NAG CL Interface
g13ffc (uni_​garch_​gjr_​forecast)

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1 Purpose

g13ffc forecasts the conditional variances, h t , t = 1 , , τ from a GJR GARCH (p,q) sequence, where τ is the forecast horizon (see Glosten et al. (1993)).

2 Specification

#include <nag.h>
void  g13ffc (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: g13ffc, nag_tsa_uni_garch_gjr_forecast or nag_forecast_garchgjr.

3 Description

Assume the 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 +γ S t-i ) ε t-i 2 + i=1 p β i h t-i ,   t = 1 , , T .  
where S t = 1 , if ε t < 0 , and S t = 0 , if ε t 0 has been modelled by g13fec and the estimated conditional variances and residuals are contained in the arrays ht and et respectively. Then g13ffc 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
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

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.
g13ffc is not threaded in any implementation.

9 Further Comments


10 Example

See the example for g13fcc.