On the limiting spectral distribution of the covariance matrices of time-lagged processes

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Robert, Christian Y.^2,3  Rosenbaum, Mathieu¹ 

[1] CMAP Ecole Polytech Paris, CNRS, UMR 7641, F-91128 Palaiseau, France

[2] CREST, F-92245 Malakoff, France

[3] ENSAE Paris Tech, F-92245 Malakoff, France

关键词: Eigenvalues of covariance matrices;    Lagged processes;    Random matrix theory;    Time lag estimation;    Adaptive estimation;   

DOI  :  10.1016/j.jmva.2010.06.014

来源: Elsevier

【 摘 要 】

We consider two continuous-time Gaussian processes, one being partially correlated to a time-lagged version of the other. We first give the limiting spectral distribution for the covariance matrices of the increments of the processes when the span between two observations tends to zero. Then, we derive the limiting distribution of the eigenvalues of the sample covariance matrices. This result is obtained when the number of paths of the processes is asymptotically proportional to the number of observations for each single path. As an application, we use the second moment of this distribution together with auxiliary volatility and correlation estimates to construct an adaptive estimator of the time lag between the two processes. Finally, we provide an asymptotic theory for our estimation procedure. (c) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free