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Sample autocorrelation learning in a capital market model

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Adaptive agent models are supposed to result in the same limit behavior as models with perfectly rational agents. In this article we show that this claim cannot by accepted in general, even in a simple capital market model, where the agents apply sample autocorrelation learning to perform their forecasts. By applying this learning algorithm, the agents use sample means, the sample autocorrelation coefficient, and the sample variances of prices to predict the future prices, and to determine the demand for the risky asset. Therefore, even if the agents are not perfectly rational, we require that the agents' forecasts are consistent with the underlying information. In this article a sufficient condition for convergence is derived analytically, and checked by means of 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. Thus, divergence of the price sequences is not a pathological example, since it possibly occurs over a wide range of parameters. Therefore, the often claimed coincidence of adaptive agents models and ration agent models cannot be observed even in a simple capital market model. (author's abstract) ; Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

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Klaus Pötzelberger, Leopold Sögner

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