GARCHM_FORESD - Volatility Forecast of GARCH-M Model

Mohamad

October 27, 2016 22:50

(Deprecated) Calculates the estimated error/standard deviation of the conditional mean forecast.

Syntax

GARCHM_FORESD ([x], [σ], order, µ, λ, [α], [β], t, local)

[X]

Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).

[σ]

Optional. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)) of the last q realized volatilities.

Order

Optional. Is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).

Value	Order
1	Ascending (the first data point corresponds to the earliest date) (default).
0	Descending (the first data point corresponds to the latest date).

µ

Optional. Is the GARCH model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.

λ

Optional. Is the volatility coefficient for the mean. In finance, lambda is referenced as the risk premium. If missing, a default of 0 is assumed.

[α]

Required. Are the parameters of the ARCH(p) component model: [αo α1, α2 … αp] (starting with the lowest lag).

[β]

Optional. Are the parameters of the GARCH(q) component model: [β1, β2 … βq] (starting with the lowest lag).

T

Optional. Is the forecast time/horizon (expressed in terms of steps beyond the end of the time series). If missing, a default of 1 is assumed.

Local

Optional. Is the type of desired volatility output (0 = Term Structure, 1 = Local Volatility). If missing, local volatility is assumed.

Warning

GARCHM_FORESD(.) function is deprecated as of version 1.63; use the GARCHM_FORE(.) function instead.

The underlying model is described here.
The time series is homogeneous or equally spaced.
The time series may include missing values (e.g., #N/A) at either end.
The number of parameters in the input argument - [α_oα_1, α₂… α_p] - determines the order of the ARCH component model.
The number of parameters in the input argument - [β_1, β₂… β_q] - determines the order of the GARCH component model.

James Douglas Hamilton; Time Series Analysis, Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.
Tsay, Ruey S.; Analysis of Financial Time Series, John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.