Time series analysis


1. Introduction. Time series.  
2. Variation over time  
3. The H-method for time dependent data.  
4. Regression including lags.  
5. Graphic analysis.  
6. Case study  
7. Filter and smoothing methods.  
8. Periodicity studies.  
9. Trend analysis.  
10. Importance of variables.  
11. CovProc methods.  
12. Regression coefficients. Analysis.  
13. Predictions.  
14. Positive solutions  
15. Analysis of residuals.  
16. Models for discrete time  
17. Confidence intervals  
18. Outlier detection  
19. Sensitivity analysis  
20. Case study  
21. Guidelines for presentation of results  

In industry there is great interest in time series, where data values are associated to fixed time points. Unfortunately, the data that are registered are of large magnitude. For instance, a company might want to study the variation of signals or samples, given as an optical spectrum, which means that at each time point there may observed a thousand data values or more. Industry is interested in making predictions of new signals. There may also the regression situation, where optical measurements are used to obtain fast estimates of important magnitudes. In these situation it is desired both to estimate the future signals and also the derived magnitudes. Traditional methods for time series analysis are only operational for models containing few variables, say less than 10. The H-method builds up a solution to the given model. It is not concerned with how many variables are given by the model. On the other hand it handles both which variables contribute to the modelling task and which samples from the historic data are relevant to use in the light of the task in question.

The applications of the H-method to handle the modern requirements from industry have proven successful. The reason is that data values are relatively stable, although the rank of data is much lower than the number of variables.