JEAN-PAUL PAQUIN, ANNICK LAMBERT AND ALAIN CHARBONNEAU 291Table 15.4Calculated Chi-square table uniform distribution ̃εt=ρε ̃t− 1 +u ̃t
kc|rho 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.00 4.7 6.1 2.9 6.8 6.8 16.2 11.1 6.9 3.5 5.7
0.05 2.8 6.5 5.0 7.0 9.5 6.2 6.9 5.4 4.1 9.3
0.10 9.4 7.9 4.0 14.3 5.2 12.8 6.419.0(∗) 5.2 2.2
0.15 8.3 7.7 3.9 7.0 9.1 8.0 9.7 15.6 7.3 2.9
0.20 9.7 10.4 4.1 14.3 6.4 12.1 9.0 6.3 7.0 17.4
0.25 17.4 13.5 5.8 19.3(∗) 11.1 5.8 12.9 11.6 6.5 13.1
0.30 8.8 16.6 16.9 12.1 4.0 9.8 12.3 10.7 10.7 10.9
0.35 15.9 15.5 15.2 20.0(∗) 10.9 20.2(∗)15.2 9.8 6.1 14.1
0.40 13.3(∗)14.8(∗)16.1(∗)21.7(∗)14.9(∗) 18.6(∗)11.913.7(∗) 19.5(∗)24.5(∗)
n= 20 NS=5,000 χ^27 (α= 0. 01 )= 18. 48 χ^27 (α= 0. 05 )= 14. 07
Table 15.5Calculated Chi-square table uniform distribution ̃εt=ρε ̃t− 1 +u ̃t
kc|rho 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.00 8.2 6.2 4.4 10.8 11.9 6.0 5.2 14.9 5.3 6.0
0.05 19.0(∗) 1.8 8.5 2.4 5.2 18.0 5.9 10.4 4.0 3.8
0.10 6.7 8.5 6.4 3.8 4.3 6.9 7.3 7.1 7.4 7.0
0.15 8.6 9.9 5.5 6.6 6.1 6.3 5.1 3.7 8.1 8.4
0.20 5.3 9.4 3.6 10.7 7.7 3.7 11.9 5.9 6.9 9.2
0.25 11.6 11.9 8.5 14.4 6.9 8.0 5.1 16.4 5.1 6.6
0.30 14.4 10.5 7.6 21.3(∗) 24.1(∗) 12.4 2.5 7.0 11.0 8.1
0.35 19.4(∗) 14.7 7.8 14.1 9.3 19.8(∗) 11.3 8.9 15.6 13.8
0.40 10.3 14.1 24.1(∗) 11.5 20.6(∗) 13.9 13.9 17.9 12.2 15.9
n= 40 NS=5,000 χ^27 (α= 0. 01 )= 18. 48 χ^27 (α= 0. 05 )= 14. 07
of significance is used. However, we see that that increasing the number
of years increases the effectiveness of the CLT. The following three tables
(Table 15.6, 15.7 and 15.8) provide us the results for double exponential dis-
tributed cash flows over three different time periods: 10, 20 and 40 years
for a first-order autoregressive process. These results make it quite clear
that highly correlated cash flows do not invalidate the effectiveness CLT.
Increasing the number of periods, however, improves the effectiveness of
the CLT for values of the discount ratekclower than 20%. However, over this
20% threshold value, the CLT does not allow convergence of the NPV prob-
ability distribution towards a Gaussian distribution. Over the 25% discount