#1

library(fBasics)
## Loading required package: timeDate
## Loading required package: timeSeries
data=read.table("d-axp3dx-0111.txt",header=T) 
head(data)
##       date       axp        vw        ew        sp
## 1 20010904  0.000824 -0.001658 -0.005708 -0.000565
## 2 20010905  0.007682 -0.003242 -0.008926 -0.001059
## 3 20010906 -0.039477 -0.020733 -0.014187 -0.022390
## 4 20010907 -0.019274 -0.017769 -0.011476 -0.018637
## 5 20010910  0.011850  0.003513 -0.007368  0.006226
## 6 20010917 -0.135961 -0.050714 -0.042398 -0.049216
tail(data)
##          date       axp        vw        ew        sp
## 2530 20110923 -0.003860  0.005754  0.007256  0.006082
## 2531 20110926  0.023897  0.021588  0.009890  0.023336
## 2532 20110927 -0.010093  0.012842  0.015739  0.010688
## 2533 20110928 -0.012957 -0.023688 -0.025358 -0.020691
## 2534 20110929  0.005380  0.008222  0.006639  0.008114
## 2535 20110930 -0.038955 -0.024625 -0.018836 -0.024974
axp0=data[,2]
basicStats(axp0)
##                    axp0
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.175949
## Maximum        0.206485
## 1. Quartile   -0.009672
## 3. Quartile    0.010540
## Mean           0.000534
## Median         0.000000
## Sum            1.353560
## SE Mean        0.000524
## LCL Mean      -0.000493
## UCL Mean       0.001561
## Variance       0.000695
## Stdev          0.026368
## Skewness       0.459773
## Kurtosis       9.592053
vw0=data[,3]
basicStats(vw0)
##                     vw0
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.089762
## Maximum        0.114889
## 1. Quartile   -0.005473
## 3. Quartile    0.006212
## Mean           0.000224
## Median         0.000848
## Sum            0.567996
## SE Mean        0.000271
## LCL Mean      -0.000308
## UCL Mean       0.000756
## Variance       0.000186
## Stdev          0.013652
## Skewness      -0.098318
## Kurtosis       7.982134
ew0=data[,4]
basicStats(ew0)
##                     ew0
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.078240
## Maximum        0.107422
## 1. Quartile   -0.004630
## 3. Quartile    0.006402
## Mean           0.000626
## Median         0.001429
## Sum            1.586462
## SE Mean        0.000240
## LCL Mean       0.000155
## UCL Mean       0.001096
## Variance       0.000146
## Stdev          0.012080
## Skewness      -0.247410
## Kurtosis       8.108428
sp0=data[,5]
basicStats(sp0)
##                     sp0
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.090350
## Maximum        0.115800
## 1. Quartile   -0.005798
## 3. Quartile    0.006117
## Mean           0.000094
## Median         0.000700
## Sum            0.238869
## SE Mean        0.000274
## LCL Mean      -0.000442
## UCL Mean       0.000631
## Variance       0.000190
## Stdev          0.013779
## Skewness       0.008152
## Kurtosis       8.532667

#another way

#mean(axp0)
#stdev(axp0)
#skewness(axp0)
#kurtosis(axp0)
#min(axp0)
#max(axp0)
axp=log(data$axp+1)
basicStats(axp)
##                     axp
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.193523
## Maximum        0.187711
## 1. Quartile   -0.009719
## 3. Quartile    0.010484
## Mean           0.000188
## Median         0.000000
## Sum            0.476584
## SE Mean        0.000522
## LCL Mean      -0.000836
## UCL Mean       0.001212
## Variance       0.000691
## Stdev          0.026294
## Skewness       0.020992
## Kurtosis       9.020499
vw=log(data$vw+1)
basicStats(vw)
##                      vw
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.094049
## Maximum        0.108755
## 1. Quartile   -0.005489
## 3. Quartile    0.006193
## Mean           0.000131
## Median         0.000848
## Sum            0.331452
## SE Mean        0.000272
## LCL Mean      -0.000402
## UCL Mean       0.000663
## Variance       0.000187
## Stdev          0.013670
## Skewness      -0.300352
## Kurtosis       7.880082
ew=log(data$ew+1)
basicStats(ew)
##                      ew
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.081470
## Maximum        0.102035
## 1. Quartile   -0.004641
## 3. Quartile    0.006382
## Mean           0.000553
## Median         0.001428
## Sum            1.400780
## SE Mean        0.000240
## LCL Mean       0.000081
## UCL Mean       0.001024
## Variance       0.000146
## Stdev          0.012100
## Skewness      -0.427315
## Kurtosis       8.017712
sp=log(data$sp+1)
basicStats(sp)
##                      sp
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.094695
## Maximum        0.109572
## 1. Quartile   -0.005815
## 3. Quartile    0.006098
## Mean          -0.000001
## Median         0.000700
## Sum           -0.001898
## SE Mean        0.000274
## LCL Mean      -0.000538
## UCL Mean       0.000536
## Variance       0.000190
## Stdev          0.013790
## Skewness      -0.206357
## Kurtosis       8.322826
t.test(axp)
## 
##  One Sample t-test
## 
## data:  axp
## t = 0.35999, df = 2534, p-value = 0.7189
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -0.0008360686  0.0012120714
## sample estimates:
##    mean of x 
## 0.0001880014

#5

library(fBasics)
ukus=read.table("d-fx-ukus-0711.txt",header=T) 
head(ukus)
##   year mon day   rate
## 1 2007   1   2 1.9736
## 2 2007   1   3 1.9498
## 3 2007   1   4 1.9443
## 4 2007   1   5 1.9305
## 5 2007   1   8 1.9385
## 6 2007   1   9 1.9400
tail(ukus)
##      year mon day   rate
## 1233 2011  11  22 1.5646
## 1234 2011  11  23 1.5511
## 1235 2011  11  25 1.5467
## 1236 2011  11  28 1.5538
## 1237 2011  11  29 1.5625
## 1238 2011  11  30 1.5705
UKUS1=ukus[,4]
head(UKUS1)
## [1] 1.9736 1.9498 1.9443 1.9305 1.9385 1.9400
tail(UKUS1)
## [1] 1.5646 1.5511 1.5467 1.5538 1.5625 1.5705
LOGUKUS=log(UKUS1+1)
basicStats(LOGUKUS)
##                 LOGUKUS
## nobs        1238.000000
## NAs            0.000000
## Minimum        0.861116
## Maximum        1.134751
## 1. Quartile    0.941100
## 3. Quartile    1.087484
## Mean           0.997025
## Median         0.966965
## Sum         1234.317034
## SE Mean        0.002130
## LCL Mean       0.992846
## UCL Mean       1.001204
## Variance       0.005618
## Stdev          0.074955
## Skewness       0.364941
## Kurtosis      -1.391234
jpus=read.table("d-fx-usjp-0711.txt",header=T) 
head(jpus)
##   year mon day   rate
## 1 2007   1   2 118.83
## 2 2007   1   3 119.58
## 3 2007   1   4 119.28
## 4 2007   1   5 118.77
## 5 2007   1   8 118.49
## 6 2007   1   9 119.45
tail(jpus)
##      year mon day  rate
## 1233 2011  11  22 77.07
## 1234 2011  11  23 77.41
## 1235 2011  11  25 77.66
## 1236 2011  11  28 78.05
## 1237 2011  11  29 77.86
## 1238 2011  11  30 77.58
JPUS1=jpus[,4]
head(JPUS1)
## [1] 118.83 119.58 119.28 118.77 118.49 119.45
tail(JPUS1)
## [1] 77.07 77.41 77.66 78.05 77.86 77.58
LOGJPUS=log(JPUS1+1)
basicStats(LOGJPUS)
##                 LOGJPUS
## nobs        1238.000000
## NAs            0.000000
## Minimum        4.340162
## Maximum        4.829033
## 1. Quartile    4.454144
## 3. Quartile    4.687648
## Mean           4.573775
## Median         4.552191
## Sum         5662.333286
## SE Mean        0.003920
## LCL Mean       4.566084
## UCL Mean       4.581466
## Variance       0.019024
## Stdev          0.137929
## Skewness       0.195236
## Kurtosis      -1.096912
head(LOGJPUS)
## [1] 4.786074 4.792313 4.789822 4.785573 4.783233 4.791235
plot(density(LOGJPUS))

t.test(LOGJPUS)
## 
##  One Sample t-test
## 
## data:  LOGJPUS
## t = 1166.8, df = 1237, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  4.566084 4.581466
## sample estimates:
## mean of x 
##  4.573775