For conditional variance model estimation, the required inputs for
estimate are a model and a vector of univariate time series data.
The model specifies the parametric form of the conditional variance model being
estimate returns fitted values for any parameters in the
input model with
NaN values. If you specify
NaN values for any parameters,
views 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
'Offset',0.3 in the model you input to
estimate views this
NaN value as an equality constraint, and does not estimate
the mean offset.
estimate also 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
estimate sets any GARCH, ARCH, or leverage coefficient with an
estimate less than
1e-12 in magnitude equal to zero.