GARCH Model

GARCH model functions. More...

Functions
int __stdcall	NDK_GARCH_GOF (double *pData, size_t nSize, double mu, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, WORD retType, double *retVal)
int __stdcall	NDK_GARCH_RESID (double *pData, size_t nSize, double mu, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, WORD retType)
int __stdcall	NDK_GARCH_PARAM (double *pData, size_t nSize, double *mu, double *Alphas, size_t p, double *Betas, size_t q, WORD nInnovationType, double *nu, WORD retType, size_t maxIter)
int __stdcall	NDK_GARCH_SIM (double mu, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, double *pData, size_t nSize, double *sigmas, size_t nSigmaSize, UINT nSeed, double *retArray, size_t nSteps)
int __stdcall	NDK_GARCH_FORE (double *pData, size_t nSize, double *sigmas, size_t nSigmaSize, double mu, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, size_t nStep, WORD retType, double alpha, double *retVal)
int __stdcall	NDK_GARCH_FITTED (double *pData, size_t nSize, double mu, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, WORD retType)
int __stdcall	NDK_GARCH_LRVAR (double mu, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu, double *retVal)
int __stdcall	NDK_GARCH_VALIDATE (double mu, const double *Alphas, size_t p, const double *Betas, size_t q, WORD nInnovationType, double nu)

Detailed Description

If an autoregressive moving average model (ARMA model) is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH, Bollerslev(1986)) model.

Function Documentation

NDK_GARCH_FITTED()

int __stdcall NDK_GARCH_FITTED	(	double *	pData,
		size_t	nSize,
		double	mu,
		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)

Note

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.

Returns

status code of the operation

Return values

NDK_SUCCESS	Operation successful
NDK_FAILED	operation is unsuccessful ( )

See also

NDK_GARCH_GOF(), NDK_GARCH_RESID(), NDK_GARCH_PARAM(), NDK_GARCH_FORE(), NDK_GARCH_VALIDATE()

Parameters

[in]	pData	is the univariate time series data (a one dimensional array).
[in]	nSize	is the number of observations in X.
[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]	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 output type ( see FIT_RETVAL_FUNC)

NDK_GARCH_FORE()

int __stdcall NDK_GARCH_FORE	(	double *	pData,
		size_t	nSize,
		double *	sigmas,
		size_t	nSigmaSize,
		double	mu,
		const double *	Alphas,
		size_t	p,
		const double *	Betas,
		size_t	q,
		WORD	nInnovationType,
		double	nu,
		size_t	nStep,
		WORD	retType,
		double	alpha,
		double *	retVal )

Calculates the out-of-sample forecast statistics.

Note

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.

Returns

status code of the operation

Return values

NDK_SUCCESS	Operation successful
NDK_FAILED	operation is unsuccessful ( )

See also

NDK_GARCH_GOF(), NDK_GARCH_RESID(), NDK_GARCH_PARAM(), NDK_GARCH_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 X.
[in]	sigmas	is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)) of the last q realized volatilities.
[in]	nSigmaSize	is the number of elements in sigmas. Only the latest q observations are used.
[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]	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 or Normal Distribution 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]	nStep	is the forecast time/horizon (expressed in terms of steps beyond end of the time series).
[in]	retType	is a switch to select the type of value returned Mean forecast Forecast Error Volatility term structure Confidence interval lower limit Confidence interval upper limit (see FORECAST_RETVAL_FUNC)
[in]	alpha	is the statistical significance level. If missing, a default of 5% is assumed.
[out]	retVal	is the calculated forecast value

NDK_GARCH_GOF()

int __stdcall NDK_GARCH_GOF	(	double *	pData,
		size_t	nSize,
		double	mu,
		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 function of the GARCH model.

Note

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.

Returns

status code of the operation

Return values

NDK_SUCCESS	Operation successful
NDK_FAILED	operation is unsuccessful ( )

See also

NDK_GARCH_RESID(), NDK_GARCH_PARAM(), NDK_GARCH_FORE(), NDK_GARCH_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 X.
[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]	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 fitness measure ( see GOODNESS_OF_FIT_FUNC)
[out]	retVal	is the calculated goodness of fit value.

NDK_GARCH_LRVAR()

int __stdcall NDK_GARCH_LRVAR	(	double	mu,
		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

Note

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 long-run variance is not affected by our choice of shock/innovation distribution

4. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.

5. The number of parameters in the input argument - beta - determines the order of the GARCH component model.

Returns

status code of the operation

Return values

NDK_SUCCESS	Operation successful
NDK_FAILED	operation is unsuccessful ( )

See also

NDK_GARCH_GOF(), NDK_GARCH_RESID(), NDK_GARCH_PARAM(), NDK_GARCH_FORE(), NDK_GARCH_VALIDATE()

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]	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 value

NDK_GARCH_PARAM()

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

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

Note

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.

Returns

status code of the operation

Return values

NDK_SUCCESS	Operation successful
NDK_FAILED	operation is unsuccessful ( )

See also

NDK_GARCH_GOF(), NDK_GARCH_RESID(), NDK_GARCH_FORE(), NDK_GARCH_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 X.
	mu	[inout] is the GARCH model conditional mean (i.e. mu).
	Alphas	[inout] are the parameters of the ARCH(p) component model (starting with the lowest lag).
[in]	p	is the number of elements in Alphas array
	Betas	[inout] 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)
	nu	[inout] is the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[in]	retType	is a switch to select the type of value returned: 1= Quick Guess, 2=Calibrated, 3= Std. Errors ( see MODEL_RETVAL_FUNC)
[in]	maxIter	is the maximum number of iterations used to calibrate the model. If missing or less than 100, the default maximum of 100 is assumed.

NDK_GARCH_RESID()

int __stdcall NDK_GARCH_RESID	(	double *	pData,
		size_t	nSize,
		double	mu,
		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 model

Note

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.

Returns

status code of the operation

Return values

NDK_SUCCESS	Operation successful
NDK_FAILED	operation is unsuccessful ( )

Deprecated

this function is being replaced by NDK_GARCH_FITTED()

See also

NDK_GARCH_GOF(), NDK_GARCH_PARAM(), NDK_GARCH_FORE(), NDK_GARCH_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 X.
[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]	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

NDK_GARCH_SIM()

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

Returns a simulated data series the underlying GARCH process.

Note

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.

Returns

status code of the operation

Return values

NDK_SUCCESS	Operation successful
NDK_FAILED	operation is unsuccessful ( )

See also

NDK_GARCH_RESID(), NDK_GARCH_PARAM(), NDK_GARCH_FORE(), NDK_GARCH_FITTED(), NDK_GARCH_VALIDATE()

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]	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)
[in]	nu	is the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.
[in]	pData	is the univariate time series of the latest observations (a one dimensional array).
[in]	nSize	is the number of observations in X.
[in]	sigmas	is the univariate time series of the latest observations (a one dimensional array of cells (e.g. rows or columns)) of the last q realized volatilities.
[in]	nSigmaSize	is the number of elements in sigmas. Only the latest q observations are used.
[in]	nSeed	is an unsigned integer for setting up the random number generators
[out]	retArray	is the calculated simulation value
[in]	nSteps	is the number of future steps to simulate for.

NDK_GARCH_VALIDATE()

int __stdcall NDK_GARCH_VALIDATE	(	double	mu,
		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.).

Note

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.

Returns

status code of the operation

Return values

NDK_TRUE	Model is stable (i.e. variance process is stationary and yield positive values)
NDK_FALSE	Model is unstable.
NDK_FAILED	operation is unsuccessful ( )

See also

NDK_AIRLINE_GOF(), NDK_AIRLINE_RESID(), NDK_AIRLINE_PARAM(), NDK_AIRLINE_FORE(), NDK_AIRLINE_FITTED()

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]	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.