# Definition:Iterative Modelling

## Definition

Let $S$ be a stochastic process based on an equispaced time series.

Suppose it has been determined that $S$ should be modelled using a hybrid mechanistic and empirical model.

It is supposed that the inputs and outputs of $S$ are available for analysis.

If possible, at least $50$ and preferably $100$ observations or more should be used.

If there are not available as many as that, it is necessary to use experience and past information to make an informed estimate of a preliminary model.

As more data becomes available, the model can be updated.

If fitting a dynamic model, a theoretical analysis can sometimes be used to estimate the approximate form of the model, as well as good estimates of the numbers to be used for its parameters.

These values can be checked and modified if necessary by later analysis of the data.

- $(1): \quad$ From the interaction of theory and practice, a useful class of models can be considered.

- $(2): \quad$ Methods for identifying an appropriate subclass of models can be developed, so as to use the Principle of Parsimony to suggest a model that may be investigated.

- $(3): \quad$ The model to be investigated is fitted to the data available and estimations are made of its parameters.

- $(4): \quad$ Diagnostic checks are then applied to uncover possible lack of fit, and if such is found, to diagnose the cause. If the model is found to be inadequate, the cycle is repeated.

## Sources

- 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel:
*Time Series Analysis: Forecasting and Control*(3rd ed.) ... (previous) ... (next):

- $1$: Introduction:
- $1.3$ Basic Ideas in Model Building:
- $1.3.2$ Iterative Stages in the Selection of a Model

- $1.3$ Basic Ideas in Model Building:

- $1$: Introduction: