Related papers: Functional Periodic ARMA Processes
We present a re-parameterization of vector autoregressive moving average (VARMA) models that allows estimation of parameters under the constraints of causality and invertibility. The parameter constraints associated with a causal invertible…
In this paper, we propose a novel variable selection approach in the framework of sparse high-dimensional GLARMA models. It consists in combining the estimation of the autoregressive moving average (ARMA) coefficients of these models with…
High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper focuses on high-dimensional time series and on the different regularized estimation procedures proposed for…
We introduce a new class of conditional autoregressive models for spatially dependent functional data, formulated through conditional means given neighboring functional observations and characterized by a covariance operator and a spatial…
Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods…
This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…
Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
This paper addresses the estimation of the second-order structure of a manifold cross-time random field (RF) displaying spatially varying Long Range Dependence (LRD), adopting the functional time series framework introduced in Ruiz-Medina…
We prove that a time series satisfying a (linear) multivariate autoregressive moving average (VARMA) model satisfies the same model assumption in the reversed time direction, too, if all innovations are normally distributed. This…
We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained result, we…
Multivariate time-series forecasting holds immense value across diverse applications, requiring methods to effectively capture complex temporal and inter-variable dynamics. A key challenge lies in uncovering the intrinsic patterns that…
In the past four decades, research on count time series has made significant progress, but research on $\mathbb{Z}$-valued time series is relatively rare. Existing $\mathbb{Z}$-valued models are mainly of autoregressive structure, where the…
In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval $(0,1)$. The proposed model accommodates a set of…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
Improvements in data acquisition and processing techniques have lead to an almost continuous flow of information for financial data. High resolution tick data are available and can be quite conveniently described by a continuous time…
Time series forecasting has attracted significant attention, leading to the de-velopment of a wide range of approaches, from traditional statistical meth-ods to advanced deep learning models. Among them, the Auto-Regressive Integrated…
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…
Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless,…
In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…