at either end (not intermediary).
3. The function removes any observations with missing values from the dataset before calculating.
4. If the value of the nSize is zero, the function will fail and return NDK_INVALID_ARG.
5. If the value of the retVal argument is NULL, the function will fails and return NDK_INVALID_ARG.
6. The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and provides estimates for the model's parameters.
7. In lite-license mode (e.g., expired license key), the size of the input data set is limited to a maximum of 25. If this limit is exceeded, the function will fail and return NDK_LOW_LICENSE_ARG_LIMIT.

Requirements

Requirement	Value
Target Platform	Windows
Header	SFSDK.h (include Windows.h)
Library	SFSDK.lib
DLL	SFSDK.dll SFLUC.dll SFLOG.dll

Since

v1.63

See also

• NDK_GARCHM_GOF
• NDK_GARCHM_RESID
• NDK_GARCHM_PARAM
• NDK_GARCHM_SIM
• NDK_GARCHM_FORE
• NDK_GARCHM_LRVAR
• NDK_GARCHM_VALIDATE

NDK_GARCHM_FORE()

int __stdcall NDK_GARCHM_FORE	(	double *	pData,
		size_t	nSize,
		double *	pVols,
		size_t	nVolSize,
		double	mu,
		double	flambda,
		const double *	Alphas,
		size_t	p,
		const double *	Betas,
		size_t	q,
		WORD	nInnovationType,
		double	nu,
		size_t	nSteps,
		WORD	retType,
		double	alpha,
		double *	retVal )

Calculates the out-of-sample forecast statistics.

Parameters

[in]	pData	(Required) The univariate time series data.
[in]	nSize	(Required) The number of observations in pData.
[in]	pVols	(Required) the univariate time series data (a one dimensional array of cells (e.g. rows or columns)) of the last q realized volatilities.
[in]	nVolSize	(Required) the number of elements in sigmas. Only the latest q observations are used.
[in]	mu	(Optional) The GARCH model conditional mean (i.e. mu).
[in]	flambda	(Optional) The volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
[in]	Alphas	(Optional) The parameters of the ARCH(p) component model (starting with the lowest lag).
[in]	p	(Optional) The number of elements in Alphas array.
[in]	Betas	(Optional) The parameters of the GARCH(q) component model (starting with the lowest lag).
[in]	q	(Optional) The number of elements in Betas array.
[in]	nInnovationType	(Optional) is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) Value Distribution 1 Gaussian Distribution (default) 2 Student's T-Distribution 3 Generalized Error Distribution (GED)
[in]	nu	(Optional) the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[in]	nSteps	(Required) is the forecast time/horizon (expressed in terms of steps beyond end of the time series).
[in]	retType	(Required) is a switch to select the type of value returned. (see FORECAST_RETVAL_FUNC). Value Return 1 Mean Value (default) 2 Forecast standard error (aka local volatility) 2 Volatility term structure. 3 Lower limit of the forecast confidence interval. 4 Upper limit of the forecast confidence interval.
[in]	alpha	(Required) is the statistical significance level. If missing, a default of 5% is assumed.
[out]	retVal	(Required) is the calculated forecast value.

Returns

status code of the function call: zero = success, positive = success with a warning, and negative = error occurred.

Return values

NDK_SUCCESS	success
NDK_INVALID_ARG	failed (see remarks)
NDK_LOW_LICENSE_ARG_LIMIT	failed (see remarks)
NDK_FAILED	failed

Remarks

1. The underlying model is described here.
2. The data sample may include one or more observation with missing values (i.e., NaN) at either end (not intermediary).
3. The function removes any observations with missing values from the dataset before calculating.
4. If the value of the nSize is zero, the function will fail and return NDK_INVALID_ARG.
5. If the value of the retVal argument is NULL, the function will fails and return NDK_INVALID_ARG.
6. The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and provides estimates for the model's parameters.
7. In lite-license mode (e.g., expired license key), the size of the input data set is limited to a maximum of 25. If this limit is exceeded, the function will fail and return NDK_LOW_LICENSE_ARG_LIMIT.

Requirements

Requirement	Value
Target Platform	Windows
Header	SFSDK.h (include Windows.h)
Library	SFSDK.lib
DLL	SFSDK.dll SFLUC.dll SFLOG.dll

Since

v1.63

See also

• NDK_GARCHM_GOF
• NDK_GARCHM_RESID
• NDK_GARCHM_PARAM
• NDK_GARCHM_SIM
• NDK_GARCHM_FITTED
• NDK_GARCHM_LRVAR
• NDK_GARCHM_VALIDATE

NDK_GARCHM_GOF()

int __stdcall NDK_GARCHM_GOF	(	double *	pData,
		size_t	nSize,
		double	mu,
		double	flambda,
		const double *	Alphas,
		size_t	p,
		const double *	Betas,
		size_t	q,
		WORD	nInnovationType,
		double	nu,
		WORD	retType,
		double *	retVal )

Computes the log-likelihood (LLF), Akaike Information Criterion (AIC) or other goodness of fit functions of the GARCH-M model.

Parameters

[in]	pData	(Required) The univariate time series data.
[in]	nSize	(Required) The number of observations in pData.
[in]	mu	(Optional) The GARCH model conditional mean (i.e. mu).
[in]	flambda	(Optional) The volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
[in]	Alphas	(Optional) The parameters of the ARCH(p) component model (starting with the lowest lag).
[in]	p	(Optional) The number of elements in Alphas array.
[in]	Betas	(Optional) The parameters of the GARCH(q) component model (starting with the lowest lag).
[in]	q	(Optional) The number of elements in Betas array.
[in]	nInnovationType	(Optional) is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) Value Distribution 1 Gaussian Distribution (default) 2 Student's T-Distribution 3 Generalized Error Distribution (GED)
[in]	nu	(Optional) the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[in]	retType	(Required) a switch to select a fitness measure ( see GOODNESS_OF_FIT_FUNC). Value Return 1 Log-likelihood goodness of fit measure (LLF) 2 Akaike information criterion goodness of fit measure (AIC) 3 Bayesian or Schwartz information criterion goodness of fit measure (BIC) 4 Hannan-Quinn information criterion goodness of fit measure. (HQC) 5 R-squared goodness of fit measure (R^2) 6 Adjusted R-squared goodness of fit measure (Adj. R^2)
[out]	retVal	(Required) is a pointer to a variable to hold the calculated GOF statistics.

Returns

status code of the function call: zero = success, positive = success with a warning, and negative = error occurred.

Return values

NDK_SUCCESS	success
NDK_INVALID_ARG	failed (see remarks)
NDK_LOW_LICENSE_ARG_LIMIT	failed (see remarks)
NDK_FAILED	failed

Remarks

1. The underlying model is described here.
2. The data sample may include one or more observation with missing values (i.e., NaN) at either end (not intermediary).
3. The function removes any observations with missing values from the dataset before calculating.
4. If the value of the nSize is zero, the function will fail and return NDK_INVALID_ARG.
5. If the value of the retVal argument is NULL, the function will fails and return NDK_INVALID_ARG.
6. The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and provides estimates for the model's parameters.
7. In lite-license mode (e.g., expired license key), the size of the input data set is limited to a maximum of 25. If this limit is exceeded, the function will fail and return NDK_LOW_LICENSE_ARG_LIMIT.

Requirements

Requirement	Value
Target Platform	Windows
Header	SFSDK.h (include Windows.h)
Library	SFSDK.lib
DLL	SFSDK.dll SFLUC.dll SFLOG.dll

Since

v1.63

See also

• NDK_GARCHM_RESID
• NDK_GARCHM_PARAM
• NDK_GARCHM_SIM
• NDK_GARCHM_FORE
• NDK_GARCHM_FITTED
• NDK_GARCHM_LRVAR
• NDK_GARCHM_VALIDATE

NDK_GARCHM_LRVAR()

int __stdcall NDK_GARCHM_LRVAR	(	double	mu,
		double	lambda,
		const double *	Alphas,
		size_t	p,
		const double *	Betas,
		size_t	q,
		WORD	nInnovationType,
		double	nu,
		double *	retVal )

Calculates the long-run average volatility for the given GARCH model

Parameters

[in]	mu	(Optional) The GARCH model conditional mean (i.e. mu).
[in]	lambda	(Optional) The volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
[in]	Alphas	(Optional) The parameters of the ARCH(p) component model (starting with the lowest lag).
[in]	p	(Optional) The number of elements in Alphas array.
[in]	Betas	(Optional) The parameters of the GARCH(q) component model (starting with the lowest lag).
[in]	q	(Optional) The number of elements in Betas array.
[in]	nInnovationType	(Optional) is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) Value Distribution 1 Gaussian Distribution (default) 2 Student's T-Distribution 3 Generalized Error Distribution (GED)
[in]	nu	(Optional) the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[out]	retVal	(Required) is a pointer to a variable to hold the calculated GOF statistics.

Returns

status code of the function call: zero = success, positive = success with a warning, and negative = error occurred.

Return values

NDK_SUCCESS	success
NDK_INVALID_ARG	failed (see remarks)
NDK_LOW_LICENSE_ARG_LIMIT	failed (see remarks)
NDK_FAILED	failed

Remarks

1. The underlying model is described here.
2. If the value of the retVal argument is NULL, the function will fails and return NDK_INVALID_ARG.

Requirements

Requirement	Value
Target Platform	Windows
Header	SFSDK.h (include Windows.h)
Library	SFSDK.lib
DLL	SFSDK.dll SFLUC.dll SFLOG.dll

Since

v1.63

See also

• NDK_GARCHM_GOF
• NDK_GARCHM_RESID
• NDK_GARCHM_PARAM
• NDK_GARCHM_SIM
• NDK_GARCHM_FORE
• NDK_GARCHM_VALIDATE
• NDK_GARCHM_FITTED

NDK_GARCHM_PARAM()

int __stdcall NDK_GARCHM_PARAM	(	double *	pData,
		size_t	nSize,
		double *	mu,
		double *	flambda,
		double *	Alphas,
		size_t	p,
		double *	Betas,
		size_t	q,
		WORD	nInnovationType,
		double *	nu,
		WORD	retType,
		size_t	maxIter )

Returns the initial (non-optimal), optimal or standard errors of the model's parameters.

Parameters

[in]	pData	(Required) The univariate time series data.
[in]	nSize	(Required) The number of observations in pData.
[in,out]	mu	(Optional) The GARCH model conditional mean (i.e. mu).
[in,out]	flambda	(Optional) The volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
[in,out]	Alphas	(Optional) The parameters of the ARCH(p) component model (starting with the lowest lag).
[in]	p	(Optional) The number of elements in Alphas array.
[in,out]	Betas	(Optional) The parameters of the GARCH(q) component model (starting with the lowest lag).
[in]	q	(Optional) The number of elements in Betas array.
[in]	nInnovationType	(Optional) is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) Value Distribution 1 Gaussian Distribution (default) 2 Student's T-Distribution 3 Generalized Error Distribution (GED)
[in,out]	nu	(Optional) the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[in]	retType	(Required) A switch to select the type of value returned: 1= Quick Guess, 2=Calibrated, 3= Std. Errors ( see MODEL_RETVAL_FUNC). Value Type 1 Quick guess (non-optimal) of parameters values 2 Run a calibration process to find optimal values for the model's parameters 3 Compute the standard error of the parameters' values
[in]	maxIter	(Required) is the maximum number of iterations used to calibrate the model. If missing or less than 100, the default maximum of 100 is assumed.

Returns

status code of the function call: zero = success, positive = success with a warning, and negative = error occurred.

Return values

NDK_SUCCESS	success
NDK_INVALID_ARG	failed (see remarks)
NDK_LOW_LICENSE_ARG_LIMIT	failed (see remarks)
NDK_FAILED	failed

Remarks

1. The underlying model is described here.
2. The data sample may include one or more observation with missing values (i.e., NaN) at either end (not intermediary).
3. The function removes any observations with missing values from the dataset before calculating.
4. If the value of the nSize is zero, the function will fail and return NDK_INVALID_ARG.
5. If the value of the retVal argument is NULL, the function will fails and return NDK_INVALID_ARG.
6. The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and provides estimates for the model's parameters.
7. In lite-license mode (e.g., expired license key), the size of the input data set is limited to a maximum of 25. If this limit is exceeded, the function will fail and return NDK_LOW_LICENSE_ARG_LIMIT.

Requirements

Requirement	Value
Target Platform	Windows
Header	SFSDK.h (include Windows.h)
Library	SFSDK.lib
DLL	SFSDK.dll SFLUC.dll SFLOG.dll

Since

v1.63

See also

• NDK_GARCHM_GOF
• NDK_GARCHM_RESID
• NDK_GARCHM_SIM
• NDK_GARCHM_FORE
• NDK_GARCHM_FITTED
• NDK_GARCHM_LRVAR
• NDK_GARCHM_VALIDATE

NDK_GARCHM_RESID()

int __stdcall NDK_GARCHM_RESID	(	double *	pData,
		size_t	nSize,
		double	mu,
		double	flambda,
		const double *	Alphas,
		size_t	p,
		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-M model.

Parameters

[in,out]	pData	(Required) The univariate time series data.
[in]	nSize	(Required) The number of observations in pData.
[in]	mu	(Optional) The GARCH model conditional mean (i.e. mu).
[in]	flambda	(Optional) The volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
[in]	Alphas	(Optional) The parameters of the ARCH(p) component model (starting with the lowest lag).
[in]	p	(Optional) The number of elements in Alphas array.
[in]	Betas	(Optional) The parameters of the GARCH(q) component model (starting with the lowest lag).
[in]	q	(Optional) The number of elements in Betas array.
[in]	nInnovationType	(Optional) is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) Value Distribution 1 Gaussian Distribution (default) 2 Student's T-Distribution 3 Generalized Error Distribution (GED)
[in]	nu	(Optional) the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[in]	retType	(Required) is a switch to select a residuals-type:raw or standardized. see RESID_RETVAL_FUNC Value Residuals Type 0 Standardized residuals 1 Raw Residuals

Returns

status code of the function call: zero = success, positive = success with a warning, and negative = error occurred.

Return values

NDK_SUCCESS	success
NDK_INVALID_ARG	failed (see remarks)
NDK_LOW_LICENSE_ARG_LIMIT	failed (see remarks)
NDK_FAILED	failed

Remarks

1. The underlying model is described here.
2. The data sample may include one or more observation with missing values (i.e., NaN) at either end (not intermediary).
3. The function removes any observations with missing values from the dataset before calculating.
4. If the value of the nSize is zero, the function will fail and return NDK_INVALID_ARG.
5. If the value of the retVal argument is NULL, the function will fails and return NDK_INVALID_ARG.
6. The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and provides estimates for the model's parameters.
7. In lite-license mode (e.g., expired license key), the size of the input data set is limited to a maximum of 25. If this limit is exceeded, the function will fail and return NDK_LOW_LICENSE_ARG_LIMIT.

Requirements

Requirement	Value
Target Platform	Windows
Header	SFSDK.h (include Windows.h)
Library	SFSDK.lib
DLL	SFSDK.dll SFLUC.dll SFLOG.dll

Since

v1.63

See also

• NDK_GARCHM_GOF
• NDK_GARCHM_PARAM
• NDK_GARCHM_SIM
• NDK_GARCHM_FORE
• NDK_GARCHM_FITTED
• NDK_GARCHM_LRVAR
• NDK_GARCHM_VALIDATE

NDK_GARCHM_SIM()

int __stdcall NDK_GARCHM_SIM	(	double	mu,
		double	flambda,
		const double *	Alphas,
		size_t	p,
		const double *	Betas,
		size_t	q,
		WORD	nInnovationType,
		double	nu,
		double *	pData,
		size_t	nSize,
		double *	pSigmas,
		size_t	nSigmaSize,
		UINT	nSeed,
		double *	retArray,
		size_t	nSteps )

Returns a simulated data series the underlying GARCH process.

Parameters

[in]	mu	(Optional) The GARCH model conditional mean (i.e. mu).
[in]	flambda	(Optional) The volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
[in]	Alphas	(Optional) The parameters of the ARCH(p) component model (starting with the lowest lag).
[in]	p	(Optional) The number of elements in Alphas array.
[in]	Betas	(Optional) The parameters of the GARCH(q) component model (starting with the lowest lag).
[in]	q	(Optional) The number of elements in Betas array.
[in]	nInnovationType	(Optional) is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) Value Distribution 1 Gaussian Distribution (default) 2 Student's T-Distribution 3 Generalized Error Distribution (GED)
[in]	nu	(Optional) the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[in]	pData	(Optional) he univariate time series of the latest observations (a one dimensional array).
[in]	nSize	(Required) The number of observations in pData.
[in]	pSigmas	(Optional) The univariate time series of the latest observations (a one dimensional array).
[in]	nSigmaSize	(Required) The number of observations in pSigmas.
[in]	nSeed	(Required) is an unsigned integer for setting up the random number generators.
[out]	retArray	(Required) is the calculated simulation value.
[in]	nSteps	(Required) is the simulation time/horizon (expressed in terms of steps beyond end of the time series).

Returns

status code of the function call: zero = success, positive = success with a warning, and negative = error occurred.

Return values

NDK_SUCCESS	success
NDK_INVALID_ARG	failed (see remarks)
NDK_LOW_LICENSE_ARG_LIMIT	failed (see remarks)
NDK_FAILED	failed

Remarks

1. The underlying model is described here.
2. The data sample may include one or more observation with missing values (i.e., NaN) at either end (not intermediary).
3. The function removes any observations with missing values from the dataset before calculating.
4. If the value of the nSize is zero, the function will fail and return NDK_INVALID_ARG.
5. If the value of the retVal argument is NULL, the function will fails and return NDK_INVALID_ARG.
6. The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and provides estimates for the model's parameters.
7. In lite-license mode (e.g., expired license key), the size of the input data set is limited to a maximum of 25. If this limit is exceeded, the function will fail and return NDK_LOW_LICENSE_ARG_LIMIT.

Requirements

Requirement	Value
Target Platform	Windows
Header	SFSDK.h (include Windows.h)
Library	SFSDK.lib
DLL	SFSDK.dll SFLUC.dll SFLOG.dll

Since

v1.63

See also

• NDK_GARCHM_GOF
• NDK_GARCHM_RESID
• NDK_GARCHM_PARAM
• NDK_GARCHM_FORE
• NDK_GARCHM_FITTED
• NDK_GARCHM_LRVAR
• NDK_GARCHM_VALIDATE

NDK_GARCHM_VALIDATE()

int __stdcall NDK_GARCHM_VALIDATE	(	double	mu,
		double	lambda,
		const double *	Alphas,
		size_t	p,
		const double *	Betas,
		size_t	q,
		WORD	nInnovationType,
		double	nu )

Examines the model's parameters for stability constraints (e.g. variance stationary, positive variance, etc.).

Parameters

[in]	mu	(Optional) The GARCH model conditional mean (i.e. mu).
[in]	lambda	(Optional) The volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
[in]	Alphas	(Optional) The parameters of the ARCH(p) component model (starting with the lowest lag).
[in]	p	(Optional) The number of elements in Alphas array.
[in]	Betas	(Optional) The parameters of the GARCH(q) component model (starting with the lowest lag).
[in]	q	(Optional) The number of elements in Betas array.
[in]	nInnovationType	(Optional) is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) Value Distribution 1 Gaussian Distribution (default) 2 Student's T-Distribution 3 Generalized Error Distribution (GED)
[in]	nu	(Optional) the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.

Returns

status code of the function call: zero = success, positive = success with a warning, and negative = error occurred.

Return values

NDK_TRUE	model is stable
NDK_FALSE	model is instable
NDK_INVALID_ARG	failed (see remarks)
NDK_FAILED	failed

Remarks

1. The underlying model is described here.

Requirements

Requirement	Value
Target Platform	Windows
Header	SFSDK.h (include Windows.h)
Library	SFSDK.lib
DLL	SFSDK.dll SFLUC.dll SFLOG.dll

Since

v1.63

See also

• NDK_GARCHM_GOF
• NDK_GARCHM_RESID
• NDK_GARCHM_PARAM
• NDK_GARCHM_SIM
• NDK_GARCHM_FORE
• NDK_GARCHM_LRVAR
• NDK_GARCHM_FITTED