Nonlinear system theory: another look at dependence.

By Wei Biao Wu. 2005

650 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

In Statistical and Nonlinear Physics

Citations in the corpus

Fairness in Criminal Justice Risk Assessments: The State of the Art (2017, background): “The IID requirement can be relaxed somewhat (Rosenblatt 1956; Wu 2005).”
Uniform change point tests in high dimension (2015, background): “For example, the dependence concept in [50] is based on ak(p).”
Testing Many Moment Inequalities (2013, neutral): “7 in Yu (1994) (see also Eberlein, 1984), we have”
Banded and tapered estimates for autocovariance matrices and the linear process bootstrap (2010, background): “We follow Wu and Pourahmadi (2009) in adopting the physical dependence measure of Wu (2005).”
Asymptotic results for the empirical process of stationary sequences (2009, neutral): “Coupling conditions of this type were first used by Wu [69].”
Break detection in the covariance structure of multivariate time series models (2009, background): “It is not immediately clear, however, whether the sharp almost sure in variance principles in [50] can be extended with reasonable effort to a multivariate setting.”
Placebo inference on treatment effects when the number of clusters is small (2018, background): “A very large class of commonly used time series (d = 1) and spatial models are of this form; see Shao and Wu (2007) and El Machkouri et al.”
Convolutional autoregressive models for functional time series (2016, positive): “…physicaldependencemeasuresdefinedinWu(2005)oftheprocess θ ( u t + z t + A t b k ) decay geometrically fast, and therefore the martingale approximation used in Wu (2005) can be applied to obtain the central limit theorem for , where Υ k is the long-run variance of the process u t + z t + A t b k .”
Towards a general theory for nonlinear locally stationary processes (2017, neutral): “, and Wu, W.B. (2009)): Given parameter curves a1, a2 : [0, 1]→ R, define”
The asymptotic size and power of the augmented Dickey–Fuller test for a unit root (2018, background): “It is based on the concept of weak dependence introduced by Wu (2005) and allows together with (2.5) for a very broad class of possible processes.”
Gaussian Approximation for High Dimensional Time Series (2015, methodology): “To perform simultaneous inference on γjk, 1 ≤ j, k ≤ p, one needs to derive asymptotic distribution of the maximum deviation maxj,k≤p |γ̂jk−γjk| or the normalized version maxj,k≤p |γ̂jk − γjk|/τjk; cf Equation (2) in Xiao and Wu (2013). Jiang (2004) established the Gumbel convergence of the maximum ”
An invariance principle for stationary random fields under Hannan's condition (2014, background): “See for example Wu [24], Dedecker et al.”
SEQUENTIAL TESTING FOR THE STABILITY OF HIGH-FREQUENCY PORTFOLIO BETAS (2011, methodology): “Similar types of approximation schemes were first used in Ibragimov (1962) for univariate random variables and lately in more general contexts also in Wu (2005) and Aue, Hörmann, Horváth, and Reimherr (2009).”
Inference of trends in time series (2007, background): “We conjecture that, like σ̂3, the other two estimates also satisfy σ̂1, σ̂2 = σ+ OP.n−1=3/ if kn n1=3. Our simulation study (which is not reported here) shows that σ̂2 is more robust whereas σ̂1 and σ̂3 are vulnerable to large jumps in μ. For autoregressive AR(1) models with IID normal innovations, ”
Robust Spectral Analysis (2011, background): “Arguing as in the proof of Theorem 1 of Wu (2005), use the Jensen inequality and the law of iterated expectations to deduce that ‖E(1{Xt ξ} | F0)− E(1{X∗t ξ} | F−1, ε∗0)‖ = ‖E(1{Xt ξ} − 1{X∗t ξ} | F0, ε∗0)‖ ≤ ‖1{Xt ξ} − 1{X∗t ξ}‖.”
Simultaneous inference of linear models with time varying coefficients (2010, background): “U, l+ j/: .36/ By theorem 1 in Wu (2005), ‖Pi−l.QiQTi /‖ ‖QiQTi − Qi,{i−l}QTi,{i−l}‖.”
Weakly dependent functional data (2010, background): “BY SIEGFRIED HÖRMANN AND PIOTR KOKOSZKA1”
LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION FOR NONLINEAR PROCESSES (2007, methodology): “For the details, see Shao and Wu (2005). I The following lemma is used in proving the asymptotic distribution of d when do = 1.”