Errors when estimating state space model

[NoraVelvet]

Hello,

I'm trying to model the effects of radio commercials, print advertising and the website activity (as well as their interactions) on a variable which consists of the residuals of a previous model.
I attached my workfile.

According to general theory, all c's in the state space model (so c(1) until c(14)) should be positive. As you can see, I enforced this on c(1), which is the carryover effect, and on c(2) until c(4), which represent the effectiveness of radio, print and website, and on c(8) until c(14), which are the variance terms. The procedure of estimating this model runs quite smooth: convergence after 19 iterations and "to be expected" likelihood and AIC values. However, the estimates for c(5) until c(7) are negative and insignificant. Like I said, this is not compatible with general theory. So I tried to enforce these coefficients to become positive as well by taking exp(c(5)), exp(c(6)) and exp(c(7)), but then the estimation output shows NA's for the standard errors and z-statistics. If I adapt my starting values for the coefficients, this problem disappears, but then the likelihood takes on extremely bad values. How do I get an outcome with positive estimates for all coefficients with a reasonable value for the likelihood?

P.S.1: in state equations 2 and 3 a certain value, respectively k1 and k2, needs to be multiplied with exp(c(1)). At this moment, grid search showed that k1 = 0.9 and k2 = 1 maximize the log likelihood. These values may, however, be changed to any value between 0 and 1.

P.S. 2: on this forum, people mainly advice to use OLS estimates for the starting values. However, I don't see how I can apply this in my setting.


Thank you in advance!

[NoraVelvet]

Is there someone who can help me with this problem?
I would very much appreciate it!

[trubador]

Either your model is ill-defined or the data does not agree with the model, since nothing seems wrong with the estimation other than the unpleasant results.