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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:

  1. Model Selection
  2. Parameter Estimation
  3. Performance Checking

The figure below gives an overview of the model finding process:

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.

Last Update: 2004-Jul-03