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We propose an empirical test to depict possible endogenous cycles within Heterogeneous Agent
Models (HAMs). We consider a 2-type HAM into a standard small-scale dynamic asset pricing framework.
On the one hand, fundamentalists base their expectations on the deviation of fundamental value
from market price expecting a convergence between them. On the other hand, chartists, subject to
self-fulling moods, consider the level of past prices and relate it to the fundamental value acting as contrarians.
These pricing strategies, by their nature, cannot be directly observed but can cause the response
of the observed data. For this reason, we consider the agents' beliefs as unobserved state components
from which, through a state space model formulation, the heterogeneity of fundamentalist-chartist trader
cycles can be mathematically derived and empirically tested. The model is estimated using the S&P500
index, for the period 1990-2020 at different time scales, specifically, daily, monthly, and quarterly.
