NAG FL Interface
g13fbf (uni_​garch_​asym1_​forecast)

1 Purpose

g13fbf 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)).

2 Specification

Fortran Interface
Subroutine g13fbf ( num, nt, ip, iq, theta, gamma, fht, ht, et, ifail)
Integer, Intent (In) :: num, nt, ip, iq
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: theta(iq+ip+1), gamma, ht(num), et(num)
Real (Kind=nag_wp), Intent (Out) :: fht(nt)
C Header Interface
#include <nag.h>
void  g13fbf_ (const Integer *num, const Integer *nt, const Integer *ip, const Integer *iq, const double theta[], const double *gamma, double fht[], const double ht[], const double et[], Integer *ifail)
The routine may be called by the names g13fbf or nagf_tsa_uni_garch_asym1_forecast.

3 Description

Assume the GARCHp,q process can be represented by:
ht=α0+i=1qαi εt-i+γ 2+i=1pβiht-i,  t=1,2,,T  
where εtψt-1=N0,ht or εtψt-1=Stdf,ht, has been modelled by g13faf and the estimated conditional variances and residuals are contained in the arrays ht and et respectively.
g13fbf 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.

4 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

5 Arguments

1: num Integer Input
On entry: the number of terms in the arrays ht and et from the modelled sequence.
Constraint: maxip,iqnum.
2: nt Integer Input
On entry: ξ, the forecast horizon.
Constraint: nt>0.
3: ip Integer Input
On entry: the number of coefficients, βi, for i=1,2,,p.
Constraints:
  • maxip,iq20;
  • ip0.
4: iq Integer Input
On entry: the number of coefficients, αi, for i=1,2,,q.
Constraints:
  • maxip,iq20;
  • iq1.
5: thetaiq+ip+1 Real (Kind=nag_wp) array Input
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.
6: gamma Real (Kind=nag_wp) Input
On entry: the asymmetry parameter γ for the GARCHp,q sequence.
7: fhtnt Real (Kind=nag_wp) array Output
On exit: the forecast values of the conditional variance, ht, for t=T+1,,T+ξ.
8: htnum Real (Kind=nag_wp) array Input
On entry: the sequence of past conditional variances for the GARCHp,q process, ht, for t=1,2,,T.
9: etnum Real (Kind=nag_wp) array Input
On entry: the sequence of past residuals for the GARCHp,q process, εt, for t=1,2,,T.
10: ifail Integer Input/Output
On entry: ifail must be set to 0, -1 or 1. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 or 1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this argument, the recommended value is 0. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or -1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
ifail=1
On entry, ip=value.
Constraint: ip0.
On entry, iq=value.
Constraint: iq1.
On entry, maxip,iq=value.
Constraint: maxip,iq20.
On entry, nt=value.
Constraint: nt>0.
On entry, num=value.
Constraint: maxip,iqnum.
ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
ifail=-399
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
ifail=-999
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g13fbf is not threaded in any implementation.

9 Further Comments

None.

10 Example

See Section 10 in g13faf.