AIC dan BIC

Model ARIMA di Python

James Fulton

Climate informatics researcher

AIC - Akaike information criterion

AIC lebih rendah menandakan model lebih baik
AIC cenderung memilih model sederhana dengan orde lebih rendah

BIC - Bayesian information criterion

Sangat mirip dengan AIC
BIC lebih rendah menandakan model lebih baik
BIC cenderung memilih model sederhana dengan orde lebih rendah

AIC vs BIC

BIC lebih menyukai model yang lebih sederhana dibanding AIC
AIC lebih baik untuk memilih model prediktif
BIC lebih baik untuk memilih model penjelas yang baik

AIC dan BIC di statsmodels

# Create model
model = ARIMA(df, order=(1,0,1))

# Fit model
results = model.fit()

# Print fit summary
print(results.summary())

                            Statespace Model Results                           
==============================================================================
Dep. Variable:                      y   No. Observations:                 1000
Model:               SARIMAX(2, 0, 0)   Log Likelihood               -1399.704
Date:                Fri, 10 May 2019   AIC                           2805.407
Time:                        01:06:11   BIC                           2820.131
Sample:                    01-01-2013   HQIC                          2811.003
                         - 09-27-2015                                         
Covariance Type:                  opg

AIC dan BIC di statsmodels

# Create model
model = ARIMA(df, order=(1,0,1))

# Fit model
results = model.fit()

# Print AIC and BIC
print('AIC:', results.aic)
print('BIC:', results.bic)

AIC: 2806.36 
BIC: 2821.09

Menelusuri AIC dan BIC

# Loop over AR order
for p in range(3):
    # Loop over MA order
    for q in range(3):

        # Fit model
        model = ARIMA(df, order=(p,0,q))
        results = model.fit()

        # print the model order and the AIC/BIC values
        print(p, q, results.aic, results.bic)

0 0 2900.13 2905.04
0 1 2828.70 2838.52
0 2 2806.69 2821.42
1 0 2810.25 2820.06
1 1 2806.37 2821.09
1 2 2807.52 2827.15
...

Menelusuri AIC dan BIC

order_aic_bic =[]
# Loop over AR order
for p in range(3):
    # Loop over MA order
    for q in range(3):

        # Fit model
        model = ARIMA(df, order=(p,0,q))
        results = model.fit()

        # Add order and scores to list
        order_aic_bic.append((p, q, results.aic, results.bic))

# Make DataFrame of model order and AIC/BIC scores
order_df = pd.DataFrame(order_aic_bic, columns=['p','q', 'aic', 'bic'])

Menelusuri AIC dan BIC

# Sort by AIC
print(order_df.sort_values('aic'))

   p  q      aic      bic
7  2  1  2804.54  2824.17
6  2  0  2805.41  2820.13
4  1  1  2806.37  2821.09
2  0  2  2806.69  2821.42
...

# Sort by BIC
print(order_df.sort_values('bic'))

   p  q      aic      bic
3  1  0  2810.25  2820.06
6  2  0  2805.41  2820.13
4  1  1  2806.37  2821.09
2  0  2  2806.69  2821.42
...

Orde model tidak stasioner

# Fit model
model = ARIMA(df, order=(2,0,1))
results = model.fit()

ValueError: Non-stationary starting autoregressive parameters
found with `enforce_stationarity` set to True.

Saat orde tertentu gagal

# Loop over AR order
for p in range(3):
    # Loop over MA order
    for q in range(3):


        # Fit model
        model = ARIMA(df, order=(p,0,q))
        results = model.fit()

        # Print the model order and the AIC/BIC values
        print(p, q, results.aic, results.bic)

Saat orde tertentu gagal

# Loop over AR order
for p in range(3):
    # Loop over MA order
    for q in range(3):

        try:
            # Fit model
            model = ARIMA(df, order=(p,0,q))
            results = model.fit()

            # Print the model order and the AIC/BIC values
            print(p, q, results.aic, results.bic)

        except:
            # Print AIC and BIC as None when fails
            print(p, q, None, None)

Ayo berlatih!

Model ARIMA di Python