Traditional Problem Definition - Computational Intelligence in Time Series Forecasting - page 20

X t () uu . St () Rt () Ct ()

Both models are useful because, in some real-life cases, time series made up of
values collected in trade or in commerce, the seasonal and trend-cycle components
can add their values to the main component or to multiply them as interrelated
factors.
Anyhow, to make a proper forecast when a multi-component time series is
given, it must first be identified to what extent the individual components are
present in the time series data. This needs the decomposition of time series data to
identify and extract the partial data superimposed to the main time series data. The
time series decomposition process can be presented as shown in Figure 2.1.

Seasonal
Removal

Cycling
Removal

Trend
Removal

Time series
data

Data
Smoothing

Regression
Methods

Ratio
Building

T, S, R, C

Figure 2.1. Time series decomposition process

For solving the decomposition problem, two methods have been mostly used.

x Census I method , to eliminate the variability within the individual seasons.
This uses the moving average windows for calculating the average time
series values within the windows. The windows have a width equal to the
length of the season. This enables the removal of both the seasonal and
random components. Depending on the representation model used,
moving-average values are subtracted from the time series values (when an
additive model is used) or the time series values are divided by the moving
average values (when the multiplicative model is used). In the first case the
seasonal component is calculated as the average value.
x Census II method , an extended and improved Census I method. This is
predominantly used in financial engineering, trading, and econometrics. It
also relies on additive and multiplicative representation models, but it is
very data-table oriented.

2.3 Classification of Time Series

Depending on the character of data that they carry, the time series could be

x stationary and nonstationary
x seasonal and non-seasonal
x linear and nonlinear
x univariate and multivariate