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We develop a class of tests for time series models such as multiple regression with growing dimension, infinite-order autoregression and nonparametric sieve regression. Examples include the Chow test and general linear restriction tests of…
In this article, we analyze three classes of time-reversal of a Markov process with Gaussian noise on a manifold. We first unveil a commutativity constraint for the most general of these time-reversals to be well defined. Then we give a…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
In this paper an easy to implement method of stochastically weighing short and long memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly…
Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at…
Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. The absence of inherent structure in metric spaces has resulted in a literature…
This paper introduces a periodic multivariate Poisson autoregression with potentially infinite memory, with a special focus on the network setting. Using contraction techniques, we study the stability of such a process and provide upper…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly…
We propose two robust methods for testing hypotheses on unknown parameters of predictive regression models under heterogeneous and persistent volatility as well as endogenous, persistent and/or fat-tailed regressors and errors. The proposed…
This paper is a survey of recent results on the adaptive robust non parametric methods for the continuous time regression model with the semi - martingale noises with jumps. The noises are modeled by the L\'evy processes, the Ornstein --…
Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be…
We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected…
We consider the analysis of continuous repeated measurement outcomes that are collected through time, also known as longitudinal data. A standard framework for analysing data of this kind is a linear Gaussian mixed-effects model within…
In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In…
This paper analyzes the limit properties of the empirical process of $\alpha$-stable random variables with long range dependence. The $\alpha$-stable random variables are constructed by non-linear transformations of bivariate sequences of…
A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust inter-nodes correlations, that…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
This work presents generalized forgetting recursive least squares (GF-RLS), a generalization of recursive least squares (RLS) that encompasses many extensions of RLS as special cases. First, sufficient conditions are presented for the 1)…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…