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#### Article: Moment approach for singular values distribution of a large auto-covariance matrix

Title Moment approach for singular values distribution of a large auto-covariance matrix Wang, QYao, JJ 2016 Annales de l'Institut Henri Poincaré Probabilités et Statistiques (Forthcoming) How to Cite? Let $\{\varepsilon_{ij}\}$ be a double array of i.i.d. real random variables with $\mathbb{E} \varepsilon_{ij}=0$, $\mathbb{E} \varepsilon_{ij}^2=1$ and $\mathbb{E} \varepsilon_{ij}^4<\infty$, and let $X_T=\frac 1T \sum_{t=s+1}^{s+T}\varepsilon_t\varepsilon^T_{t-s}$ be the lag-$s$ ($s$ is a fixed positive integer) auto-covariance matrix of $\varepsilon_t$. We investigate the limiting behaviors of the singular values of $X_T$ in two aspects. First, we show that the empirical distribution of these singular values converges to a nonrandom limit $F$. Second, we establish the convergence of the largest singular value to the right edge of $F$. Both results are derived using moment methods. http://hdl.handle.net/10722/231312

DC FieldValueLanguage
dc.contributor.authorWang, Q-
dc.contributor.authorYao, JJ-
dc.date.accessioned2016-09-20T05:22:15Z-
dc.date.available2016-09-20T05:22:15Z-
dc.date.issued2016-
dc.identifier.citationAnnales de l'Institut Henri Poincaré Probabilités et Statistiques (Forthcoming)-
dc.identifier.urihttp://hdl.handle.net/10722/231312-
dc.description.abstractLet $\{\varepsilon_{ij}\}$ be a double array of i.i.d. real random variables with $\mathbb{E} \varepsilon_{ij}=0$, $\mathbb{E} \varepsilon_{ij}^2=1$ and $\mathbb{E} \varepsilon_{ij}^4<\infty$, and let $X_T=\frac 1T \sum_{t=s+1}^{s+T}\varepsilon_t\varepsilon^T_{t-s}$ be the lag-$s$ ($s$ is a fixed positive integer) auto-covariance matrix of $\varepsilon_t$. We investigate the limiting behaviors of the singular values of $X_T$ in two aspects. First, we show that the empirical distribution of these singular values converges to a nonrandom limit $F$. Second, we establish the convergence of the largest singular value to the right edge of $F$. Both results are derived using moment methods.-
dc.languageeng-
dc.relation.ispartofAnnales de l'Institut Henri Poincaré Probabilités et Statistiques-
dc.titleMoment approach for singular values distribution of a large auto-covariance matrix-
dc.typeArticle-
dc.identifier.emailYao, JJ: jeffyao@hku.hk-
dc.identifier.authorityYao, JJ=rp01473-
dc.identifier.hkuros263170-