Paper Structural Decomposition

*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: Tue, 28 Dec 2010 23:01:27 +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/29/t1293577210ms4evp531ldj894.htm/, Retrieved Wed, 29 Dec 2010 00:00:11 +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/29/t1293577210ms4evp531ldj894.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 «

1203 1319 1328 1260 1286 1274 1389 1255 1244 1336 1214 1239 1174 1061 1116 1123 1086 1074 965 1035 1016 941 1003 998 891 828 833 887 842 793 778 699 686 727 641 619 627 593 535 536 504 487 477 435 433 393 389 377 339 370 350 341 367 396 408 405 391 396 368 356

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Structural Time Series Model t Observed Level Slope Seasonal Stand. Residuals 1 1203 1203 0 0 0 2 1319 1271.33768238461 6.05011974973103 5.45719047236403 2.13680144797764 3 1328 1301.5509745245 7.8596620751904 6.62285334544699 0.913744894947211 4 1260 1279.88171476133 5.56614948577158 5.72141857710112 -1.15670593386498 5 1286 1282.70372258676 5.3273897633946 5.66448771565941 -0.106850817282098 6 1274 1277.44177730629 4.29435416107412 5.50474629024856 -0.405381880146181 7 1389 1337.13832482564 10.2247562896793 6.14549735804713 2.08292772605223 8 1255 1293.15393476915 4.00331410640721 5.64681477531442 -2.00599739860565 9 1244 1264.5200394644 0.0632398169072989 5.40232066141286 -1.19232186340311 10 1336 1301.46446948977 4.67956545202945 5.6305334717465 1.33400781316754 11 1214 1251.24567703662 -2.37018062562429 5.34761169860572 -1.97077075598029 12 1239 1240.29597316713 -3.49198556254219 5.31061435031826 -0.306261799708889 13 1174 1235.13552694535 -3.66968062081088 -59.9134187155649 -0.0707135415833912 14 1061 1123.43141275073 -18.5022337243168 2.18890309220458 -3.2560081436769 15 1116 1110.03442129365 -17.8127622219657 2.26684120330256 0.175038143358962 16 1123 1108.4224787782 -15.6267107631587 2.38500438867741 0.569389273276767 17 1086 1087.57968016565 -16.3319268507968 2.36795896296858 -0.183848843083739 18 1074 1071.46639629124 -16.3023084006126 2.36823982400927 0.00769841210980477 19 965 1002.45965182791 -23.4527949653169 2.35065343484883 -1.85351910030537 20 1035 1009.58023427643 -19.300150875874 2.34758052470137 1.0743638727477 21 1016 1003.60567272486 -17.4886729714544 2.34385966011454 0.468054865037274 22 941 959.052858598201 -21.1700651972516 2.35290836771339 -0.950378993977456 23 1003 973.676343017156 -16.2989967661841 2.34102253715549 1.25675633114193 24 998 979.209394297848 -13.3268935192337 2.33435728158025 0.76650184259075 25 891 943.521224888383 -16.265335219752 -36.4529886950164 -0.858695912553732 26 828 866.024541826562 -24.5904254891867 2.12590025102563 -1.95978073100647 27 833 835.381901686831 -25.4118989363191 2.06964532461525 -0.209382487492236 28 887 852.654868242657 -19.6060321627232 2.24296182966763 1.49808194978023 29 842 836.86948644346 -19.0856830264347 2.24862666983006 0.134274672713953 30 793 802.374060078955 -21.1853869903085 2.24461182611986 -0.541219401232844 31 778 778.089737729936 -21.6076766232377 2.24549275534144 -0.108779907139429 32 699 722.407492963085 -26.2507761333725 2.26239817256737 -1.19578181891547 33 686 689.07115728401 -27.2162140722858 2.26628532802501 -0.248636281396004 34 727 697.728796472308 -22.3284646017127 2.24732480723948 1.25886289734498 35 641 654.493149536096 -25.1769716462127 2.25733621084937 -0.733706977773668 36 619 622.143570050058 -26.1542040337182 2.26035083650177 -0.251730243543539 37 627 623.119983715367 -22.5262429013667 -15.8670056255188 1.01440217042801 38 593 595.262961825551 -23.2500465041479 1.36456441868317 -0.174843971626167 39 535 550.049067495107 -26.2322792100498 1.21255232197458 -0.762908927134954 40 536 530.065888275873 -25.3820089536488 1.23118843258667 0.219357698894115 41 504 503.592791277614 -25.5306361592116 1.23004198861049 -0.0383354495839676 42 487 482.456536046761 -24.9317988887803 1.23065511413187 0.154317811797882 43 477 467.930670726792 -23.5136654025035 1.22792316948307 0.365272356578948 44 435 438.344535275654 -24.341186555607 1.23044217505364 -0.21311716062041 45 433 424.138601946363 -22.9601017690299 1.22590133761821 0.355687497801202 46 393 395.813615949552 -23.6911155427449 1.22819474324193 -0.188280842889908 47 389 381.049442065686 -22.4747710186004 1.2247538831816 0.313308515487044 48 377 368.38596794487 -21.1379401244782 1.22144322089657 0.344367634763589 49 339 349.859686094565 -20.7869245209572 -12.7763263043198 0.0962978215120284 50 370 352.373755865043 -17.621578085175 1.43551149495441 0.774890669983178 51 350 342.651197781017 -16.5483656954187 1.47934086632961 0.274969712272711 52 341 333.747400642999 -15.5079253959154 1.4975801269348 0.268359548560303 53 367 345.171387116108 -11.8389842787608 1.52011564201883 0.946132259232507 54 396 368.194997151457 -7.08809746490329 1.5238212760086 1.22423361118309 55 408 386.982298431636 -3.56176997886117 1.51824120464556 0.908332395619856 56 405 394.863625713048 -2.00235730356484 1.51438271613638 0.401638325218341 57 391 390.935708334571 -2.2647499800114 1.51508210403931 -0.0675824121439657 58 396 391.9873260262 -1.81285191137947 1.51393405269161 0.116398959607753 59 368 376.662805628962 -3.65395227359053 1.51814916260386 -0.474258104875292 60 356 362.441685267873 -5.09382407681189 1.52103418361381 -0.370924786860383

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577210ms4evp531ldj894/11zmr1293577282.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577210ms4evp531ldj894/11zmr1293577282.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577210ms4evp531ldj894/21zmr1293577282.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577210ms4evp531ldj894/21zmr1293577282.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577210ms4evp531ldj894/3tq3u1293577282.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577210ms4evp531ldj894/3tq3u1293577282.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577210ms4evp531ldj894/4tq3u1293577282.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577210ms4evp531ldj894/4tq3u1293577282.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577210ms4evp531ldj894/54i3f1293577282.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577210ms4evp531ldj894/54i3f1293577282.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$resid) myfit <- mylevel+myseas mylagmax <- nx/2 bitmap(file='test2.png') op <- par(mfrow = c(2,2)) acf(as.numeric(x),lag.max = mylagmax,main='Observed') acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level') acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal') acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals') par(op) dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) spectrum(as.numeric(x),main='Observed') spectrum(mylevel,main='Level') spectrum(myseas,main='Seasonal') spectrum(myresid,main='Standardized Residals') par(op) dev.off() bitmap(file='test4.png') op <- par(mfrow = c(2,2)) cpgram(as.numeric(x),main='Observed') cpgram(mylevel,main='Level') cpgram(myseas,main='Seasonal') cpgram(myresid,main='Standardized Residals') par(op) dev.off() bitmap(file='test1.png') plot(as.numeric(m$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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