Related papers: A review and comparative study on functional time …
Periodicity is a common feature of time series. For finite-dimensional data, periodic autoregressive moving average (ARMA) models have been extensively studied. In functional time series analysis, AR models have been extended to incorporate…
We extend the notion of cointegration for time series taking values in a potentially infinite dimensional Banach space. Examples of such time series include stochastic processes in C[0,1] equipped with the supremum distance and those in a…
In data rich environments we may sometimes deal with time series that are probability density-function valued, such as observations of cross-sectional income distributions over time. To apply the methods of functional time series analysis…
High-frequency financial data can be collected as a sequence of curves over time; for example, as intra-day price, currently one of the topics of greatest interest in finance. The Functional Data Analysis framework provides a suitable tool…
We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the…
We introduce and study a new model for functional data. The ARHD is an autoregressive model in which the first order derivative of the random curves appears explicitely. Convergent estimates are obtained through a double penalization…
The autoregressive Hilbertian model (ARH) was introduced in the early 90's by Denis Bosq. It was the subject of a vast literature and gave birth to numerous extensions. The model generalizes the classical multidimensional autoregressive…
In this article, a new nonparametric and robust method of forecasting hierarchical functional time series is presented. The method is compared with Hyndman and Shang's method with respect to their unbiasedness, effectiveness, robustness,…
This is an expository paper on approximating functions from general Hilbert or Banach spaces in the worst case, average case and randomized settings with error measured in the $L_p$ sense. We define the power function as the ratio between…
As objects of study in functional analysis, Hilbert spaces stand out as special objects of study as do nuclear spaces in view of a rich geometrical structure they possess as Banach and Frechet spaces, respectively. On the other hand, there…
This work derives new results on strong consistent estimation and prediction for autoregressive processes of order 1 in a separable Banach space B. The consistency results are obtained for the component-wise estimator of the autocorrelation…
The paper deals with variational approaches to the segmentation of time series into smooth pieces, but allowing for sharp breaks. In discrete time, the corresponding functionals are of Blake-Zisserman type. Their natural counterpart in…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
In this paper we develop statistical inference tools for high dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis…
This work derives new results on strong consistent estimation and prediction for autoregressive processes of order 1 in a separable Banach space B. The consistency results are obtained for the componentwise estimator of the autocorrelation…
Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…
The first-order autoregressive process, AR (1), has been widely used and implemented in time series analysis. Different estimation methods have been employed in order to estimate the autoregressive parameter. This article focuses on…
Functional times series have become an integral part of both functional data and time series analysis. This paper deals with the functional autoregressive model of order 1 and the autoregression bootstrap for smooth functions. The…
In this article, we prove Herglotz's theorem for Hilbert-valued time series. This requires the notion of an operator-valued measure, which we shall make precise for our setting. Herglotz's theorem for functional time series allows to…
The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential…