1.3.3.1.2. Autocorrelation Plot: Weak Autocorrelation

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

1.3.3.1.2. Autocorrelation Plot: Weak Autocorrelation

Autocorrelation Plot

Conclusions

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 improved predictability.

Recommended Next Step

The next step would be to determine the parameters for the autoregressive model:

Such estimation can be done by least squares linear regression or by fitting a Box-Jenkins autoregressive (AR) model.

The randomness assumption for least squares fitting applies to the residuals (i.e., the E_i). That is, even though the original data exhibits randomness, the residuals after fitting Y_i against Y_i-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