报告题目：Some recent developments on linear processes and linear random fields

报告人：桑海林 教授 （University of Mississippi，美国密西西比大学）

时间：2019年7月5 日上午9：00-12：00

地点：数学馆 金融实验室

摘要：The linear processes and linear random fields are tools for studying stationary time series and stationary random fields. One can have a better understanding of many important time series and random fields by studying the corresponding linear processes and linear random fields.

   In this talk we survey some recent developments on linear processes and linear random fields. One part is the moderate and large deviations under different conditions. This part research plays an important role in many applied fields, for instance, the premium calculation problem, risk management in insurance, non-parametric estimation and network information theory. We also study the memory properties of transformations of linear processes which have application in econometrics and financial data analysis when the time series observations have non-Gaussian heavy tails. Entropy is widely applied in the fields of information theory, statistical classification, pattern recognition and so on since it is a measure of uncertainty in a probability distribution. At the end, we focus on the estimation of the quadratic entropy for linear processes. With a Fourier transform on the kernel function and the projection method, it is shown that, the kernel estimator has similar asymptotical properties as the i.i.d. case if the linear process has the defined short range dependence.

   Part of the results are confirmed by simulation studies. We also obtain very promising results in some real data analysis.