[R] help for segmented package

pw2233 at columbia.edu pw2233 at columbia.edu
Sat Dec 8 11:18:59 CET 2007


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))



-------------- next part --------------
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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