Traditional Problem Definition - Computational Intelligence in Time Series Forecasting - page 24

and the predicted value to be

ˆ ˆ

x I x I x

t 2 1 t 1 2 t

or

x ˆ I II I ( x x ) x .

t 2 1 1 t 2 t 1 2 t

2.4.2 Time Series Modelling

In engineering, modelling of dynamic phenomena has long been seen as a valuable
support tool for winning a deep insight into the structure and behaviour of dynamic
systems. Much research and development efforts have been made in development
and application of system models. In control engineering, system models have
been widely used for design and implementation of advanced control strategies,
such as adaptive, predictive, and self-tuning control. In business and financial
engineering, as well as in water, gas, fuel, and electrical power distribution
systems, the mathematical models have for a long time been used for quantity
demand forecasting. This is, in fact, the most significant aspect of time series
analysis, which also helps to reduce, or even to eliminate, the inherent disturbances
or fluctuating components present in observed or in measured values.

2.4.3 Time Series Models

In statistics, two basic mathematical system models are used:

x deterministic models , mathematically viewed as analytical models
represented by deterministic relations like

x

ft () ,

or by recurrence equations like

xf ( xx , ,...)

t t 1 t 2

x stochastic models , statistically viewed as functions of random variables .

Mathematical models used for time series analysis are generally

x regression models
x time-domain models
x frequency-domain models ,
whereas, again, the time-domain models could be

x transfer function models