As a useful tool in functional data analysis, the functional linear regression model has become increasingly common and been studied extensively in recent years. In this paper, we consider a sparse functional linear regression model which is generated by a finite number of basis functions in an...

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...

We consider large and moderate deviations for the empirical mean and covariance of hilbertian autoregressive processes. As an application we obtain moderate deviation principles for the eigenvalues and associated projectors of the empirical covariance sequence.