NAG Library Function Document

nag_rand_garchGJR (g05pfc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     dist – Nag_ErrorDistnInput

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

$\mathbf{dist}=\mathrm{Nag\_NormalDistn}$

A Normal distribution is used.

$\mathbf{dist}=\mathrm{Nag\_Tdistn}$

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

Constraint: $\mathbf{dist}=\mathrm{Nag\_NormalDistn}$ or $\mathrm{Nag\_Tdistn}$.

2:     num – IntegerInput

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

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

3:     ip – IntegerInput

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

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

4:     iq – IntegerInput

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

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

5:     theta[$\mathbf{iq}+\mathbf{ip}+1$] – const doubleInput

On entry: the first element must contain the coefficient ${\alpha }_o$, 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 $\mathit{j}=1,2,\dots ,p$.

Constraints:

• ${\displaystyle \sum _{\mathit{i}=2}^{\mathbf{iq}+\mathbf{ip}+1}}\mathbf{theta}\left[\mathit{i}-1\right]<1.0$;
• $\mathbf{theta}\left[\mathit{i}-1\right]\ge 0.0$, for $i=1$ and $i=\mathbf{iq}+2,\dots ,\mathbf{iq}+\mathbf{ip}+1$.

6:     gamma – doubleInput

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

Constraint: $\mathbf{gamma}+\mathbf{theta}\left[\mathit{i}-1\right]\ge 0.0$, for $\mathit{i}=2,3,\dots ,\mathbf{iq}+1$.

7:     df – IntegerInput

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

If $\mathbf{dist}=\mathrm{Nag\_NormalDistn}$, df is not referenced.

Constraint: if $\mathbf{dist}=\mathrm{Nag\_Tdistn}$, $\mathbf{df}>2$.

8:     ht[num] – doubleOutput

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

9:     et[num] – doubleOutput

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

10:   fcall – Nag_BooleanInput

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

11:   r[lr] – doubleInput/Output

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

On exit: contains information that can be used in a subsequent call of nag_rand_garchGJR (g05pfc), with $\mathbf{fcall}=\mathrm{Nag\_FALSE}$.

12:   lr – IntegerInput

On entry: the dimension of the array r.

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

13:   state[$\mathit{dim}$] – IntegerCommunication Array

Note: the actual argument supplied must be the array state supplied to the initialization functions nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).

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

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

14:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

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

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, lr is not large enough, $\mathbf{lr}=〈\mathit{\text{value}}〉$: minimum length required $=〈\mathit{\text{value}}〉$.

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

NE_INVALID_STATE

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

NE_PREV_CALL

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 $\mathbf{iq}=〈\mathit{\text{value}}〉$.

NE_REAL_2

On entry, $\mathbf{theta}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$ and $\gamma =〈\mathit{\text{value}}〉$.
Constraint: ${\alpha }_i+\gamma \ge 0$.

NE_REAL_ARRAY

On entry, sum of $\mathbf{theta}\left[i\right]=〈\mathit{\text{value}}〉$.
Constraint: sum of $\mathbf{theta}\left[\mathit{i}\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{ip}+\mathbf{iq}$ is $<1.0$.

On entry, $\mathbf{theta}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{theta}\left[i\right]\ge 0.0$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g05pfce.c)

9.2  Program Data

9.3  Program Results

Program Results (g05pfce.r)