*The author of this computation has been verified*

R Software Module: /rwasp_structuraltimeseries.wasp (opens new window with default values)

Title produced by software: Structural Time Series Models

Date of computation: Sat, 12 Dec 2009 10:02:22 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi.htm/, Retrieved Sat, 12 Dec 2009 18:11:04 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

4716.99 4926.65 4920.10 5170.09 5246.24 5283.61 4979.05 4825.20 4695.12 4711.54 4727.22 4384.96 4378.75 4472.93 4564.07 4310.54 4171.38 4049.38 3591.37 3720.46 4107.23 4101.71 4162.34 4136.22 4125.88 4031.48 3761.36 3408.56 3228.47 3090.45 2741.14 2980.44 3104.33 3181.57 2863.86 2898.01 3112.33 3254.33 3513.47 3587.61 3727.45 3793.34 3817.58 3845.13 3931.86 4197.52 4307.13 4229.43 4362.28 4217.34 4361.28 4327.74 4417.65 4557.68 4650.35 4967.18 5123.42 5290.85 5535.66 5514.06 5493.88 5694.83 5850.41 6116.64 6175.00 6513.58 6383.78 6673.66 6936.61 7300.68 7392.93 7497.31 7584.71 7160.79 7196.19 7245.63 7347.51 7425.75 7778.51 7822.33 8181.22 8371.47 8347.71 8672.11 8802.79 9138.46 9123.29 9023.21 8850.41 8864.58 9163.74 8516.66 8553.44 7555.20 7851.22 7442.00 7992.53 8264.04 7517.39 7200.40 7193.69 6193.58 5104.21 4800.46 4461.61 4398.59 4243.63 4293.82

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Structural Time Series Model t Observed Level Slope Seasonal Stand. Residuals 1 4716.99 4716.99 0 0 0 2 4926.65 4915.82389346482 12.2917766479807 10.8261065351772 0.474143182426502 3 4920.1 4909.32683329282 11.4783583557380 10.7731667071821 -0.0734824681006915 4 5170.09 5158.68754853415 26.0141984409625 11.4024514658532 0.921510114350787 5 5246.24 5234.71537176125 29.8425338269466 11.5246282387540 0.192107471638571 6 5283.61 5272.0686665272 30.5149302589782 11.5413334727969 0.0286401383000769 7 4979.05 4968.1779507151 -2.97703075555560 10.8720492848993 -1.26741586773592 8 4825.2 4814.5966152821 -19.3439670193376 10.6033847178987 -0.56796472904498 9 4695.12 4684.69108854291 -32.1016949099125 10.4289114570866 -0.415292614347238 10 4711.54 4701.04384669712 -26.2575725887026 10.4961533028767 0.181431462760696 11 4727.22 4716.67296336093 -21.0373994941140 10.5470366390665 0.156452449748119 12 4384.96 4374.75299305129 -62.0106907111784 10.2070069487136 -1.19624486917932 13 4378.75 4436.73343869824 -47.7041255128459 -57.983438698239 0.54484929709266 14 4472.93 4465.89583591745 -37.4123459112682 7.03416408255052 0.242844075962779 15 4564.07 4557.04150936607 -20.3317398518579 7.02849063393283 0.477273329575311 16 4310.54 4303.50260130892 -51.5562773248639 7.0373986910815 -0.865276390319022 17 4171.38 4164.33970554415 -63.3536491347295 7.04029445584965 -0.324906830983984 18 4049.38 4042.33802915334 -71.2852190313923 7.04197084666357 -0.217436545685577 19 3591.37 3584.31847453474 -123.754103295220 7.05152546526229 -1.43345909869020 20 3720.46 3713.41387187157 -89.3681082060259 7.04612812843154 0.937033817508478 21 4107.23 4100.19265105717 -24.5004804807337 7.03734894282743 1.76431044845353 22 4101.71 4094.67295328399 -21.9112363000397 7.03704671600866 0.0703241064200002 23 4162.34 4155.30408812257 -10.6402515458678 7.03591187743475 0.305797827925542 24 4136.22 4129.18390437811 -12.7555488039746 7.03609562189286 -0.0573458877171195 25 4125.88 4188.23893747785 -3.11678906716208 -62.3589374778513 0.289731068152174 26 4031.48 4028.10070478333 -24.3810111134591 3.37929521666738 -0.529160684893247 27 3761.36 3757.92118652420 -58.0148360519227 3.43881347580425 -0.9102431428449 28 3408.56 3405.05956319205 -98.3669595349494 3.50043680794973 -1.09190368296418 29 3228.47 3224.95481818324 -109.554868427549 3.51518181676425 -0.302705118195113 30 3090.45 3086.93038547113 -113.452045168433 3.51961452886704 -0.105435258230845 31 2741.14 2737.58868550287 -145.745286927794 3.55131449712617 -0.87361740661691 32 2980.44 2976.93335069631 -93.0233982195095 3.50664930369296 1.42620229767075 33 3104.33 3100.84506724284 -63.3218588624774 3.48493275716462 0.803442188384188 34 3181.57 3178.09721279508 -44.0745472717793 3.47278720492115 0.520636908689185 35 2863.86 2860.36680639736 -81.5444359146892 3.49319360264471 -1.01353612875065 36 2898.01 2894.524252856 -65.7017773773218 3.48574714399963 0.428527702181873 37 3112.33 3111.68071084429 -27.2929400636639 0.64928915571192 1.11018305782392 38 3254.33 3252.58198045968 -4.4912995017168 1.74801954032212 0.582396729051283 39 3513.47 3511.77645591089 31.6219920270312 1.69354408910864 0.97645256497049 40 3587.61 3585.9240369021 37.4458089755348 1.68596309789715 0.157481621939537 41 3727.45 3725.77979330157 51.470194610832 1.67020669843369 0.379257671785835 42 3793.34 3791.67170831907 53.445109342064 1.66829168092609 0.0534096839371694 43 3817.58 3815.90836093006 49.4453560447877 1.67163906993779 -0.108173430408701 44 3845.13 3843.4561950466 46.4467768814015 1.67380495339840 -0.0810988394344724 45 3931.86 3930.18963414255 51.963480196427 1.67036585745173 0.149206410047856 46 4197.52 4195.86537960764 81.2283664072787 1.65462039235670 0.791518731463537 47 4307.13 4305.47718442853 85.1150777748934 1.65281557146737 0.105123906839561 48 4229.43 4227.76824868805 62.818604263389 1.66175131195165 -0.603057870740139 49 4362.28 4372.18265897977 73.9279075564652 -9.90265897977322 0.315786596542491 50 4217.34 4218.37893707788 43.0006322761441 -1.03893707788023 -0.800393009891683 51 4361.28 4362.33587906628 56.8272562125938 -1.05587906628336 0.373865937961279 52 4327.74 4328.78278946027 44.4496948531407 -1.04278946026654 -0.334710182348936 53 4417.65 4418.69847246062 50.676034628179 -1.04847246062223 0.168380595553360 54 4557.68 4558.73811278851 62.9136494584889 -1.05811278851137 0.330959548503073 55 4650.35 4651.41088350667 66.9888554396978 -1.06088350666693 0.110215274502267 56 4967.18 4968.26096115749 101.204453736285 -1.08096115748658 0.92539436899065 57 5123.42 5124.50477822304 108.741413871920 -1.08477822303992 0.203848137453370 58 5290.85 5291.93829122378 116.778547518771 -1.08829122377515 0.217378977263251 59 5535.66 5536.75490546699 134.311707600534 -1.09490546698773 0.474221112831057 60 5514.06 5515.14795391804 112.960656443390 -1.08795391804169 -0.577488284858046 61 5493.88 5492.96246396063 94.5375324987235 0.91753603936832 -0.518577928452614 62 5694.83 5694.16102348844 109.042743155212 0.66897651155731 0.378444331402451 63 5850.41 5849.74752593441 115.417098603227 0.662474065587506 0.172368407652804 64 6116.64 6115.99571780659 136.073161637524 0.644282193408487 0.558595597647032 65 6175 6174.34762749772 125.429674930768 0.652372502275441 -0.287842657372996 66 6513.58 6512.94677845454 154.621460576209 0.633221545458092 0.789492014875746 67 6383.78 6383.12472368476 115.669790054040 0.655276315244423 -1.05347679181640 68 6673.66 6673.01638240153 139.527523588693 0.64361759846787 0.645263145153977 69 6936.61 6935.97351108528 156.429744271382 0.636488914719063 0.457149231481348 70 7300.68 7300.05386168012 184.864961277996 0.626138319881116 0.769087320776314 71 7392.93 7392.29987717766 172.181938433169 0.630122822339113 -0.343040591962557 72 7497.31 7496.67735964767 162.896952975821 0.632640352333754 -0.251134670148619 73 7584.71 7595.98851243948 154.222183930943 -11.2785124394809 -0.242587193683522 74 7160.79 7163.2985799774 74.3251537458699 -2.50857997740033 -2.09615699538332 75 7196.19 7198.69391742458 68.9936342680549 -2.50391742457799 -0.144174533300344 76 7245.63 7248.13190073559 66.3155428998391 -2.50190073558575 -0.0724248136395152 77 7347.51 7350.01506636859 71.1863083849607 -2.50506636859111 0.131727794391126 78 7425.75 7428.25560823944 72.1523257701151 -2.50560823943748 0.0261263476820294 79 7778.51 7781.03421262287 110.581288348258 -2.52421262287331 1.03935167459402 80 7822.33 7824.85039249436 101.438538125693 -2.52039249436380 -0.247279570629184 81 8181.22 8183.75310663398 136.695291393995 -2.53310663397975 0.953584763074233 82 8371.47 8374.0053892257 144.029288724178 -2.53538922570406 0.198363566572881 83 8347.71 8350.23921710754 121.051700658928 -2.52921710754449 -0.621482221174525 84 8672.11 8674.64567291107 148.898712863899 -2.53567291106812 0.753191119910407 85 8802.79 8777.56885015513 142.623015852787 25.221149844873 -0.174676268283618 86 9138.46 9139.60046868351 172.514008884709 -1.14046868350967 0.78741058187347 87 9123.29 9124.41088022865 146.807886384767 -1.12088022865161 -0.695162404777605 88 9023.21 9024.30864954734 112.994450835427 -1.09864954733887 -0.91445080278711 89 8850.41 8851.4864399484 73.8537513436139 -1.07643994839492 -1.05856010987136 90 8864.58 8865.6524370118 65.6800280022417 -1.07243701180828 -0.221064351685476 91 9163.74 9164.82595179866 97.6546400260065 -1.08595179865886 0.864794429344212 92 8516.66 8517.70874699143 -4.33384005982002 -1.0487469914273 -2.75845109364271 93 8553.44 8554.49051964635 1.29647987327590 -1.05051964635045 0.152283249500874 94 7555.2 7556.21332555107 -135.583616982515 -1.01332555107067 -3.70222671546491 95 7851.22 7852.24718672509 -76.478617885217 -1.02718672508902 1.59863617553322 96 7442 7443.01796394945 -122.044951144962 -1.01796394944658 -1.23245629015078 97 7992.53 7949.43349181159 -36.2246524676038 43.0965081884122 2.38027621180336 98 8264.04 8266.31332300849 11.9085426029695 -2.27332300849068 1.27191057413278 99 7517.39 7519.59311124382 -91.9852621817703 -2.20311124382117 -2.80962772561542 100 7200.4 7202.58513439162 -122.80114939434 -2.18513439162517 -0.833398554455185 101 7193.69 7195.88313928954 -106.902176930406 -2.19313928953686 0.429992843692330 102 6193.58 6195.71998412694 -229.226474643052 -2.13998412693853 -3.30838015469042 103 5104.21 5106.30580661488 -347.020669364046 -2.0958066148797 -3.18591649669571 104 4800.46 4802.55772467492 -341.094948687163 -2.09772467491556 0.160271944492674 105 4461.61 4463.70781055924 -340.787516058197 -2.09781055923776 0.0083151603860756 106 4398.59 4400.69698180428 -302.749137257229 -2.10698180428214 1.02883541325194 107 4243.63 4245.74119322935 -282.510520532841 -2.11119322934705 0.547402958611653 108 4293.82 4295.93937561659 -236.949847608641 -2.11937561659008 1.23230507978733

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi/1cmdo1260637339.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi/1cmdo1260637339.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi/22dhk1260637339.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi/22dhk1260637339.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi/39eu01260637339.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi/39eu01260637339.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi/42lvp1260637339.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi/42lvp1260637339.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi/5hh5e1260637339.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606378572oe8qk40bzae7gi/5hh5e1260637339.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 0.2 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;

Parameters (R input):

par1 = 12 ; par2 = 0.2 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) nx <- length(x) x <- ts(x,frequency=par1) m <- StructTS(x,type='BSM') m$coef m$fitted m$resid mylevel <- as.numeric(m$fitted[,'level']) myslope <- as.numeric(m$fitted[,'slope']) myseas <- as.numeric(m$fitted[,'sea']) myresid <- as.numeric(m$resid) myfit <- mylevel+myseas mylagmax <- nx/2 bitmap(file='test2.png') op <- par(mfrow = c(2,2)) acf(as.numeric(x),lag.max = mylagmax,main='Observed') acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level') acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal') acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals') par(op) dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) spectrum(as.numeric(x),main='Observed') spectrum(mylevel,main='Level') spectrum(myseas,main='Seasonal') spectrum(myresid,main='Standardized Residals') par(op) dev.off() bitmap(file='test4.png') op <- par(mfrow = c(2,2)) cpgram(as.numeric(x),main='Observed') cpgram(mylevel,main='Level') cpgram(myseas,main='Seasonal') cpgram(myresid,main='Standardized Residals') par(op) dev.off() bitmap(file='test1.png') plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b') grid() dev.off() bitmap(file='test5.png') op <- par(mfrow = c(2,2)) hist(m$resid,main='Residual Histogram') plot(density(m$resid),main='Residual Kernel Density') qqnorm(m$resid,main='Residual Normal QQ Plot') qqline(m$resid) plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit') par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Structural Time Series Model',6,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Level',header=TRUE) a<-table.element(a,'Slope',header=TRUE) a<-table.element(a,'Seasonal',header=TRUE) a<-table.element(a,'Stand. Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nx) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,x[i]) a<-table.element(a,mylevel[i]) a<-table.element(a,myslope[i]) a<-table.element(a,myseas[i]) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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