In UCM regression coefficients are part of the state vector. They make up the section of the model state vector that has diffuse prior. Diffuse Kalman filter recursively computes one-step-ahead forecasts of the model state and response values. This recursive process also produces the one-step-ahead residuals. The one-step-ahead forecasts and residuals are set to missing until enough observations are processed so that all the diffuse state elements can be estimated. This scenario is similar to recursive estimation of regression vector in ordinary regression setting where the observation are processed one-at-a-time in a sequential fashion. In this setting one must first process sufficient number of observations so that the resulting design matrix is invertible before one can produce a valid estimate of the regression vector. When you specify an ntervention variable in such a setting, say the intervention is at 10th observation, i.e., the variable is zero for the first nine observations and is 1 thereafter, you must process at least 10 observations for the design matrix to become invertible. Because of this recursive nature of diffuse state estimation, the number of residuals available to compute residuals based fit statistics (such as RSuare) can become quite small when intervention variables are introduced as regressors in a UCM model. UCM one-step-ahead residuals are not the same as regression residuals (i.e. PROC REG residuals). For UCM models RSquare statistic need not increase because one adds a regressor in the model (in fact, in many time series model settings, including ARIMA and UCM, RSquare can even be negative).
Whether adding intervention improves the model can be determined based on a variety of other considerations: first, is the regression coefficient significant, have information criteria such as AIC, BIC improved, and so on.
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