Intro to ACF and PACF

ARIMA Models in Python

James Fulton

Climate informatics researcher

Motivation

ACF and PACF

ACF - Autocorrelation Function
PACF - Partial autocorrelation function

What is the ACF

lag-1 autocorrelation $\rightarrow$ $corr(y_t, y_{t-1})$
lag-2 autocorrelation $\rightarrow$ $corr(y_t, y_{t-2})$
...
lag-n autocorrelation $\rightarrow$ $corr(y_t, y_{t-n})$

What is the ACF

What is the PACF

Using ACF and PACF to choose model order

AR(2) model $\rightarrow$

Using ACF and PACF to choose model order

MA(2) model $\rightarrow$

Using ACF and PACF to choose model order

Using ACF and PACF to choose model order

Implementation in Python

from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

# Create figure
fig, (ax1, ax2) = plt.subplots(2,1, figsize=(8,8))

# Make ACF plot
plot_acf(df, lags=10, zero=False, ax=ax1)

# Make PACF plot
plot_pacf(df, lags=10, zero=False, ax=ax2)

plt.show()

Implementation in Python

Over/under differencing and ACF and PACF

Over/under differencing and ACF and PACF

Let's practice!

ARIMA Models in Python

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