Some Nonparametric Regression Problems for Gaussian Subordinated Time Series Observations with Long-Memory
Sucharita Ghosh
Swiss Federal Researh Institute WSL, Switzerland

Consider the nonparametric regression problem Y(i) = m(t(i)) + e(i), i=1,2,...n, t(i) = i/n, where Y(i), i=1,...,n, are time series observations, m is smooth, and the errors e(i) have zero mean and are one dimensional transformations e(i) = G(Z(i)) of a stationary unobserved Gaussian process Z(i), i=1,2,.... The function G is unknown and arbitrary except that it allows for a Hermite polynomial expansion. This assumption means that the residuals are stationary but they need not be Gaussian. In addition, often in environmental applications, the traditional assumption of constant error variance of the errors need not hold, and more importantly, the probability distribution of the errors may change with time. The Gaussian subordination model for the errors can be tailored to accommodate also this problem. For instance, we may assume that e(i) = G(Z(i), t(i)), so that the model allows for non-Gaussianity of the data and also, the shape of the underlying probability distribution function may be time dependent. Of special interest is when Z(i) has long-memory, in which case the data may display trend-like features, where there may be none. We will consider theory, some real data applications and address a selection of problems. For instance, since the data may have time-varying distributions, estimation of selected exceedance probabilities as functions of time are of interest, having direct implications for risk management strategies. Another special topic of interest is the rapid change-point estimation problem, having applications in palaeo-climatology, where however, the time series data may not be evenly spaced in time, requiring the use of continuous time stochastic processes. Examples of such data include deep core data such as oxygen isotope ratios from ice or lake-sedimdents.

Keywords: Nonparametric regression; Change point estimation; Long-range dependence; Time series

Biography: Sucharita Ghosh is statistician at the WSL, a federal research institute located near Zurich. Her research interests include empirical moment generating functions, smoothing and long-memory and applications of statistics in the environment.