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GJR conditional variance time series model

A `gjr`

model object specifies the
functional form and stores the parameter values of a Glosten, Jagannathan,
and Runkle (GJR) model [1],
which is a generalized autoregressive conditional heteroscedastic
(GARCH) model generalization. GJR models attempt to address volatility
clustering in an innovations process. Volatility clustering occurs
when an innovations process does not exhibit significant autocorrelation,
but the variance of the process changes with time. GJR models are
appropriate when negative shocks contribute more to volatility than
positive shocks [2].

The GJR(*P*,*Q*) conditional
variance model includes:

*P*past conditional variances that compose the GARCH component polynomial*Q*past squared innovations that compose the ARCH and leverage component polynomials

To create a `gjr`

model object, use `gjr`

. Specify only the GARCH and ARCH (and
leverage) polynomial degrees *P* and *Q*,
respectively, using the shorthand syntax `gjr(P,Q)`

.
Then, pass the model and time series data to `estimate`

to fit the
model to the data. Or, specify the values of some parameters, and
then estimate others.

Use a completely specified model (i.e., all parameter values of the model are known) to:

Create `gjr`

models using `gjr`

.

You can specify a `gjr`

model as part of a
composition of conditional mean and variance models. For details,
see `arima`

.

Conditional Variance Model Properties | Specify conditional variance model functional form and parameter values |

`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 |

`print` | Display parameter estimation results for conditional variance models |

`simulate` | Monte Carlo simulation of conditional variance models |

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