WS9 Populaire technieken

*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 07:17:26 -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/t1259936291iwqesmwqcgd8cwo.htm/, Retrieved Fri, 04 Dec 2009 15:18:19 +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/t1259936291iwqesmwqcgd8cwo.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 «

7.1 6.9 6.8 7.5 7.6 7.8 8.0 8.1 8.2 8.3 8.2 8.0 7.9 7.6 7.6 8.3 8.4 8.4 8.4 8.4 8.6 8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8.0 8.2 8.1 8.1 8.0 7.9 7.9 8.0 8.0 7.9 8.0 7.7 7.2 7.5 7.3 7.0 7.0 7.0 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9 7.7 8.0 8.0 7.7 7.3 7.4 8.1 8.3 8.2

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 7.1 7.1 0 0 0 2 6.9 6.90727003089972 -0.193330798072277 -0.00727003089972077 -0.704226735768314 3 6.8 6.78850306280179 -0.125492050946939 0.0114969371982098 0.252756347173876 4 7.5 7.44591083795652 0.583043511915296 0.0540891620434831 2.52588990561095 5 7.6 7.6428322681507 0.234136871314490 -0.0428322681506953 -1.24908457651851 6 7.8 7.79831776638186 0.163006920426251 0.00168223361814192 -0.254542711717144 7 8 7.99604011720555 0.194403161063487 0.0039598827944467 0.112354031319325 8 8.1 8.10674705227073 0.118713362298507 -0.00674705227072498 -0.270861433124373 9 8.2 8.20026103489564 0.0959246813346164 -0.00026103489563794 -0.0815509497598487 10 8.3 8.2993394342541 0.0987767140041689 0.00066056574590474 0.0102062058851642 11 8.2 8.21342016981819 -0.0682513346322619 -0.0134201698181885 -0.597721993050808 12 8 8.00650145456995 -0.193653803787009 -0.0065014545699481 -0.44876183614508 13 7.9 7.89147459508063 -0.122595520072838 0.0085254049193685 0.254523475645755 14 7.6 7.59217121082318 -0.282536962946179 0.0078287891768185 -0.577275216605326 15 7.6 7.64182416917516 0.00596598444299717 -0.041824169175161 1.04483237081638 16 8.3 8.16655525806636 0.459782393795423 0.133444741933641 1.62336816872578 17 8.4 8.45965219770558 0.314615543694299 -0.0596521977055777 -0.519354045982309 18 8.4 8.43612740944127 0.0198809399027283 -0.0361274094412692 -1.05486589780462 19 8.4 8.38716986626877 -0.0401338706277877 0.0128301337312255 -0.214765078397047 20 8.4 8.39576081350222 0.00234381489326167 0.00423918649778433 0.152009931540260 21 8.6 8.59081817877229 0.170341920771762 0.00918182122771118 0.601193315489384 22 8.9 8.87851676311519 0.272648613683221 0.0214832368848141 0.366112006440112 23 8.8 8.831832584746 -0.00574093890677252 -0.0318325847460061 -0.99624165140994 24 8.3 8.36200481191443 -0.410263807497274 -0.0620048119144279 -1.44762769201956 25 7.5 7.4932303197456 -0.809740169950117 0.00676968025439419 -1.43130618328905 26 7.2 7.15511012989834 -0.398327005872472 0.0448898701016636 1.47498680004554 27 7.4 7.45583114313896 0.201888958538703 -0.0558311431389586 2.15555527228033 28 8.8 8.58039119628602 0.998089410556252 0.219608803713978 2.85296047944670 29 9.3 9.35577571761805 0.806473459701432 -0.0557757176180474 -0.685193450912207 30 9.3 9.39936618674591 0.150037179689955 -0.099366186745913 -2.34951319211936 31 8.7 8.74806931594868 -0.539751201203634 -0.0480693159486781 -2.46844625115379 32 8.2 8.19999718750983 -0.546913970464848 2.81249016968841e-06 -0.025632464797672 33 8.3 8.25928087668654 -0.0251096822778961 0.0407191233134559 1.86731544749477 34 8.5 8.4541253571834 0.164224349065813 0.0458746428165990 0.677547023955088 35 8.6 8.60161411509725 0.149818621850856 -0.00161411509725253 -0.051552241481579 36 8.5 8.50057399688722 -0.0660559400168866 -0.00057399688721909 -0.772568313369397 37 8.2 8.2246425368067 -0.246655836751749 -0.0246425368067008 -0.647074252099913 38 8.1 8.09442967950603 -0.146446877730986 0.00557032049397373 0.358638820560745 39 7.9 8.09142844421346 -0.0238997809579522 -0.191428444213459 0.439135973489429 40 8.6 8.37454691802018 0.23914639186227 0.225453081979815 0.942689687612276 41 8.7 8.68584769092942 0.300882146710618 0.0141523090705795 0.220765088877582 42 8.7 8.70569724624342 0.0605463043947875 -0.00569724624342114 -0.860125487706866 43 8.5 8.53430383931603 -0.137888066608808 -0.0343038393160259 -0.71013274749021 44 8.4 8.46329550245308 -0.0806649634861769 -0.063295502453075 0.204775138201458 45 8.5 8.48368698787787 0.00579914097279904 0.0163130121221290 0.309418719666709 46 8.7 8.65267841536439 0.145426081298132 0.0473215846356103 0.499669444396183 47 8.7 8.68824865126332 0.0514402107595554 0.0117513487366797 -0.336333862244121 48 8.6 8.579968496711 -0.0851648468510307 0.0200315032890044 -0.488923484234839 49 8.5 8.52374288160539 -0.0604079103247379 -0.0237428816053893 0.0886787778566803 50 8.3 8.31311180350983 -0.188854972835606 -0.0131118035098312 -0.459524459102798 51 8 8.22776220341937 -0.100708917528796 -0.227762203419365 0.315642902356651 52 8.2 8.01447943356547 -0.196744756131382 0.185520566434526 -0.344087289326769 53 8.1 8.03298858416205 -0.0132014923308079 0.0670114158379463 0.656468788902478 54 8.1 8.06255105661335 0.0232368452714625 0.0374489433866447 0.130392330938489 55 8 8.03970540050667 -0.0160420623676027 -0.0397054005066689 -0.140570424063523 56 7.9 7.97802831168556 -0.0549450064838047 -0.0780283116855602 -0.139215456420619 57 7.9 7.91615239554774 -0.0608535176785578 -0.0161523955477431 -0.0211441138149328 58 8 7.93545198060208 0.00747467701808595 0.0645480193979246 0.244520744789192 59 8 7.96520068167508 0.0264601922469266 0.0347993183249160 0.0679404175326343 60 7.9 7.89872396132192 -0.0527355078436937 0.00127603867807973 -0.283469326265611 61 8 7.98623349051895 0.0668121636373034 0.0137665094810453 0.428103429163364 62 7.7 7.75631952395923 -0.185943521580317 -0.0563195239592275 -0.904194443637885 63 7.2 7.41481367387593 -0.318120961263392 -0.214813673875928 -0.473185742016671 64 7.5 7.32354846566041 -0.125148099870672 0.176451534339589 0.6912281262927 65 7.3 7.23829098133275 -0.091217044934376 0.0617090186672505 0.121381259628967 66 7 6.97357700991644 -0.238688393993744 0.0264229900835601 -0.527675275800038 67 7 7.00535343574502 -0.00874736864003431 -0.00535343574501785 0.822912848967152 68 7 7.0669277434401 0.051048683953149 -0.0669277434400967 0.213983038118568 69 7.2 7.21776890431996 0.135906561874758 -0.0177689043199547 0.303671323684131 70 7.3 7.25071420025048 0.0483568380781457 0.049285799749519 -0.313307336039727 71 7.1 7.07611430569738 -0.141195911550297 0.0238856943026192 -0.678325316143238 72 6.8 6.8441745721063 -0.218330676964357 -0.0441745721063067 -0.276101577646014 73 6.4 6.3681186017649 -0.437471930072982 0.0318813982351018 -0.784590556971931 74 6.1 6.10687663620297 -0.287734886356914 -0.00687663620296603 0.535674493546359 75 6.5 6.6695206129733 0.433565869984015 -0.169520612973299 2.58186942735932 76 7.7 7.49087366362227 0.762752725324344 0.209126336377733 1.17890596097675 77 7.9 7.83639480139802 0.408516713160404 0.063605198601978 -1.26737687852553 78 7.5 7.57333104585269 -0.161303494489143 -0.0733310458526862 -2.03882164460811 79 6.9 6.96011983928894 -0.544773139016027 -0.060119839288939 -1.37234651814663 80 6.6 6.66851579883087 -0.329902993657074 -0.0685157988308718 0.768927974988306 81 6.9 6.86471913468883 0.116633535003733 0.0352808653111663 1.59796866010482 82 7.7 7.56928691897711 0.615626983916892 0.130713081022887 1.78570242190926 83 8 7.98183495809932 0.44329926183928 0.0181650419006784 -0.616691422072169 84 8 8.01339896912546 0.0939464808181325 -0.0133989691254577 -1.25050214367421 85 7.7 7.69547686589742 -0.255609700124928 0.00452313410258257 -1.25133186123122 86 7.3 7.43848397623087 -0.256782819675197 -0.138483976230873 -0.00419692932001889 87 7.4 7.62531941992596 0.118993667319690 -0.225319419925961 1.34498147436459 88 8.1 7.85409050603119 0.212037450252055 0.245909493968811 0.333163348864071 89 8.3 8.13400594812843 0.269582263292263 0.165994051871569 0.205901647277511 90 8.2 8.1955038702557 0.0932682385149048 0.00449612974429121 -0.630844684103213

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936291iwqesmwqcgd8cwo/16s5s1259936244.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936291iwqesmwqcgd8cwo/16s5s1259936244.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936291iwqesmwqcgd8cwo/2wscx1259936244.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936291iwqesmwqcgd8cwo/2wscx1259936244.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936291iwqesmwqcgd8cwo/39qy01259936244.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936291iwqesmwqcgd8cwo/39qy01259936244.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936291iwqesmwqcgd8cwo/4shgt1259936244.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936291iwqesmwqcgd8cwo/4shgt1259936244.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936291iwqesmwqcgd8cwo/595v41259936244.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936291iwqesmwqcgd8cwo/595v41259936244.ps (open in new window)

Parameters (Session):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;

Parameters (R input):

par1 = 12 ; par2 = 0.99 ; par3 = 0.005 ;

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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