Graduate Student Seminar

Speaker 1: Peter Linton

Title

A Drunk and His Dog

Abstract

I will present definitions and background on two important concepts in stochastic processes: Integrated and Co-integrated processes. These topics may be unfamiliar to most graduate students but they are of recent import, especially with regards to economic interpretation. The title represents one of the most accessible and fun examples to cement the idea of cointegration. Given time we may explore the spectral density properties of cointegration or the issues of incorporating cointegration constraints into Vector autoregressive moving average models.

Speaker 2: Ricardo Moura

Title

Behrens Fisher Statistic -- Exact and Near-Exact Distributions

Abstract

The Behrens-Fisher problem consists on the well known equality test between mean values of two different normal populations, however, when considering that the variance of both are unknown, i.e., the fact that they could have different variances. With this presentation we propose to find the exact distributions for the Behrens-Fisher statistic for samples with both odd and both even dimensions. For the case of being alternatively odd and even dimensions the work will be similar to the case of both even. For that objective we will construct the distributions using the notion of distribution mixtures, the Generalizes Integer Gamma (GIG)  distribution and Generalized Near-Integer Gamma (GNIG) obtaining a finite mixture of distributions that we will call "pseudo-t-student" for the odd case and obtaining a infinite mixture for the even case. After we will compare the obtained approximations with the ones obtained by Welch (1947).