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x model-based , particularly used in modelling of time series data to capture
the feature of long-time behaviour of the underlying dynamic system.
In the following, various traditional approaches to time series classification,
modelling, and forecasting are considered and their application in engineering
demonstrated on practical examples taken from process and production industry
sectors. This should help in better understanding the modern approaches to time
series analysis and forecasting using the methods and tools of artificial intelligence
exposed in the chapters to follow. The items presented here should also serve as a
source of definitions and explanations of terms used in this field of data processing.
It will, however, be supposed that the time series, the model of which should be
built, are homogeneous, made up of uniformly sampled discrete data values.
2.2 Traditional Problem Definition
Traditionally, time series analysis is defined as a branch of statistics that generally
deals with the structural dependencies between the observation data of random
phenomena and the related parameters. The observed phenomena are indexed by
time as the only parameter; therefore, the name time series is used.
Basically, there are two approaches to time series analysis:
x time domain approach , mainly based on the use of the covariance function
of the time series
x frequency domain approach , based on spectral density function analysis
and Fourier analysis.
Both approaches are appropriate for application to a wide range of disciplines, but
the time domain approach is mostly used in engineering practice. This is
particularly due to the availability of the Box-Jenkins approach to time series
analysis, which is primarily concerned with the linear modelling of stationary
phenomena. However, Box and Jenkins have pointed out that their approach is also
applicable to the analysis of nonstationary time series, after their differencings
(trend removal).
2.2.1 Characteristic Features
The major characteristic features of time series are the stationarity , linearity ,
trend , and seasonality . Although a time series can exhibit one or more of these
features, for presentation, analysis, and prediction of time series values each
feature is rather treated separately.
2.2.1.1 Stationarity
This property of a random process is related to the mean value and variance of
observation data, both of which should be constant over time, and the covariance
between the observations x t and x t-d should only depend on the distance between
the two observations and does not change over time, i.e. the following relationships
should hold:
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