1.3.3.15.2. Lag Plot: Weak Autocorrelation

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

1.3.3.15.2. Lag Plot: Weak Autocorrelation

Lag Plot

Conclusions

Underlying autoregressive model with moderate positive autocorrelation
No outliers

Discussion

In the plot above for lag = 1, note how the points tend to cluster (albeit noisily) along the diagonal. Such clustering is the lag plot signature of moderate autocorrelation.

If the process were completely random, knowledge of a current observation (say Y_i-1 = 0) would yield virtually no knowledge about the next observation Y_i. If the process has moderate autocorrelation as above, and if Y_i-1 = 0, then the range of possible values for Y_i is seen to be restricted to a smaller range (.01 to +.01) which suggests prediction is possible using an autoregressive model.

Recommended Next Step

Determine the parameters for the autoregressive model:

Since Y_i and Y_i-1 are precisely the axes of the lag plot, such estimation is a linear regression straight from the lag plot.

The residual standard deviation for the autoregressive model will be much smaller than the residual standard deviation for the default model