Data preparation, model specification and residual checking

4 Data preparation, model specification and residual checking 

The previous section points out which structure of a time series model to choose depending on the general type of the production plant to be modelled. Once a model class is selected, the corresponding model s parameters have to specified based on historical records of the investigated plant. The model fitted to the historical records has then to be checked for adequacy, i.e. the residuals of the model have to be checked for the assumptions inherent to the chosen model (typically white noise). 

To give an example for the influence of the length of the recording interval, let y(t) denote the value of an Ornstein-Uhlenbeck process as introduced in (2.23) at time t. For this specific process the autocorrelation p for ( oo can be expressed as  

Note that (2.61) represents the autocorrelation function of an AR(1) process with pa- 

In principle, the measured flow rates may vary either due to fluctuations of the underlying production process or due to measurement errors. For the analysis of the production system, one is interested in the former variation only. However, the latter cannot be excluded since there is no infinitely precise and reliable sensor. Flow measures can be affected by turbulences or pollutions. Hence, implicitly it has to be assumed that the sensors measures of the corresponding flow rates are unbiased and that the measurement error does not dominate the error process of the production process. Since these sensors are also used for the automatic control systems, continuous efforts are expended for checking their accurateness. Hence, it can be assumed that the sensors work properly in the sense that they are unbiased and have measurement errors that are as small as (technically) possible. 

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