Technical Discussion—509

•Make Gradient Group creates a group object with series containing the gradients of the log likelihood. These series are named “GRAD##” where ## is a unique number in the workfile.

•Make Kalman Filter creates a new state space object containing the current specification, but with all parameters replaced by their estimated values. In this way you can “freeze” the current state space for additional analysis. This procedure is similar to the Make Model procedure found in other estimation objects.

•Make Model creates a model object containing the state space equations.

•Update Coefs from Sspace will place the estimated parameters in the appropriate coefficient vectors.

Converting from Version 3 Sspace

Those of you who have worked with the EViews Version 3 sspace object will undoubtedly be struck by the large number of changes and additional features in Version 4 and later. In addition to new estimation options, views and procedures, we have changed the underlying specification syntax to provide you with considerable additional flexibility. A wide variety of specifications that were not supported in earlier versions may be estimated with the current sspace object.

The cost of these additional features and added flexibility is that Version 3 sspace objects are not fully compatible with those in the current version. This has two important practical effects:

•If you load in a workfile which contains a Version 3 sspace object, all previous estimation results will be cleared and the text of the specification will be translated to the current syntax. The original text will be retained as comments at the bottom of your sspace specification.

•If you take a workfile which contains a new sspace object created with EViews 4 or later and attempt to read it into an earlier version of EViews, the object will not be read, and EViews will warn you that a partial load of the workfile was performed. If you subsequently save the workfile, the original sspace object will not be saved with the workfile.

Technical Discussion

Initial Conditions

If there are no @MPRIOR or @VPRIOR statements in the specification, EViews will either:

(1) solve for the initial state mean and variance, or (2) initialize the states and variances using diffuse priors.

510—Chapter 33. State Space Models and the Kalman Filter

Solving for the initial conditions is only possible if the state transition matrices T , and variance matrices P and Q are non time-varying and satisfy certain stability conditions (see Harvey, 1989, p. 121). If possible, EViews will solve for the conditions P1 0 using the familiar relationship: (I – T ƒ T) ¥ vec(P) = vec(Q). If this is not possible, the states will be treated as diffuse unless otherwise specified.

When using diffuse priors, EViews follows the method adopted by Koopman, Shephard and Doornik (1999) in setting a1 0 = 0 , and P1 0 = kIM , where the k is an arbitrarily chosen large number. EViews uses the authors’ recommendation that one first set k = 106 and then adjust it for scale by multiplying by the largest diagonal element of the residual covariances.

References

Box, George E. P. and Gwilym M. Jenkins (1976). Time Series Analysis: Forecasting and Control, Revised Edition, Oakland, CA: Holden-Day.

Hamilton, James D. (1994a). Time Series Analysis, Princeton University Press.

Hamilton, James D. (1994b). “State Space Models,” Chapter 50 in Robert F. Engle and Daniel L. McFadden (eds.), Handbook of Econometrics, Volume 4, Amsterdam: Elsevier Science B.V.

Harvey, Andrew C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge: Cambridge University Press.

Koopman, Siem Jan, Neil Shephard, and Jurgen A. Doornik (1999). “Statistical Algorithms for Models in State Space using SsfPack 2.2,” Econometrics Journal, 2(1), 107-160.