GJR conditional variance time series model
Use gjr
to specify a univariate GJR (Glosten, Jagannathan, and Runkle) model. The gjr
function returns a gjr
object specifying the functional form of a GJR(P,Q) model, and stores its parameter values.
The key components of a gjr
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.
Leverage polynomial, which is composed of lagged squared, negative innovations.
Maximum of the ARCH and leverage polynomial degrees, denoted by Q.
P is the maximum nonzero lag in the GARCH polynomial, and Q is the maximum nonzero lag in the ARCH and leverage polynomials. 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
= gjrgjr
object.
creates a GJR conditional variance model object (Mdl
= gjr(P
,Q
)Mdl
) with a GARCH polynomial with a degree of P
and ARCH and leverage polynomials each with a degree of Q
. All 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 property name in quotes. For example, Mdl
= gjr(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 gjr
model as part of a composition of conditional mean and variance models. For details, see arima
.
[1] Glosten, L. R., R. Jagannathan, and D. E. Runkle. “On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” The Journal of Finance. Vol. 48, No. 5, 1993, pp. 1779–1801.
[2] Tsay, R. S. Analysis of Financial Time Series. 3rd ed. Hoboken, NJ: John Wiley & Sons, Inc., 2010.