Time Series
Model Finding
Setting up a model is a common approach to analyzing
time series. Once a suitable model is found, it can be used for forecasting
future time series elements. However, finding such a model is not straightforward.
Typically, a standard model is chosen, and estimates of its parameters
are determined based on a part of the data set. Then, its performance is
checked on an independent test set. Since another model may provide better
results, the original model is altered, its parameters are estimated, and
the new model is also checked. This process of testing various models can
be repeated until one of the models is accepted. If it models the time
series satisfactorily, it may be applied to as yet unseen data.
To summarize, the following phases can be distinguished:
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Model Selection
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Parameter Estimation
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Performance Checking
The figure below gives an overview of the
model finding process:
Due to the lack of algorithmic solutions, the process
of finding an appropriate model is mainly based on experiments. However,
the space of potential models is huge. So, numerous heuristics for guiding
the model selection process have been developed. For instance, detailed
guidelines exist for selecting a single suitable model out of the group
of the so-called ARIMA-models (auto-regressive
integrated moving average models). This collection is well suited to modeling
a large variety of common types of time series. An introduction to the
world of ARIMA models is provided by Box
and Jenkins.
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