nag_forecast_garchGJR (g13ffc) (PDF version)
g13 Chapter Contents
g13 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_forecast_garchGJR (g13ffc)

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

nag_forecast_garchGJR (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>
#include <nagg13.h>
void  nag_forecast_garchGJR (Integer num, Integer nt, Integer p, Integer q, const double theta[], double gamma, double fht[], const double ht[], const double et[], NagError *fail)

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 nag_estimate_garchGJR (g13fec) and the estimated conditional variances and residuals are contained in the arrays ht and et respectively. Then nag_forecast_garchGJR (g13ffc) will use the last maxp,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:     numIntegerInput
On entry: the number of terms in the arrays ht and et from the modelled sequence.
Constraint: maxp,q num .
2:     ntIntegerInput
On entry: τ , the forecast horizon.
Constraint: nt>0 .
3:     pIntegerInput
On entry: the GARCH p,q  argument p .
Constraint: 0 < maxp,q num , ​ p0 .
4:     qIntegerInput
On entry: the GARCH p,q  argument q .
Constraint: 0 < maxp,q num , ​ q1 .
5:     theta[q+p+1]const doubleInput
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:     gammadoubleInput
On entry: the asymmetry argument γ  for the GARCH p,q  sequence.
7:     fht[nt]doubleOutput
On exit: the forecast values of the conditional variance, h t , for t=1,2,,τ.
8:     ht[num]const doubleInput
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 doubleInput
On entry: the sequence of past residuals for the GARCH p,q  process, ε t , for t=1,2,,T.
10:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_2_INT_ARG_LT
On entry, num=value  while maxp,q = value. These arguments must satisfy num maxp,q .
NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_INT_ARG_LT
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  Further Comments

None.

9  Example

See the example for nag_estimate_agarchII (g13fcc).

nag_forecast_garchGJR (g13ffc) (PDF version)
g13 Chapter Contents
g13 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012