|1.||Introduction. Dynamic systems.|
|2.||Explorative study of dynamics.|
|3.||The H-method for dynamic data.|
|4.||Regression including lags.|
|7.||Kalman Filter type of methods.|
|10.||Importance of variables.|
|13.||Predictions in dynamic systems.|
|15.||Analysis of residuals.|
|16.||Inertia in dynamic systems|
|21.||Guidelines for presentation of results|
In industry there is great interest in methods that can handle dynamic systems containing many variables. The reason is the importance of getting measurements and also that measurement instruments are getting cheaper. A great challenge for industry is that many modern measurement instruments provide with numerous measurement values. For instance, a NIR (Near Infra-Red) instrument may give 1056 values for each sample. In process control environments it can be considerable savings to use NIR instruments to supervise the processes compared with traditional process control instruments.
The H-method has been applied with success to analyse dynamic systems, where many variables have been measured. The background for the success is that data often show sign of reduced rank. The H-method appropriately identifies the appropriate rank and the subset of variables that should be used in the analysis.
Kalman Filer type of methods are popular in many industrial applications. The experience in industry is that these methods function well when there are few variables, say less than 10. If there are more than around 20 they typically break down. Already with 10 to 20 variables the predictions derived from these methods deteriorates.
The H-method provides with stable solutions to Kalman Filter type of methods. See a short introduction to some of the ideas.