6.6.2.4. Model Validation

6. Process or Product Monitoring and Control
6.6. Case Studies in Process Monitoring
6.6.2. Aerosol Particle Size

6.6.2.4. Model Validation

Residuals

After fitting the model, we should validate the time series model.

As with standard non-linear least squares fitting, the primary tool for validating the model is residual analysis. As this topic is covered in detail in the process modeling chapter, we do not discuss it in detail here.

4-Plot of Residuals

The 4-plot is a convenient graphical technique for model validation in that it tests the assumptions for the residuals on a single graph.

Interpretation of the 4-Plot

We can make the following conclusions based on the above 4-plot.

The run sequence plot shows that the residuals do not violate the assumption of constant location and scale. It also shows that most of the residuals are in the range (-1, 1).

The lag plot indicates that the residuals appear to be random.

The histogram and normal probability plot indicate that the normal distribution provides an adequate fit for this model.

This 4-plot of the residuals indicates that the fitted model is an adequate model for these data.

We generate the individual plots from the 4-plot as separate plots to show more detail.

Run Sequence Plot of Residuals

Lag Plot of Residuals

Histogram of Residuals

Normal Probability Plot of Residuals