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We propose a new, computationally efficient, sparsity adaptive changepoint estimator for detecting changes in unknown subsets of a high-dimensional data sequence. Assuming the data sequence is Gaussian, we prove that the new method…
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…
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…
Many real-life dynamical systems change abruptly followed by almost stationary periods. In this paper, we consider streams of data with such abrupt behavior and investigate the problem of tracking their statistical properties in an online…
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…
In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…
High-dimensional time series are characterized by a large number of measurements and complex dependence, and often involve abrupt change points. We propose a new procedure to detect change points in the mean of high-dimensional time series…
In a variety of different settings cumulative sum (CUSUM) procedures have been applied for the sequential detection of structural breaks in the parameters of stochastic models. Yet their performance depends strongly on the time of change…
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…
Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires…
We study the problem of detecting a common change point in large panel data based on a mean shift model, wherein the errors exhibit both temporal and cross-sectional dependence. A least squares based procedure is used to estimate the…
Detecting changes in high-dimensional time series is difficult because it involves the comparison of probability densities that need to be estimated from finite samples. In this paper, we present the first feature extraction method tailored…
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…
We consider the problem of estimating the location of a single change point in a dynamic stochastic block model. We propose two methods of estimating the change point, together with the model parameters. The first employs a least squares…
This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of…
We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…
Change-point detection and estimation procedures have been widely developed in the literature. However, commonly used approaches in change-point analysis have mainly been focusing on detecting change-points within an entire time series…
This paper is a survey of methods for solving smooth (strongly) monotone stochastic variational inequalities. To begin with, we give the deterministic foundation from which the stochastic methods eventually evolved. Then we review methods…
In this paper we consider the problem of detecting a change in the parameters of an autoregressive process, where the moments of the innovation process do not necessarily exist. An empirical likelihood ratio test for the existence of a…
Automated analysis of complex systems based on multiple readouts remains a challenge. Change point detection algorithms are aimed to locating abrupt changes in the time series behaviour of a process. In this paper, we present a novel change…