## Event Date:

## Event Date Details:

refreshments served at 3:15 p.m.

## Event Location:

- Sobel Seminar Room; South Hall 5607F

- Department Seminar Series

### Speaker:

György Terdik (University of Debrecen Hungary)

### Abstract:

Time Series methods are often used for the analysis of data coming from various fields, such as economics, finance, environment and medical sciences, atmospheric pollution and sensor networking etc. One of the important objects in time series analysis is to develop methods for understanding the underlying dynamics of the given data, and based on this knowledge to find suitable linear (or non linear) time series models which could be used for obtaining optimal forecasts. There is an extensive literature on model building,forecasting of time series. Many times the data we come across is not only a function of time t, but also a function of the spatial locations. The problem of interest here is that of finding an estimate of unobservable data at a given location when spatial data at neighboring locations are available.. The estimation requires knowledge of spatial covariance function (or a suitable spatial model). Our object here is to obtain a class of spatio-temporal covariance functions and use the function obtained to obtain optimal forecasts. To achieve these objectives, we use Discrete Fourier Transforms of the data rather than the data itself which will substantially reduces the number of arithmetic operations required to compute the statistics. Let us denote the measurement at time t∈Z, at the location s by Z(s,t). We assume s∈R^{2}. Here Z is the set of integers and R is the real line. Suppose we have an observation regularly collected at several locations, say m locations, and at n time points. Our first object is to validate the data at location, using the data we collected in the neighborhood of it. To achieve this objective, we need a spatio-temporal covariance function, and in this paper we derive an expression for such a function when the process satisfies a partial second order stochastic differential equation. In order to obtain this covariance function we assume the process is spatially, temporally second order stationary and also it is isotropic. Joint work with T. Subba Rao.

Keywords: Complex Stochastic Partial Differential Equations, Covariance Functions, Discrete Fourier Transforms, ,Spatio-Temporal Processes, Prediction (Kriging), Frequency Variogram.