Publications by Shahin Tavakoli

Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics

Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of localizing any inferred differences ...

American Statistical Association2016

Fourier Analysis of Functional Time Series, with Applications to DNA Dynamics

Shahin Tavakoli

This work is about time series of functional data (functional time series), and consists of three main parts. In the first part (Chapter 2), we develop a doubly spectral decomposition for functional time series that generalizes the Karhunen–Loève expansion ...

EPFL2014

Cramer-Karhunen-Loeve representation and harmonic principal component analysis of functional time series

Victor Panaretos, Shahin Tavakoli

We develop a doubly spectral representation of a stationary functional time series, and study the properties of its empirical version. The representation decomposes the time series into an integral of uncorrelated frequency components (Cramer representatio ...

Elsevier2013

Fourier Analysis Of Stationary Time Series In Function Space

Victor Panaretos, Shahin Tavakoli

We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which gen ...

Institute of Mathematical Statistics2013