Related papers: On Locally Dyadic Stationary Processes
We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…
The local regularity of functional time series is studied under $L^p-m-$appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity…
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
We propose the use of indirect inference estimation to conduct inference in complex locally stationary models. We develop a local indirect inference algorithm and establish the asymptotic properties of the proposed estimator. Due to the…
Irregular multivariate time series data is characterized by varying time intervals between consecutive observations of measured variables/signals (i.e., features) and varying sampling rates (i.e., recordings/measurement) across these…
In order to capture the dependence in the upper tail of a time series, we develop non-negative regularly-varying time series models that are constructed similarly to classical non-extreme ARMA models. Rather than fully characterizing tail…
With regard to a three-step estimation procedure, proposed without theoretical discussion by Li and You in Journal of Applied Statistics and Management, for a nonparametric regression model with time-varying regression function, local…
We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic relationships in the model make it effectively impossible to use the EM algorithm for learning model parameters. To…
We propose an $L^2$ norm for stationary Autoregressive Moving Average (ARMA) models. We look at ARMA models within the Hilbert space of the past with present of a true purely linearly non-deterministic stationary process $X_t$, and compute…
This paper challenges the dominance of stochastic trend models by introducing the Seasonal-Trend-Stationary ARMA (STSA) framework, which represents univariate nonstationary time series as stationary fluctuations around deterministic trend…
In this paper we propose a nonparametric procedure for validating the assumption of stationarity in multivariate locally stationary time series models. We develop a bootstrap assisted test based on a Kolmogorov-Smirnov type statistic, which…
We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of…
The Mat\'ern covariance model is ubiquitous in spatial modelling, but there is no default choice for spatio-temporal modelling. In this paper, we consider the recently proposed ``diffusion-based'' extension of the spatial Mat\'ern…
We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…
This paper investigates locally linear regression for locally stationary time series and develops theoretical results for locally linear smoothing and transfer learning. Existing analyses have focused on local constant estimators and given…
Linear processes on functional spaces were born about fifteen years ago. And this original topic went through the same fast development as the other areas of functional data modeling such as PCA or regression. They aim at generalizing to…
In this study, we develop an asymptotic theory of nonparametric regression for a locally stationary functional time series. First, we introduce the notion of a locally stationary functional time series (LSFTS) that takes values in a…
In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform…
The standard approach for studying the periodic ARMA model with coefficients that vary over the seasons is to express it in a vector form. In this paper we introduce an alternative method which views the periodic formulation as a time…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…