GARCH conditional variance time series model
Use garch
to specify a univariate GARCH (generalized autoregressive conditional heteroscedastic) model. The garch
function returns a garch
object specifying the functional form of a GARCH(P,Q) model, and stores its parameter values.
The key components of a garch
model include the:
GARCH polynomial, which is composed of lagged conditional variances. The degree is denoted by P.
ARCH polynomial, which is composed of the lagged squared innovations. The degree is denoted by Q.
P and Q are the maximum nonzero lags in the GARCH and ARCH polynomials, respectively. Other model components include an innovation mean model offset, a conditional variance model constant, and the innovations distribution.
All coefficients are unknown (NaN
values) and estimable unless you specify their values using name-value pair argument syntax. To estimate models containing all or partially unknown parameter values given data, use estimate
. For completely specified models (models in which all parameter values are known), simulate or forecast responses using simulate
or forecast
, respectively.
returns a zero-degree conditional variance Mdl
= garchgarch
object.
creates a GARCH conditional variance model object (Mdl
= garch(P
,Q
)Mdl
) with a GARCH polynomial with a degree of P
and an ARCH polynomial with a degree of Q
. The GARCH and ARCH polynomials contain all consecutive lags from 1 through their degrees, and all coefficients are NaN
values.
This shorthand syntax enables you to create a template in which you specify the polynomial degrees explicitly. The model template is suited for unrestricted parameter estimation, that is, estimation without any parameter equality constraints. However, after you create a model, you can alter property values using dot notation.
sets properties or additional options using name-value pair arguments. Enclose each name in quotes. For example, Mdl
= garch(Name,Value
)'ARCHLags',[1 4],'ARCH',{0.2 0.3}
specifies the two ARCH coefficients in ARCH
at lags 1
and 4
.
This longhand syntax enables you to create more flexible models.
estimate | Fit conditional variance model to data |
filter | Filter disturbances through conditional variance model |
forecast | Forecast conditional variances from conditional variance models |
infer | Infer conditional variances of conditional variance models |
simulate | Monte Carlo simulation of conditional variance models |
summarize | Display estimation results of conditional variance model |
You can specify a garch
model as part of a composition of conditional mean and variance models. For details, see arima
.
[1] Tsay, R. S. Analysis of Financial Time Series. 3rd ed. Hoboken, NJ: John Wiley & Sons, Inc., 2010.