Structural Time Series Models

*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: Wed, 02 Dec 2009 14:19:07 -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/02/t1259788791ptpftisy5n0sjo6.htm/, Retrieved Wed, 02 Dec 2009 22:19:57 +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/02/t1259788791ptpftisy5n0sjo6.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 «

0.0314796223103059 -3.00870920563557 -2.07677512619799 -1.25010391965540 0.817975239137125 0.0252076485413113 0.554937772830776 0.230027371950115 2.35672227418686 1.41350455171120 2.73311719024401 1.31551925971717 -2.70076272244080 -0.721411049152714 -0.149388576811997 -0.118199629770334 -0.676562489695275 1.79699928690761 1.79845572032988 0.245100010770855 1.80710848932636 -1.75934771184948 -0.0186697168761931 0.189651523600062 -1.84149562719087 -1.07019530156943 -0.507291477584104 0.866365633831705 -1.76077926699189 -0.580719393339347 -0.435702079860853 -0.994868534845203 1.63136048315789 -1.1949403709466 -1.00525975426991 1.32302234837564 -0.628357549594746 0.632048410440518 -2.16903155809288 2.53779364144266 -0.632933703679292 -1.41749196342200 -0.455343045381255 0.812255211942954 0.627897309219833 0.650904313655623 -1.29800419154382 0.74391671726854 -1.50461634127457 -1.42734677658523 0.263353807408564 - etc...

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Structural Time Series Model t Observed Level Slope Seasonal Stand. Residuals 1 0.0314796223103059 0.0314796223103059 0 0 0 2 -3.00870920563557 -0.337859984836871 -0.123113202382392 -0.153436759095376 -2.05955749182822 3 -2.07677512619799 -0.709604203587071 -0.185270956474344 -0.185865735543112 -0.995014943027091 4 -1.2501039196554 -0.928920685940089 -0.192080061650079 -0.18529031273494 -0.116144616839291 5 0.817975239137125 -0.689068229444243 -0.120091308625758 -0.0910683381002602 1.37353653543211 6 0.0252076485413113 -0.609751814053241 -0.0916044909090781 -0.091244966301525 0.623809170681526 7 0.554937772830776 -0.425316061107351 -0.0570994604272071 -0.0447892531669484 0.876900194796564 8 0.230027371950115 -0.328188351538081 -0.0399631082053763 -0.0375253125168191 0.506663681018811 9 2.35672227418686 0.161182279398779 0.0129702657088473 0.0455911680914143 1.8165914954529 10 1.4135045517112 0.401884775082881 0.0336731957065978 0.0338586903486665 0.820736271441635 11 2.73311719024401 0.833407095198025 0.06682728940731 0.0902280373892896 1.50930109389431 12 1.31551925971717 0.960867064477248 0.0714913417051494 0.0624532429412668 0.24228216916783 13 -2.7007627224408 0.912510468505958 0.0629307747282609 -0.732463638908291 -2.17933242704605 14 -0.721411049152714 0.668085691631248 0.0424404046213962 0.00909657936452334 -1.17069055337286 15 -0.149388576811997 0.558253656218478 0.0329233771192608 0.0302213377362605 -0.614818643709566 16 -0.118199629770334 0.476092980363506 0.0261537269443059 0.00813932661654078 -0.498521227947173 17 -0.676562489695275 0.322020025646073 0.0161411335186538 0.0135541398248013 -0.832626770711557 18 1.79699928690761 0.536684282562967 0.0265897189606664 0.0713173531641533 0.973152758639384 19 1.79845572032988 0.723544336598844 0.0346032357144269 0.0562168571589747 0.83006549095896 20 0.245100010770855 0.693826219618397 0.0315403141575282 -0.0166323523779194 -0.350703795086036 21 1.80710848932636 0.84757694205539 0.0370953327156857 0.0948890622698778 0.69932370728707 22 -1.75934771184948 0.580412785196599 0.0238666592559258 -0.0795039836124123 -1.82235595792003 23 -0.0186697168761931 0.526893172336354 0.0206422312510853 0.0564684343821266 -0.484013558286986 24 0.189651523600062 0.504624042992753 0.0189257768272979 0.0349609929985976 -0.280503374220937 25 -1.84149562719087 0.38927014086954 0.0137611737907398 -0.254724170071894 -1.52794292646426 26 -1.07019530156943 0.246067427505414 0.00794769648870773 -0.0183011781312519 -1.0452326201295 27 -0.507291477584104 0.172584823601882 0.00503947147469917 0.0104305576599460 -0.555639151846882 28 0.866365633831705 0.242548388680557 0.00727823332311213 0.0491730028938489 0.461484830401469 29 -1.76077926699189 0.0644389081634554 0.00109864286177167 -0.114862540034759 -1.37061423861296 30 -0.580719393339347 0.00122788551389760 -0.00097586247730348 0.0351870300457735 -0.493580940212733 31 -0.435702079860853 -0.0414523212142378 -0.00227912323514198 0.0212395364642590 -0.331709514079693 32 -0.994868534845203 -0.119441415399855 -0.00457336477909578 -0.093674439949029 -0.623085277070507 33 1.63136048315789 0.0108240738219333 -0.000607516132010945 0.179733754595189 1.14661034875885 34 -1.1949403709466 -0.0756029597806416 -0.00305950234545563 -0.171689005949062 -0.75307597417658 35 -1.00525975426991 -0.154820057768571 -0.00517499111330214 0.0176248386783926 -0.688907865313166 36 1.32302234837564 -0.0542808312175853 -0.00231785009534840 0.127192218812249 0.990379756576892 37 -0.628357549594746 -0.0829553485932472 -0.00301144660272508 -0.101866706160584 -0.345612060624114 38 0.632048410440518 -0.0344549765229294 -0.00169063073931372 0.0413418884526878 0.49732768724465 39 -2.16903155809288 -0.186727500127953 -0.00545517806095646 -0.138095474337901 -1.46759701218477 40 2.53779364144266 -0.0110938868259967 -0.00103837827161713 0.267429836906598 1.81368136259316 41 -0.632933703679292 -0.0430496195485981 -0.00177450575854533 -0.189162105198873 -0.3182282809543 42 -1.417491963422 -0.139152857514633 -0.00396819720523114 -0.0217179566559275 -0.996947869794296 43 -0.455343045381255 -0.167905679693075 -0.00453148413644047 0.0516160745682807 -0.268740639518525 44 0.812255211942954 -0.103133724382716 -0.00299140770428937 -0.0573571650138387 0.770343197484806 45 0.627897309219833 -0.0716115302370842 -0.00224111201189978 0.202855581014120 0.392986893703714 46 0.650904313655623 -0.0202645828473225 -0.00110094053526868 -0.118848634120266 0.624625821615639 47 -1.29800419154382 -0.0947240222227177 -0.00262924259443798 -0.0957231302269195 -0.875016785424487 48 0.74391671726854 -0.0588193515525736 -0.00184283620128325 0.202286259675681 0.473798361432027 49 -1.50461634127457 -0.119992930518855 -0.00302945105658321 -0.208417934589222 -0.920249067996743 50 -1.42734677658523 -0.202142045837650 -0.00458081702250893 0.0415931699430216 -1.00334328447356 51 0.263353807408564 -0.172088230247541 -0.00391476639534321 -0.119825198802325 0.440015640864886 52 -0.430830854870631 -0.203879200209112 -0.00444073250036638 0.229128885971704 -0.361218271192151 53 0.379576092518008 -0.169737289497339 -0.00372623910754898 -0.0955298814100973 0.510410469441461 54 1.70309353400146 -0.0743187411439252 -0.00192360660825874 0.0854053465408092 1.33848623748116 55 -3.12314448117342 -0.229786100389650 -0.00466545933392777 -0.219038676757315 -2.11437705674836 56 -1.32526207118689 -0.289519204058890 -0.0056315583573543 -0.0573483874067931 -0.77312700438829 57 -0.60032490743804 -0.320613976735117 -0.0060705792938866 0.181570918253374 -0.364317983495049 58 1.23607137604666 -0.247719439131744 -0.00473218748206865 0.0258235548943518 1.15092684830282 59 0.738007075905376 -0.198020565092148 -0.00382500312337423 -0.088422186146746 0.808299372178697 60 0.899100896289585 -0.160382719072617 -0.00314528428496595 0.256487101264982 0.632971369509908

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788791ptpftisy5n0sjo6/1qofq1259788745.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788791ptpftisy5n0sjo6/1qofq1259788745.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788791ptpftisy5n0sjo6/2jhmi1259788745.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788791ptpftisy5n0sjo6/2jhmi1259788745.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788791ptpftisy5n0sjo6/36hpb1259788745.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788791ptpftisy5n0sjo6/36hpb1259788745.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788791ptpftisy5n0sjo6/4aj9r1259788745.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788791ptpftisy5n0sjo6/4aj9r1259788745.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788791ptpftisy5n0sjo6/591151259788745.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788791ptpftisy5n0sjo6/591151259788745.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')

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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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