statistical modelling

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Models are useful to  predict or reproduce behaviours of the phenomenon and express a role (function) the phenomenon plays, where the models are formulae which can express various state by the numerical values based on rules. Models are conventionally built based on the basic principles. However, when the basic principles are not explained sufficiently we cannot build the models by the conventional approach. On the other hand, we can observe phenomena and can obtain the observational data relative easily. There are cases where there are some elements involved in a phenomenon. However, we might not be able to always obtain all the elements data.? In difficult situations that the obtained information is not complete and sufficient we can build statistical models from the data. A present state is influenced by the past states in many cases. Hence, it is very important to know the underlying relationship among time delays in the phenomenon. When a model sufficiently extracts the peculiarities of the data we can consider that the model reflects the essence of the basic principle, although the structure of the model is not similar to that of a model based on the basic principle. Such a model can make accurate predictions, generate similar behaviours to the analysis target data, and produce various behaviours.

Original time series data and simulation time series (free-run) data generated by a statistical model built using the original time series data only.