NAG CL Interface
g13fbc (uni_​garch_​asym1_​forecast)

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1 Purpose

g13fbc forecasts the conditional variances, h t , t = 1 , , τ from a type I AGARCH (p,q) sequence, where τ is the forecast horizon (see Engle and Ng (1993)).

2 Specification

#include <nag.h>
void  g13fbc (Integer num, Integer nt, Integer p, Integer q, const double theta[], double gamma, double fht[], const double ht[], const double et[], NagError *fail)
The function may be called by the names: g13fbc, nag_tsa_uni_garch_asym1_forecast or nag_forecast_agarchi.

3 Description

Assume the standard (γ=0) GARCH (p,q) process can be represented by:
ε t ψ t-1 N (0, h t )  
h t = α 0 + i=1 q α i ε t-i 2 + i=1 p β i h t-i ,   t = 1 , , T .  
or type I AGARCH (p,q) process with conditional variance h t given by:
h t = α 0 + i=1 q α i ( ε t-i +γ) 2 + i=1 p β i h t-i ,   t = 1 , , T .  
has been modelled by g13fac and the estimated conditional variances and residuals are contained in the arrays ht and et respectively. Then g13fbc will use the last max(p,q) elements of the arrays ht and et to estimate the conditional variance forecasts, h t ψ T , where t = T + 1 , , T + τ and τ 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: max(p,q) num .
2: nt Integer Input
On entry: τ , the forecast horizon.
Constraint: nt>0 .
3: p Integer Input
On entry: the GARCH (p,q) argument p .
Constraint: 0 < max(p,q) num , ​ p0 .
4: q Integer Input
On entry: the GARCH (p,q) argument q .
Constraint: 0 < max(p,q) num , ​ q1 .
5: theta[q+p+1] const double Input
On entry: the first element must contain the coefficient α o and the next q elements must contain the coefficients α i , for i=1,2,,q. The remaining p elements must contain the coefficients β j , for j=1,2,,p.
6: gamma double Input
On entry: the asymmetry argument γ for the GARCH (p,q) sequence.
7: fht[nt] double Output
On exit: the forecast values of the conditional variance, h t , for t=1,2,,τ.
8: ht[num] const double Input
On entry: the sequence of past conditional variances for the GARCH (p,q) process, h t , for t=1,2,,T.
9: et[num] const double Input
On entry: the sequence of past residuals for the GARCH (p,q) process, ε t , for t=1,2,,T.
10: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

On entry, num=value while max(p,q) = value. These arguments must satisfy num max(p,q) .
Dynamic memory allocation failed.
On entry, nt=value.
Constraint: nt1.
On entry, num=value.
Constraint: num0.
On entry, p=value.
Constraint: p0.
On entry, q=value.
Constraint: q1.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g13fbc is not threaded in any implementation.

9 Further Comments


10 Example

See the example for g13fac.