Mini-Course: Regression Models For Time Series Analysis

by:  Benjamin Kedem
 
Abstract:
 
    A time series is a sequence of observations in time. Examples
include, monthly unemployment figures, daily stock prices, EEG
records, hourly rainfall speed averaged over College Park during
June 2003, etc. By "regression" we mean relating time series to
useful predictors. Thus, a daily stock price may depend on economic
and political indices which would help investors predict future
returns.
 
     Regression methods have been an integral part of time series analysis
for a long time dating back at least one hundred years to the
work of Schuster (1898) on sinusoidal regression applied in the
estimation of "hidden periodicities."

    We shall concentrate on a relatively recent statistical development
as "generalized linear models" (GLM) that was introduced by Nelder and
Wedderburn (1972), and which provides under some conditions a unified
regression theory suitable for continuous, categorical, and and count
data. The theory of GLM  was originally intended for independent data,
but it can be extended to dependent data under various assumptions.