LARGE COVARIANCE AND AUTOCOVARIANCE MATRICES

"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. Arup Bose is a professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in mathematical statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been editor of Sankhya for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of Indi