STSM Yuan

*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: Sun, 26 Dec 2010 13:34:39 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5.htm/, Retrieved Sun, 26 Dec 2010 14:34:13 +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/2010/Dec/26/t12933704489gelqhclm6j7am5.htm/}, year = {2010}, } @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 = {2010}, 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 «

7,4271 7,7662 7,6289 7,5281 7,3831 7,2355 7,0617 7,1237 7,4533 7,5411 7,4978 7,3525 7,3862 7,311 7,2013 7,249 7,3321 7,59 7,9082 8,2123 8,0929 8,118 8,1206 8,2883 8,4281 8,7917 8,9168 8,9446 8,9786 9,5862 9,6533 9,4125 9,2195 9,2882 9,6774 9,6857 10,1688 10,4399 10,4675 10,149 9,9163 9,9268 10,0529 10,1622 10,083 10,1134 10,3423 10,7536 11,0967 10,8588 10,7719 10,9262 10,708 10,5062 10,0683 9,8954 9,9589 9,9177 9,7189 9,5273 9,5746 9,763 9,6117 9,6581 9,8361 10,2353 10,1285 10,1347 10,2141 10,0971 9,9651 10,1286 10,3356 10,1238 10,1326 10,2467 10,44 10,3689 10,2415 10,3899 10,3162 10,4533 10,6741 10,8957 10,7404 10,6568 10,5682 10,9833 11,0237 10,8462 10,7287 10,7809 10,2609 9,8252 9,1071 8,695 9,2205 9,0496 8,7406 8,921 9,011 9,3157 9,5786 9,6246 9,7485 9,9431 10,1152 10,1827 9,9777 9,7436 9,3462 9,2623 9,1505 8,5794 8,3245 8,6538 8,752 8,8104 9,2665 9,0895

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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Structural Time Series Model t Observed Level Slope Seasonal Stand. Residuals 1 7.4271 7.4271 0 0 0 2 7.7662 7.74856679927801 0.0176331995292359 0.0176332007219904 0.825877318167806 3 7.6289 7.61188406459956 0.0170159354004443 0.0170159354004442 -0.661595985910299 4 7.5281 7.51155158818015 0.0165484118198462 0.0165484118198463 -0.503101789956956 5 7.3831 7.36719011948947 0.0159098805105273 0.0159098805105273 -0.689855194930098 6 7.2355 7.22023385921398 0.015266140786018 0.015266140786018 -0.698236648345201 7 7.0617 7.04717529510318 0.0145247048968225 0.0145247048968225 -0.807375867194713 8 7.1237 7.10898984472097 0.0147101552790265 0.0147101552790265 0.202737000576945 9 7.4533 7.43736459233642 0.0159354076635825 0.0159354076635825 1.34470590560733 10 7.5411 7.52488604738892 0.0162139526110766 0.0162139526110766 0.306892949711581 11 7.4978 7.48181583100285 0.0159841689971484 0.0159841689971483 -0.254152275382592 12 7.3525 7.33713615476503 0.0153638452349719 0.0153638452349720 -0.688763596946793 13 7.3862 7.49082703120338 0.00951154773345023 -0.104627031203376 0.716470157387364 14 7.311 7.30618854113065 0.00481145386874014 0.00481145886935236 -0.708145117511599 15 7.2013 7.19669637117913 0.00460362882086875 0.00460362882086866 -0.489519150764006 16 7.249 7.24431829803187 0.00468170196813193 0.00468170196813197 0.184230783904569 17 7.3321 7.32727649277123 0.00482350722876448 0.00482350722876455 0.335227487381897 18 7.59 7.58471967593275 0.00528032406725284 0.00528032406725283 1.08186912529155 19 7.9082 7.90235585661733 0.00584414338267313 0.00584414338267312 1.33769313735252 20 8.2123 8.20591942514503 0.00638057485497425 0.00638057485497426 1.27500918252747 21 8.0929 8.08674524308493 0.00615475691506779 0.00615475691506778 -0.537698233757084 22 8.118 8.11181129103163 0.00618870896836901 0.00618870896836902 0.080988977620993 23 8.1206 8.11441771090546 0.00618228909453932 0.0061822890945393 -0.0153413886407199 24 8.2883 8.2818292863814 0.00647071361860732 0.00647071361860738 0.690473917528906 25 8.4281 8.46179133425479 0.00306284801665976 -0.0336913342547889 0.818601556492607 26 8.7917 8.78368516940102 0.00801482247115776 0.00801483059897778 1.24003322931279 27 8.9168 8.90864759183822 0.00815240816177794 0.00815240816177787 0.500681867600775 28 8.9446 8.93642453127938 0.008175468720616 0.00817546872061604 0.0840174597427016 29 8.9786 8.97039425632403 0.00820574367596635 0.00820574367596634 0.110431498653719 30 9.5862 9.5772923893604 0.00890761063960619 0.00890761063960619 2.56314628831903 31 9.6533 9.64432432807147 0.00897567192852698 0.008975671928527 0.248844074632262 32 9.4125 9.40381612214418 0.00868387785582337 0.00868387785582337 -1.06809909581460 33 9.2195 9.21105145927563 0.00844854072437134 0.00844854072437132 -0.862447943432769 34 9.2882 9.27968123611439 0.00851876388561243 0.00851876388561244 0.257649659802235 35 9.6774 9.66843806810671 0.00896193189328686 0.00896193189328687 1.62788517945411 36 9.6857 9.67673883779513 0.00896116220487228 0.00896116220487235 -0.00283058303596371 37 10.1688 10.1956272147361 0.00243883702459244 -0.0268272147360572 2.3302832078919 38 10.4399 10.4347549486031 0.00514504233724613 0.00514505139687149 0.946054341828682 39 10.4675 10.4623354485162 0.00516455148382581 0.00516455148382574 0.0960370709468288 40 10.149 10.1441164074107 0.00488359258926055 0.00488359258926065 -1.38427315174270 41 9.9163 9.91162246435983 0.00467753564016824 0.004677535640168 -1.01611594756798 42 9.9268 9.9221174188953 0.00468258110469757 0.00468258110469758 0.0249019768194336 43 10.0529 10.0481122955581 0.00478770444189335 0.00478770444189336 0.519287830573666 44 10.1622 10.1573218869715 0.00487811302852447 0.00487811302852445 0.44698680027863 45 10.083 10.0781945560619 0.00480544393810591 0.00480544393810588 -0.359592338651841 46 10.1134 10.1085724536754 0.00482754632458231 0.00482754632458232 0.109464988891711 47 10.3423 10.3372791210446 0.00502087895537148 0.00502087895537149 0.958332613345804 48 10.7536 10.7482288803209 0.00537111967911264 0.00537111967911271 1.73761062708716 49 11.0967 11.1177932051967 0.00191756317614841 -0.0210932051966607 1.63754274746305 50 10.8588 10.8592388201639 -0.00043882862533931 -0.000438820163883977 -1.05700731964457 51 10.7719 10.7723984161219 -0.000498416121887206 -0.000498416121887273 -0.369816768412151 52 10.9262 10.9265918056032 -0.000391805603189859 -0.000391805603189806 0.662113049167792 53 10.708 10.7085417080633 -0.000541708063327919 -0.000541708063328226 -0.931622464493622 54 10.5062 10.5068801250963 -0.00068012509632438 -0.000680125096324359 -0.86083441836604 55 10.0683 10.0692806199662 -0.000980619966180281 -0.000980619966180217 -1.87010434255196 56 9.8954 9.89649869650684 -0.00109869650683532 -0.00109869650683532 -0.73534455672841 57 9.9589 9.95995435970504 -0.00105435970503512 -0.00105435970503516 0.276305737273075 58 9.9177 9.91878189444785 -0.00108189444784958 -0.00108189444784959 -0.171713578639576 59 9.7189 9.7201174106768 -0.00121741067680137 -0.00121741067680139 -0.845693111439456 60 9.5273 9.52864780975836 -0.00134780975835926 -0.00134780975835916 -0.814317341839422 61 9.5746 9.5572887373518 -0.001573752320421 0.0173112626481884 0.133525103871349 62 9.763 9.76302221599718 -2.22303268542917e-05 -2.22159971758409e-05 0.849405033275063 63 9.6117 9.6118086257439 -0.000108625743893207 -0.000108625743893309 -0.647092334169511 64 9.6581 9.65818207971288 -8.20797128773598e-05 -8.20797128773532e-05 0.198941214799181 65 9.8361 9.83608049262872 1.95073712810654e-05 1.95073712808516e-05 0.761748395622014 66 10.2353 10.235052909579 0.000247090420996112 0.000247090420996105 1.70749998983046 67 10.1285 10.1283139050991 0.000186094900913675 0.000186094900913739 -0.457895460541517 68 10.1347 10.1345104803225 0.000189519677540222 0.000189519677540216 0.0257245692638785 69 10.2141 10.2138653975021 0.000234602497859056 0.000234602497859039 0.338824072597873 70 10.0971 10.0969320838811 0.000167916118884755 0.000167916118884758 -0.501472933122704 71 9.9651 9.96500722201324 9.27779867556013e-05 9.27779867555776e-05 -0.565350518289300 72 10.1286 10.1284143769598 0.00018562304019171 0.000185623040191803 0.698977295694115 73 10.3356 10.3241947314723 -0.00103684416425714 0.0114052685276979 0.865187932216387 74 10.1238 10.1260944738573 -0.0022944897398976 -0.00229447385732355 -0.812833396653992 75 10.1326 10.1348890803987 -0.00228908039872485 -0.00228908039872496 0.0474588583440954 76 10.2467 10.2489323605446 -0.00223236054463706 -0.00223236054463705 0.497876496958151 77 10.44 10.4421371182350 -0.00213711823503504 -0.00213711823503530 0.836427076632708 78 10.3689 10.3710706931705 -0.00217069317047501 -0.00217069317047502 -0.295001954014176 79 10.2415 10.2437316320374 -0.00223163203738306 -0.00223163203738299 -0.535692442765182 80 10.3899 10.3920583675871 -0.00215836758709928 -0.00215836758709930 0.644355850244483 81 10.3162 10.3183931472027 -0.00219314720271426 -0.00219314720271427 -0.306033163223771 82 10.4533 10.4554254634228 -0.00212546342281789 -0.00212546342281787 0.595853436012474 83 10.6741 10.6761171945650 -0.00201719456496722 -0.00201719456496726 0.953606991469831 84 10.8957 10.8976086424729 -0.00190864247285206 -0.00190864247285196 0.956566118672814 85 10.7404 10.7291856447054 -0.00101948803565176 0.0112143552945983 -0.733096489221792 86 10.6568 10.6582086272326 -0.00140863983037296 -0.00140862723257189 -0.289969789961864 87 10.5682 10.5696457269530 -0.00144572695298487 -0.00144572695298498 -0.372989184023579 88 10.9833 10.9845686240732 -0.00126862407319025 -0.00126862407319025 1.78190922424800 89 11.0237 11.0249509153402 -0.00125091534020962 -0.00125091534020985 0.178251047854762 90 10.8462 10.8475257875530 -0.00132578755295218 -0.00132578755295220 -0.75396266519479 91 10.7287 10.7300751184579 -0.00137511845786048 -0.00137511845786038 -0.496972945510703 92 10.7809 10.7822523785809 -0.00135237858091410 -0.00135237858091412 0.229184999542216 93 10.2609 10.2624724243711 -0.00157242437110091 -0.00157242437110094 -2.2186841393223 94 9.8252 9.8269565328663 -0.00175653286630728 -0.00175653286630727 -1.85712227994783 95 9.1071 9.10916019708398 -0.00206019708397825 -0.00206019708397833 -3.06439306605472 96 8.695 8.69723394286558 -0.00223394286557603 -0.00223394286557591 -1.75407929214146 97 9.2205 9.17149612413693 -0.00445489969857698 0.0490038758630709 2.09041248191656 98 9.0496 9.05460915222478 -0.00500917223789506 -0.00500915222477997 -0.467769222051947 99 8.7406 8.74572384318586 -0.00512384318586281 -0.00512384318586302 -1.30045029130411 100 8.921 8.92605388693901 -0.00505388693901072 -0.00505388693901074 0.793657405081196 101 9.011 9.01601805808482 -0.00501805808481796 -0.00501805808481813 0.406633591233611 102 9.3157 9.32060135941713 -0.00490135941712902 -0.00490135941712907 1.32495134319441 103 9.5786 9.58340049254804 -0.0048004925480378 -0.0048004925480377 1.14563483398549 104 9.6246 9.62938136584386 -0.00478136584385678 -0.00478136584385684 0.21732084594893 105 9.7485 9.75323293473685 -0.00473293473684889 -0.0047329347368489 0.550489648082331 106 9.9431 9.9477579411074 -0.00465794110739321 -0.00465794110739315 0.85273204979304 107 10.1152 10.1197914657187 -0.00459146571873962 -0.00459146571873969 0.756157893846958 108 10.1827 10.1872643636460 -0.004564363645976 -0.00456436364597582 0.308402182078795 109 9.9777 9.93859600195647 -0.00355491085774163 0.0391039980435285 -1.06794725927161 110 9.7436 9.74798286374374 -0.00438288378423411 -0.0043828637437393 -0.780547988618482 111 9.3462 9.35071606568596 -0.00451606568596075 -0.00451606568596104 -1.68133044681761 112 9.2623 9.26684295728252 -0.00454295728251458 -0.00454295728251455 -0.339605162554386 113 9.1505 9.15507927869193 -0.00457927869193504 -0.00457927869193530 -0.458846589450193 114 8.5794 8.58417105971429 -0.00477105971428671 -0.00477105971428675 -2.42358085906393 115 8.3245 8.32935570578031 -0.00485570578030867 -0.00485570578030855 -1.07005396962358 116 8.6538 8.65854266249459 -0.00474266249458824 -0.00474266249458831 1.42952134810355 117 8.752 8.7567078492587 -0.00470784925870629 -0.0047078492587063 0.44038973311464 118 8.8104 8.81508651460832 -0.00468651460832123 -0.00468651460832117 0.269976021682733 119 9.2665 9.27103079076425 -0.00453079076425134 -0.00453079076425138 1.97124951379478 120 9.0895 9.09408905743197 -0.00458905743197106 -0.00458905743197088 -0.737825117461123

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5/1kfaa1293370472.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5/1kfaa1293370472.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5/2d79v1293370472.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5/2d79v1293370472.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5/3d79v1293370472.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5/3d79v1293370472.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5/45gqg1293370472.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5/45gqg1293370472.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5/5yp711293370472.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933704489gelqhclm6j7am5/5yp711293370472.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

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$resid) myfit <- mylevel+myseas bitmap(file='test1.png') plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time') grid() dev.off() 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='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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