# Linear Stationary Non-Gaussian Time Series

Monday, November 12, 2001 - 9:30am - 10:30am

Keller 3-180

Murray Rosenblatt (University of California, San Diego)

Linear stationary time series are generated by passing an independent, identically distributed sequence of random variables through a linear filter whose transfer function is square integrable. The probability structure of a Gaussian sequence is determined by the modulus of the transfer function while that of a non-Gaussian process is determined by the transfer function itself (and the distribution of the i.i.d. random variables generating the process). In a certain sense the non-Gaussian sequences are a much richer class of processes than the Gaussian sequences. Detailed comments are made about autoregressive moving average (ARMA) models where the transfer function is a ratio of polynomials evaluated on the boundary of the unit disc in the complex plane. If the zeros of the polynomials are outside the unit disc the sequence is called minimum phase.Gaussian ARMA schemes can always be taken to be minimum phase. Prediction and estimation questions are discussed for non-Gaussian nonminimum phase models.