g13fb forecasts the conditional variances ht, for t=T+1,…,T+ξ, from a type I AGARCHp,q sequence, where ξ is the forecast horizon and T is the current time (see Engle and Ng (1993)).

Syntax

C#
public static void g13fb(
	int num,
	int nt,
	int ip,
	int iq,
	double[] theta,
	double gamma,
	double[] fht,
	double[] ht,
	double[] et,
	out int ifail
)
Visual Basic
Public Shared Sub g13fb ( _
	num As Integer, _
	nt As Integer, _
	ip As Integer, _
	iq As Integer, _
	theta As Double(), _
	gamma As Double, _
	fht As Double(), _
	ht As Double(), _
	et As Double(), _
	<OutAttribute> ByRef ifail As Integer _
)
Visual C++
public:
static void g13fb(
	int num, 
	int nt, 
	int ip, 
	int iq, 
	array<double>^ theta, 
	double gamma, 
	array<double>^ fht, 
	array<double>^ ht, 
	array<double>^ et, 
	[OutAttribute] int% ifail
)
F#
static member g13fb : 
        num : int * 
        nt : int * 
        ip : int * 
        iq : int * 
        theta : float[] * 
        gamma : float * 
        fht : float[] * 
        ht : float[] * 
        et : float[] * 
        ifail : int byref -> unit

Parameters

num
Type: System..::..Int32
On entry: the number of terms in the arrays ht and et from the modelled sequence.
Constraint: maxip,iq≤num.
nt
Type: System..::..Int32
On entry: ξ, the forecast horizon.
Constraint: nt>0.
ip
Type: System..::..Int32
On entry: the number of coefficients, βi, for i=1,2,…,p.
Constraints:
  • maxip,iq≤20;
  • ip≥0.
iq
Type: System..::..Int32
On entry: the number of coefficients, αi, for i=1,2,…,q.
Constraints:
  • maxip,iq≤20;
  • iq≥1.
theta
Type: array<System..::..Double>[]()[][]
An array of size [iq+ip+1]
On entry: the first element must contain the coefficient αo and the next iq elements must contain the coefficients αi, for i=1,2,…,q. The remaining ip elements must contain the coefficients βj, for j=1,2,…,p.
gamma
Type: System..::..Double
On entry: the asymmetry parameter γ for the GARCHp,q sequence.
fht
Type: array<System..::..Double>[]()[][]
An array of size [nt]
On exit: the forecast values of the conditional variance, ht, for t=T+1,…,T+ξ.
ht
Type: array<System..::..Double>[]()[][]
An array of size [num]
On entry: the sequence of past conditional variances for the GARCHp,q process, ht, for t=1,2,…,T.
et
Type: array<System..::..Double>[]()[][]
An array of size [num]
On entry: the sequence of past residuals for the GARCHp,q process, εt, for t=1,2,…,T.
ifail
Type: System..::..Int32%
On exit: ifail=0 unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Description

Assume the GARCHp,q process can be represented by:
ht=α0+∑i=1qαiεt-i+γ2+∑i=1pβiht-i,  t=1,2,…,T
where εt∣ψt-1=N0,ht or εt∣ψt-1=Stdf,ht, has been modelled by g13fa and the estimated conditional variances and residuals are contained in the arrays ht and et respectively.
g13fb will then use the last maxp,q elements of the arrays ht and et to estimate the conditional variance forecasts, ht∣ψT, where t=T+1,…,T+ξ and ξ is the forecast horizon.

References

Bollerslev T (1986) Generalised autoregressive conditional heteroskedasticity Journal of Econometrics 31 307–327
Engle R (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation Econometrica 50 987–1008
Engle R and Ng V (1993) Measuring and testing the impact of news on volatility Journal of Finance 48 1749–1777
Hamilton J (1994) Time Series Analysis Princeton University Press

Error Indicators and Warnings

Errors or warnings detected by the method:
ifail=1
On entry,num<maxip,iq,
oriq<1,
orip<0,
ormaxip,iq>20,
ornt≤0.
ifail=-9000
An error occured, see message report.
ifail=-8000
Negative dimension for array value
ifail=-6000
Invalid Parameters value

Accuracy

Not applicable.

Parallelism and Performance

None.

Further Comments

None.

Example

See [Example] in g13fa.

See Also