Unobserved Components Models and Trend Term

[jaweriahh]

I have a very simply question about Unobserved Components Model.

I have a data set of 63 years. The data is declining for the entire time period but the slope is stochastic. The parameter of my slope term is negative but the level is positive [in the Trend Information  (Based on the Final State) table]. I can interpret the slope but should the level not be negative if the data is decreasing?

I use the command 

      proc ucm data = lan;
      id year interval = year;
      model Eco ;
      irregular ;
      level  variance=0 noest;
      slope ;
      run ;

[rselukar · Accepted solution]

Slope is the rate of change of the level component.  The level component tracks the series pattern.  You say the series is decreasing so the level component will be decreasing and since it is decreasing the slope will be negative.  Series can be decreasing without being negative so the level need not be negative.