## Documentation Center |

Infer ARMAX/GARCH model innovations

`garchinfer` has been removed. Use `infer` instead.

`[Innovations,Sigmas,LLF]
= garchinfer(Spec,Series)[...] = garchinfer(Spec,Series,X)[...] = garchinfer(Spec,Series,X,... PreInnovations,PreSigmas,PreSeries)`

`[Innovations,Sigmas,LLF] = garchinfer(Spec,Series)`, given a conditional mean specification of ARMAX form and conditional variance specification of GARCH, EGARCH, or GJR form, infers the innovations and conditional standard deviations from an observed univariate return series. Since`garchinfer`is an interface to the appropriate loglikelihood objective function, the loglikelihood value is also computed for convenience.`[...] = garchinfer(Spec,Series,X)`accepts a time series regression matrix`X`of observed explanatory data.`garchinfer`treats each column of`X`as an individual time series, and uses it as an explanatory variable in the regression component of the conditional mean.`[...] = garchinfer(Spec,Series,X,...`uses presample observations, represented by the time series matrices or column vectors

PreInnovations,PreSigmas,PreSeries)`PreInnovations`,`PreSigmas`, and`PreSeries`, to infer the outputs`Innovations`and`Sigmas`. These vectors form the conditioning set used to initiate the inverse filtering, or inference, process.

If you specify the presample data as matrices, the number of
columns (paths) of each *must* be the same as the
number of columns (paths) of the `Series` input.
In this case, `garchinfer` uses the presample information
of a given column to infer the residuals and standard deviations of
the corresponding column of `Series`. If you specify
the presample data as column vectors, `garchinfer` applies
the vectors to each column of `Series`.

If you provide no explicit presample data, `garchinfer` derives
the necessary presample observations using conventional time series
techniques.

GARCH specification structure that contains the conditional
mean and variance specifications. It also contains the optimization
parameters needed for the estimation. Create this structure by calling | |

Time series matrix or column vector of observations of
the underlying univariate return series of interest. | |

Time series regression matrix of explanatory variables.
Typically, The
number of valid (non- | |

Time series matrix or column vector of presample innovations
on which the recursive mean and variance models are conditioned. This
array can have any number of rows, provided it contains sufficient
observations to initialize the mean and variance equations. That is,
if If the number
of rows exceeds | |

Time series matrix or column vector of positive presample
conditional standard deviations on which the recursive variance model
is conditioned. This array can have any number of rows, provided it
contains sufficient observations to initialize the conditional variance
equation. For example, if At least `P`rows for GARCH and GJR models, andAt least `max(P,Q)`rows for EGARCH models.
If the number of rows exceeds the requirement, then | |

Time series matrix or column vector of presample observations
of the return series of interest on which the recursive mean model
is conditioned. This array can have any number of rows, provided it
contains sufficient observations to initialize the conditional mean
equation. Thus, if |

Innovations time series matrix inferred from | |

Conditional standard deviation time series matrix corresponding
to | |

Row vector of loglikelihood objective function values
for each path of |

[1] Box, G. E. P., G. M. Jenkins, and G. C.
Reinsel. *Time Series Analysis: Forecasting and Control*.
3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.

[2] Hamilton, J. D. *Time Series
Analysis*. Princeton, NJ: Princeton University Press, 1994.

`garchpred` | `garchset` | `garchsim `

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