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In this paper, we follow the methodology developed in Bathia et al. (2010) to model the dynamics of the probability density functions (pdf's) of IBOVESPA intraday returns over business days. As a byproduct, we obtain filtered estimates of these intraday return pdf's, in a sense that whatever noise that may occur in previously estimating non-parametrically the pdf's is removed. Furthermore, we find that the pdf's dynamic behavior reduces to a ${R}^{2}$-valued process, and that this process is well represented by a VAR(1) model. Its effect on the pdf's is shown to be a dispersion-symmetry deforming. Moreover, by taking into account the dynamics of the curve process, we generate one-step-ahead forecasts of upcoming pdf's.

Autocovariance. Dimension reduction. Functional time series. High frequency financial data. Karhunen-Loève expansion.