DEPARTMENT OF Statistics

No. MRP(S)-402/08-09/KLMG023/UGC-SWRO dated 30-Mar-09

Executive Summary

The research focuses on developing new techniques for giving a single framework for Gaussian and non-Gaussian autoregressive processes. Using the concept of convolution, Gaussian non-Gaussian random variables can be developed and applied to construct autoregressive processes.

            The project is organized into 5 chapters. Chapter 1 is an introductory chapter which gives a review of literature and a brief summary of the project work. Chapter 2 introduces autoregressive processes with a convolution of normal and asymmetric Laplace distributions as marginals, which also deals with many properties of the processes developed. The innovations can be obtained as the convolution of the Normal and exponentially tailed densities.

            Chapter 3 deals with estimation of parameters and data analysis on normal-Laplace processes. The sample path behaviour of the process is established through simulation studies. The developed theory is applied to generated data sets. Chapter 4 proposes a general method to give a unified framework for Gaussian non-Gaussian autoregressive processes with additive structure. The unified theory is illustrated through generalized normal semi alpha-Laplace processes.

            In Chapter 5, a generalization of the unification of Gaussian non-Gaussian processes is obtained as stable non- Gaussian processes. Since stable distributions play a vital role in statistical theory as a natural generalization of normal distribution, stable non-Gaussian processes are developed.