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Dynamics of financial returns densities: A functional approach applied to the Bovespa intraday index

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  • Horta, Eduardo
  • Ziegelmann, Flavio

Abstract

We model the stochastic evolution of the probability density functions (PDFs) of Ibovespa intraday returns over business days, in a functional time series framework. We find evidence that the dynamic structure of the PDFs reduces to a vector process lying in a two-dimensional space. Our main contributions are as follows. First, we provide further insights into the finite-dimensional decomposition of the curve process: it is shown that its evolution can be interpreted as a dynamic dispersion-symmetry shift. Second, we provide an application to realized volatility forecasting, with a forecasting ability that is comparable to those of HAR realized volatility models in the model confidence set framework.

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  • Horta, Eduardo & Ziegelmann, Flavio, 2018. "Dynamics of financial returns densities: A functional approach applied to the Bovespa intraday index," International Journal of Forecasting, Elsevier, vol. 34(1), pages 75-88.
    • Handle: RePEc:eee:intfor:v:34:y:2018:i:1:p:75-88
    DOI: 10.1016/j.ijforecast.2017.08.001
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    1. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2020. "Forecasting value at risk with intra-day return curves," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1023-1038.
    2. Rodney V. Fonseca & Aluísio Pinheiro, 2020. "Wavelet estimation of the dimensionality of curve time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1175-1204, October.
    3. Kokoszka, Piotr & Miao, Hong & Petersen, Alexander & Shang, Han Lin, 2019. "Forecasting of density functions with an application to cross-sectional and intraday returns," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1304-1317.
    4. Petersen, Alexander & Zhang, Chao & Kokoszka, Piotr, 2022. "Modeling Probability Density Functions as Data Objects," Econometrics and Statistics, Elsevier, vol. 21(C), pages 159-178.
    5. Chao Zhang & Piotr Kokoszka & Alexander Petersen, 2022. "Wasserstein autoregressive models for density time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 30-52, January.

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