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

## Autocorrelation Plot: Moderate Autocorrelation

Autocorrelation Plot The following is a sample autocorrelation plot.

Conclusions We can make the following conclusions from this plot.
1. The data come from an underlying autoregressive model with moderate positive autocorrelation.
Discussion The plot starts with a moderately high autocorrelation at lag 1 (approximately 0.75) that gradually decreases. The decreasing autocorrelation is generally linear, but with significant noise. Such a pattern is the autocorrelation plot signature of "moderate autocorrelation", which in turn provides moderate predictability if modeled properly.
Recommended Next Step The next step would be to estimate the parameters for the autoregressive model:
$Y_{i} = A_0 + A_1*Y_{i-1} + E_{i}$
Such estimation can be performed by using least squares linear regression or by fitting a Box-Jenkins autoregressive (AR) model.

The randomness assumption for least squares fitting applies to the residuals of the model. That is, even though the original data exhibit non-randomness, the residuals after fitting Yi against Yi-1 should result in random residuals. Assessing whether or not the proposed model in fact sufficiently removed the randomness is discussed in detail in the Process Modeling chapter.

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

$Y_{i} = A_0 + E_{i}$