Can the Lasota(1977)’s model compete with the Mackey-Glass(1977)’s model in nonlinear modelling of financial time series?

The existence of nonlinear structures in the mean equation leads some authors [43, 44] to model financial time series by a Mackey-Glass equation, which is a differential equation with delay. We propose, in this paper, to compare the contributions of the [52]’s equation in the modelling of nonlinear structures in the mean equation with that of [48], published the same year but which may lead to different results in finance. Theoretical results point out that these two equations can describe mean dynamics’ of financial time series. These dynamics reflect the interaction between two types of agents, fundamentalists and chartists, that creates chaotic structures. To verify this, we apply these two models to two Europeans stock markets indices [CAC 40 and DAX 30] on the period [2003-2011]. We show the adequacy of these models, associated with a GARCH specification, to financial time series, comparatively to the ARMA-GARCH model. Moreover, it seems that the [48]’s model is more suitable than the [52]’s model for strongly leptokurtic financial time series: these findings are based on the backtesting results’ conducted on VaR forecasts’.