Sample autocorrelation learning in a capital market model

In this article we analytically derive a sufficient condition for convergence in a simple asset pricing model and check this result through simulations. The price sequence as well as the sequence of parameters, estimated by means of sample autocorrelation learning, converge if the initial value of the price sequence is sufficiently close to the steady-state equilibrium and a random variable derived from the dividend process is not too volatile to skip the price trajectory out of the attracting region. Therefore, the market price can even diverge, and the region of convergence could become very small depending on the underlying parameters.