Autocorrelation Function

Time Series Analysis in Python

Rob Reider

Adjunct Professor, NYU-Courant Consultant, Quantopian

Autocorrelation Function

Autocorrelation Function (ACF): The autocorrelation as a function of the lag
Equals one at lag-zero
Interesting information beyond lag-one

ACF Example 1: Simple Autocorrelation Function

Can use last two values in series for forecasting

ACF Example 2: Seasonal Earnings

Earnings for H&R Block

ACF for H&R Block

ACF Example 3: Useful for Model Selection

Model selection

Plot ACF in Python

Import module:

from statsmodels.graphics.tsaplots import plot_acf

Plot the ACF:
```
plot_acf(x, lags= 20, alpha=0.05)
```

Confidence Interval of ACF

Confidence Interval of ACF

Argument alpha sets the width of confidence interval
Example: alpha=0.05
- 5% chance that if true autocorrelation is zero, it will fall outside blue band
Confidence bands are wider if:
- Alpha lower
- Fewer observations
Under some simplifying assumptions, 95% confidence bands are $\pm 2/\sqrt{N}$
If you want no bands on plot, set alpha=1

ACF Values Instead of Plot

from statsmodels.tsa.stattools import acf
print(acf(x))

[ 1.         -0.6765505   0.34989905 -0.01629415 -0.02507013  0.01930354
 -0.03186545  0.01399904 -0.03518128  0.02063168 -0.02620646 -0.00509828
...
  0.07191516 -0.12211912  0.14514481 -0.09644228  0.05215882]

Let's practice!

Time Series Analysis in Python

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