Functional data analysis for volatility. (English) Zbl 1441.62817

Summary: We introduce a functional volatility process for modeling volatility trajectories for high frequency observations in financial markets and describe functional representations and data-based recovery of the process from repeated observations. A study of its asymptotic properties, as the frequency of observed trades increases, is complemented by simulations and an application to the analysis of intra-day volatility patterns of the S&P 500 index. The proposed volatility model is found to be useful to identify recurring patterns of volatility and for successful prediction of future volatility, through the application of functional regression and prediction techniques.


62P20 Applications of statistics to economics
62G07 Density estimation
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M05 Markov processes: estimation; hidden Markov models
62H25 Factor analysis and principal components; correspondence analysis
62R10 Functional data analysis


fda (R)
Full Text: DOI


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