Related papers: High-frequency sampling of multivariate CARMA proc…
Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modeling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form $Y_{n\Delta}, n=0,1,2,...$, where…
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…
We consider the parametric estimation of the driving L\'evy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid $(0,h,2h,...)$. Beginning with a new state…
Interest in continuous-time processes has increased rapidly in recent years, largely because of high-frequency data available in many applications. We develop a method for estimating the kernel function $g$ of a second-order stationary…
We consider high-frequency sampled continuous-time autoregressive moving average (CARMA) models driven by finite-variance zero-mean L\'evy processes. An L^2-consistent estimator for the increments of the driving L\'evy process without order…
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.…
A spectral representation for regularly varying L\'evy processes with index between one and two is established and the properties of the resulting random noise are discussed in detail giving also new insight in the $L^2$-case where the…
In this article we study multivariate continuous-time autoregressive moving-average (MCARMA) processes with values in convex cones. More specifically, we introduce matrix-valued MCARMA processes with L\'evy noise and present necessary and…
In this paper we show that stationary and non-stationary multivariate continuous-time ARMA (MCARMA) processes have the representation as a sum of multivariate complex-valued Ornstein-Uhlenbeck processes under some mild assumptions. The…
Continuous-time autoregressive and moving average (CARMA) models are extensively used to model high-frequency and irregularly sampled data. We study Whittle estimation for the model parameters when the process is observed at renewal times.…
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) either over time or…
We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-ime linear state space models and equidistantly observed multivariate L\'evy-driven continuoustime autoregressive moving average (MCARMA) processes. In…
Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…
This paper considers a continuous time analogue of the classical autoregressive moving average processes, L\'evy-driven CARMA processes. First we describe limiting properties of the periodogram by means of the so-called truncated Fourier…
We discuss simulation schemes for continuous-time autoregressive moving average (CARMA) processes driven by tempered stable L\'evy noises. CARMA processes are the continuous-time analogue of ARMA processes as well as a generalization of…
This paper is about vector autoregressive-moving average (VARMA) models with time-dependent coefficients to represent non-stationary time series. Contrarily to other papers in the univariate case, the coefficients depend on time but not on…
The paper considers an extension of factor analysis to moving average processes. The problem is formulated as a rank minimization of a suitable spectral density. It is shown that it can be adequately approximated via a trace norm convex…
We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of…
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…
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…