1.
Exploratory Data Analysis
1.3. EDA Techniques 1.3.3. Graphical Techniques: Alphabetic 1.3.3.15. Lag Plot


Lag Plot  
Conclusions 
We can make the following conclusions based on the above plot of
the random walk data set.


Discussion 
Note the tight clustering of points along the diagonal. This is the
lag plot signature of a process with strong positive autocorrelation.
Such processes are highly nonrandomthere is strong association
between an observation and a succeeding observation. In short, if you
know Y_{i1} you can make a strong guess as to
what Y_{i} will be.
If the above process were completely random, the plot would have a shotgun pattern, and knowledge of a current observation (say Y_{i1} = 3) would yield virtually no knowledge about the next observation Y_{i} (it could here be anywhere from 2 to +8). On the other hand, if the process had strong autocorrelation, as seen above, and if Y_{i1} = 3, then the range of possible values for Y_{i} is seen to be restricted to a smaller range (2 to 4)still wide, but an improvement nonetheless (relative to 2 to +8) in predictive power. 

Recommended Next Step 
When the lag plot shows a strongly autoregressive pattern and only
successive observations appear to be correlated, the
next steps are to:
