NAG FL Interface
g13fhf (uni_​garch_​exp_​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: $\max (\mathbf{ip},\mathbf{iq})\le \mathbf{num}$.

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:

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

4: $\mathbf{iq}$ – Integer Input

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

Constraints:

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

5: $\mathbf{theta}\left(2\times \mathbf{iq}+\mathbf{ip}+1\right)$ – Real (Kind=nag_wp) array Input

On entry: the initial parameter estimates for the vector $\theta$. The first element must contain the coefficient ${\alpha }_o$ and the next iq elements must contain the autoregressive coefficients ${\alpha }_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,q$. The next iq elements must contain the coefficients ${\varphi }_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,q$. The next ip elements must contain the moving average coefficients ${\beta }_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,p$.

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

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

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

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

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

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

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

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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, $\max (\mathbf{ip},\mathbf{iq})=⟨\mathit{\text{value}}⟩$.
Constraint: $\max (\mathbf{ip},\mathbf{iq})\le 20$.

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

On entry, $\mathbf{num}=⟨\mathit{\text{value}}⟩$.
Constraint: $\max (\mathbf{ip},\mathbf{iq})\le \mathbf{num}$.

$\mathbf{ifail}=-99$

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