g13fc Method
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g13fc estimates the parameters of a univariate regression-type II AGARCHp,q process.

Syntax

C#
public static void g13fc(
	string dist,
	double[] yt,
	double[,] x,
	int num,
	int ip,
	int iq,
	int nreg,
	int mn,
	int npar,
	double[] theta,
	double[] se,
	double[] sc,
	double[,] covr,
	ref double hp,
	double[] et,
	double[] ht,
	out double lgf,
	bool[] copts,
	int maxit,
	double tol,
	out int ifail
)
Visual Basic (Declaration)
Public Shared Sub g13fc ( _
	dist As String, _
	yt As Double(), _
	x As Double(,), _
	num As Integer, _
	ip As Integer, _
	iq As Integer, _
	nreg As Integer, _
	mn As Integer, _
	npar As Integer, _
	theta As Double(), _
	se As Double(), _
	sc As Double(), _
	covr As Double(,), _
	ByRef hp As Double, _
	et As Double(), _
	ht As Double(), _
	<OutAttribute> ByRef lgf As Double, _
	copts As Boolean(), _
	maxit As Integer, _
	tol As Double, _
	<OutAttribute> ByRef ifail As Integer _
)
Visual C++
public:
static void g13fc(
	String^ dist, 
	array<double>^ yt, 
	array<double,2>^ x, 
	int num, 
	int ip, 
	int iq, 
	int nreg, 
	int mn, 
	int npar, 
	array<double>^ theta, 
	array<double>^ se, 
	array<double>^ sc, 
	array<double,2>^ covr, 
	double% hp, 
	array<double>^ et, 
	array<double>^ ht, 
	[OutAttribute] double% lgf, 
	array<bool>^ copts, 
	int maxit, 
	double tol, 
	[OutAttribute] int% ifail
)
F#
static member g13fc : 
        dist:string * 
        yt:float[] * 
        x:float[,] * 
        num:int * 
        ip:int * 
        iq:int * 
        nreg:int * 
        mn:int * 
        npar:int * 
        theta:float[] * 
        se:float[] * 
        sc:float[] * 
        covr:float[,] * 
        hp:float byref * 
        et:float[] * 
        ht:float[] * 
        lgf:float byref * 
        copts:bool[] * 
        maxit:int * 
        tol:float * 
        ifail:int byref -> unit 

Parameters

dist
Type: System..::.String
On entry: the type of distribution to use for et.
dist="N"
A Normal distribution is used.
dist="T"
A Student's t-distribution is used.
yt
Type: array< System..::.Double >[]()[]
An array of size [num]
On entry: the sequence of observations, yt, for t=1,2,,T.
x
Type: array< System..::.Double ,2>[,](,)[,]
An array of size [ldx, dim2]
Note: ldx must satisfy the constraint: ldxnum
Note: the second dimension of the array x must be at least max1,nreg+mn.
On entry: row t of x must contain the time dependent exogenous vector xt , where xtT = xt1,,xtk , for t=1,2,,T.
num
Type: System..::.Int32
On entry: T, the number of terms in the sequence.
Constraints:
  • nummaxip,iq;
  • numnreg+mn.
ip
Type: System..::.Int32
On entry: the number of coefficients, βi, for i=1,2,,p.
Constraint: ip0 (see also npar).
iq
Type: System..::.Int32
On entry: the number of coefficients, αi, for i=1,2,,q.
Constraint: iq1 (see also npar).
nreg
Type: System..::.Int32
On entry: k, the number of regression coefficients.
Constraint: nreg0 (see also npar).
mn
Type: System..::.Int32
On entry: if mn=1, the mean term b0 will be included in the model.
Constraint: mn=0 or 1.
npar
Type: System..::.Int32
On entry: the number of parameters to be included in the model. npar=2+iq+ip+mn+nreg when dist="N" and npar=3+iq+ip+mn+nreg when dist="T".
Constraint: npar<20.
theta
Type: array< System..::.Double >[]()[]
An array of size [npar]
Note: npar must satisfy the constraint: npar<20
On entry: the initial parameter estimates for the vector θ.
The first element must contain the coefficient αo and the next iq elements must contain the coefficients αi, for i=1,2,,q.
The next ip elements must contain the coefficients βj, for j=1,2,,p.
The next element must contain the asymmetry parameter γ.
If dist="T", the next element must contain df, the number of degrees of freedom of the Student's t-distribution.
If mn=1, the next element contains the mean term bo.
If copts[1]=false, the remaining nreg elements are taken as initial estimates of the linear regression coefficients bi, for i=1,2,,k.
On exit: the estimated values θ^ for the vector θ.
The first element contains the coefficient αo, the next iq elements contain the coefficients αi, for i=1,2,,q.
The next ip elements are the coefficients βj, for j=1,2,,p.
The next element contains the estimate for the asymmetry parameter γ.
If dist="T", the next element contains an estimate for df, the number of degrees of freedom of the Student's t-distribution.
If mn=1, the next element contains an estimate for the mean term bo.
The final nreg elements are the estimated linear regression coefficients bi, for i=1,2,,k.
se
Type: array< System..::.Double >[]()[]
An array of size [npar]
Note: npar must satisfy the constraint: npar<20
On exit: the standard errors for θ^.
The first element contains the standard error for αo and the next iq elements contain the standard errors for αi, for i=1,2,,q.
The next ip elements are the standard errors for βj, for j=1,2,,p.
The next element contains the standard error for γ.
If dist="T", the next element contains the standard error for df, the number of degrees of freedom of the Student's t-distribution.
If mn=1, the next element contains the standard error for bo.
The final nreg elements are the standard errors for bj, for j=1,2,,k.
sc
Type: array< System..::.Double >[]()[]
An array of size [npar]
Note: npar must satisfy the constraint: npar<20
On exit: the scores for θ^.
The first element contains the score for αo and the next iq elements contain the score for αi, for i=1,2,,q.
The next ip elements are the scores for βj, for j=1,2,,p.
The next element contains the score for γ.
If dist="T", the next element contains the score for df, the number of degrees of freedom of the Student's t-distribution.
If mn=1, the next element contains the score for bo.
The final nreg elements are the scores for bj, for j=1,2,,k.
covr
Type: array< System..::.Double ,2>[,](,)[,]
An array of size [ldcovr, npar]
Note: ldcovr must satisfy the constraint: ldcovrnpar
Note: npar must satisfy the constraint: npar<20
On exit: the covariance matrix of the parameter estimates θ^, that is the inverse of the Fisher Information Matrix.
hp
Type: System..::.Double %
On entry: if copts[1]=false, hp is the value to be used for the pre-observed conditional variance; otherwise hp is not referenced.
On exit: if copts[1]=true, hp is the estimated value of the pre-observed conditional variance.
et
Type: array< System..::.Double >[]()[]
An array of size [num]
On exit: the estimated residuals, εt, for t=1,2,,T.
ht
Type: array< System..::.Double >[]()[]
An array of size [num]
On exit: the estimated conditional variances, ht, for t=1,2,,T.
lgf
Type: System..::.Double %
On exit: the value of the log-likelihood function at θ^.
copts
Type: array< System..::.Boolean >[]()[]
An array of size [2]
On entry: the options to be used by g13fc.
copts[0]=true
Stationary conditions are enforced, otherwise they are not.
copts[1]=true
The method provides initial parameter estimates of the regression terms, otherwise these are to be provided by you.
maxit
Type: System..::.Int32
On entry: the maximum number of iterations to be used by the optimization method when estimating the GARCHp,q parameters. If maxit is set to 0, the standard errors, score vector and variance-covariance are calculated for the input value of θ in theta; however the value of θ is not updated.
Constraint: maxit0.
tol
Type: System..::.Double
On entry: the tolerance to be used by the optimization method when estimating the GARCHp,q parameters.
ifail
Type: System..::.Int32 %
On exit: ifail=0 unless the method detects an error (see [Error Indicators and Warnings]).

Description

g13fc provides an estimate for the parameter vector θ=bo,bT,ωT where bT=b1,,bk, ωT=α0,α1,,αq,β1,,βp,γ when dist="N" and ωT=α0,α1,,αq,β1,,βp,γ,df when dist="T".
mn and nreg can be used to simplify the GARCHp,q expression in (1) as follows:
No Regression and No Mean
  • yt=εt,
  • mn=0,
  • nreg=0 and
  • θ is a p+q+2 vector when dist="N" and a p+q+3 vector when dist="T".
No Regression
  • yt=bo+εt,
  • mn=1,
  • nreg=0 and
  • θ is a p+q+3 vector when dist="N" and a p+q+4×1 vector when dist="T".
Note:  if the yt=μ+εt, where μ is known (not to be estimated by g13fc) then (1) can be written as ytμ=εt, where ytμ=yt-μ. This corresponds to the case No Regression and No Mean, with yt replaced by yt-μ.
No Mean
  • yt = xtT b + εt ,
  • mn=0,
  • nreg=k and
  • θ is a p+q+k+2 vector when dist="N" and a p+q+k+3 vector when dist="T".

References

Error Indicators and Warnings

Accuracy

Further Comments

Example

See Also