1.
Exploratory Data Analysis
1.4. EDA Case Studies 1.4.2. Case Studies 1.4.2.3. 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, Y_{i} versus Y_{i1}, a good candidate model is a model of the form


Fit Output 
The results of a linear fit
of this model generated the following results.
Coefficient Estimate Stan. Error tValue A_{0} 0.050165 0.024171 2.075 A_{1} 0.987087 0.006313 156.350 Residual Standard Deviation = 0.2931 Residual Degrees of Freedom = 497 The slope parameter, A_{1}, 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. 