NAG FL Interface
g05pgf (times_​garch_​exp)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{dist}$ – Character(1) Input

On entry: the type of distribution to use for ${\epsilon }_t$.

$\mathbf{dist}=\text{'N'}$

A Normal distribution is used.

$\mathbf{dist}=\text{'T'}$

A Student's $t$-distribution is used.

Constraint: $\mathbf{dist}=\text{'N'}$ or $\text{'T'}$.

2: $\mathbf{num}$ – Integer Input

On entry: $T$, the number of terms in the sequence.

Constraint: $\mathbf{num}\ge 0$.

3: $\mathbf{ip}$ – Integer Input

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

Constraint: $\mathbf{ip}\ge 0$.

4: $\mathbf{iq}$ – Integer Input

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

Constraint: $\mathbf{iq}\ge 1$.

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 $\mathit{j}=1,2,\dots ,p$.

Constraints:

• ${\displaystyle \sum _{\mathit{i}=1}^p}{\beta }_i\ne 1.0$;
• $\frac{{\alpha }_0}{1-{\displaystyle \sum _{\mathit{i}=1}^p}{\beta }_i}\le -\log \left(\mathbf{x02amf}\right)$.

6: $\mathbf{df}$ – Integer Input

On entry: the number of degrees of freedom for the Student's $t$-distribution.

If $\mathbf{dist}=\text{'N'}$, df is not referenced.

Constraint: if $\mathbf{dist}=\text{'T'}$, $\mathbf{df}>2$.

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

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

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

On exit: the observations ${\epsilon }_{\mathit{t}}$, for $\mathit{t}=1,2,\dots ,T$, for the $\text{GARCH}(p,q)$ sequence.

9: $\mathbf{fcall}$ – Logical Input

On entry: if $\mathbf{fcall}=\mathrm{.TRUE.}$, a new sequence is to be generated, otherwise a given sequence is to be continued using the information in r.

10: $\mathbf{r}\left(\mathbf{lr}\right)$ – Real (Kind=nag_wp) array Communication Array

On entry: the array contains information required to continue a sequence if $\mathbf{fcall}=\mathrm{.FALSE.}$.

On exit: contains information that can be used in a subsequent call of g05pgf, with $\mathbf{fcall}=\mathrm{.FALSE.}$.

11: $\mathbf{lr}$ – Integer Input

On entry: the dimension of the array r as declared in the (sub)program from which g05pgf is called.

Constraint: $\mathbf{lr}\ge 2\times (\mathbf{ip}+2\times \mathbf{iq}+2)$.

12: $\mathbf{state}(*)$ – Integer array Communication Array

Note: the actual argument supplied must be the array state supplied to the initialization routines g05kff or g05kgf.

On entry: contains information on the selected base generator and its current state.

On exit: contains updated information on the state of the generator.

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

On entry: ifail must be set to $0$, $\mathrm{-1}$ 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 $\mathrm{-1}$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $\mathrm{-1}$ 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, dist is not valid: $\mathbf{dist}=⟨\mathit{\text{value}}⟩$.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

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

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=6$

On entry, $\mathbf{df}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{df}\ge 3$.

$\mathbf{ifail}=10$

ip or iq is not the same as when r was set up in a previous call.
Previous value of $\mathbf{ip}=⟨\mathit{\text{value}}⟩$ and $\mathbf{ip}=⟨\mathit{\text{value}}⟩$.
Previous value of $\mathbf{iq}=⟨\mathit{\text{value}}⟩$ and $\mathbf{iq}=⟨\mathit{\text{value}}⟩$.

$\mathbf{ifail}=11$

On entry, lr is not large enough, $\mathbf{lr}=⟨\mathit{\text{value}}⟩$: minimum length required $=⟨\mathit{\text{value}}⟩$.

$\mathbf{ifail}=12$

On entry, state vector has been corrupted or not initialized.

$\mathbf{ifail}=20$

Invalid sequence generated, use different parameters.

$\mathbf{ifail}=-99$

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

10.1 Program Text

10.2 Program Data

10.3 Program Results