`refine(`

finds
a set of initial parameter values to use when fitting the state-space
model `Mdl`

,`Y`

,`params0`

)`Mdl`

to the response data `Y`

,
using the crude set of initial parameter values `params0`

.
The software uses several routines, and displays the resulting loglikelihood
and initial parameter values for each routine.

`refine(`

displays
results of the routines with additional options specified by one or
more `Mdl`

,`Y`

,`params0`

,`Name,Value`

)`Name,Value`

pair arguments. For example,
you can include a linear regression component composed of predictors
and an initial value for the coefficients.

returns
a structure array (`Output`

= refine(___)`Output`

) containing a vector
of refined, initial parameter values, the loglikelihood corresponding
the initial parameter values, and the method the software used to
obtain the values. You can use any of the input arguments in the previous
syntaxes.

Likelihood surfaces of state-space models can be complicated, for example, they might contain multiple local maxima. If

`estimate`

fails to converge, or converges to an unsatisfactory solution, then`refine`

might find a better set of initial parameter values to pass to`estimate`

.The refined initial parameter values returned by

`refine`

might appear similar to each other and to`params0`

. Choose a set yielding estimates that make economic sense and correspond to relatively large loglikelihood values.If a refinement attempt fails, then the software displays errors and sets the corresponding loglikelihood to

`-Inf`

. It also sets its initial parameter values to`[]`

.

The Kalman filter accommodates missing data by not updating
filtered state estimates corresponding to missing observations. In
other words, suppose that your data has a missing observation at period *t*.
Then, the state forecast for period *t*, based on
the previous *t* – 1 observations, is equivalent
to the filtered state for period *t*.

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