Mathematical and Statistical Methods for Actuarial Sciences and Finance

Checking financial markets via Benford’s law: the S&P 500 case 99

Ta b le 2 .Most rejected days and related calculated chi-square

Rank Day χ^2 Rank Day χ^2 Rank Day χ^2

1 02.27.2007 265.55 16 10.01.2002 100.19 31 06.22.2007 80.86

2 07.29.2002 201.43 17 08.04.1998 99.96 32 09.26.2002 78.90

3 01.02.2003 177.33 18 03.17.2003 98.81 33 03.10.2003 78.44

4 03.24.2003 152.84 19 06.07.2007 96.93 34 10.01.2003 77.21

5 01.24.2003 122.93 20 06.17.2002 93.67 35 03.21.2003 75.63

6 10.27.1997 122.89 21 12.27.2002 92.29 36 04.14.2000 75.22

7 03.13.2007 119.38 22 08.05.2002 90.05 37 06.05.2006 74.57

8 08.29.2007 118.19 23 03.30.2005 86.39 38 07.20.2007 74.27

9 07.24.2002 117.10 24 04.14.2003 85.39 39 08.22.2003 74.10

10 03.08.1996 115.01 25 02.24.2003 84.14 40 02.22.2005 73.40

11 08.06.2002 113.42 26 08.08.2002 84.05 41 08.05.2004 72.96

12 08.03.2007 111.14 27 03.02.2007 82.86 42 05.30.2003 72.24

13 08.28.2007 106.23 28 05.25.2004 81.47 43 07.10.2007 71.97

14 05.10.2007 101.04 29 06.13.2007 81.47 44 04.11.1997 71.44

15 09.03.2002 100.76 30 09.07.2007 81.29 45 10.28.2005 71.23

syad detpecca tsom dna detcejer tsom eht fo ruoivaheb tigid tnacifingis tsrif snruteR

000000.0

000050.0

000001.0

000051.0

000002.0

000052.0

000003.0

000053.0

1 2 3 4 5 6 7 8 9

tigid tnacifingis tsriF

Probability

drofneB

mrofinU

7002.72.20

5991.50.90

Fig. 3.Empirical probability distributions of the most rejected and mostaccepted days

Finally, we spend a few words on the day of the Twin Towers attack, which
has been chosen as the central one of the data set. We remark that 42.89% of all
the rejected days falls before this day and 57.11% of them after. Moreover, if we
limit our attention to the first 45 most rejected days, the difference between such
percentages considerably increases to 11.11% before and 88.89% after, respectively.