g13fh forecasts the conditional variances, ht,t=T+1,,T+ξ from an exponential GARCHp,q sequence, where ξ is the forecast horizon and T is the current time (see Engle and Ng (1993)).

Syntax

C#
public static void g13fh(
	int num,
	int nt,
	int ip,
	int iq,
	double[] theta,
	double[] fht,
	double[] ht,
	double[] et,
	out int ifail
)
Visual Basic
Public Shared Sub g13fh ( _
	num As Integer, _
	nt As Integer, _
	ip As Integer, _
	iq As Integer, _
	theta As Double(), _
	fht As Double(), _
	ht As Double(), _
	et As Double(), _
	<OutAttribute> ByRef ifail As Integer _
)
Visual C++
public:
static void g13fh(
	int num, 
	int nt, 
	int ip, 
	int iq, 
	array<double>^ theta, 
	array<double>^ fht, 
	array<double>^ ht, 
	array<double>^ et, 
	[OutAttribute] int% ifail
)
F#
static member g13fh : 
        num : int * 
        nt : int * 
        ip : int * 
        iq : int * 
        theta : 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,iqnum.
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,iq20;
  • ip0.
iq
Type: System..::..Int32
On entry: the number of coefficients, αi, for i=1,2,,q.
Constraints:
  • maxip,iq20;
  • iq1.
theta
Type: array<System..::..Double>[]()[][]
An array of size [2×iq+ip+1]
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 autoregressive coefficients αi, for i=1,2,,q. The next iq elements must contain the coefficients ϕi, for i=1,2,,q. The next ip elements must contain the moving average coefficients βj, for j=1,2,,p.
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 represented by:
lnht=α0+i=1qαizt-i+j=1qϕizt-j-Ezt-i+j=1pβilnht-j,  t=1,2,,T.
where εtψt-1=N0,ht or εtψt-1=Stdf,ht, and zt=εtht, Ezt-i denotes the expected value of zt-i, has been modelled by g13fg, and the estimated conditional variances and residuals are contained in the arrays ht and et respectively.
g13fh will then use the last maxp,q elements of the arrays ht and et to estimate the conditional variance forecasts, htψT, 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
Glosten L, Jagannathan R and Runkle D (1993) Relationship between the expected value and the volatility of nominal excess return on stocks Journal of Finance 48 1779–1801
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,
ornt0.
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 Also