NAG Library Function Document

nag_forecast_garchGJR (g13ffc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{num}$ – IntegerInput

On entry: the number of terms in the arrays ht and et from the modelled sequence.

Constraint: $\max \left(\mathbf{p},\mathbf{q}\right)\le \mathbf{num}$.

2:    $\mathbf{nt}$ – IntegerInput

On entry: $\tau$, the forecast horizon.

Constraint: $\mathbf{nt}>0$.

3:    $\mathbf{p}$ – IntegerInput

On entry: the GARCH$\left(p,q\right)$ argument $p$.

Constraint: $0<\max \left(\mathbf{p},\mathbf{q}\right)\le \mathbf{num}\text{, }\mathbf{p}\ge 0$.

4:    $\mathbf{q}$ – IntegerInput

On entry: the GARCH$\left(p,q\right)$ argument $q$.

Constraint: $0<\max \left(\mathbf{p},\mathbf{q}\right)\le \mathbf{num}\text{, }\mathbf{q}\ge 1$.

5:    $\mathbf{theta}\left[\mathbf{q}+\mathbf{p}+1\right]$ – const doubleInput

On entry: the first element must contain the coefficient ${\alpha }_o$ and the next q elements must contain the coefficients ${\alpha }_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,q$. The remaining p elements must contain the coefficients ${\beta }_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,p$.

6:    $\mathbf{gamma}$ – doubleInput

On entry: the asymmetry argument $\gamma$ for the GARCH$\left(p,q\right)$ sequence.

7:    $\mathbf{fht}\left[\mathbf{nt}\right]$ – doubleOutput

On exit: the forecast values of the conditional variance, $h_{\mathit{t}}$, for $\mathit{t}=1,2,\dots ,\tau$.

8:    $\mathbf{ht}\left[\mathbf{num}\right]$ – const doubleInput

On entry: the sequence of past conditional variances for the GARCH$\left(p,q\right)$ process, $h_{\mathit{t}}$, for $\mathit{t}=1,2,\dots ,T$.

9:    $\mathbf{et}\left[\mathbf{num}\right]$ – const doubleInput

On entry: the sequence of past residuals for the GARCH$\left(p,q\right)$ process, ${\epsilon }_{\mathit{t}}$, for $\mathit{t}=1,2,\dots ,T$.

10:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_2_INT_ARG_LT

On entry, $\mathbf{num}=〈\mathit{\text{value}}〉$ while $\max \left(\mathbf{p},\mathbf{q}\right)=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{num}\ge \max \left(\mathbf{p},\mathbf{q}\right)$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_INT_ARG_LT

On entry, $\mathbf{nt}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nt}\ge 1$.

On entry, $\mathbf{num}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{num}\ge 0$.

On entry, $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{p}\ge 0$.

On entry, $\mathbf{q}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{q}\ge 1$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example