Hi,
I am trying to find m breakpoints of a linear regression model. I
used the segmented package. It works fine for small number of
predicators and breakpoints.(3 r.v. 3 points). However, my model has
14 variables it even would not work even for just one breakpoints!.
The error message is always estimated breakpoints are out of range.
Since my problem is time related problem. So I hink the
breakpoints should be all at the same time for all variables. Can I
achieve this requiement with this package? How?
Thanks
Best Regards
Peter
Here is the code I used and the data is also attached.
reduceddata <- read.table("reduceddata.txt")
detach()
attach(reduceddata)
library(segmented)
dat=data.frame(y=V2,x1=V3,x2=V4,x3=V5,
x4=V6,x5=V7,x6=V8,x7=V9,x8=V10,x9=V11,
x10=V12,x11=V13,x12=V14,x13=V15,x14=V16,x15=V16)
m=2
psi <- array(0, c(15,m))
for (i in 1:m)
{
psi[1,i]=range(V3)[1]+(i)/(m+1)*(range(V3)[2]-range(V3)[1])
psi[2,i]=range(V4)[1]+(i)/(m+1)*(range(V4)[2]-range(V4)[1])
psi[3,i]=range(V5)[1]+(i)/(m+1)*(range(V5)[2]-range(V5)[1])
psi[4,i]=range(V6)[1]+(i)/(m+1)*(range(V6)[2]-range(V6)[1])
psi[5,i]=range(V7)[1]+(i)/(m+1)*(range(V7)[2]-range(V7)[1])
psi[6,i]=range(V8)[1]+(i)/(m+1)*(range(V8)[2]-range(V8)[1])
psi[7,i]=range(V9)[1]+(i)/(m+1)*(range(V9)[2]-range(V9)[1])
psi[8,i]=range(V10)[1]+(i)/(m+1)*(range(V10)[2]-range(V10)[1])
psi[9,i]=range(V11)[1]+(i)/(m+1)*(range(V11)[2]-range(V11)[1])
psi[10,i]=range(V12)[1]+(i)/(m+1)*(range(V12)[2]-range(V12)[1])
psi[11,i]=range(V13)[1]+(i)/(m+1)*(range(V13)[2]-range(V13)[1])
psi[12,i]=range(V14)[1]+(i)/(m+1)*(range(V14)[2]-range(V14)[1])
psi[13,i]=range(V15)[1]+(i)/(m+1)*(range(V15)[2]-range(V15)[1])
psi[14,i]=range(V16)[1]+(i)/(m+1)*(range(V16)[2]-range(V16)[1])
psi[15,i]=range(V17)[1]+(i)/(m+1)*(range(V17)[2]-range(V17)[1])
}
out.lm=glm(y~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13+x14
,data=dat)
o=segmented(out.lm,seg.Z=~x1+x2+x3+x4+x5+x6+ x7+x9+x8+x9+
x10+x11+x12+x13+x14,
psi=list(x1=0,x2=psi[2,],x3=psi[3,],
x4=psi[4],x7=psi[7],x9=psi[9],
x5=psi[5], x6=psi[6],x8=psi[8],
x10=psi[10],x11=psi[11],x12=psi[12,],
x13=psi[13],x14=psi[14,]),control=seg.control(display=TRUE))
Jan-91 7.858 6.64 7.38 7.7 6.3 6.34 7.7758 7.48 6.969
7.125 7.313 8.065 7.76 7.17 9.52 9.54
Feb-91 7.848 6.27 7.08 7.47 5.95 5.93 7.6225 7.33 7.063
6.891 7.063 7.9233 7.68 6.51 9.05 9.49
Mar-91 7.654 6.4 7.35 7.77 5.91 5.91 7.46 7.3 6.328
6.531 7 7.765 7.58 6.5 9 9.26
Apr-91 7.501 6.24 7.23 7.7 5.67 5.73 7.28 7.16 6.078
6.313 6.75 7.5683 7.47 6.16 9 9.24
May-91 7.329 6.13 7.12 7.7 5.51 5.65 7.0975 7.07 5.953
6.188 6.625 7.365 7.31 6.03 8.5 9.23
Jun-91 7.155 6.36 7.39 7.94 5.6 5.76 6.9525 6.94 6.078
6.563 7 7.185 7.11 6.26 8.5 9.12
Jul-91 6.998 6.31 7.38 7.91 5.58 5.71 6.8167 6.85 5.953
6.313 6.625 7.0083 6.94 6.25 8.5 9.12
Aug-91 6.845 5.78 6.8 7.43 5.39 5.47 6.65 6.76 5.75
5.875 6 6.815 6.76 5.79 8.5 9.1
Sep-91 6.714 5.57 6.5 7.14 5.25 5.29 6.4675 6.61 5.5
5.688 5.813 6.5992 6.62 5.6 8.2 8.93
Oct-91 6.566 5.33 6.23 6.87 5.03 5.08 6.2825 6.53 5.25
5.359 5.5 6.3717 6.54 5.32 8 8.78
Nov-91 6.414 4.89 5.9 6.62 4.6 4.66 6.0808 6.4 4.813
4.938 5.063 6.1142 6.42 4.92 7.58 8.43
Dec-91 6.245 4.38 5.39 6.19 4.12 4.16 5.8583 6.25 4.328
4.25 4.375 5.835 6.29 4.41 7.21 8.25
Jan-92 6.002 4.15 5.4 6.24 3.84 3.88 5.6508 6.01 4.141
4.25 4.625 5.575 6.09 4.07 6.5 8.02
Feb-92 5.8 4.29 5.72 6.58 3.84 3.94 5.4858 5.78 4.25
4.375 4.75 5.3708 5.85 4.13 6.5 8.15
Mar-92 5.611 4.63 6.18 6.95 4.05 4.19 5.3383 5.63 4.25
4.547 5.063 5.1875 5.66 4.42 6.5 8.14
Apr-92 5.427 4.3 5.93 6.78 3.81 3.93 5.1767 5.48 3.969
4.266 4.703 5.0158 5.5 4.13 6.5 8.26
May-92 5.29 4.19 5.81 6.69 3.66 3.78 5.015 5.38 4.016
4.25 4.75 4.8417 5.35 3.96 6.5 8.2
Jun-92 5.258 4.17 5.6 6.48 3.7 3.81 4.8325 5.25 3.922
4.125 4.375 4.6575 5.17 3.97 6.5 8.04
Jul-92 5.069 3.6 4.91 5.84 3.28 3.36 4.6067 5.13 3.391
3.625 3.75 4.44 5.07 3.5 6.02 7.78
Aug-92 4.874 3.47 4.72 5.6 3.14 3.23 4.4142 4.98 3.5
3.625 3.75 4.245 4.98 3.4 6 7.58
Sep-92 4.805 3.18 4.42 5.38 2.97 3.01 4.215 4.84 3.188
3.313 3.375 4.05 4.87 3.17 6 7.44
Oct-92 4.597 3.3 4.64 5.6 2.84 2.98 4.0458 4.74 3.281
3.641 3.938 3.8775 4.76 3.27 6 7.4
Nov-92 4.508 3.68 5.14 6.04 3.14 3.35 3.945 4.59 3.172
3.891 4.141 3.7642 4.6 3.6 6 7.49
Dec-92 4.432 3.71 5.21 6.08 3.25 3.39 3.8892 4.51 3.344
3.641 4.078 3.6817 4.5 3.55 6 7.53
Jan-93 4.36 3.5 4.93 5.83 3.06 3.17 3.835 4.44 3.203
3.438 3.75 3.61 4.4 3.33 6 7.49
Feb-93 4.333 3.39 4.58 5.43 2.95 3.08 3.76 4.34 3.203
3.328 3.578 3.5308 4.34 3.22 6 7.28
Mar-93 4.245 3.33 4.4 5.19 2.97 3.08 3.6517 4.31 3.203
3.375 3.625 3.4358 4.29 3.2 6 7.17
Apr-93 4.171 3.24 4.3 5.13 2.89 3 3.5633 4.24 3.141
3.313 3.563 3.36 4.25 3.16 6 7.06
May-93 4.103 3.36 4.4 5.2 2.96 3.07 3.4942 4.18 3.203
3.438 3.75 3.3 4.24 3.2 6 7.08
Jun-93 4.05 3.54 4.53 5.22 3.1 3.23 3.4417 4.1 3.203
3.563 3.781 3.2458 4.2 3.36 6 7.02
Jul-93 3.998 3.47 4.43 5.09 3.05 3.15 3.4308 4.09 3.188
3.563 3.813 3.2283 4.16 3.34 6 6.95
Aug-93 3.958 3.44 4.36 5.03 3.05 3.17 3.4283 4.04 3.203
3.438 3.563 3.2142 4.1 3.32 6 6.87
Sep-93 3.881 3.36 4.17 4.73 2.96 3.06 3.4433 3.96 3.188
3.375 3.531 3.2133 4.07 3.24 6 6.75
Oct-93 3.823 3.39 4.18 4.71 3.04 3.13 3.4508 3.95 3.188
3.5 3.688 3.2117 4.02 3.25 6 6.59
Nov-93 3.822 3.58 4.5 5.06 3.12 3.27 3.4425 3.9 3.578
3.516 3.781 3.1925 3.98 3.39 6 6.6
Dec-93 3.879 3.61 4.54 5.15 3.08 3.25 3.4342 3.9 3.297
3.5 3.813 3.1742 3.96 3.35 6 6.65
Jan-94 3.71 3.54 4.48 5.09 3.02 3.19 3.4375 3.87 3.141
3.391 3.703 3.1708 3.92 3.29 6 6.73
Feb-94 3.687 3.87 4.83 5.4 3.21 3.38 3.4775 3.76 3.594
4 4.344 3.1967 3.89 3.62 6 6.68
Mar-94 3.629 4.32 5.4 5.94 3.52 3.79 3.56 3.81 3.703
4.25 4.75 3.2517 3.84 4.03 6.06 6.84
Apr-94 3.672 4.82 5.99 6.52 3.74 4.13 3.6917 3.81 3.938
4.625 5.25 3.3283 3.79 4.38 6.45 7.04
May-94 3.726 5.31 6.34 6.78 4.19 4.64 3.8542 3.85 4.375
5 5.516 3.4458 3.76 4.9 6.99 7.33
Jun-94 3.804 5.27 6.27 6.7 4.18 4.58 3.9983 3.86 4.563
5.25 5.828 3.555 3.77 4.85 7.25 7.36
Jul-94 3.86 5.48 6.48 6.91 4.39 4.81 4.1658 3.91 4.516
5.328 5.828 3.6858 3.82 5.15 7.25 7.49
Aug-94 3.945 5.56 6.5 6.88 4.5 4.91 4.3425 3.97 4.875
5.328 5.813 3.825 3.88 5.17 7.51 7.59
Sep-94 4.039 5.76 6.69 7.08 4.64 5.02 4.5425 4.01 5
5.688 6.188 3.9842 3.94 5.4 7.75 7.57
Oct-94 4.187 6.11 7.04 7.4 4.96 5.39 4.7692 4.11 5.078
6 6.563 4.1733 4.05 5.79 7.75 7.6
Nov-94 4.367 6.54 7.44 7.72 5.25 5.69 5.0158 4.17 6
6.438 7.078 4.3767 4.17 6.11 8.15 7.56
Dec-94 4.589 7.14 7.71 7.78 5.64 6.21 5.31 4.32 5.984
7 7.75 4.6292 4.34 6.78 8.5 7.75
Jan-95 4.747 7.05 7.66 7.76 5.81 6.31 5.6025 4.44 6.078
6.688 7.25 4.8867 4.57 6.71 8.5 7.77
Feb-95 4.925 6.7 7.25 7.37 5.8 6.1 5.8383 4.49 6.125
6.438 6.75 5.1142 4.82 6.44 9 8
Mar-95 5.007 6.43 6.89 7.05 5.73 5.91 6.0142 4.69 6.141
6.438 6.75 5.3125 4.99 6.34 9 8.09
Apr-95 5.064 6.27 6.68 6.86 5.67 5.8 6.135 4.79 6.079
6.313 6.563 5.4875 5.14 6.27 9 7.99
May-95 5.141 6 6.27 6.41 5.7 5.73 6.1925 4.91 6.063
6.063 6.055 5.6133 5.27 6.07 9 7.87
Jun-95 5.179 5.64 5.8 5.93 5.5 5.46 6.2233 4.93 6.079
5.875 5.766 5.7283 5.33 5.8 9 7.62
Jul-95 5.144 5.59 5.89 6.01 5.47 5.41 6.2325 4.98 5.875
5.875 5.875 5.815 5.32 5.73 8.8 7.56
Aug-95 5.133 5.75 6.1 6.24 5.41 5.4 6.2483 5.01 5.907
5.938 5.954 5.895 5.3 5.79 8.75 7.6
Sep-95 5.111 5.62 5.89 6 5.26 5.28 6.2367 4.98 5.922
5.985 5.969 5.9533 5.25 5.73 8.75 7.61
Oct-95 5.116 5.59 5.77 5.86 5.3 5.34 6.1933 5.03 5.844
5.954 5.883 5.9767 5.22 5.76 8.75 7.53
Nov-95 5.119 5.43 5.57 5.69 5.35 5.29 6.1008 4.92 6.032
5.735 5.672 5.9725 5.18 5.64 8.75 7.48
Dec-95 5.059 5.31 5.39 5.51 5.16 5.15 5.9483 5.01 5.735
5.563 5.454 5.9167 5.16 5.49 8.65 7.22
Jan-96 5.033 5.09 5.2 5.36 5.02 4.97 5.785 5.01 5.469
5.336 5.196 5.8458 5.15 5.28 8.5 7.18
Feb-96 4.975 4.94 5.14 5.38 4.87 4.79 5.6383 4.9 5.352
5.289 5.274 5.7617 5.15 5.03 8.25 7.13
Mar-96 4.874 5.34 5.79 5.97 4.96 4.96 5.5475 4.92 5.454
5.516 5.704 5.69 5.08 5.3 8.25 7.29
Apr-96 4.841 5.54 6.11 6.3 4.99 5.08 5.4867 4.87 5.454
5.422 5.829 5.6275 5.01 5.42 8.25 7.55
May-96 4.823 5.64 6.27 6.48 5.02 5.12 5.4567 4.87 5.446
5.641 5.977 5.5725 4.97 5.47 8.25 7.72
Jun-96 4.809 5.81 6.49 6.69 5.11 5.26 5.4708 4.82 5.516
5.844 6.172 5.5358 4.93 5.64 8.25 7.77
Jul-96 4.819 5.85 6.45 6.64 5.17 5.32 5.4925 4.87 5.493
5.922 6.243 5.5158 4.92 5.75 8.25 7.87
Aug-96 4.839 5.67 6.21 6.39 5.09 5.17 5.4858 4.87 5.43
5.743 6.055 5.485 4.93 5.57 8.25 7.76
Sep-96 4.834 5.83 6.41 6.6 5.15 5.29 5.5033 4.84 5.438
5.75 5.985 5.4667 4.92 5.71 8.25 7.78
Oct-96 4.839 5.55 6.08 6.27 5.01 5.12 5.5 4.89 5.375
5.579 5.719 5.435 4.95 5.51 8.25 7.68
Nov-96 4.835 5.42 5.82 5.97 5.03 5.07 5.4992 4.76 5.391
5.547 5.696 5.405 4.96 5.43 8.25 7.55
Dec-96 4.842 5.47 5.91 6.07 4.87 5.02 5.5125 4.87 5.547
5.618 5.789 5.39 4.96 5.47 8.25 7.45
Jan-97 4.821 5.61 6.16 6.33 5.05 5.11 5.5558 4.92 5.461
5.711 5.954 5.3933 4.98 5.54 8.25 7.55
Feb-97 4.759 5.53 6.03 6.2 5 5.05 5.605 4.79 5.469
5.68 5.954 5.4117 5.01 5.47 8.25 7.53
Mar-97 4.78 5.8 6.38 6.54 5.14 5.24 5.6433 4.9 5.719
5.961 6.282 5.4317 4.99 5.69 8.3 7.61
Apr-97 4.822 5.99 6.61 6.76 5.17 5.35 5.6808 4.89 5.704
6.079 6.454 5.4608 4.98 5.9 8.5 7.73
May-97 4.864 5.87 6.42 6.57 5.13 5.35 5.7 4.94 5.711
6.008 6.289 5.4892 5 5.87 8.5 7.75
Jun-97 4.853 5.69 6.24 6.38 4.92 5.14 5.69 4.9 5.719
5.938 6.141 5.5058 5.07 5.78 8.5 7.67
Jul-97 4.887 5.54 6 6.12 5.07 5.12 5.6642 4.96 5.641
5.829 5.977 5.5117 5.1 5.7 8.5 7.52
Aug-97 4.904 5.56 6.06 6.16 5.13 5.17 5.655 4.97 5.68
5.86 6.079 5.5283 5.1 5.71 8.5 7.47
Sep-97 4.941 5.52 5.98 6.11 4.97 5.11 5.6292 4.92 5.672
5.852 6.008 5.5358 5.09 5.71 8.5 7.46
Oct-97 4.957 5.46 5.84 5.93 4.95 5.09 5.6217 4.98 5.633
5.805 5.922 5.5558 5.08 5.72 8.5 7.37
Nov-97 4.949 5.46 5.76 5.8 5.15 5.17 5.625 4.93 5.766
6.039 6.11 5.5858 5.07 5.78 8.5 7.34
Dec-97 4.963 5.53 5.74 5.77 5.16 5.24 5.63 4.97 5.852
6.008 6.079 5.6158 5.04 5.82 8.5 7.26
Jan-98 4.987 5.24 5.38 5.42 5.09 5.07 5.5992 4.96 5.704
5.75 5.774 5.625 5.04 5.56 8.5 7.12
Feb-98 4.968 5.31 5.43 5.49 5.11 5.07 5.5808 4.85 5.789
5.782 5.836 5.6392 5.04 5.55 8.5 7.06
Mar-98 4.917 5.39 5.57 5.61 5.03 5.04 5.5467 4.92 5.719
5.797 5.914 5.6433 5.02 5.61 8.5 7.07
Apr-98 4.903 5.38 5.58 5.61 5 5.08 5.4958 4.91 5.688
5.868 6.024 5.6325 5.02 5.63 8.5 7.09
May-98 4.881 5.44 5.61 5.63 5.03 5.15 5.46 4.91 5.696
5.805 5.93 5.6233 5.03 5.67 8.5 7.08
Jun-98 4.881 5.41 5.52 5.52 4.99 5.12 5.4367 4.87 5.748
5.871 5.94 5.6183 5.01 5.65 8.5 7.06
Jul-98 4.911 5.36 5.47 5.46 4.96 5.03 5.4217 4.9 5.696
5.822 5.897 5.6175 4.99 5.65 8.5 7.01
Aug-98 4.899 5.21 5.24 5.27 4.94 4.97 5.3925 4.9 5.727
5.692 5.648 5.6158 4.95 5.61 8.5 6.98
Sep-98 4.882 4.71 4.62 4.62 4.74 4.75 5.325 4.85 5.4
5.359 5.186 5.6 4.92 5.33 8.49 6.88
Oct-98 4.762 4.12 4.18 4.18 4.08 4.15 5.2133 4.84 5.277
5.131 4.865 5.5633 4.91 4.99 8.12 6.74
Nov-98 4.691 4.53 4.57 4.54 4.44 4.43 5.1358 4.77 5.048
5.28 5.244 5.5217 4.85 5.07 7.89 6.77
Dec-98 4.655 4.52 4.48 4.45 4.42 4.43 5.0517 4.74 5.118
5.172 5.213 5.4667 4.79 5.01 7.75 6.76
Jan-99 4.608 4.51 4.61 4.6 4.34 4.36 4.9908 4.63 4.946
5.036 5.108 5.4125 4.67 4.9 7.75 6.77
Feb-99 4.562 4.7 4.9 4.91 4.45 4.43 4.94 4.57 5.003
5.168 5.405 5.3592 4.63 4.95 7.75 6.82
Mar-99 4.519 4.78 5.11 5.14 4.48 4.52 4.8892 4.54 4.94
5.083 5.307 5.3033 4.6 4.98 7.75 6.91
Apr-99 4.49 4.69 5.03 5.08 4.28 4.36 4.8317 4.53 4.902
5.075 5.303 5.245 4.58 4.94 7.75 6.94
May-99 4.48 4.85 5.33 5.44 4.51 4.55 4.7825 4.48 4.93
5.193 5.503 5.1892 4.55 5.03 7.75 6.96
Jun-99 4.504 5.1 5.7 5.81 4.59 4.81 4.7567 4.48 5.223
5.633 5.803 5.15 4.52 5.31 7.75 7.14
Jul-99 4.5 5.03 5.62 5.68 4.6 4.62 4.7292 4.47 5.178
5.68 5.836 5.1208 4.5 5.58 8 7.35
Aug-99 4.562 5.2 5.77 5.84 4.76 4.88 4.7283 4.46 5.37
5.913 6.023 5.1067 4.47 5.83 8.06 7.48
Sep-99 4.608 5.25 5.75 5.8 4.73 4.91 4.7733 4.49 5.396
5.974 6.053 5.1142 4.48 5.89 8.25 7.57
Oct-99 4.666 5.43 5.94 6.03 4.88 4.98 4.8825 4.52 5.41
6.144 6.313 5.1908 4.5 6.04 8.25 7.56
Nov-99 4.773 5.55 5.92 5.97 5.07 5.17 4.9675 4.57 6.503
6.063 6.261 5.2542 4.56 5.97 8.37 7.56
Dec-99 4.852 5.84 6.14 6.19 5.23 5.43 5.0775 4.6 5.832
6.136 6.508 5.33 4.64 6.07 8.5 7.55
Jan-00 4.901 6.12 6.49 6.58 5.34 5.52 5.2117 4.63 5.856
6.238 6.659 5.4183 4.69 6.15 8.5 7.79
Feb-00 4.967 6.22 6.65 6.68 5.57 5.75 5.3383 4.67 5.907
6.328 6.76 5.5108 4.75 6.26 8.73 7.95
Mar-00 5.002 6.22 6.53 6.5 5.72 5.85 5.4583 4.68 6.133
6.53 6.97 5.6133 4.78 6.36 8.83 8.01
Apr-00 5.078 6.15 6.36 6.26 5.67 5.82 5.58 4.73 6.197
6.614 6.964 5.73 4.84 6.5 9 8
May-00 5.196 6.33 6.77 6.69 5.92 6.12 5.7033 4.83 6.641
7.064 7.453 5.8792 4.96 6.94 9.24 8.08
Jun-00 5.357 6.17 6.43 6.3 5.74 6.02 5.7925 4.88 6.649
7.014 7.214 6.0125 5.03 6.91 9.5 8.17
Jul-00 5.456 6.08 6.28 6.18 5.93 5.99 5.88 4.96 6.625
6.887 7.047 6.1317 5.11 6.86 9.5 8.09
Aug-00 5.509 6.18 6.17 6.06 6.1 6.09 5.9617 5.05 6.628
6.831 6.978 6.2317 5.25 6.76 9.5 8
Sep-00 5.548 6.13 6.02 5.93 6.03 6 6.035 5.09 6.62
6.761 6.811 6.3233 5.28 6.68 9.5 7.89
Oct-00 5.589 6.01 5.85 5.78 6.1 6.04 6.0833 5.13 6.621
6.721 6.725 6.3683 5.37 6.65 9.5 7.81
Nov-00 5.607 6.09 5.79 5.7 6.19 6.08 6.1283 5.2 6.827
6.678 6.618 6.4225 5.46 6.61 9.5 7.73
Dec-00 5.617 5.6 5.26 5.17 5.9 5.77 6.1083 5.21 6.565
6.208 5.997 6.4558 5.52 6.3 9.5 7.59
Jan-01 5.514 4.81 4.77 4.86 5.21 5 5.9992 5.22 5.622
5.361 5.284 6.4283 5.54 5.45 9.05 7.25
Feb-01 5.426 4.68 4.71 4.89 4.93 4.78 5.8708 5.17 5.278
4.955 4.925 6.3658 5.47 5.12 8.5 7.1
Mar-01 5.198 4.3 4.43 4.64 4.5 4.36 5.7108 5.09 5.078
4.711 4.67 6.2617 5.35 4.74 8.32 7.02
Apr-01 4.946 3.98 4.42 4.76 3.92 3.89 5.53 5.01 4.435
4.231 4.33 6.1158 5.21 4.41 7.8 7.01
May-01 4.745 3.78 4.51 4.93 3.68 3.69 5.3175 4.9 4.059
3.99 4.259 5.8917 5.47 4.01 7.24 7.08
Jun-01 4.498 3.58 4.35 4.81 3.51 3.46 5.1017 4.78 3.835
3.827 4.055 5.6425 5.03 3.74 6.98 7.1
Jul-01 4.274 3.62 4.31 4.76 3.54 3.48 4.8967 4.68 3.76
3.694 3.835 5.3917 4.6 3.7 6.75 7.1
Aug-01 4.106 3.47 4.04 4.57 3.39 3.31 4.6708 4.59 3.584
3.479 3.6 5.1308 4.39 3.49 6.67 6.99
Sep-01 3.974 2.82 3.45 4.12 2.87 2.84 4.395 4.45 2.637
2.532 2.65 4.82 4.19 2.84 6.28 6.86
Oct-01 3.628 2.33 3.14 3.91 2.22 2.19 4.0883 4.27 2.321
2.173 2.311 4.4567 3.89 2.26 5.53 6.66
Nov-01 3.368 2.18 3.22 3.97 1.93 1.94 3.7625 4.09 2.145
2.101 2.492 4.0717 3.59 2.03 5.1 6.56
Dec-01 3.074 2.22 3.62 4.39 1.72 1.81 3.4808 3.9 1.876
1.983 2.445 3.6867 3.39 1.9 4.84 6.69
Jan-02 2.823 2.16 3.56 4.34 1.64 1.72 3.26 3.79 1.829
1.989 2.42 3.3633 3.27 1.85 4.75 6.81
Feb-02 2.744 2.23 3.55 4.3 1.73 1.83 3.0558 3.65 1.883
2.068 2.496 3.0767 3.15 1.95 4.75 6.77
Mar-02 2.653 2.57 4.14 4.74 1.8 1.99 2.9117 3.55 1.88
2.332 3.006 2.8283 3.04 2.16 4.75 6.77
Apr-02 2.723 2.48 4.01 4.65 1.72 1.97 2.7867 3.48 1.842
2.1 2.613 2.6067 2.98 2.11 4.75 6.88
May-02 2.772 2.35 3.8 4.49 1.74 1.88 2.6675 3.38 1.844
2.09 2.634 2.4233 2.94 1.93 4.75 6.74
Jun-02 2.847 2.2 3.49 4.19 1.71 1.83 2.5525 3.32 1.836
1.948 2.251 2.2625 2.92 1.92 4.75 6.62
Jul-02 2.821 1.96 3.01 3.81 1.68 1.71 2.4142 3.28 1.818
1.863 2.07 2.1067 2.89 1.84 4.75 6.48
Aug-02 2.763 1.76 2.52 3.29 1.63 1.62 2.2717 3.21 1.82
1.815 1.943 1.9608 2.85 1.72 4.75 6.32
Sep-02 2.759 1.72 2.32 2.94 1.63 1.61 2.18 3.13 1.819
1.751 1.813 1.8683 2.81 1.74 4.75 6.23
Oct-02 2.708 1.65 2.25 2.95 1.61 1.58 2.1233 3.1 1.741
1.618 1.664 1.82 2.74 1.69 4.75 6.09
Nov-02 2.537 1.49 2.32 3.05 1.31 1.33 2.0658 3 1.38
1.471 1.705 1.7667 2.63 1.4 4.35 6.03
Dec-02 2.375 1.45 2.23 3.03 1.2 1.26 2.0017 2.9 1.382
1.383 1.447 1.7258 2.56 1.36 4.25 6.04
Jan-03 2.308 1.36 2.18 3.05 1.2 1.26 1.935 2.83 1.339
1.353 1.477 1.6883 2.47 1.3 4.25 5.91
Feb-03 2.257 1.3 2.05 2.9 1.16 1.18 1.8575 2.73 1.334
1.336 1.368 1.6425 2.3 1.27 4.25 5.88
Mar-03 2.21 1.24 1.98 2.78 1.13 1.12 1.7467 2.7 1.306
1.262 1.34 1.5858 2.25 1.2 4.25 5.76
Apr-03 2.208 1.27 2.06 2.93 1.14 1.15 1.6458 2.62 1.318
1.29 1.362 1.5333 2.17 1.23 4.25 5.68
May-03 2.13 1.18 1.75 2.52 1.08 1.09 1.5483 2.57 1.3189
1.2232 1.2214 1.4833 2.14 1.19 4.25 5.58
Jun-03 2.113 1.01 1.51 2.27 0.95 0.94 1.4492 2.5 1.1232
1.1239 1.2014 1.4192 2.12 1.02 4.22 5.36
Jul-03 2.018 1.12 1.93 2.87 0.89 0.94 1.3792 2.41 1.1036
1.1507 1.2789 1.3575 2.06 1.06 4 5.34
Aug-03 1.946 1.31 2.44 3.37 0.95 1.02 1.3417 2.36 1.117
1.2098 1.4714 1.3033 2.03 1.13 4 5.61
Sep-03 1.923 1.24 2.23 3.18 0.95 1.02 1.3017 2.32 1.1214
1.1795 1.2857 1.2467 1.95 1.13 4 5.89
Oct-03 1.909 1.25 2.26 3.19 0.93 1.01 1.2683 2.28 1.1201
1.2207 1.4551 1.1942 1.87 1.14 4 5.78
Nov-03 1.821 1.34 2.45 3.29 0.94 1.02 1.2558 2.25 1.1157
1.2295 1.4867 1.1708 1.86 1.17 4 5.79
Dec-03 1.902 1.31 2.44 3.27 0.9 1 1.2442 2.22 1.1195
1.2192 1.4582 1.1508 1.85 1.17 4 5.74
Jan-04 1.811 1.24 2.27 3.12 0.89 0.98 1.2342 2.22 1.0982
1.2107 1.4607 1.1317 1.85 1.12 4 5.63
Feb-04 1.841 1.24 2.25 3.07 0.92 0.99 1.2292 2.15 1.0973
1.1695 1.3645 1.1133 1.85 1.11 4 5.69
Mar-04 1.815 1.19 2 2.79 0.94 0.99 1.225 2.14 1.0914
1.1595 1.3401 1.0983 1.85 1.09 4 5.43
Apr-04 1.802 1.43 2.57 3.39 0.94 1.06 1.2383 2.12 1.1007
1.3682 1.8082 1.085 1.85 1.21 4 5.37
May-04 1.708 1.78 3.1 3.85 1.04 1.31 1.2883 2.08 1.1089
1.5789 2.0764 1.0833 1.85 1.46 4 5.73
Jun-04 1.758 2.12 3.26 3.93 1.27 1.58 1.3808 2.09 1.3582
1.942 2.4682 1.1183 1.88 1.76 4 5.96
Jul-04 1.816 2.1 3.05 3.69 1.36 1.69 1.4625 2.09 1.4929
1.9857 2.4632 1.1617 1.91 1.85 4.25 5.88
Aug-04 1.875 2.02 2.88 3.47 1.48 1.72 1.5217 2.11 1.6482
1.9907 2.3001 1.2117 1.94 1.89 4.42 5.77
Sep-04 1.931 2.12 2.83 3.36 1.64 1.84 1.595 2.15 1.8401
2.1695 2.4445 1.2767 1.97 2.04 4.58 5.63
Oct-04 1.96 2.23 2.85 3.35 1.74 1.99 1.6767 2.16 1.987
2.3007 2.5289 1.355 2 2.18 4.75 5.64
Nov-04 2.025 2.5 3.09 3.53 2.08 2.28 1.7733 2.18 2.2826
2.6239 2.9607 1.4508 2.02 2.46 4.93 5.65
Dec-04 2.118 2.67 3.21 3.6 2.2 2.45 1.8867 2.22 2.4178
2.7751 3.1004 1.5633 2.08 2.66 5.14 5.71
Jan-05 2.183 2.86 3.39 3.71 2.32 2.6 2.0217 2.27 2.5892
2.9582 3.271 1.6925 2.19 2.85 5.25 5.72
Feb-05 2.317 3.03 3.54 3.77 2.53 2.76 2.1708 2.3 2.6895
3.1495 3.5114 1.8358 2.28 3 5.49 5.68
Mar-05 2.4 3.3 3.91 4.17 2.74 2.98 2.3467 2.34 2.8582
3.3876 3.842 1.9958 2.39 3.23 5.58 5.76
Apr-05 2.515 3.32 3.79 4 2.78 3.07 2.5042 2.39 3.0826
3.4151 3.7101 2.1633 2.52 3.34 5.75 5.86
May-05 2.622 3.33 3.72 3.85 2.86 3.1 2.6333 2.43 3.1126
3.5314 3.7789 2.3317 2.61 3.44 5.98 5.8
Jun-05 2.676 3.36 3.69 3.77 2.97 3.11 2.7367 2.48 3.3401
3.6914 3.8632 2.4917 2.7 3.56 6.01 5.65
Jul-05 2.757 3.64 3.91 3.98 3.19 3.37 2.865 2.54 3.5107
3.9235 4.1745 2.6583 2.78 3.8 6.25 5.68
Aug-05 2.87 3.87 4.08 4.12 3.45 3.67 3.0192 2.61 3.6942
4.0817 4.3123 2.8325 2.89 3.99 6.44 5.83
Sep-05 2.972 3.85 3.96 4.01 3.47 3.68 3.1633 2.67 3.8584
4.2154 4.4067 3 2.97 4.01 6.59 5.85
Oct-05 3.074 4.18 4.29 4.33 3.7 3.98 3.3258 2.74 4.0882
4.4467 4.6765 3.1742 3.06 4.32 6.75 5.98
Nov-05 3.19 4.33 4.43 4.45 3.9 4.16 3.4783 2.82 4.2954
4.5795 4.7379 3.345 3.14 4.52 7 6.22
Dec-05 3.296 4.35 4.39 4.39 3.89 4.19 3.6183 2.86 4.3857
4.6901 4.8226 3.5117 3.24 4.62 7.15 6.29
Jan-06 3.347 4.45 4.35 4.35 4.2 4.3 3.7508 2.94 4.572
4.8126 4.9412 3.6742 3.36 4.69 7.26 6.3
Feb-06 3.604 4.68 4.64 4.57 4.41 4.51 3.8883 3 4.631
4.9907 5.1526 3.8367 3.46 4.88 7.5 6.31
Mar-06 3.624 4.77 4.74 4.72 4.51 4.61 4.0108 3.06 4.826
5.1196 5.2476 3.9958 3.56 5.01 7.53 6.43
Apr-06 3.759 4.9 4.89 4.9 4.59 4.72 4.1425 3.11 5.0245
5.2879 5.4217 4.1575 3.66 5.17 7.75 6.5
May-06 3.884 5 4.97 5 4.72 4.81 4.2817 3.21 5.1071
5.3215 5.4139 4.3183 3.79 5.25 7.93 6.61
Jun-06 4.09 5.16 5.09 5.07 4.79 4.95 4.4317 3.28 5.3451
5.6382 5.766 4.4825 3.94 5.46 8.02 6.65
Jul-06 4.177 5.22 5.07 5.04 4.96 5.09 4.5633 3.35 5.4045
5.5473 5.591 4.64 4.11 5.54 8.25 6.77
Aug-06 4.277 5.08 4.85 4.82 4.98 5 4.6642 3.45 5.3314
5.4501 5.4501 4.7742 4.34 5.44 8.25 6.75
Sep-06 4.382 4.97 4.69 4.67 4.85 4.91 4.7575 3.52 5.3229
5.3704 5.2985 4.8967 4.49 5.37 8.25 6.59
Oct-06 4.346 5.01 4.72 4.69 4.89 4.91 4.8267 3.57 5.3198
5.3898 5.3348 4.9967 4.6 5.35 8.25 6.54
Nov-06 4.358 5.01 4.64 4.58 4.96 4.96 4.8833 3.63 5.3479
5.3495 5.2439 5.0808 4.65 5.33 8.25 6.45
Dec-06 4.396 4.94 4.58 4.53 4.86 4.89 4.9325 3.67 5.3279
5.3651 5.3139 5.1533 4.69 5.31 8.25 6.4
Jan-07 4.392 5.06 4.79 4.75 4.96 4.94 4.9833 3.71 5.3201
5.4014 5.4414 5.2167 4.73 5.34 8.25 6.37
Feb-07 4.376 5.05 4.75 4.71 5.02 4.97 5.0142 3.71 5.3214
5.3723 5.3328 5.2658 4.75 5.34 8.25 6.4
Mar-07 4.299 4.92 4.51 4.48 4.97 4.9 5.0267 3.74 5.3195
5.3212 5.2009 5.3008 4.77 5.28 8.25 6.33
Apr-07 4.224 4.93 4.6 4.59 4.88 4.87 5.0292 3.76 5.3201
5.3581 5.2967 5.3242 4.79 5.31 8.25 6.28
May-07 4.293 4.91 4.69 4.67 4.77 4.8 5.0217 3.79 5.321
5.3844 5.3885 5.3375 4.76 5.32 8.25 6.37
Jun-07 4.283 4.96 5 5.03 4.66 4.78 5.005 3.79 5.3195
5.3817 5.4048 5.3358 4.76 5.36 8.25 6.58
Jul-07 4.277 4.96 4.82 4.88 4.84 4.86 4.9833 3.81 5.32
5.3768 5.3914 5.3242 4.78 5.34 8.25 6.74
Aug-07 4.359 4.47 4.34 4.43 4.34 4.56 4.9325 3.84 5.4801
5.3683 5.1847 5.3333 4.79 5.4 8.25 6.73
Sep-07 4.383 4.14 4.06 4.2 4.01 4.13 4.8633 3.85 5.5121
5.3655 5.0703 5.3433 4.79 5.33 8.03 6.59
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