For conditional variance model estimation, the required inputs
estimate are a model and a vector of univariate
time series data. The model specifies the parametric form of the conditional
variance model being estimated.
fitted values for any parameters in the input model with
If you specify non-
NaN values for any parameters,
these values as equality constraints and honors them during estimation.
For example, suppose you are estimating a model with a mean
offset known to be 0.3. To indicate this, specify
the model you input to
NaN value as an equality constraint, and
does not estimate the mean offset.
honors all specified equality constraints during estimation of the
parameters without equality constraints.
estimate optionally returns the variance-covariance
matrix for estimated parameters. The parameters in the variance-covariance
matrix are ordered as follows:
Nonzero GARCH coefficients at positive lags
Nonzero ARCH coefficients at positive lags
Nonzero leverage coefficients at positive lags (EGARCH and GJR models only)
Degrees of freedom (t innovation distribution only)
Offset (models with nonzero offset only)
If any parameter known to the optimizer has an equality constraint, the corresponding row and column of the variance-covariance matrix has all zeros.
In addition to user-specified equality constraints, note that
any GARCH, ARCH, or leverage coefficient with an estimate less than
magnitude equal to zero.