Box-Jenkins method

ARIMA Models in Python

James Fulton

Climate informatics researcher

The Box-Jenkins method

From raw data $\rightarrow$ production model

• identification
• estimation
• model diagnostics

Identification

• Is the time series stationary?
• What differencing will make it stationary?
• What transforms will make it stationary?
• What values of p and q are most promising?

Identification tools

• Plot the time series
  • df.plot()
• Use augmented Dicky-Fuller test
  • adfuller()
• Use transforms and/or differencing
  • df.diff(), np.log(), np.sqrt()
• Plot ACF/PACF
  • plot_acf(), plot_pacf()

Estimation

• Use the data to train the model coefficients
• Done for us using model.fit()
• Choose between models using AIC and BIC
  • results.aic, results.bic

Model diagnostics

• Are the residuals uncorrelated
• Are residuals normally distributed
  • results.plot_diagnostics()
  • results.summary()

Decision

Repeat

• We go through the process again with more information
• Find a better model

Production

• Ready to make forecasts
  • results.get_forecast()

Box-Jenkins

Let's practice!

ARIMA Models in Python