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hurd@stat.unc.edu hhurd@email.unc.edu
103 Hanes Hall 
Education
Positions
Research Interests
Our book with A.G. Miamee entitled, "Periodically Correlated Sequences: Spectral Theory and Practice", John Wiley, Hoboken, NJ, 2007, gives both theoretical and practical aspects(see paragraph below). My theoretical interests include Fourier theory of correlation; the role of unitary operators and process representation; harmonizable processes; nonstationary random fields; prediction theory; generalized harmonic analysis; periodically perturbed dynamical systems. My applicationoriented interests are primarily focused on issues of timeseries analysis for the aforementioned nonstationary process. These include estimation of the family of coefficient functions describing the correlation; estimation of the corresponding spectral densities; testing a time series for the presence of periodic correlation; statistical inference in the presence of nonstationary measurement errors; modeling by parametric systems (such as ARMA) with periodically timevarying coefficients. ARMA systems with timeperiodic coefficients are often called PARMA systems. In 2004 I became interested in statistical issues arising in medical research, particularly problems connected with analysis of large proteomic and microarray datasets. This lead to an interest in clustering. Publications
Periodically Correlated Sequences: Spectral Theory and Practice", John Wiley, Hoboken, NJ, 2007. From the preface: Chapters 1 and 2 present basic definitions, simple mathematical models, and simulations whose intent is to motivate and give insight. In this we present a number of examples that illustrate that the usual periodogram analysis cannot be expected to reveal the presence of periodic correlation in a time series. We give a historical review of the topic that mainly emphasizes the early develop ment but gives references to applicationspecific bibliographies. Chapters 3–8 give background and theoretical structure, beginning with a review of Hilbert space including the spectral theorem for unitary operators and correlation and spectral theory for multivariate stationary sequences. We present the (spectral) theory of harmonizable sequences and then the Fourier theory for the covariance of PC sequences. This is naturally followed by representations for PC sequences and here is where the unitary operator plays its part. We then treat the prediction problem for PC sequences and introduce the rank of a PC sequence. The last three chapters (Chapters 9–11) treat issues of time series analysis for PC sequences. We first treat the nonparametric estimation of mean, cor relation, and spectrum. Chapter 11 summarizes the methods into a paradigm for nonparametric time series analysis of possibly PC sequences. The book web pages provide the Table of Contents, the Preface along with MATLAB scripts and programs that were used to produce the figures in the book. In addition, some data and a broader collection of scripts and programs for analysis of PC time series are provided. Teaching:
Teaching notes. These are short notes on various subjects. The intent is to help the prospective or current student.
These are to be taken as work in progress and comments and suggestions would be appreciated.
