Your data is not suitable. Raw (points) index changes now cannot be compared with those 20 years ago. You must look at relative changes (returns). I sourced my data from
Yahoo! I used only the closing prices.
I constructed monthly relative returns by calculating the differences between the logs of monthly closing prices. A cursory examination of the data indicated that Oct 87 was an outlier, with a value of -0.55. After excluding this point the returns data were adequately normal. See attached aoxm.csv.
aoxm.csv
I then constructed return vectors for each month and compared them to the whole sample using the standard R function t.test. The (rather tedious) results are shown below.
In summary, the only month significantly different from the whole sample was December, which was more profitable than average at the 5% confidence level. However, we've mined through 12 different months to find this apparent anomaly, so the real significance level is more like 41%, ie completely insignificant.
Cheers,
Chemist
> t.test(ret.dec,Return)
Welch Two Sample t-test
data: ret.dec and Return
t = 2.133, df = 24.952, p-value = 0.04294
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.0005114338 0.0292618736
sample estimates:
mean of x mean of y
0.023929489 0.009042835
> t.test(ret.nov,Return)
Welch Two Sample t-test
data: ret.nov and Return
t = -0.8923, df = 22.159, p-value = 0.3818
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.02718518 0.01082427
sample estimates:
mean of x mean of y
0.000862381 0.009042835
> t.test(ret.oct,Return)
Welch Two Sample t-test
data: ret.oct and Return
t = -0.202, df = 19.569, p-value = 0.842
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.02826812 0.02328408
sample estimates:
mean of x mean of y
0.006550815 0.009042835
> t.test(ret.sep,Return)
Welch Two Sample t-test
data: ret.sep and Return
t = -1.2074, df = 21.934, p-value = 0.2401
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.031100232 0.008215084
sample estimates:
mean of x mean of y
-0.002399739 0.009042835
> t.test(ret.aug,Return)
Welch Two Sample t-test
data: ret.aug and Return
t = -0.4159, df = 21.573, p-value = 0.6816
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.02506644 0.01669987
sample estimates:
mean of x mean of y
0.004859554 0.009042835
> t.test(ret.jul,Return)
Welch Two Sample t-test
data: ret.jul and Return
t = 0.9792, df = 21.336, p-value = 0.3385
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.01154739 0.03213362
sample estimates:
mean of x mean of y
0.019335951 0.009042835
> t.test(ret.jun,Return)
Welch Two Sample t-test
data: ret.jun and Return
t = -1.1463, df = 24.237, p-value = 0.2629
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.023620609 0.006745979
sample estimates:
mean of x mean of y
0.0006055197 0.0090428351
> t.test(ret.may,Return)
Welch Two Sample t-test
data: ret.may and Return
t = 0.0518, df = 24.565, p-value = 0.9591
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.01442015 0.01516286
sample estimates:
mean of x mean of y
0.009414191 0.009042835
> t.test(ret.apr,Return)
Welch Two Sample t-test
data: ret.apr and Return
t = 1.6191, df = 24.83, p-value = 0.1181
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.003433481 0.028638043
sample estimates:
mean of x mean of y
0.021645116 0.009042835
> t.test(ret.mar,Return)
Welch Two Sample t-test
data: ret.mar and Return
t = 0.0877, df = 22.852, p-value = 0.9309
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.01946730 0.02119027
sample estimates:
mean of x mean of y
0.009904317 0.009042835
> t.test(ret.feb,Return)
Welch Two Sample t-test
data: ret.feb and Return
t = -0.8648, df = 23.714, p-value = 0.3958
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.02557027 0.01047567
sample estimates:
mean of x mean of y
0.001495534 0.009042835
> t.test(ret.jan,Return)
Welch Two Sample t-test
data: ret.jan and Return
t = 0.3597, df = 25.203, p-value = 0.7221
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.01281183 0.01823589
sample estimates:
mean of x mean of y
0.011754867 0.009042835