Detrend: Auxiliary function for removing trends and mean from...
In SpecsVerification: Forecast Verification Routines for Ensemble Forecasts of Weather and Climate
Description
Usage
Arguments
Value
Examples
Description
Detrend fits a linear function to a time-series of observations or to the time-series of ensemble means of an ensemble matrix. The linear trend is removed, and if option demean is true, the total mean is removed as well.
Usage
1
Arguments
x
A vector, matrix, or data.frame.
demean
logical; if true, the total mean is removed from x
Value
The function returns an object of the same dimensions as the argument 'x', but with its linear trend and (possibly) its mean removed.
Examples
1
2
3
Example output
member
year Member_1 Member_2 Member_3 Member_4 Member_5
1983 0.224243193 0.02058097 -0.21812198 -0.17548875 -0.041049870
1984 -0.588337216 -0.26446326 0.19389875 -0.56058218 0.041324537
1985 -0.183617741 -0.12446701 -0.49824487 -0.35604499 -0.453454633
1986 -0.005988570 -0.18677469 0.14478233 0.07602119 0.001452767
1987 -0.173069522 -0.42089392 -0.21977703 -0.02996378 -0.318588703
1988 0.088533540 -0.30113842 0.24658764 -0.25959381 -0.043747042
1989 0.094683168 -0.15455630 0.43127963 0.31329862 0.002674435
1990 0.462838071 0.62171150 0.68572662 0.59923495 0.101201467
1991 0.131197151 0.13257595 0.14719545 -0.03290239 0.076597728
1992 -0.217245502 0.13980558 -0.05402605 -0.11408626 0.100141675
1993 -0.015207897 -0.26828176 -0.17099717 -0.27341119 -0.368333439
1994 -0.091473122 -0.01202222 -0.54894628 0.01361302 0.240496344
1995 0.009016113 0.17446993 0.19432360 0.09209769 -0.268031643
1996 -0.071085152 -0.36220475 -0.08552849 -0.11684387 -0.140453815
1997 -0.222743963 -0.66982615 -0.06448129 -0.41826349 -0.073489201
1998 -0.002473617 -0.41102585 -0.28965852 0.09454211 0.096657607
1999 -0.260839196 -0.24753465 0.22665183 -0.14259549 0.111191102
2000 -0.107501772 -0.07553613 0.02755440 0.49168463 -0.043298466
2001 -0.295031012 0.01671005 0.28401188 -0.53906878 -0.137033458
2002 -0.078187283 -0.09513088 0.02397206 -0.34571179 -0.085091813
2003 -0.235317875 -0.32653007 -0.22093720 -0.57858110 -0.540387700
2004 -0.177721093 -0.22433662 -0.07220388 0.04787351 0.095346857
2005 0.086986530 -0.21804144 -0.06838436 -0.02806483 -0.058087184
2006 -0.133089680 -0.40863023 0.16178587 0.21704069 -0.110136435
2007 -0.292662954 -0.09573197 -0.10153750 -0.15636896 -0.292225326
2008 0.457016004 -0.16229053 -0.17623685 -0.12419610 -0.137274034
2009 -0.236527489 -0.21535850 -0.05868528 -0.21266918 0.016552784
member
year Member_6 Member_7 Member_8 Member_9 Member_10
1983 -0.10182747 -0.2127347666 -0.194463715 -0.298384030 0.07683883
1984 0.06012341 -0.1975983870 -0.393438918 -0.032050172 -0.02934397
1985 -0.59758211 -0.3269145865 -0.878133567 -0.329373142 0.21983492
1986 0.11239146 -0.1520492223 -0.075404837 -0.070225872 0.20844471
1987 0.19727326 -0.1453855221 -0.102486880 0.001702837 -0.36743120
1988 -0.25684924 -0.2285280761 0.141871031 -0.384658313 -0.18516001
1989 -0.36107327 -0.2775153836 0.143775628 0.148093567 0.39600883
1990 0.21489690 0.6945180450 0.279834557 0.416171079 0.69178440
1991 -0.43440055 -0.1651397992 0.452987534 0.242438184 0.07967355
1992 0.31147358 0.0580589049 -0.031618328 -0.144048173 -0.09286893
1993 -0.44307301 -0.0850714899 -0.152513283 0.180853094 -0.36514001
1994 -0.24010087 -0.0954862997 0.009454157 0.270885201 -0.37902078
1995 0.54055676 0.3755335741 0.385264239 -0.180025419 0.29727117
1996 -0.44395680 -0.2306973205 -0.346876682 -0.330126371 -0.65438492
1997 -0.02488590 0.0074482307 -0.448030577 -0.454908365 -0.13131271
1998 -0.08885070 -0.0279810373 -0.164107635 0.078980675 -0.31046550
1999 -0.06774371 -0.2666081392 -0.027233730 0.181223105 -0.19835449
2000 0.27510938 0.0718297541 -0.091377808 -0.078346369 -0.41111012
2001 0.01247720 -0.0583763128 -0.360859354 0.548919208 0.14642500
2002 -0.08701343 -0.5061936282 -0.440765702 0.006957807 -0.01857610
2003 -0.11077798 -0.2095472934 -0.407362713 -0.108452286 -0.02735962
2004 -0.29094701 0.0009275265 -0.187798511 -0.232454097 0.43691106
2005 -0.37653254 0.1491190532 -0.126310394 0.026713751 0.44220050
2006 -0.15654452 0.2025529367 -0.374510383 0.218553794 -0.02693596
2007 0.29378127 0.0972273521 0.037519200 0.228246048 -0.06362224
2008 0.40913037 0.1658828902 -0.093553780 0.245010551 0.19185513
2009 -0.09228893 0.2338260654 0.020171218 0.318466971 -0.09512760
member
year Member_11 Member_12 Member_13 Member_14 Member_15
1983 0.133219022 -0.072899690 -0.13663798 0.590866173 -0.018791027
1984 -0.157717613 0.336201993 0.08821937 -0.104455603 0.053370105
1985 -0.141761321 0.079444947 -0.46939731 -0.439693854 -0.538141496
1986 -0.095197685 -0.169568314 0.04029884 -0.003415435 0.219791266
1987 0.382923736 -0.281879673 -0.12918865 0.031420669 -0.169401899
1988 0.059538949 0.124241878 -0.19952287 0.293457376 -0.330156125
1989 -0.085668662 0.240231831 0.03485325 0.205938021 0.524564416
1990 0.614302152 0.256959912 0.44235109 0.794488665 0.335509234
1991 0.078177222 0.081433301 0.65904316 0.257899177 0.376042961
1992 0.169485926 0.210843454 -0.13228390 0.150307851 0.032467042
1993 -0.656560054 -0.035107077 0.24895725 -0.095270312 -0.056119364
1994 -0.081465056 0.108980513 -0.11301455 0.196800318 -0.071884058
1995 0.258200212 0.246571601 0.14854190 0.068467729 -0.012268479
1996 0.059594263 -0.498478116 -0.09214539 0.009235637 -0.150058023
1997 -0.008273435 -0.361508143 -0.04502743 -0.271989766 -0.188002518
1998 -0.224790868 0.394353524 0.07517009 -0.098272317 -0.014494893
1999 0.015408230 0.249632300 0.09745867 -0.294951628 -0.006688905
2000 -0.429752489 0.204961045 -0.04538269 0.052820109 -0.169220011
2001 -0.163235725 -0.116589548 0.33389520 -0.481490802 0.291988945
2002 0.241176061 0.002121516 -0.19888381 0.031585242 0.155239608
2003 -0.050581008 -0.020007260 -0.16255754 -0.238834011 -0.026953054
2004 -0.068310931 0.264186026 0.13223447 -0.160589057 -0.101655119
2005 -0.073070087 0.079936444 -0.24565762 -0.078203980 0.111619834
2006 -0.093279498 0.172173418 -0.05573383 0.072731677 0.282664891
2007 0.475996489 0.182023540 0.09702364 0.229281840 -0.133256055
2008 0.092770289 0.013255590 0.30607047 0.427503947 0.161806998
2009 -0.121851840 0.122756617 -0.43354940 0.045743144 -0.058441748
member
year Member_16 Member_17 Member_18 Member_19 Member_20
1983 0.10083913 -0.218593837 -0.04626021 0.11873925 0.198006077
1984 -0.02877604 0.382790093 0.19795372 -0.03098834 0.227071785
1985 -0.01931156 -0.237867464 -0.20814753 -0.17291246 -0.262187287
1986 -0.39516006 0.081307891 -0.14231294 -0.30839066 -0.142499282
1987 0.02482124 0.007416013 -0.04155360 0.18267799 -0.086147874
1988 -0.47204743 -0.233466367 0.41024546 0.13494471 -0.003213928
1989 -0.09325894 0.059170740 0.61812094 0.10063458 -0.017245906
1990 0.42494438 0.148057067 0.48882762 0.88052193 0.415867646
1991 0.17305224 -0.001112024 0.21455242 0.41174581 0.140715868
1992 -0.04448038 0.187921916 -0.17463308 -0.03470629 0.114547821
1993 -0.15941863 0.311118270 -0.10377152 -0.22048773 0.164499090
1994 0.17275891 0.426140531 0.27441135 -0.03784930 -0.117751387
1995 0.12035896 0.301819084 0.49506821 0.45249500 0.001810500
1996 0.10638037 -0.428093669 -0.14889219 0.04731837 -0.143346385
1997 0.13432818 -0.203178969 -0.28892222 -0.28723171 -0.353920113
1998 0.08332601 -0.261834391 0.20005248 -0.10564190 -0.028552437
1999 -0.09760023 0.244622303 -0.09541025 0.38544059 0.586146456
2000 0.27223180 -0.278647817 0.13985049 -0.35244519 0.021671933
2001 0.15474666 0.472954726 0.20076253 0.33083552 0.202088874
2002 -0.17633051 0.036455351 0.37989993 -0.18402491 0.112261746
2003 0.01063423 0.437755071 -0.11355361 0.14581989 0.199178702
2004 -0.19044844 0.121633964 -0.61633648 0.10054605 0.079892113
2005 0.32684728 -0.103874559 -0.12844394 0.08438689 -0.001784106
2006 0.30390537 0.109528338 0.31588190 0.13281478 0.168604703
2007 -0.16470150 -0.195717385 0.06205322 -0.22381557 -0.367087899
2008 -0.08154839 -0.032433832 -0.09000826 0.66390430 0.300956689
2009 -0.10747465 0.090801994 0.03756714 -0.19811345 0.303986566
member
year Member_21 Member_22 Member_23 Member_24
1983 0.03969397 0.168884019 0.381421563 0.241115070
1984 0.06419470 0.057597704 -0.002249154 0.058554874
1985 0.19463703 -0.254730524 -0.154967333 -0.091289261
1986 0.22551956 0.112994471 0.244639468 0.215794607
1987 -0.14833819 -0.133495501 -0.028501529 -0.115284843
1988 0.26265008 0.014363611 -0.040124944 0.380059890
1989 -0.08660980 -0.016856676 0.194443757 0.005586182
1990 0.55386071 0.918800809 0.595932010 0.472444641
1991 0.13931609 0.153577177 0.279288359 -0.148015119
1992 -0.01950782 0.194385666 -0.084494675 -0.200426643
1993 -0.13842470 0.069851083 -0.193356067 -0.142020822
1994 0.18159751 0.045811968 -0.447742800 -0.089714612
1995 0.19756076 -0.007481871 0.218894921 0.135960811
1996 -0.60673607 -0.368020347 0.146563527 -0.203742209
1997 -0.40358491 -0.095828471 0.042117662 -0.281287584
1998 0.13805016 -0.043042381 0.386173953 -0.044322532
1999 0.19085602 -0.015879378 0.315711043 0.049062560
2000 0.22225708 0.198681203 -0.208041303 0.180180556
2001 0.04954959 0.042466032 -0.179869295 0.658870151
2002 -0.38720115 -0.154433298 0.080737368 -0.183630558
2003 0.16613190 0.316465306 -0.139873135 0.276199554
2004 -0.05363144 -0.021659969 -0.263143587 -0.081065480
2005 -0.39864174 0.166100896 0.146740676 0.193077057
2006 0.27245236 0.108008805 0.204630385 0.250035342
2007 0.03557969 0.305256493 0.192916274 0.138001906
2008 0.26183178 0.106007794 -0.060303680 -0.035395838
2009 -0.10070913 -0.023430488 0.073797255 -0.287002637
1983 1984 1985 1986 1987 1988 1989 1990
18.87151 18.36583 18.82377 18.90162 18.57678 19.22003 18.99650 18.96617
1991 1992 1993 1994 1995 1996 1997 1998
19.02706 18.70294 18.24303 18.92342 18.79909 18.39295 18.66132 18.76153
1999 2000 2001 2002 2003 2004 2005 2006
18.93651 18.55802 18.82772 19.05711 19.32125 18.52795 18.64528 19.01122
2007 2008 2009
18.78305 18.60365 18.76050
SpecsVerification documentation built on March 26, 2020, 7:55 p.m.
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Description Usage Arguments Value Examples
Description
Detrend fits a linear function to a time-series of observations or to the time-series of ensemble means of an ensemble matrix. The linear trend is removed, and if option demean is true, the total mean is removed as well.
Usage
1 |
Arguments
x |
A vector, matrix, or data.frame. |
demean |
logical; if true, the total mean is removed from x |
Value
The function returns an object of the same dimensions as the argument 'x', but with its linear trend and (possibly) its mean removed.
Examples
1 2 3 |
Example output
member
year Member_1 Member_2 Member_3 Member_4 Member_5
1983 0.224243193 0.02058097 -0.21812198 -0.17548875 -0.041049870
1984 -0.588337216 -0.26446326 0.19389875 -0.56058218 0.041324537
1985 -0.183617741 -0.12446701 -0.49824487 -0.35604499 -0.453454633
1986 -0.005988570 -0.18677469 0.14478233 0.07602119 0.001452767
1987 -0.173069522 -0.42089392 -0.21977703 -0.02996378 -0.318588703
1988 0.088533540 -0.30113842 0.24658764 -0.25959381 -0.043747042
1989 0.094683168 -0.15455630 0.43127963 0.31329862 0.002674435
1990 0.462838071 0.62171150 0.68572662 0.59923495 0.101201467
1991 0.131197151 0.13257595 0.14719545 -0.03290239 0.076597728
1992 -0.217245502 0.13980558 -0.05402605 -0.11408626 0.100141675
1993 -0.015207897 -0.26828176 -0.17099717 -0.27341119 -0.368333439
1994 -0.091473122 -0.01202222 -0.54894628 0.01361302 0.240496344
1995 0.009016113 0.17446993 0.19432360 0.09209769 -0.268031643
1996 -0.071085152 -0.36220475 -0.08552849 -0.11684387 -0.140453815
1997 -0.222743963 -0.66982615 -0.06448129 -0.41826349 -0.073489201
1998 -0.002473617 -0.41102585 -0.28965852 0.09454211 0.096657607
1999 -0.260839196 -0.24753465 0.22665183 -0.14259549 0.111191102
2000 -0.107501772 -0.07553613 0.02755440 0.49168463 -0.043298466
2001 -0.295031012 0.01671005 0.28401188 -0.53906878 -0.137033458
2002 -0.078187283 -0.09513088 0.02397206 -0.34571179 -0.085091813
2003 -0.235317875 -0.32653007 -0.22093720 -0.57858110 -0.540387700
2004 -0.177721093 -0.22433662 -0.07220388 0.04787351 0.095346857
2005 0.086986530 -0.21804144 -0.06838436 -0.02806483 -0.058087184
2006 -0.133089680 -0.40863023 0.16178587 0.21704069 -0.110136435
2007 -0.292662954 -0.09573197 -0.10153750 -0.15636896 -0.292225326
2008 0.457016004 -0.16229053 -0.17623685 -0.12419610 -0.137274034
2009 -0.236527489 -0.21535850 -0.05868528 -0.21266918 0.016552784
member
year Member_6 Member_7 Member_8 Member_9 Member_10
1983 -0.10182747 -0.2127347666 -0.194463715 -0.298384030 0.07683883
1984 0.06012341 -0.1975983870 -0.393438918 -0.032050172 -0.02934397
1985 -0.59758211 -0.3269145865 -0.878133567 -0.329373142 0.21983492
1986 0.11239146 -0.1520492223 -0.075404837 -0.070225872 0.20844471
1987 0.19727326 -0.1453855221 -0.102486880 0.001702837 -0.36743120
1988 -0.25684924 -0.2285280761 0.141871031 -0.384658313 -0.18516001
1989 -0.36107327 -0.2775153836 0.143775628 0.148093567 0.39600883
1990 0.21489690 0.6945180450 0.279834557 0.416171079 0.69178440
1991 -0.43440055 -0.1651397992 0.452987534 0.242438184 0.07967355
1992 0.31147358 0.0580589049 -0.031618328 -0.144048173 -0.09286893
1993 -0.44307301 -0.0850714899 -0.152513283 0.180853094 -0.36514001
1994 -0.24010087 -0.0954862997 0.009454157 0.270885201 -0.37902078
1995 0.54055676 0.3755335741 0.385264239 -0.180025419 0.29727117
1996 -0.44395680 -0.2306973205 -0.346876682 -0.330126371 -0.65438492
1997 -0.02488590 0.0074482307 -0.448030577 -0.454908365 -0.13131271
1998 -0.08885070 -0.0279810373 -0.164107635 0.078980675 -0.31046550
1999 -0.06774371 -0.2666081392 -0.027233730 0.181223105 -0.19835449
2000 0.27510938 0.0718297541 -0.091377808 -0.078346369 -0.41111012
2001 0.01247720 -0.0583763128 -0.360859354 0.548919208 0.14642500
2002 -0.08701343 -0.5061936282 -0.440765702 0.006957807 -0.01857610
2003 -0.11077798 -0.2095472934 -0.407362713 -0.108452286 -0.02735962
2004 -0.29094701 0.0009275265 -0.187798511 -0.232454097 0.43691106
2005 -0.37653254 0.1491190532 -0.126310394 0.026713751 0.44220050
2006 -0.15654452 0.2025529367 -0.374510383 0.218553794 -0.02693596
2007 0.29378127 0.0972273521 0.037519200 0.228246048 -0.06362224
2008 0.40913037 0.1658828902 -0.093553780 0.245010551 0.19185513
2009 -0.09228893 0.2338260654 0.020171218 0.318466971 -0.09512760
member
year Member_11 Member_12 Member_13 Member_14 Member_15
1983 0.133219022 -0.072899690 -0.13663798 0.590866173 -0.018791027
1984 -0.157717613 0.336201993 0.08821937 -0.104455603 0.053370105
1985 -0.141761321 0.079444947 -0.46939731 -0.439693854 -0.538141496
1986 -0.095197685 -0.169568314 0.04029884 -0.003415435 0.219791266
1987 0.382923736 -0.281879673 -0.12918865 0.031420669 -0.169401899
1988 0.059538949 0.124241878 -0.19952287 0.293457376 -0.330156125
1989 -0.085668662 0.240231831 0.03485325 0.205938021 0.524564416
1990 0.614302152 0.256959912 0.44235109 0.794488665 0.335509234
1991 0.078177222 0.081433301 0.65904316 0.257899177 0.376042961
1992 0.169485926 0.210843454 -0.13228390 0.150307851 0.032467042
1993 -0.656560054 -0.035107077 0.24895725 -0.095270312 -0.056119364
1994 -0.081465056 0.108980513 -0.11301455 0.196800318 -0.071884058
1995 0.258200212 0.246571601 0.14854190 0.068467729 -0.012268479
1996 0.059594263 -0.498478116 -0.09214539 0.009235637 -0.150058023
1997 -0.008273435 -0.361508143 -0.04502743 -0.271989766 -0.188002518
1998 -0.224790868 0.394353524 0.07517009 -0.098272317 -0.014494893
1999 0.015408230 0.249632300 0.09745867 -0.294951628 -0.006688905
2000 -0.429752489 0.204961045 -0.04538269 0.052820109 -0.169220011
2001 -0.163235725 -0.116589548 0.33389520 -0.481490802 0.291988945
2002 0.241176061 0.002121516 -0.19888381 0.031585242 0.155239608
2003 -0.050581008 -0.020007260 -0.16255754 -0.238834011 -0.026953054
2004 -0.068310931 0.264186026 0.13223447 -0.160589057 -0.101655119
2005 -0.073070087 0.079936444 -0.24565762 -0.078203980 0.111619834
2006 -0.093279498 0.172173418 -0.05573383 0.072731677 0.282664891
2007 0.475996489 0.182023540 0.09702364 0.229281840 -0.133256055
2008 0.092770289 0.013255590 0.30607047 0.427503947 0.161806998
2009 -0.121851840 0.122756617 -0.43354940 0.045743144 -0.058441748
member
year Member_16 Member_17 Member_18 Member_19 Member_20
1983 0.10083913 -0.218593837 -0.04626021 0.11873925 0.198006077
1984 -0.02877604 0.382790093 0.19795372 -0.03098834 0.227071785
1985 -0.01931156 -0.237867464 -0.20814753 -0.17291246 -0.262187287
1986 -0.39516006 0.081307891 -0.14231294 -0.30839066 -0.142499282
1987 0.02482124 0.007416013 -0.04155360 0.18267799 -0.086147874
1988 -0.47204743 -0.233466367 0.41024546 0.13494471 -0.003213928
1989 -0.09325894 0.059170740 0.61812094 0.10063458 -0.017245906
1990 0.42494438 0.148057067 0.48882762 0.88052193 0.415867646
1991 0.17305224 -0.001112024 0.21455242 0.41174581 0.140715868
1992 -0.04448038 0.187921916 -0.17463308 -0.03470629 0.114547821
1993 -0.15941863 0.311118270 -0.10377152 -0.22048773 0.164499090
1994 0.17275891 0.426140531 0.27441135 -0.03784930 -0.117751387
1995 0.12035896 0.301819084 0.49506821 0.45249500 0.001810500
1996 0.10638037 -0.428093669 -0.14889219 0.04731837 -0.143346385
1997 0.13432818 -0.203178969 -0.28892222 -0.28723171 -0.353920113
1998 0.08332601 -0.261834391 0.20005248 -0.10564190 -0.028552437
1999 -0.09760023 0.244622303 -0.09541025 0.38544059 0.586146456
2000 0.27223180 -0.278647817 0.13985049 -0.35244519 0.021671933
2001 0.15474666 0.472954726 0.20076253 0.33083552 0.202088874
2002 -0.17633051 0.036455351 0.37989993 -0.18402491 0.112261746
2003 0.01063423 0.437755071 -0.11355361 0.14581989 0.199178702
2004 -0.19044844 0.121633964 -0.61633648 0.10054605 0.079892113
2005 0.32684728 -0.103874559 -0.12844394 0.08438689 -0.001784106
2006 0.30390537 0.109528338 0.31588190 0.13281478 0.168604703
2007 -0.16470150 -0.195717385 0.06205322 -0.22381557 -0.367087899
2008 -0.08154839 -0.032433832 -0.09000826 0.66390430 0.300956689
2009 -0.10747465 0.090801994 0.03756714 -0.19811345 0.303986566
member
year Member_21 Member_22 Member_23 Member_24
1983 0.03969397 0.168884019 0.381421563 0.241115070
1984 0.06419470 0.057597704 -0.002249154 0.058554874
1985 0.19463703 -0.254730524 -0.154967333 -0.091289261
1986 0.22551956 0.112994471 0.244639468 0.215794607
1987 -0.14833819 -0.133495501 -0.028501529 -0.115284843
1988 0.26265008 0.014363611 -0.040124944 0.380059890
1989 -0.08660980 -0.016856676 0.194443757 0.005586182
1990 0.55386071 0.918800809 0.595932010 0.472444641
1991 0.13931609 0.153577177 0.279288359 -0.148015119
1992 -0.01950782 0.194385666 -0.084494675 -0.200426643
1993 -0.13842470 0.069851083 -0.193356067 -0.142020822
1994 0.18159751 0.045811968 -0.447742800 -0.089714612
1995 0.19756076 -0.007481871 0.218894921 0.135960811
1996 -0.60673607 -0.368020347 0.146563527 -0.203742209
1997 -0.40358491 -0.095828471 0.042117662 -0.281287584
1998 0.13805016 -0.043042381 0.386173953 -0.044322532
1999 0.19085602 -0.015879378 0.315711043 0.049062560
2000 0.22225708 0.198681203 -0.208041303 0.180180556
2001 0.04954959 0.042466032 -0.179869295 0.658870151
2002 -0.38720115 -0.154433298 0.080737368 -0.183630558
2003 0.16613190 0.316465306 -0.139873135 0.276199554
2004 -0.05363144 -0.021659969 -0.263143587 -0.081065480
2005 -0.39864174 0.166100896 0.146740676 0.193077057
2006 0.27245236 0.108008805 0.204630385 0.250035342
2007 0.03557969 0.305256493 0.192916274 0.138001906
2008 0.26183178 0.106007794 -0.060303680 -0.035395838
2009 -0.10070913 -0.023430488 0.073797255 -0.287002637
1983 1984 1985 1986 1987 1988 1989 1990
18.87151 18.36583 18.82377 18.90162 18.57678 19.22003 18.99650 18.96617
1991 1992 1993 1994 1995 1996 1997 1998
19.02706 18.70294 18.24303 18.92342 18.79909 18.39295 18.66132 18.76153
1999 2000 2001 2002 2003 2004 2005 2006
18.93651 18.55802 18.82772 19.05711 19.32125 18.52795 18.64528 19.01122
2007 2008 2009
18.78305 18.60365 18.76050
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