Exploratory Data Analysis
1.4. EDA Case Studies
1.4.2. Case Studies
188.8.131.52. Random Walk
|Lag Plot Suggests Better Model||
Since the underlying assumptions did not hold, we need to develop
a better model.
The lag plot showed a distinct linear pattern. Given the definition of the lag plot, Yi versus Yi-1, a good candidate model is a model of the form
The results of a linear fit
of this model generated the following results.
Coefficient Estimate Stan. Error t-Value A0 0.050165 0.024171 2.075 A1 0.987087 0.006313 156.350 Residual Standard Deviation = 0.2931 Residual Degrees of Freedom = 497
The slope parameter, A1, has a t value of 156.350 which is statistically significant. Also, the residual standard deviation is 0.2931. This can be compared to the standard deviation shown in the summary table, which is 2.078675. That is, the fit to the autoregressive model has reduced the variability by a factor of 7.
|Time Series Model||This model is an example of a time series model. More extensive discussion of time series is given in the Process Monitoring chapter.|