majority of the agents was following the fundamental forecasting rule and already had short positions before the turn in price direction, volume drops sharply after the change of direction in the price trend. As price returns to the fundamental value, agents following the fundamental belief are closing their short positions, while traders following the moving average belief are holding more and more short positions, causing volume to increase. After prices dropped back to the fundamental value, prices keep on declining due to the moving average traders, with negative but increasing returns, so that the price sequence is convex. Volume increases, because traders following the fundamental belief are now holding more and more long positions as price moves below the fundamental value. Then, if the short position held by the moving average traders is not profitable anymore, the fraction of fundamental traders increases sharply turning the downward trend in price to an upward trend in price. The moving average traders detect the change in trend and will change their short position to a long position in the risky asset, causing price to increase back to the fundamental value. Because a majority of the agents was following the fundamental forecasting rule and already had long positions, volume drops sharply after the change of direction in the price trend. The price cycle is thus characterized by a period of small price changes when moving average traders dominate the market and periods of rapid decrease or increase of prices when fundamental traders temporarily dominate the market. Furthermore, volume goes by the prevailing trend as can be seen in figure 6.6d. That is, if the primary trend is upwards, then volume increases. Volume drops during a change in directional trend. Then, if the primary trend is downwards, volume also increases. This is a very important concept in technical analysis and the relation has been shown in many price charts.
Adding dynamic noise to the deterministic skeleton leads to irregular price behavior as can be seen in figure 6.7a. Clearly periods with trending behavior can be identified. Figure 6.7c shows that the fraction of fundamental traders is switching irregular between its lower- and upperbound. Because little autocorrelation, volatility clustering and fat tails are important characteristics of real financial time series, we check our return series for these features. Figures 6.8b and 6.8c show the autocorrelation function plots of the returns and the squared returns up to order 36. Figure 6.8b shows that the return series does not exhibit any serial autocorrelation, which means that price changes are linearly independent. Further, according to figure 6.8c the squared return series does not exhibit any serial autocorrelation, which means that there is no volatility clustering present in the data. The return distribution does show excess kurtosis relatively to the normal distribution (see figure 6.8a). Thus our theoretical heterogeneous agents model only fails in mimicking the feature of volatility clustering.