Autoregressive Moving Average Models 175
AIC) when there are seven lags—denoted by AR(7). For the BIC, however,
the model is optimal is when n is one (i.e., AR(1)).
In practice it is important to check for the adequacy of the selected
model. If the model is adequate, the residual series of the model should
behave as white noise or should have no autocorrelation. For this purpose,
the Q-statistic can be employed. The Q-statistic tests whether the joint
table 9.2 Autoregressive Model: Akaike Information Criterion (AIC) and
Bayesian Information Criterion (BIC) for the Weekly Sample Returns of CRSP
Value-Weighted Index (yt) from January 1998 through October 2012
Lags AIC BIC
1 2.032 2.044*
2 2.030 2.048
3 2.030 2.054
4 2.031 2.061
5 2.033 2.069
6 2.029 2.071
7 2.025* 2.074
8 2.029 2.083
9 2.031 2.092
10 2.035 2.102
11 2.038 2.111
12 2.039 2.118
13 2.043 2.128
14 2.046 2.137
15 2.041 2.138
16 2.045 2.148
17 2.048 2.158
18 2.052 2.169
19 2.056 2.179
20 2.060 2.189
21 2.064 2.199
22 2.066 2.208
23 2.070 2.218
24 2.073 2.227
A model is selected based on the calculated minimum of either AIC or BIC.
- Denotes minimum values.