We study the impact of autoregressive forecasting rules in the CAPM with heterogeneous investors with CARA utilities which are characterized as so called fundamentalists or chartist. Forecasts by chartists are made according to an adaptive mean reverting principle for the first two conditional moments of the asset price process. Fundamentalists’ forecasts also use a mean reverting process, however, relative to a perceived so called fund amental value of asset price assumed to follow a stationary random walk.
We investigate the role of mean reversion on asset prices and returns showing the occurrence of a Neimark-Sacker bifurcation after a period doubling. For a large range of parameters these induce significant autocorrelations for long lags. These results provide evidence that adaptive expectations in many cases do not have a stabilizing influence on the asset price process.
We extends the analysis to study the impact of different random influences on aggregate asset supply, asset dividends, and on the fundamental asset price using numerical methods. For small enough noise, the period doubling and the Neimark-Sacker bifurcations are preserved inducing similar persistent autocorrelations. However, with larger perturbations and/or group switching, the bifurcations and autocorrelations disappear showing conver gence to stationary solutions (random fixed points) without significant autocorrelations.