CHAPTER 1
 INTRODUCTION

 1.1 Goal

 Good data analysis and forecast are essential for the scientific, industrial and even

economic communities. Recent years have seen an ever-increasing interest in analyzing

time series, which are collections over time of measurements gathered from a dynamic

process. Norbert Wiener initiated the field broadly referred to as "signal processing" in

the 1940's when he started considering a time series as a stochastic process. Areas of

time series collection range from meteorology to banking, telecommunications,

earthquakes, biology or medicine; and main objectives for time series analysis include

describing the data (usually by a time plot or statistics), modeling the data (i.e.,

identifying a statistical model able to describe the data given its past values) and

forecasting (or predicting future values of the series). Good predictions then allow taking

actions to control the process generating the time series, particularly when it exhibits

abrupt statistical changes.

 A basic requirement for traditional time series modeling is stationarity [1], since

only one global model is usually used to explain a whole process. But real world time

series data are hardly ever stationary. Non-stationarity can be classified in two groups:

quasi-stationary signals, and piecewise stationary signals. In the first case, the process'

parameters changes occur gradually over time, and an appropriate way to deal with this

problem is by "tracking" the data, or adapting a chosen model to fit the local incoming

values, forgetting at the same time other previously learned properties. In the latter case,