(Ebook) Large Covariance and Autocovariance Matrices by Arup Bose, Monika Bhattacharjee ISBN 9781351398169, 9780367734107, 9781138303867, 9780203730652, 1351398164, 0367734109, 1138303860, 0203730658, 9781351398168

(Ebook) Large Covariance and Autocovariance Matrices by Arup Bose, Monika Bhattacharjee ISBN 9781351398169, 9780367734107, 9781138303867, 9780203730652, 1351398164, 0367734109, 1138303860, 0203730658, 9781351398168

Large Covariance and Autocovariance Matrices brings together a collection of recent results on sample covariance and autocovariance matrices in high-dimensional models and novel ideas on how to use them for statistical inference in one or more high-dimensional time series models. The prerequisites include knowledge of elementary multivariate analysis, basic time series analysis and basic results in stochastic convergence.

Part I is on different methods of estimation of large covariance matrices and auto-covariance matrices and properties of these estimators. Part II covers the relevant material on random matrix theory and non-commutative probability. Part III provides results on limit spectra and asymptotic normality of traces of symmetric matrix polynomial functions of sample auto-covariance matrices in high-dimensional linear time series models. These are used to develop graphical and significance tests for different hypotheses involving one or more independent high-dimensional linear time series.

The book should be of interest to people in econometrics and statistics (large covariance matrices and high-dimensional time series), mathematics (random matrices and free probability) and computer science (wireless communication). Parts of it can be used in post-graduate courses on high-dimensional statistical inference, high-dimensional random matrices and high-dimensional time series models. It should be particularly attractive to researchers developing statistical methods in high-dimensional time series models.