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,