Estimate Order of Model: Information Criteria

Another tool to identify the order of a model is to look at the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). These measures compute the goodness of fit with the estimated parameters, but apply a penalty function on the number of parameters in the model. You will take the AR(2) simulated data from the last exercise, saved as simulated_data_2, and compute the BIC as you vary the order, p, in an AR(p) from 0 to 6.

This exercise is part of the course

Time Series Analysis in Python

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Exercise instructions

Import the ARIMA module for estimating the parameters and computing BIC.
Initialize a numpy array BIC, which we will use to store the BIC for each AR(p) model.
Loop through order p for p = 0,…,6.
- For each p, fit the data to an AR model of order p.
- For each p, save the value of BIC using the .bic attribute (no parentheses) of res.
Plot BIC as a function of p (for the plot, skip p=0 and plot for p=1,…6).

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Import the module for estimating an ARIMA model
from statsmodels.tsa.arima.model import ARIMA

# Fit the data to an AR(p) for p = 0,...,6 , and save the BIC
BIC = np.zeros(7)
for p in range(7):
    mod = ARIMA(simulated_data_2, order=(___,___,___))
    res = mod.fit()
# Save BIC for AR(p)    
    BIC[p] = res.___
    
# Plot the BIC as a function of p
plt.plot(range(1,7), BIC[1:7], marker='o')
plt.xlabel('Order of AR Model')
plt.ylabel('Bayesian Information Criterion')
plt.show()

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