g13fd forecasts the conditional variances,

h_{t}, t = T + 1, \dots, T + ξ

from a type II

AGARCH (p, q)

sequence, where

ξ

is the forecast horizon and

T

is the current time (see Engle and Ng (1993)).

Syntax

C#
public static void g13fd( int num, int nt, int ip, int iq, double[] theta, double gamma, double[] fht, double[] ht, double[] et, out int ifail )

Visual Basic
Public Shared Sub g13fd ( _ num As Integer, _ nt As Integer, _ ip As Integer, _ iq As Integer, _ theta As Double(), _ gamma As Double, _ fht As Double(), _ ht As Double(), _ et As Double(), _ <OutAttribute> ByRef ifail As Integer _ )

Visual Basic

Public Shared Sub g13fd ( _
	num As Integer, _
	nt As Integer, _
	ip As Integer, _
	iq As Integer, _
	theta As Double(), _
	gamma As Double, _
	fht As Double(), _
	ht As Double(), _
	et As Double(), _
	<OutAttribute> ByRef ifail As Integer _
)

Visual C++
public: static void g13fd( int num, int nt, int ip, int iq, array<double>^ theta, double gamma, array<double>^ fht, array<double>^ ht, array<double>^ et, [OutAttribute] int% ifail )

F#
static member g13fd : num : int * nt : int * ip : int * iq : int * theta : float[] * gamma : float * fht : float[] * ht : float[] * et : float[] * ifail : int byref -> unit

Parameters

num: Type: System..::..Int32
On entry: the number of terms in the arrays ht and et from the modelled sequence.

Constraint: $\max (ip, iq) \leq num$ .

nt: Type: System..::..Int32
On entry: $ξ$ , the forecast horizon.

Constraint: $nt > 0$ .

ip

Type: System..::..Int32

On entry: the number of coefficients,

β_{i}

, for

i = 1, 2, \dots, p

Constraints:

$\max (ip, iq) \leq 20$ ;
$ip \geq 0$ .

iq

Type: System..::..Int32

On entry: the number of coefficients,

α_{i}

, for

i = 1, 2, \dots, q

Constraints:

$\max (ip, iq) \leq 20$ ;
$iq \geq 1$ .

theta: Type: array<System..::..Double>[]()[][]
An array of size [ $iq + ip + 1$ ]
On entry: the first element must contain the coefficient $α_{o}$ and the next iq elements must contain the coefficients $α_{i}$ , for $i = 1, 2, \dots, q$ . The remaining ip elements must contain the coefficients $β_{j}$ , for $j = 1, 2, \dots, p$ .

gamma: Type: System..::..Double
On entry: the asymmetry parameter $γ$ for the $GARCH (p, q)$ sequence.

fht: Type: array<System..::..Double>[]()[][]
An array of size [nt]
On exit: the forecast values of the conditional variance, $h_{t}$ , for $t = T + 1, \dots, T + ξ$ .

ht: Type: array<System..::..Double>[]()[][]
An array of size [num]
On entry: the sequence of past conditional variances for the $GARCH (p, q)$ process, $h_{t}$ , for $t = 1, 2, \dots, T$ .

et: Type: array<System..::..Double>[]()[][]
An array of size [num]
On entry: the sequence of past residuals for the $GARCH (p, q)$ process, $ε_{t}$ , for $t = 1, 2, \dots, T$ .

ifail: Type: System..::..Int32%
On exit: $ifail = 0$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Description

Assume the

GARCH (p, q)

process can be represented by:

h_{t} = α_{0} + \sum_{i = 1}^{q} α_{i} {(|ε_{t - i}| + γ ε_{t - i})}^{2} + \sum_{i = 1}^{p} β_{i} h_{t - i}, t = 1, 2, \dots, T .

where

ε_{t} ∣ ψ_{t - 1} = N (0, h_{t})

ε_{t} ∣ ψ_{t - 1} = S_{t} (df, h_{t})

, has been modelled by g13fc and the estimated conditional variances and residuals are contained in the arrays ht and et respectively.

g13fd will then use the last

\max (p, q)

elements of the arrays ht and et to estimate the conditional variance forecasts,

h_{t} ∣ ψ_{T}

, where

t = T + 1, \dots, T + ξ

and

ξ

is the forecast horizon.

References

Bollerslev T (1986) Generalised autoregressive conditional heteroskedasticity Journal of Econometrics 31 307–327

Engle R (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation Econometrica 50 987–1008

Engle R and Ng V (1993) Measuring and testing the impact of news on volatility Journal of Finance 48 1749–1777

Hamilton J (1994) Time Series Analysis Princeton University Press

Error Indicators and Warnings

Errors or warnings detected by the method:

$ifail = 1$

On entry,	$num < \max (ip, iq)$ ,
or	$iq < 1$ ,
or	$ip < 0$ ,
or	$\max (ip, iq) > 20$ ,
or	$nt \leq 0$ .

$ifail = -9000$: An error occured, see message report.
$ifail = -8000$: Negative dimension for array $〈value〉$
$ifail = -6000$: Invalid Parameters $〈value〉$

Accuracy

Not applicable.

Parallelism and Performance

None.

Further Comments