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Fractionally integrated autoregressive moving average (FIARMA) processes have been widely and successfully used to model and predict univariate time series exhibiting long range dependence. Vector and functional extensions of these…

Functional Analysis · Mathematics 2022-10-07 Amaury Durand , François Roueff

In this paper we suggest two continuous-time models which exhibit an autoregressive structure. We obtain existence and uniqueness results and study the structure of the solution processes. One of the models, which corresponds to general…

Probability · Mathematics 2018-11-13 Andreas Basse-O'Connor , Mikkel Slot Nielsen , Jan Pedersen , Victor Rohde

We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses…

Statistics Theory · Mathematics 2007-06-13 James L. Cantor , David F. Findley

Producing probabilistic guarantee for several steps of a predicted signal follow a temporal logic defined behavior has its rising importance in monitoring. In this paper, we derive a method to compute the joint probability distribution of…

Systems and Control · Computer Science 2019-01-15 Xin Qin , Jyotirmoy V. Deshmukh

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…

Methodology · Statistics 2025-12-18 Sebastian Kühnert , Juhyun Park

A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Bernhard Kaufmann

This paper presents new variants of the averaged alternating modified reflections (AAMR) method for the best approximation problem. Under a mild constraint qualification, we first show its weak convergence and then establish a convergence…

Optimization and Control · Mathematics 2016-09-06 Shin-ya Matsushita

In this paper we define and characterize cointegrated continuous-time linear state-space models. A main result is that a cointegrated continuous-time linear state-space model can be represented as a sum of a L\'evy process and a stationary…

Probability · Mathematics 2018-01-03 Vicky Fasen-Hartmann , Markus Scholz

We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems…

Systems and Control · Electrical Eng. & Systems 2019-08-15 Romeo Ortega , Stanislav Aranovskiy , Anton A. Pyrkin , Alessandro Astolfi , Alexey A. Bobtsov

The paper considers high frequency sampled multivariate continuous-time ARMA (MCARMA) models, and derives the asymptotic behavior of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behavior…

Statistics Theory · Mathematics 2015-08-10 Vicky Fasen

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…

Symbolic Computation · Computer Science 2015-07-16 Sébastien Maulat , Bruno Salvy

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

Statistics Theory · Mathematics 2007-05-23 Teo Sharia

In this paper we derive the asymptotic properties of the least squares estimator (LSE) of autoregressive moving-average (ARMA) models with regime changes under the assumption that the errors are uncorrelated but not necessarily independent.…

Statistics Theory · Mathematics 2019-07-11 Yacouba Boubacar Maïnassara , Landy Rabehasaina

The autoregressive moving average (ARMA) model is one of the most important models in time series analysis.We consider the Bayesian estimation of an unknown spectral density in the ARMA model.In the i.i.d. cases, Komaki showed that Bayesian…

Statistics Theory · Mathematics 2021-05-27 Fuyuhiko Tanaka , Fumiyasu Komaki

Functional variables are often used as predictors in regression problems. A commonly-used parametric approach, called {\it scalar-on-function regression}, uses the $\ltwo$ inner product to map functional predictors into scalar responses.…

Methodology · Statistics 2020-06-02 Kyungmin Ahn , J. Derek Tucker , Wei Wu , Anuj Srivastava

This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the…

Methodology · Statistics 2023-12-12 J. Klepsch , C. Klüppelberg , T. Wei

In this study we show how to represent a continuous time autoregressive moving average (CARMA) as a higher order stochastic delay differential equation, which may be thought of as a continuous-time equivalent of the AR($\infty$)…

Probability · Mathematics 2018-03-12 Andreas Basse-O'Connor , Mikkel Slot Nielsen , Jan Pedersen , Victor Rohde

We provide a closed-form estimator based on the VARMA representation for the unrestricted multivariate GARCH(1,1). We show that all parameters can be derived using basic linear algebra tools. We show that the estimator is consistent and…

Statistics Theory · Mathematics 2014-08-26 Giacomo Sbrana , Federico Poloni

The class of multivariate L\'{e}vy-driven autoregressive moving average (MCARMA) processes, the continuous-time analogs of the classical vector ARMA processes, is shown to be equivalent to the class of continuous-time state space models.…

Statistics Theory · Mathematics 2012-03-02 Eckhard Schlemm , Robert Stelzer

This paper proposes the quantile unit-log-symmetric autoregressive moving average (QULS--ARMA) model for bounded time series on the open unit interval $(0,1)$. The model extends the unit-log-symmetric family by introducing a quantile-based…

Computation · Statistics 2026-05-26 Helton Saulo , Roberto Vila , Filidor Vilca