ACF and PACF plots §

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ACF plots §

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Partial Autocorrelation Function (PACF) §

• PACF is a component of the Autocorrelation Function (ACF).

• The Partial Autocorrelation at lag is given by:

  { are fixed})

  This measures the direct correlation between and when the intervening lags are controlled for.

Idea §

• Consider indirect correlation through intervening periods as demonstrated in the following example:

  January → Food Festival February March → Food Festival

  There is direct correlation between the Food Festivals of January and March.

Estimating PACF §

• To estimate at lag , consider:

Where is the coefficient from Multiple Regression (MR) that measures how and are related, given all the rest are fixed.

Interpretation of PACF §

PACF Plots §

• AR(p) shows cutoff behavior after lag .
• MA(q) shows tapering off or damping behavior.
• ARMA(p,q) may show a mix of these behaviors.

Model Selection Criteria §

AIC and BIC §

Choose the model with the smallest AIC/BIC value.

Note: Fit the model with all the data to calculate AIC/BIC. No train-test method should be combined here.

Key words: §

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TAGS: §

#timeseries