Multiscale Representation of Agents Heterogeneous Beliefs in Analysis of CAC40 Prices with Frequency Decomposition

This paper focuses on the time series’ decomposition and economic representation of its constituent parts. Wavelet transforms are used for adaptive analysis of local behaviour of heterogeneous agents. Unlike fully revealing equilibrium of homogeneous beliefs, in the environment with heterogeneous beliefs prices are driven by prevailing expectations of market participants. Thus, forecasting future prices, one must form expectations of others forecasts. Evolution of agents' expectations largely governs the adaptive nature of market prices. Overlapping beliefs of heterogeneous agents prevent the effective examination of expectation formation and price forecasting by traditional methods. In the approach proposed in this paper, a time series is decomposed into a combination of underlying series, representing beliefs of major clusters of agents. The analysis of individual parts improves statistical inference, isolating effectively nonstationary and nonlinearly features. Emergent local behaviour is also more receptive to prediction. The overall forecast (weighted combination of individual forecasts) is found to be determined and evolved depending on specific market conditions. On the statistical level, the data generating mechanism is considered as complex multi-structured system, with individual layers corresponding to particular frequencies. Reflecting the time preferences of agents, trading strategies being homogeneous intra-type are heterogeneous inter-type for agents with distinct time preferences. Overall market activity at each moment, providing the dynamic feedback across agents' types, generates market prices. The frequency decomposition of a time series identifies the local and global structures and separates short and long time dynamics. The Genetic Algorithm is applied to determine the optimal decomposition of the signal and representation of heterogeneous traders. The Artificial Neural Network is trained to learn information at the scale level that is hidden in the aggregate. The resulting models seek to enhance the understanding of the underlying data generating mechanisms of financial time series and to develop new approaches for financial forecasting.