相关论文: Multivariate stochastic delay differential equatio…
In this paper we study solutions to multivariate stochastic delay differential equations (MSDDEs) which have stationary increments, and we show that this modeling framework is in many ways similar to the discrete-time cointegrated VAR…
In this paper, we examine continuous-time autoregressive moving-average (CARMA) processes on Banach spaces driven by L\'evy subordinators. We show their existence and cone-invariance, investigate their first and second order moment…
High-frequency sampled multivariate continuous time autoregressive moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process $(Y_{n\Delta})_{n \in \mathbb{Z}}$ as…
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…
A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed…
The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with 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.…
One of the important and widely used classes of models for non-Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time…
In this paper we introduce a model, the stochastic fractional delay differential equation (SFDDE), which is based on the linear stochastic delay differential equation and produces stationary processes with hyperbolically decaying…
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…
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…
Multivariate dynamic time series models are widely encountered in practical studies, e.g., modelling policy transmission mechanism and measuring connectedness between economic agents. To better capture the dynamics, this paper proposes a…
In this paper we introduce the class of beta seasonal autoregressive moving average ($\beta$SARMA) models for modeling and forecasting time series data that assume values in the standard unit interval. It generalizes the class of beta…
The autoregressive moving average (ARMA) model takes the significant position in time series analysis for a wide-sense stationary time series. The difference operator and seasonal difference operator, which are bases of ARIMA and SARIMA…
Existing models for high-dimensional time series are overwhelmingly developed within the finite-order vector autoregressive (VAR) framework. However, the more flexible vector autoregressive moving averages (VARMA) have been much less…
We clarify relationships between conditional (CAR) and simultaneous (SAR) autoregressive models. We review the literature on this topic and find that it is mostly incomplete. Our main result is that a SAR model can be written as a unique…
Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are…
Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…
For the large family of ARMA models with variable coefficients (TV-ARMA), either deterministic or stochastic, we provide an explicit and computationally tractable representation based on the general solution of the associated linear…