Recently, Vogelsang (1999) proposed a method to detect outliers which explicitly imposes the null hypothesis of a unit root. It works in an iterative fashion to select multiple outliers in a given series. We show, via simulations, that under the null hypothesis of no outliers, it has the right size in ...nite samples to detect a single outlier but when applied in an iterative fashion to select ...

We study a new class of nonlinear autoregressive models for vector time series, where the current vector depends on single-indexes defined on the past lags and the effects of different lags have an additive form. A sufficient condition is provided for stationarity of such models. We also study estimation of the proposed model using P-splines, hypothesis testing, asymptotics, selection of the or...

We consider the dynamics of the Hénon and Ikeda maps in the presence of additive and dynamical noise. We show that, from the point of view of computations of some statistical quantities, dynamical noise corrupting these deterministic systems can be considered effectively as an additive "pseudonoise" with the Cauchy distribution. In the case of the Hénon and Ikeda maps, this effect occurs only f...

Let K be a real quadratic number field. Let p be a prime which is inert in K. We denote the completion of K at the place p by Kp. Let f > 1 be a positive integer coprime to p. In this thesis we give a p-adic construction of special elements u(r, τ) ∈ K× p for special pairs (r, τ) ∈ (Z/fZ)× × Hp where Hp = P(Cp)\P(Qp) is the so called p-adic upper half plane. These pairs (r, τ) can be thought of...

We present a nonparametric way to retrieve an additive system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long-term predictions. We apply our method to a modified chaotic Chua oscillator in order to demonstrate its potential.

I consider models for binary time series, starting with autoregression models and then developing generalizations of them which allow nonparametric additive covariates. I show that several apparently different binary AR(1) models are equivalent. Three possible nonparametric additive regression models which allow for autocorrelation are considered; one is a generalization of an ARX model, the ot...

Pointwise consistent, feasible procedures for estimating contemporaneous linear causal structure from time series data have been developed using multiple conditional independence tests, but no such procedures are available for non-linear systems. We describe a feasible procedure for learning a class of non-linear time series structures, which we call additive non-linear time series. We show tha...

Cylindrical probability measures are finitely additive measures on Banach spaces that have sigma-additive projections to Euclidean spaces of all dimensions. They are naturally associated to notions of weak (cylindrical) random variable and hence weak (cylindrical) stochastic processes. In this paper we focus on cylindrical Lévy processes. These have (weak) Lévy-Itô decompositions and an associa...

One of the widely acknowledged drawbacks of exible statistical models is that the tted models are often extremely diicult to interpret. However, if exible models are constrained to be additive the tted models are much easier to interpret, as each input can be considered independently. The problem with additive models is that they cannot provide an accurate model if the phenomenon being modeled ...