WS 9 ADC3

*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 09:36:20 -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/t12599446265csguk8a9p9gf2d.htm/, Retrieved Fri, 04 Dec 2009 17:37:15 +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/t12599446265csguk8a9p9gf2d.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 «

100 96.21064363 96.31280765 107.1793443 114.9066592 92.56060184 114.9995356 107.1236185 117.7765394 107.3650971 106.2970187 114.5072908 98.0031578 103.0649206 100.2879168 104.6066685 111.1544534 104.9874617 109.9284852 111.5352466 132.4974459 100.3436426 123.0983561 114.2379493 104.569518 109.0833101 106.9843039 133.6769759 124.8537197 122.5132349 116.8013374 116.0118882 129.7575926 125.1973623 143.7912139 127.9465032 130.2962757 108.4424631 129.3675118 143.6797622 131.8844618 117.6186496 118.9560695 104.8202842 134.624315 140.401226 143.8005015 153.4317823 153.2924677 127.3149438 153.5525216 136.9276493 131.7730101 144.3391845 107.4208229 113.6249652 124.2221603 102.0618557 96.36853348 111.6838488

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 1 100 100 0 0 0 2 96.21064363 97.5373664216195 -0.143860738292253 -0.681713868392448 -0.310174879296508 3 96.31280765 96.6760509472387 -0.182276624682697 -0.144890115938404 -0.104994466129451 4 107.1793443 102.125001317525 0.00431775095857434 2.95980937768869 0.941466825970646 5 114.9066592 109.326575464091 0.156170054727744 2.75277519839507 1.24356833811129 6 92.56060184 101.430566752015 0.0252577203837679 -5.66563470086604 -1.40104564217902 7 114.9995356 107.562350334838 0.114662006986720 4.9995967082029 1.06408405220087 8 107.1236185 108.007538646737 0.119328933509450 -1.0159502009055 0.0576107766798939 9 117.7765394 113.096456050171 0.188359028989258 2.69464567648684 0.866223746173037 10 107.3650971 110.673947380498 0.152550876628292 -2.26567070631723 -0.455090770842998 11 106.2970187 108.113252137745 0.115808853761867 -0.732036952416045 -0.472946361965449 12 114.5072908 111.118466637522 0.154429596875019 2.23410031605172 0.503668723013701 13 98.0031578 106.472888785763 0.414337131190102 -6.45891247343987 -0.982996154118947 14 103.0649206 104.793290573314 0.384711891470705 -1.00189560057220 -0.341894201405566 15 100.2879168 103.265417850362 0.332871414993055 -2.35600891534035 -0.303056727939821 16 104.6066685 103.158761780015 0.322987967264927 1.60098536129036 -0.0736046776521629 17 111.1544534 104.520224576655 0.339372330782016 6.25675763957954 0.179007298202614 18 104.9874617 108.518329757763 0.381587089940069 -4.88095255380001 0.636389304796465 19 109.9284852 107.483906879900 0.367956484128434 2.96942262879167 -0.246870615250935 20 111.5352466 110.592102739825 0.392634153969483 -0.07361318227802 0.477967006690232 21 132.4974459 119.837232149212 0.471586343333092 9.37517163551574 1.54419184670030 22 100.3436426 112.470961452559 0.402403526426611 -9.21849160530255 -1.36727296540452 23 123.0983561 117.509007141891 0.438267830724493 3.86752661261286 0.808537090003388 24 114.2379493 114.727062266186 0.429886069330814 0.711360168868876 -0.562282210151758 25 104.569518 112.551668836231 0.470105710817692 -6.98151023549014 -0.477190049090728 26 109.0833101 110.915173169624 0.457697890339571 -1.07565709961084 -0.359892618309900 27 106.9843039 109.983190909314 0.434290852352844 -2.52689959933962 -0.229175799060881 28 133.6769759 120.861246994074 0.614237464854623 9.1986348531375 1.75790143069973 29 124.8537197 121.645608577595 0.61659383412269 3.14749309771558 0.0292558078729798 30 122.5132349 124.569337586340 0.641096411599984 -2.89062720104175 0.40073672140986 31 116.8013374 120.873236868002 0.603558851863338 -2.49373761979692 -0.756001444435605 32 116.0118882 119.742012937850 0.590103457234771 -3.09761354982556 -0.302711668609346 33 129.7575926 118.837636137810 0.579110776684702 11.4652107637988 -0.260852507739305 34 125.1973623 126.918193294708 0.629649392723849 -4.45893862682025 1.30918637823193 35 143.7912139 133.447811965066 0.658628731854828 8.18777016889364 1.02927781592778 36 127.9465032 131.082578853865 0.656420039702151 -2.02734274814574 -0.528788945849175 37 130.2962757 133.956547300811 0.645690061002581 -4.48348273528640 0.393540209390653 38 108.4424631 123.360960113657 0.598266384917787 -10.8729771123176 -1.93772917178489 39 129.3675118 128.617960295039 0.652702167793489 -0.870336582269216 0.78432292370667 40 143.6797622 132.214235107705 0.692565429371402 10.4393604201909 0.49877130129205 41 131.8844618 131.334246791444 0.673483320587388 1.10783648963995 -0.270291521121996 42 117.6186496 125.467601075613 0.608359721831748 -5.49990446070787 -1.13463224923134 43 118.9560695 122.834285159525 0.581681911463347 -2.70625237973415 -0.564789576711221 44 104.8202842 115.881280415165 0.527876482405619 -8.32920641147409 -1.31489170196049 45 134.624315 120.405721171360 0.55330266576413 12.7678528642587 0.697746654075396 46 140.401226 133.503394351087 0.620345664161638 2.34143232472684 2.18952252820420 47 143.8005015 135.631304691255 0.625666354365005 7.62116717600659 0.263049380675878 48 153.4317823 145.509494285397 0.633616176319047 4.55045585367862 1.61736831017654 49 153.2924677 150.935197354566 0.629860458357961 0.604827815954346 0.840666907504257 50 127.3149438 147.016532344007 0.612005981142804 -18.0664934715461 -0.785919297864018 51 153.5525216 150.957897458098 0.641620206288358 1.42289157287978 0.566753374934996 52 136.9276493 139.300227795195 0.506927433297731 1.94534276917646 -2.09631850488088 53 131.7730101 132.741924800545 0.432088942104753 1.53592589784868 -1.21531374933431 54 144.3391845 139.169482868079 0.48735961171528 3.02255579781256 1.03945457243554 55 107.4208229 125.187595445665 0.374528298462071 -12.5518191970416 -2.51970021396263 56 113.6249652 123.793713769037 0.362771627241023 -9.52929085096324 -0.308552980171308 57 124.2221603 120.500314042097 0.342135327213839 5.04593022686359 -0.638265185866724 58 102.0618557 111.408680827611 0.299890062570385 -5.92800102403571 -1.64646165455361 59 96.36853348 101.872386612429 0.271006811103152 -1.93685180440652 -1.71630925625182 60 111.6838488 103.916254118627 0.273360173772435 7.12383290362036 0.309605310926179

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599446265csguk8a9p9gf2d/1jua81259944577.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599446265csguk8a9p9gf2d/1jua81259944577.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599446265csguk8a9p9gf2d/20ycl1259944577.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599446265csguk8a9p9gf2d/20ycl1259944577.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599446265csguk8a9p9gf2d/3k5qr1259944577.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599446265csguk8a9p9gf2d/3k5qr1259944577.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599446265csguk8a9p9gf2d/4wvqf1259944577.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599446265csguk8a9p9gf2d/4wvqf1259944577.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599446265csguk8a9p9gf2d/5k84k1259944577.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599446265csguk8a9p9gf2d/5k84k1259944577.ps (open in new window)

Parameters (Session):

par1 = TRUE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

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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