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: Moderate Autocorrelation

Lag Plot

Conclusions

We can make the conclusions based on the above plot of the FLICKER.DAT data set.

1. The data are from an underlying autoregressive model with moderate positive autocorrelation
2. The data contain 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). This suggests prediction is possible using an autoregressive model.

Recommended Next Step

Estimate the parameters for the autoregressive model:

\[ Y_{i} = A_0 + A_1*Y_{i-1} + E_{i} \]

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

\[ Y_{i} = A_0 + E_{i} \]