Building business models

With our increasing need for predictability in our lives and investments, we have to rely on past events, whether related directly or not to guide us in our decisions. Plotting the output of these events over a long period forms the basis of most series analysis, whether financial or biological. Using systems to achieve these predictions with increasing accuracy is very important to many professionals. However diverse the fields, the background platform is rather similar. This is what we hope to discuss and make rather explanatory.

Firstly, a univariate analyses of input- and output series is fundamental.

The series should be plotted with available discrete data.Is the series stationary? If not: difference the series: (Xt = Xt-Xt-1.

Identification: what process generated the series? Tools: ACF and PACF.On the basis of ACF and PACF: estimate a model for the series with AR-and/or MA-parameters.

Testing the model: Does white noise represent the residuals? If not: modify the model on the basis of the ACF and PACF of the residuals.

For multivariate analysis, the approach is rather different.

Bivariate analysis of the relationship between Xt and Yt. Here, we plot (scattergram) (Yt against (Xt to detect outlier points. ((Yt = Yt-Yt-1)

Pre-whiten Xt and Yt. The residuals from the univariate model of Xt is the pre-whitened Xt given that the residuals are white noise. Estimate the cross-correlations (CCF) between the pre-whitened Xt and the pre-whitened Yt.

Are there any indications of a lag-structure? If so: construct a weighted input series that incorporates the lag-structure.

Determine the functional form between Xt and Yt .Estimate a bivariate model without noise parameters.

Identify the structure of the noise term on the basis of the ACF and PACF of the residuals.

Re-estimate the model including noise parameters.

Testing the model: Does white noise constitute the residuals. If not: modify the noise parameters on the basis of the ACF and PACF of the residuals, and re-estimate the model.

This gives a sound and direct approach for analysing time-series and providing an understanding of system dynamics.