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 i...

Mid-level processes on images often return outputs in functional form. In this context the use of functional data analysis (FDA) in image analysis is considered. In particular, attention is focussed on shape analysis, where the use of FDA in the functional approach (contour functions) shows its superiority over other approaches, such as the landmark based approach or the set theory approach, on...

Certain functions of the covariance operator such as the square root of a regularized inverse are important components of many statistics employed for functional data analysis. If Σ is a covariances operator on a Hilbert space, ̂ Σ a sample analogue of this operator, and φ a function on the complex plane, which is analytic on a domain containing a contour around the spectrum of Σ, a tool of gene...

The Bass model has been the standard for predicting the market penetration of new products. Recently a new class of non-parametric techniques, Functional Data Analysis (FDA), has shown impressive results within the statistics community. The authors test the predictive performance of FDA versus variations of the Bass model on 760 new categories across numerous products and countries. Ten fold cr...

We show how the Model-Free Prediction Principle of Politis (2013) can be applied to nonparametric regression with a univariate response and regressors that are high-dimensional or even infinite-dimensional, i.e., functional. Without assuming an additive model with i.i.d. errors, the Model-Free Principle is capable of yielding both consistent predictors as well as prediction intervals. 39.

In this paper, we measure productivity growth of the information technology (IT) industries in fourteen OECD countries over the thirteen-year period of 1978 through 1990. The IT industries are the providers of IT capital goods, and this macro-level analysis seeks to find out how efficiently IT capital goods are produced. The basic unit of analysis employed is the Malmquist Total Factor Producti...

A wavelet-based method is proposed to obtain accurate estimates of curves in more than one dimension and of their derivatives. By means of simulation studies, this novel method is compared to another locally-adaptive estimation technique for multidimensional functional data, based on free-knot regression splines. This comparison shows that the proposed method is particularly attractive when the...

In this paper, we use functional data analysis to model a time varying unconditional distribution of financial intraday returns. This is in the spirit of the recent development of realized volatility modeling (e.g. Andersen et al, 2001), where one of the moments of this uncondional distribution, the realized volatility, is assumed to change smoothly over time. In the approach used in this paper...