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variables that can be observed. The second part of the model is the noise
introduced by the variables that cannot be observed.
This applies to both the underlying process and to the mechanisms of
measure. Any tool used to measure data can also be modeled in the same
way as the underlying process, and it can have large effects on the outcome.
For example, if the same data is being collected by several different systems,
knowing the bias and variance of each collection system allows them to be
normalized.
Toward this end, this section introduces some of the methods used to
identify the underlying model in the presence of noise. As this topic is
focused on real-time data, the first part of this section focuses on some
of the simpler methods for modeling time-series models. (Real-time data
is inherently time-series data due to the nature of data collection.) These
methods are widely used in forecasting procedures in all different fields.
The second part of this section discusses linear models, also known as
regression models. These models are a classic technique in statistics and
are probably the most-used modeling technique in the world. They describe
linear relationships between variables being measured and some outcome,
which is also being measured. One variant, logistic regression, is a popular
method for producing models for the odds that an event will occur.
When the data is highly nonlinear or its structure is poorly understood,
the Artificial Neural Network has become a popular option for modeling
time-seriesdata.Thefinaldiscussioninthissectionisaboutthebasicneural
network model. Neural network models are easily adapted to real-time
problems as the training and prediction cycles are identical.
Simple Time-Series Models
Any real-time data system is essentially made up of a series of sequential
values. Asdiscussed in Chapter 8,thesevalues are computed foraparticular
time “bucket” or quantization, and then they are analyzed. Most of these
measurements are inherently noisy, so time-series models attempt to get at
the underlying shape of the time series by smoothing over the noise, usually
through some sort of averaging technique, several of which are presented in
this section.
