NAG Library Function Document

nag_generate_agarchII (g05hlc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     num – IntegerInput

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

Constraints:

• $\mathbf{num}\ge 1$;
• $\mathbf{num}>\mathbf{p}+\mathbf{q}+1$.

2:     p – IntegerInput

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

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

3:     q – IntegerInput

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

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

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

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

5:     gamma – doubleInput

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

6:     ht[num] – doubleOutput

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

7:     et[num] – doubleOutput

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

8:     fcall – Nag_Garch_Fcall_TypeInput

On entry: if $\mathbf{fcall}=\mathrm{Nag\_Garch\_Fcall\_True}$, a new sequence is to be generated, else if $\mathbf{fcall}=\mathrm{Nag\_Garch\_Fcall\_False}$ a given sequence is to be continued using the information in rvec.

9:     rvec[$2\times \left(\mathbf{p}+\mathbf{q}+1\right)$] – doubleInput/Output

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

On exit: contains information that can be used in a subsequent call of nag_generate_agarchII (g05hlc), with $\mathbf{fcall}=\mathrm{Nag\_Garch\_Fcall\_False}$.

10:   fail – NagError *Input/Output

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

6  Error Indicators and Warnings

NE_2_INT_ARG_LT

On entry, $\mathbf{num}=〈\mathit{\text{value}}〉$ while $\mathbf{p}+\mathbf{q}+1=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{num}\ge \mathbf{p}+\mathbf{q}+1$.

NE_BAD_PARAM

On entry, argument fcall had an illegal value.

NE_INT_ARG_LT

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

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  Further Comments

9  Example