Stable Noisy K-State Markov Sunspots

We consider a linear stochastic univariate rational expectations model, with a predetermined variable, and consider solutions driven by an extraneous finite state Markov process as well as by the fundamental noise. We obtain conditions for existence of noisy k-state sunspot equilibria (noisy k-SSEs) and, for the case k=2, of noisy k-state dependent sunspot equilibria (noisy k-*SDSs). k-*SDSs are driven by a finite state sunspot but have an infinite range of values even in the nonstochastic model. Stability under econometric learning is analyzed using representations that nest both types of solution. For the case k=2, we find that noisy 2-SSEs and noisy 2-*SDSs are learnable for parameters in proper subsets of the regions of their existence