Darling–Erdős limit results for change-point detection in panel data

Chan, Julian; Horváth, Lajos; Hušková, Marie

doi:10.1016/j.jspi.2012.11.004

Cited by 35 publications

(20 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…L −1 C n = (c (ν) n,i+1 ) i≥0,1≤ν≤dn . We shall impose the following condition on the decay of the coefficients c (ν) nj , which is similar to the assumption imposed in Johnstone and Lu (2009), where it controls the principal component eigenvectors within a factor model (also see our discussion below), and to condition (2.4) in Chan et al (2013), where it controls the error terms of a panel time series model.…”

Section: )mentioning

confidence: 99%

Large-sample approximations for variance-covariance matrices of high-dimensional time series

Steland¹,

Sachs²

2017

Bernoulli

View full text Add to dashboard Cite

Distributional approximations of (bi-) linear functions of sample variancecovariance matrices play a critical role to analyze vector time series, as they are needed for various purposes, especially to draw inference on the dependence structure in terms of second moments and to analyze projections onto lower dimensional spaces as those generated by principal components. This particularly applies to the high-dimensional case, where the dimension d is allowed to grow with the sample size n and may even be larger than n. We establish large-sample approximations for such bilinear forms related to the sample variance-covariance matrix of a high-dimensional vector time series in terms of strong approximations by Brownian motions. The results cover weakly dependent as well as many long-range dependent linear processes and are valid for uniformly ℓ 1 -bounded projection vectors, which arise, either naturally or by construction, in many statistical problems extensively studied for high-dimensional series. Among those problems are sparse financial portfolio selection, sparse principal components, the LASSO, shrinkage estimation and change-point analysis for high-dimensional time series, which matter for the analysis of big data and are discussed in greater detail.

show abstract

Section: )mentioning

confidence: 99%

Large-sample approximations for variance-covariance matrices of high-dimensional time series

Steland¹,

Sachs²

2017

Bernoulli

View full text Add to dashboard Cite

show abstract

“…Hawkins (1986), Csörgő and Horváth (1997, Sects. 2.1 and 2.8.1) for the case when N = 1, and Chan et al (2013). Due to the weight (t (T − t)) −1 in the definition of t * N ,T , the limit distribution of t * N ,T does not depend on the break fraction θ ; see Bai (2010).…”

Section: )mentioning

confidence: 97%

“…In our study we used the time period 03/13/2001-03/11/2003 so we have N = 23 panels and each panel has T = 500 observations. Using the testing method in Horváth and Hušková (2013) the no change in the mean of the panels null hypothesis is rejected. The estimated time of change ist 23,500 = 297 so the change is indicated on 05/16/2002.…”

Section: Applicationsmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic Properties of the Cusum Estimator for the Time of Change in Linear Panel Data Models

et al. 2016

Self Cite

View full text Add to dashboard Cite

We consider the problem of estimating the common time of a change in the mean parameters of panel data when dependence is allowed between the cross-sectional units in the form of a common factor. A CUSUM type estimator is proposed, and we establish first and second order asymptotics that can be used to derive consistent confidence intervals for the time of change. Our results improve upon existing theory in two primary directions. Firstly, the conditions we impose on the model errors only pertain to the order of their long run moments, and hence our results hold for nearly all stationary time series models of interest, including nonlinear time series like the ARCH and GARCH processes. Secondly, we study how the asymptotic distribution and norming sequences of the estimator depend on the magnitude of the changes in each cross-section and the common factor loadings. The performance of our results in finite samples is demonstrated with a Monte Carlo simulation study, and we consider applications to two real data sets: the exchange rates of 23 currencies with respect to the US dollar, and the GDP per capita in 113 countries.

show abstract

“…For good sources of references to research literature in this area along with statistical applications, the reader may consult Brodsky and Darkhovsky (1993), and Chen and Gupta (2000). For recent references on the subject we may refer, among many others, to Bouzebda (2012), Aue and Horváth (2013), Chan et al (2013), Horváth and Rice (2014), Alvarez-Andrade and Bouzebda (2014) and Bouzebda (2014). In this section, we deal with testing changes in d.f.…”

Section: The Change-point Problemmentioning

confidence: 99%

Some asymptotic results for the integrated empirical process with applications to statistical tests

Alvarez-Andrade

Bouzebda

Lachal

2016

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on the Komlós et al. (1975)'s results. Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of the integrated empirical process when the parameters are estimated. Finally, we study the behavior of the self-intersection local time of the partial sum process representation of the integrated empirical process.

show abstract

Darling–Erdős limit results for change-point detection in panel data

Cited by 35 publications

References 12 publications

Large-sample approximations for variance-covariance matrices of high-dimensional time series

Large-sample approximations for variance-covariance matrices of high-dimensional time series

Asymptotic Properties of the Cusum Estimator for the Time of Change in Linear Panel Data Models

Some asymptotic results for the integrated empirical process with applications to statistical tests

Contact Info

Product

Resources

About