Related papers: Modeling and estimation of multivariate discrete a…

We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…

In this article, we introduce and study a one sided tempered stable first order autoregressive model called TAR(1). Under the assumption of stationarity of the model, the marginal probability density function of the error term is found. It…

In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point $t-1$ with observations about the time point $t$ to yield an…

In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under mild and reasonable assumptions, the existence of…

Cross-sectional observations from a dynamical system can be modeled via steady-state distributions of Markov processes. The major challenge is then to determine whether the process parameters can be identified and estimated from the…

This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

This study aims to develop the limit theorems on the sample autocovariances and sample autocorrelations for certain stationary infinitely divisible processes. We consider the case where the infinitely divisible process has heavy tail…

Here we develop a first order autoregressive model {Xn} that is marginally stationary where Xn is the sum/ extreme of k i.i.d observations. We prove that stationary solutions to these models are either semi-selfdecomposable/…

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence $(c_0,c_1,\dots,c_n)$ of covariance lags $c_k=\mathbb{E}\{y(t+k)\overline{y(t)}\}$ emanating from a stationary periodic…

A stochastic model, the product of a circulant matrix and a random normal vector, is shown to produce an evolutive long memory time series with a power law spectral density. The distribution of the time series, a beta location scale family…

In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal…

This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials and driven by L\'evy noise. For such systems, the time evolution of the characteristic function is…

Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…

We present a bivariate vector valued discrete autoregressive model of order $1$ (BDAR($1$)) for discrete time series. The BDAR($1$) model assumes that each time series follows its own univariate DAR($1$) model with dependent random…

Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algebraic Riccati equations is included. The approach is…

In this paper we consider multivariate time series obtained as solution to multidimensional nonlinear stochastic difference equations whose coefficients are allowed to be locally degenerate and to present discontinuities. We provide simple…

We use characteristic functions to construct alpha(x)-multistable measures and integrals, where the measures behave locally like alpha-stable measures, but with the stability index alpha(x) varying with time x. This enables us to construct…

For a multivariate stationary process, we develop explicit representations for the finite predictor coefficient matrices, the finite prediction error covariance matrices and the partial autocorrelation function (PACF) in terms of the…