WS 9 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: Fri, 04 Dec 2009 03:23:01 -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/04/t1259922225ohkno5kv3pm2ev7.htm/, Retrieved Fri, 04 Dec 2009 11:23:53 +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/04/t1259922225ohkno5kv3pm2ev7.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:

SHW WS 9 Structural Time Series Models

Dataseries X:

» Textbox « » Textfile « » CSV «

14.2 13.5 11.9 14.6 15.6 14.1 14.9 14.2 14.6 17.2 15.4 14.3 17.5 14.5 14.4 16.6 16.7 16.6 16.9 15.7 16.4 18.4 16.9 16.5 18.3 15.1 15.7 18.1 16.8 18.9 19 18.1 17.8 21.5 17.1 18.7 19 16.4 16.9 18.6 19.3 19.4 17.6 18.6 18.1 20.4 18.1 19.6 19.9 19.2 17.8 19.2 22 21.1 19.5 22.2 20.9 22.2 23.5 21.5 24.3 22.8 20.3 23.7 23.3 19.6 18 17.3 16.8 18.2 16.5 16 18.4

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 14.2 14.2 0 0 0 2 13.5 13.6962936202158 -0.0218460906336913 -0.196293620215784 -0.510961302574374 3 11.9 12.5702624714998 -0.0799509747537027 -0.670262471499777 -1.28905027878636 4 14.6 13.5370438654530 -0.0461511236863038 1.06295613454698 1.46329923993990 5 15.6 14.8464248791018 -0.0239254680788868 0.753575120898171 1.95715040105429 6 14.1 14.6933425081781 -0.0252516531120534 -0.593342508178087 -0.186791276444708 7 14.9 14.7846758745439 -0.0241722368094329 0.115324125456086 0.168450679883035 8 14.2 14.4884285371524 -0.026809952089474 -0.288428537152382 -0.392773401016692 9 14.6 14.5009388600968 -0.0264128347322480 0.0990611399032352 0.0567382164401477 10 17.2 15.9906933974858 -0.0109231754860895 1.20930660251417 2.18754213010685 11 15.4 15.9531568795025 -0.0111935144893430 -0.55315687950249 -0.0383985440214962 12 14.3 15.0428351737731 -0.0202241712770097 -0.742835173773071 -1.29732709720659 13 17.5 15.8445774986595 -0.0439215903861529 1.65542250134053 1.28248841532129 14 14.5 15.1386898929531 -0.0440762184398627 -0.638689892953074 -0.956503842745318 15 14.4 15.3125085376162 -0.0395886555083069 -0.912508537616215 0.290041437516813 16 16.6 15.7595887304915 -0.0285755810519530 0.840411269508474 0.669989945447174 17 16.7 15.8833206620207 -0.0260199957618279 0.816679337979287 0.217177605013153 18 16.6 16.5663305059722 -0.0181442950745629 0.0336694940277693 1.02223378168815 19 16.9 16.7138164028435 -0.0167963714325205 0.186183597156455 0.239206876790042 20 15.7 16.4580578485087 -0.0185438447733307 -0.758057848508664 -0.345069547894469 21 16.4 16.6882200247152 -0.0166973840672004 -0.288220024715194 0.359040185774239 22 18.4 16.9319367557831 -0.0148072290730592 1.46806324421694 0.375838750550512 23 16.9 17.0767935804617 -0.0139431355412167 -0.176793580461684 0.230235386400481 24 16.5 17.3491456998188 -0.0137442623144000 -0.849145699818803 0.41346327500924 25 18.3 16.9193860039223 -0.0116906700844613 1.38061399607775 -0.609305430076157 26 15.1 16.3534377019843 -0.0125862934937511 -1.2534377019843 -0.79657961809902 27 15.7 16.5418742525155 -0.0103600918800077 -0.841874252515507 0.279518673783194 28 18.1 17.0212199201116 -0.00290334362451252 1.07878007988838 0.682027894419079 29 16.8 16.7142445080592 -0.00723011557934332 0.0857554919407617 -0.43139289913556 30 18.9 17.7838474680002 0.00487658768126743 1.11615253199985 1.54656750785754 31 19 18.4208611098164 0.0103573765296951 0.579138890183553 0.911993503563147 32 18.1 18.8217904250746 0.0131587939088284 -0.721790425074643 0.564106828493199 33 17.8 18.5966672148395 0.0116609695805094 -0.796667214839529 -0.344116422627190 34 21.5 19.3717207720338 0.0156081321537201 2.12827922796619 1.10155994887272 35 17.1 18.4481432137171 0.0125830048153362 -1.34814321371715 -1.35410045289478 36 18.7 18.7456577462286 0.0128163868799370 -0.0456577462286247 0.411320851329926 37 19 18.1060238119363 0.0128228094228599 0.89397618806374 -0.94318038422607 38 16.4 17.8638916026368 0.012031102129274 -1.46389160263678 -0.364909874229781 39 16.9 17.8719629558072 0.0119996193423882 -0.971962955807191 -0.00558288949162498 40 18.6 17.6989694758117 0.00993532789428276 0.901030524188335 -0.260187794118112 41 19.3 18.7753544015383 0.0223781798086232 0.524645598461683 1.51362961246257 42 19.4 18.8600531426583 0.0230238900156075 0.539946857341671 0.0893083145149912 43 17.6 18.0297507890655 0.0157359945700344 -0.429750789065486 -1.22942482034335 44 18.6 18.5809601148936 0.0194460942434223 0.0190398851063878 0.77294592443537 45 18.1 18.9541157807890 0.0214121214346974 -0.854115780788967 0.51059396860266 46 20.4 18.4442703095337 0.0192026570312551 1.95572969046633 -0.766288873106567 47 18.1 18.9065524914277 0.0203767240500655 -0.80655249142769 0.638717058582607 48 19.6 19.1761600539987 0.0207527011184142 0.423839946001302 0.359315647383104 49 19.9 19.0705280477479 0.0205402529781829 0.829471952252136 -0.181938014290561 50 19.2 19.8980707578793 0.0235132400234149 -0.698070757879328 1.15412229369438 51 17.8 19.4901506804105 0.0206687710323164 -1.69015068041052 -0.611959182569259 52 19.2 19.0818366549179 0.0168603129674556 0.118163345082099 -0.60712352175694 53 22 20.2248169408139 0.0277871043690181 1.77518305918609 1.60147036004313 54 21.1 20.3966885582917 0.0291123025897494 0.703311441708282 0.206319304538089 55 19.5 20.3314861417559 0.0283612770781370 -0.831486141755915 -0.135715902666664 56 22.2 21.3243372868315 0.0346525444628367 0.875662713168459 1.39088119093849 57 20.9 21.5988155316594 0.0358768768914523 -0.698815531659421 0.345947200063953 58 22.2 21.0810932714245 0.0337927449160374 1.11890672857555 -0.7981356278653 59 23.5 22.7452561272502 0.0380830958354673 0.754743872749791 2.3493292309355 60 21.5 22.1671161311025 0.0368199501355184 -0.667116131102471 -0.887476799362390 61 24.3 22.9300612000130 0.0385877168929082 1.36993879998703 1.04361331108593 62 22.8 23.2308831796378 0.0396008318279125 -0.430883179637832 0.375146174328563 63 20.3 22.6375674740528 0.0359232147716827 -2.33756747405279 -0.900854601113942 64 23.7 23.3517188547394 0.0409833004893464 0.348281145260555 0.963769543552018 65 23.3 22.5656292225158 0.0341608227293757 0.73437077748417 -1.17859557606987 66 19.6 20.6388584469645 0.0182954704975575 -1.03885844696454 -2.80788066228598 67 18 19.7138562561804 0.0114594678733042 -1.71385625618036 -1.35616078818596 68 17.3 17.9630226369832 0.000778064530874426 -0.663022636983215 -2.53892632526007 69 16.8 17.4806259685557 -0.00153895237867139 -0.680625968555701 -0.696448362145635 70 18.2 17.5804328557332 -0.00117067445069441 0.619567144266806 0.146037657290146 71 16.5 16.5566294477317 -0.00400215643104431 -0.0566294477316673 -1.47289973064485 72 16 16.6527506842698 -0.00375817701028089 -0.652750684269753 0.144091047663971 73 18.4 16.8769270349950 -0.00311478899010797 1.52307296500497 0.327384222430384

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922225ohkno5kv3pm2ev7/1j98d1259922178.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922225ohkno5kv3pm2ev7/1j98d1259922178.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922225ohkno5kv3pm2ev7/2djn81259922178.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922225ohkno5kv3pm2ev7/2djn81259922178.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922225ohkno5kv3pm2ev7/3uxum1259922178.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922225ohkno5kv3pm2ev7/3uxum1259922178.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922225ohkno5kv3pm2ev7/4dija1259922178.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922225ohkno5kv3pm2ev7/4dija1259922178.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922225ohkno5kv3pm2ev7/5zuv81259922178.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922225ohkno5kv3pm2ev7/5zuv81259922178.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = 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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