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I am trying to run a time-varying stock beta model.

I define a measurement equation without constant since I use returns over risk free rate both for the stock and the market index. my measurement equation is as follows:

rex_stock = beta*rex_market + error term

I define want to define state equation (beta) as a random walk, therefore I input rex_market in the "random walk coefficients box" in the second tab (stochastic regressors) of the auto-specification menu.

Therefore in the specification text I end up with:

@signal rex_stock = sv1*rex_market + [var = exp(c(1))]

@state sv1 = sv1(-1) + [var = exp(c(2))]

and when I estimate this I get a WARNING message saying "singular covariance - coefficients are not unique" BUT the final state value of the beta is pretty much OK.

when instead modify the state equation and get rid of the error term "[var = exp(c(2))]", and define state equation as @state sv1=sv1(-1) the error message disappears, but the thing is I want to define state equation as a random walk process.

What may be the problem?

The error message pretty much says it all. The moment matrix used to compute the covariance is singular at the coefficient estimates you have. As with multicollinearity in regression analysis, this could mean a number of things. Often in state space estimation it means that the model that you have provided simply isn't identified with the data at hand.

I would certainly first look at the coefficient and gradient values for my state space object. In particular, if the variance implied by your random walk coefficient is close to zero, it suggests that the coefficient simply may not be a random walk....