Working with the State Space

770—Chapter 25. State Space Models and the Kalman Filter

mary and visual information about the gradients of the log likelihood at estimated parameters (if the sspace is estimated) or at current parameter values.

•Actual, Predicted, Residual Graph displays, in graphical form, the actual and onestep ahead fitted values of the signal dependent variable(s), yt t − 1 , and the one-

step ahead standardized residuals, et t − 1 .

•Select Coefficient Covariance Matrix to view the estimated coefficient covariance.

•Wald Coefficient Tests… allows you to perform hypothesis tests on the estimated coefficients. For details, see “Wald Test (Coefficient Restrictions)” on page 572.

•Label allows you to annotate your object. See “Labeling Objects” on page 82.

Note that with the exception of the Label and Specification... views, these views are available only following successful estimation of your state space model.

Signal Views

When you click on View/Signal Views, EViews displays a submenu containing additional view selections. Two of these selections are always available, even if the state space model has not yet been estimated:

•Actual Signal Table and Actual Signal Graph display the dependent signal variables in spreadsheet and graphical forms, respectively. If there are multiple signal equations, EViews will display a each series with its own axes.

The remaining views are only available following estimation.

•Graph Signal Series... opens a dialog with choices for the results to be displayed. The dialog allows you to choose between the onestep ahead predicted signals, yt t − 1 , the cor-

responding one-step residuals, t t − 1 , or standardized one-step residuals, et t − 1 , the

smoothed signals, ˆ t , smoothed signal distur- y

bances, ˆt , or the standardized smoothed sig-

nal disturbances, ˆ t . ± (root mean square) e 2

standard error bands are plotted where appropriate.

•Std. Residual Correlation Matrix and Std. Residual Covariance Matrix display the correlation and covariance matrix of the standardized one-step ahead signal residual, et t − 1 .

Working with the State Space—771

State Views

To examine the unobserved state components, click on View/ State Views to display the state submenu. EViews allows you to examine the initial or final values of the state components, or to graph the full time-path of various filtered or smoothed state data.

Two of the views are available either before or after estimation:

•Initial State Vector and Initial State Covariance Matrix display the values of the

initial state vector, α0 , and covariance matrix, P0 . If the unknown parameters have previously been estimated, EViews will evaluate the initial conditions using the esti-

mated values. If the sspace has not been estimated, the current coefficient values will be used in evaluating the initial conditions.

This information is especially relevant in models where EViews is using the current values of the system matrices to solve for the initial conditions. In cases where you are having difficulty starting your estimation, you may wish to examine the values of the initial conditions at the starting parameter values for any sign of problems.

The remainder of the views are only available following successful estimation:

•Final State Vector and Final State Covariance Matrix display the values of the final state vector, αT , and covariance matrix, PT , evaluated at the estimated parameters.

•Select Graph State Series... to display a dialog containing several choices for the state information. You can graph the one-step ahead predicted states, at t − 1 , the filtered

(contemporaneous) states, at , the smoothed

state estimates, ˆ t , smoothed state distur-

α

bance estimates, ˆ t , or the standardized v

smoothed state disturbances, ˆ t . In each

η

case, the data are displayed along with corresponding ±2 standard error bands.

State Space Procedures

You can use the EViews procedures to create, estimate, forecast, and generate data from your state space specification. Select Proc in the sspace toolbar to display the available procedures:

772—Chapter 25. State Space Models and the Kalman Filter

•Define State Space... calls up the Auto-Specification dialog (see “Auto-Specification” on page 766). This feature provides a method of specifying a variety of common state space specifications using interactive menus.

•Select Estimate... to estimate the parameters of the specification (see “Estimating a State Space Model” on page 767).

These above items are available both before and after estimation. The automatic specification tool will replace the existing state space specification and will clear any results.

Once you have estimated your sspace, EViews provides additional tools for generating data:

•The Forecast... dialog allows you to generate forecasts of the states, signals, and the associated standard errors using alternative methods and initialization approaches.

First, select the forecast method. You can select between dynamic, smoothed, and n-period ahead forecasting, as described in “Forecasting” on page 756. Note that any lagged endogenous variables on the right-hand side of your signal equations will be treated as predetermined for purposes of forecasting.

EViews allows you to save various types of forecast output in series in your workfile. Simply check any of the output boxes, and specify the names for the series in the corresponding edit field.

You may specify the names either as a list or using a wildcard expression. If you choose to list the names, the number of identifiers must match the

number of signals in your specification. You should be aware that if an output series with a specified name already exists in the workfile, EViews will overwrite the entire contents of the series.

If you use a wildcard expression, EViews will substitute the name of each signal in the appropriate position in the wildcard expression. For example, if you have a model with signals Y1 and Y2, and elect to save the one-step predictions in “PRED*”, EViews will use the series PREDY1 and PREDY2 for output. There are two limitations to this feature: (1) you may not use the wildcard expression “*” to save

774—Chapter 25. State Space Models and the Kalman Filter

You may select the one-step ahead

predicted signals, ˜ t t − 1 , one- yy

step prediction residuals, t t − 1 ,

smoothed signal, ˆ t , or signal dis- y

turbance estimates, ˆt . EViews

also allows you to save the corresponding standard errors for each of these components (square roots of the diagonal elements of

ˆ

Ft t − 1 , St , and Ωt ), or the standardized values of the one-step residuals and smoothed disturbances, et t − 1

Next, specify the names of your series in the edit field using a list or wildcards as described above. Click OK to generate a group containing the desired signal series.

As above, if your signal dependent variable is an expression, EViews will only export results based upon the entire expression.

•Make State Series... opens a dialog allowing you to create series containing results for the state variables computed over the estimation sample. You can choose to save

the corresponding standard error series (square roots of the diagonal elements of

ˆ

Pt t − 1 , Pt , Vt and Ωt ).

Simply select one of the output types, and enter the names of the output series in the edit field. The rules for specifying the output names are the same as for the Forecast...

procedure described above. Note that the wildcard expression “*” is permitted when saving state results. EViews will simply use the state names defined in your specification.

We again caution you that if an out-

put series exists in the workfile, EViews will overwrite the entire contents of the series.

•Click on Make Endogenous Group to create a group object containing the signal dependent variable series.