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

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{num}$ – Integer Input

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

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

2: $\mathbf{nt}$ – Integer Input

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

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

3: $\mathbf{ip}$ – Integer Input

On entry: the number of coefficients, ${\beta }_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,p$.

Constraints:

• $\max \left(\mathbf{ip},\mathbf{iq}\right)\le 20$;
• $\mathbf{ip}\ge 0$.

4: $\mathbf{iq}$ – Integer Input

On entry: the number of coefficients, ${\alpha }_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,q$.

Constraints:

• $\max \left(\mathbf{ip},\mathbf{iq}\right)\le 20$;
• $\mathbf{iq}\ge 1$.

5: $\mathbf{theta}\left(\mathbf{iq}+\mathbf{ip}+1\right)$ – Real (Kind=nag_wp) array Input

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

6: $\mathbf{gamma}$ – Real (Kind=nag_wp) Input

On entry: the asymmetry parameter $\gamma$ for the $\text{GARCH}\left(p,q\right)$ sequence.

7: $\mathbf{fht}\left(\mathbf{nt}\right)$ – Real (Kind=nag_wp) array Output

On exit: the forecast values of the conditional variance, $h_t$, for $\mathit{t}=T+1,\dots ,T+\xi$.

8: $\mathbf{ht}\left(\mathbf{num}\right)$ – Real (Kind=nag_wp) array Input

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

9: $\mathbf{et}\left(\mathbf{num}\right)$ – Real (Kind=nag_wp) array Input

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

10: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. 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 $-1\text{ or }1$ 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 $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

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

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

On entry, $\max \left(\mathbf{ip},\mathbf{iq}\right)=〈\mathit{\text{value}}〉$.
Constraint: $\max \left(\mathbf{ip},\mathbf{iq}\right)\le 20$.

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

On entry, $\mathbf{num}=〈\mathit{\text{value}}〉$.
Constraint: $\max \left(\mathbf{ip},\mathbf{iq}\right)\le \mathbf{num}$.

$\mathbf{ifail}=-99$

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.

$\mathbf{ifail}=-399$

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.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example