174 The Basics of financial economeTrics
table 9.1 Partial Autocorrelations (PAC) for the Weekly Sample Returns of CRSP
Value-Weighted Index from January 1998 through October 2012
Lags PAC Q-Statistic ρ-Value
1 −0.069 3.667 0.055
2 0.048 5.851 0.054
3 −0.046 7.971 0.047
4 −0.051 9.324 0.053
5 0.046 11.033 0.051
6 0.076 14.520 0.024
7 −0.086 20.094 0.005
8 0.009 20.566 0.008
9 −0.034 23.042 0.006
10 0.010 23.399 0.009
11 0.022 23.997 0.013
12 −0.046 25.739 0.012
13 −0.002 25.739 0.018
14 0.015 25.818 0.027
15 0.095 31.608 0.007
16 0.008 31.810 0.011
17 0.010 31.931 0.015
18 −0.004 32.319 0.020
19 0.005 32.341 0.029
20 0.018 32.647 0.037
21 0.012 33.218 0.044
22 0.019 33.259 0.058
23 0.003 33.260 0.077
24 −0.033 34.742 0.072
Bayesian (or Schwarz) information criterion (BIC). By selecting an autore-
gressive model, we mean determining number of lags. The AIC and BIC are
described in Appendix E, where we discuss model selection. Both informa-
tion criteria involve finding the minimum value of a measure.
Table 9.2 shows the results when the calculations for the AIC and BIC
are applied to the CRSP value-weighted weekly index returns. The second
and third columns show the AIC and BIC, respectively, at different lags. The
AIC shows that the model is optimal (i.e., the n that provides the minimum