Related papers: Functional Periodic ARMA Processes
Periodicity is a fundamental characteristic of time series data and has long played a central role in forecasting. Recent deep learning methods strengthen the exploitation of periodicity by treating patches as basic tokens, thereby…
In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;\alpha)$. We call it fractional Fourier series of the order $\alpha$. Extending the basis functions of the linear space…
In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to…
The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data…
We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely that the time series can be interpolated by a periodic…
This paper explores the identification and estimation of nonseparable panel data models. We show that the structural function is nonparametrically identified when it is strictly increasing in a scalar unobservable variable, the conditional…
We consider $\alpha$-mixing observations and deal with the estimation of the conditional mode of a scalar response variable $Y$ given a random variable $X$ taking values in a semi-metric space. We provide a convergence rate in $L^p$ norm of…
Functional principal component analysis (FPCA) has played an important role in the development of functional time series analysis. This note investigates how FPCA can be used to analyze cointegrated functional time series and proposes a…
We propose an extension of the zone-based algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than set-theoretic. We study duration probabilistic automata (DPA),…
In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
This paper is motivated by modeling the cycle-to-cycle variability associated with the resistive switching operation behind memristors. As the data are by nature curves, functional principal component analysis is a suitable candidate to…
In this paper, a new model-free anomaly detection framework is proposed for time-series induced by industrial dynamical systems.The framework lies in the category of conventional approaches which enable appealing features such as a learning…
In contrast to the fixed parameter analysis (FPA), in the variable parameter analysis (VPA) the value of the target problem parameter is not fixed, it rather depends on the structure of a given problem instance and tends to have a favorable…
We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial,…
In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…
This paper tackles one of the most fundamental goals in functional time series analysis which is to provide reliable predictions for future functions. Existing methods for predicting a complete future functional observation use only…
An approach is presented for making predictions about functional time series. The method is applied to data coming from periodically correlated processes and electricity demand, obtaining accurate point forecasts and narrow prediction bands…
Many biomedical studies have identified important imaging biomarkers that are associated with both repeated clinical measures and a survival outcome. The functional joint model (FJM) framework, proposed in Li and Luo (2017), investigates…
There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the…