Related papers: Note on AR(1)-characterisation of stationary proce…
While considerable advances have been made in estimating high-dimensional structured models from independent data using Lasso-type models, limited progress has been made for settings when the samples are dependent. We consider estimating…
Heteroskedasticity is a common feature of financial time series and is commonly addressed in the model building process through the use of ARCH and GARCH processes. More recently multivariate variants of these processes have been in the…
Autoregressive (AR) modeling is invaluable in signal processing, in particular in speech and audio fields. Attempts in the literature can be found that regularize or constrain either the time-domain signal values or the AR coefficients,…
The approximation of a stationary time-series by finite order autoregressive (AR) and moving averages (MA) is a problem that occurs in many applications. In this paper we study asymptotic behavior of the spectral density of finite order…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares…
Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient…
New results on strong-consistency, in the Hilbert-Schmidt and trace operator norms, are obtained, in the parameter estimation of an autoregressive Hilbertian process of order one (ARH(1) process). In particular, a strongly-consistent…
We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
A new sufficient condition for the existence of a stationary causal solution of an ARCH($\infty$) equation is provided. This condition allows to consider polynomially decaying coefficients, so that it can be applied to the so-called FIGARCH…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
This paper presents new results on prediction of linear processes in function spaces. The autoregressive Hilbertian process framework of order one (ARH(1) process framework) is adopted. A componentwise estimator of the autocorrelation…
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…
In this paper we introduce a modified version of a gaussian standard first-order autoregressive process where we allow for a dependence structure between the state variable $Y_{t-1}$ and the next innovation $\xi_t$. We call this model…
We study a generalized ARCH model with liquidity given by a general stationary process. We provide minimal assumptions that ensure the existence and uniqueness of the stationary solution. In addition, we provide consistent estimators for…
Previous results pertaining to algebraic state and parameter estimation of linear systems based on a special construction of a forward-backward kernel representation of linear differential invariants are extended to handle large noise in…
This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised.…
In this note we review several situations in which stochastic PDEs exhibit ergodic properties. We begin with the basic dissipative conditions, as stated by Da Prato and Zabczyk in their classical monograph. Then we describe the singular…
In this paper, we present the asymptotic properties of the moment estimator for autoregressive (AR for short) models subject to Markovian changes in regime under the assumption that the errors are uncorrelated but not necessarily…