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

Lag Plot: Moderate Autocorrelation

Lag Plot lag plot with no outliers and moderate positive autocorrelation
Conclusions We can make the conclusions based on the above plot.
  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 Yi-1 = 0) would yield virtually no knowledge about the next observation Yi. If the process has moderate autocorrelation, as above, and if Yi-1 = 0, then the range of possible values for Yi 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 Yi and Yi-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

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