The use of various moving average rules remains popular with financial market practitioners. These rules have recently become the focus of empirical studies. However there have been very few studies on the analysis of financial market dynamics resulting from the fact that some agents engage in such strategies. In this paper we seek to fill this gap in the literature by proposing a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between a long run and a short run moving average. Both types of traders are boundedly rational in the sense that, based on a certain fitness measure, traders switch from a strategy with low fitness to the one with high fitness. We characterise first the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag lengths used for moving averages. By increasing the switching intensity, we then examine various rational routes to randomness for different, but fixed, long run moving averages. The price dynamics of the moving average rule is also examined and it is found that an increase of the window length of the long moving average can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including market crashes, price switching between different levels and price resistance.
