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: Mon, 07 Dec 2009 15:48:25 -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/07/t12602261623sm3szhvivf8hxx.htm/, Retrieved Mon, 07 Dec 2009 23:49:28 +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/07/t12602261623sm3szhvivf8hxx.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:

Structural Time Series Models

Dataseries X:

» Textbox « » Textfile « » CSV «

220206 220115 218444 214912 210705 209673 237041 242081 241878 242621 238545 240337 244752 244576 241572 240541 236089 236997 264579 270349 269645 267037 258113 262813 267413 267366 264777 258863 254844 254868 277267 285351 286602 283042 276687 277915 277128 277103 275037 270150 267140 264993 287259 291186 292300 288186 281477 282656 280190 280408 276836 275216 274352 271311 289802 290726 292300 278506 269826 265861 269034 264176 255198 253353 246057 235372 258556 260993 254663 250643 243422 247105 248541 245039 237080 237085 225554 226839 247934 248333 246969 245098 246263 255765 264319 268347 273046 273963 267430 271993 292710 295881 293299 288576

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 'Gwilym Jenkins' @ 72.249.127.135 Structural Time Series Model t Observed Level Slope Seasonal Stand. Residuals 1 220206 220206 0 0 0 2 220115 220151.947561343 -57.105956069184 -36.9475613429499 -0.0241578908683742 3 218444 218884.832710419 -825.237855151883 -440.832710418858 -0.257968044864550 4 214912 215807.635089226 -2313.37718911019 -895.6350892258 -0.527721428071982 5 210705 211283.377214379 -3774.90936620938 -578.377214378565 -0.479226635424588 6 209673 208881.96866542 -2884.886369516 791.031334580144 0.293510621151455 7 237041 228413.507291201 11674.1162482406 8627.49270879926 4.82514873367526 8 242081 243632.844898227 13982.9247329545 -1551.84489822655 0.763704401832559 9 241878 246732.243968709 6892.89399700677 -4854.24396870908 -2.34470007420332 10 242621 244809.28116615 1150.94170799541 -2188.28116614989 -1.89908005699550 11 238545 239904.48547557 -2792.34611975729 -1359.48547556992 -1.30415484917333 12 240337 238931.777842675 -1607.58355473100 1405.22215732499 0.391831081100997 13 244752 242658.719840158 1852.95961913864 2093.28015984247 1.14900380079447 14 244576 244677.849582123 1961.25480932071 -101.849582123406 0.0364069440670138 15 241572 242094.817409794 -924.33898095333 -522.817409794261 -0.945829032128195 16 240541 239259.420223356 -2118.81099437688 1281.57977664350 -0.40053041610154 17 236089 237147.009246986 -2114.75867793284 -1058.00924698640 0.00135060985011902 18 236997 242297.925045259 2460.46145689813 -5300.92504525874 1.50664286547255 19 264579 254795.253354148 8746.13104022008 9783.74664585243 2.07748339526408 20 270349 267772.905303327 11400.2863477810 2576.0946966728 0.87860459636238 21 269645 273762.972432773 8001.5633362573 -4117.97243277296 -1.12407224299349 22 267037 270811.588798617 1119.49118215211 -3774.58879861729 -2.27607867707033 23 258113 263028.443330783 -4471.29014092542 -4915.44333078321 -1.84911114869343 24 262813 261672.552954001 -2517.20450622156 1140.44704599920 0.646608876382176 25 267413 263694.834714795 330.998185231379 3718.16528520452 0.945007737571297 26 267366 265008.563021343 948.438860638996 2357.4369786569 0.204561220854836 27 264777 264104.939732210 -206.068971212011 672.060267789575 -0.380643411426417 28 258863 258737.122490497 -3404.43215604157 125.877509502864 -1.06137009388874 29 254844 257664.911934918 -1952.28530881217 -2820.911934918 0.482682294448132 30 254868 262613.782166726 2347.54295820549 -7745.78216672599 1.42071120739347 31 277267 269030.037705688 4873.29548896407 8236.96229431205 0.83397540008689 32 285351 279099.429717225 8096.83140331357 6251.57028277479 1.06620121409361 33 286602 286654.998894965 7760.65485853806 -52.9988949654144 -0.111202917135502 34 283042 286469.754399201 2823.21138281052 -3427.75439920139 -1.63296438615244 35 276687 284431.267887248 -196.634488030494 -7744.26788724804 -0.998871775327268 36 277915 280209.941286073 -2695.76440348411 -2294.94128607324 -0.827219284042565 37 277128 274662.903502512 -4467.68254471405 2465.09649748757 -0.586966422333203 38 277103 272191.034043496 -3227.63641403206 4911.9659565044 0.410087234379275 39 275037 270967.602949350 -1987.37327935046 4069.39705064973 0.409571799619892 40 270150 270146.799993162 -1267.41195688991 3.20000683824838 0.238446656662148 41 267140 271477.918684309 339.845263588217 -4337.91868430927 0.53310467720651 42 264993 274189.763076174 1808.96867566131 -9196.76307617405 0.486008904553596 43 287259 280282.373759483 4457.47027069849 6976.62624051714 0.874882867546938 44 291186 285196.974844635 4739.74820741193 5989.02515536527 0.0933112628916727 45 292300 289682.099837851 4582.48068372311 2617.90016214859 -0.0520160290744053 46 288186 291018.132138596 2576.57305337064 -2832.13213859644 -0.663516900184109 47 281477 289001.116672355 -261.713807785126 -7524.11667235522 -0.93904242071879 48 282656 284947.388112201 -2605.23589926443 -2291.38811220076 -0.775685943000199 49 280190 279282.544137391 -4497.20050282367 907.45586260913 -0.626181624029428 50 280408 275442.358122193 -4091.17857353071 4965.64187780673 0.134220052351034 51 276836 272488.48132049 -3390.09459460652 4347.51867951020 0.231660115571597 52 275216 274046.018825338 -344.604524095429 1169.98117466171 1.00804906563687 53 274352 278283.79037747 2479.59117482337 -3931.79037746988 0.935797187822265 54 271311 282128.862140493 3322.15763959838 -10817.8621404931 0.278826417869663 55 289802 284067.260795632 2468.99537078949 5734.73920436849 -0.281959040822644 56 290726 285400.425975654 1769.57790937026 5325.57402434617 -0.231164278915934 57 292300 288233.123611895 2423.96290862889 4066.87638810483 0.216402825998896 58 278506 282792.322991091 -2417.77686281426 -4286.3229910909 -1.60175727125959 59 269826 276479.159996527 -4816.5113818281 -6653.15999652672 -0.79377699727771 60 265861 267887.661453307 -7142.15368993512 -2026.66145330681 -0.769699633530674 61 269034 265705.385787276 -4085.54161084321 3328.61421272369 1.01121325919332 62 264176 260408.221499890 -4831.66883045008 3767.77850010972 -0.246629111376303 63 255198 253481.744716514 -6119.42339965102 1716.25528348597 -0.425634405871612 64 253353 252071.997462188 -3226.82930077746 1281.00253781236 0.957208783067707 65 246057 250421.130360352 -2258.0893904175 -4364.13036035204 0.320827585888107 66 235372 246662.910193551 -3181.1115861402 -11290.9101935510 -0.305468682572277 67 258556 250312.126552545 1019.97664312930 8243.87344745534 1.38881791005744 68 260993 255167.591180550 3376.41626196456 5825.40881945026 0.778828074810524 69 254663 250705.812578547 -1435.79846382531 3957.18742145281 -1.59121978123962 70 250643 251538.340040763 -43.2226585710357 -895.340040762983 0.460719772320593 71 243422 249883.725968071 -1032.87649947438 -6461.72596807086 -0.327525653689344 72 247105 250235.144316805 -182.240937093511 -3130.14431680489 0.281506885416021 73 248541 246019.043699973 -2661.42790024907 2521.95630002731 -0.820018267294366 74 245039 241029.604878746 -4091.12437736475 4009.39512125386 -0.472581702373198 75 237080 236849.355489554 -4145.78554897385 230.644510445671 -0.0180695605610081 76 237085 235047.703499156 -2708.99656879391 2037.29650084392 0.475399087899224 77 225554 230583.823851440 -3785.29650494648 -5029.82385143955 -0.35634510597235 78 226839 237077.358557541 2523.95829881631 -10238.3585575406 2.08795128167729 79 247934 241031.911583277 3401.91576245242 6902.08841672315 0.290288509152947 80 248333 240984.169001294 1286.89224192128 7348.83099870631 -0.699075647119443 81 246969 243287.301413909 1909.45377150278 3681.69858609122 0.205848112758371 82 245098 245746.145697483 2245.96768923106 -648.145697483318 0.111332515081609 83 246263 251809.795164201 4585.36704998856 -5546.79516420071 0.77424331249251 84 255765 257149.46187222 5047.84083996436 -1384.46187222021 0.153040188435924 85 264319 261069.258279305 4356.16008026155 3249.74172069465 -0.228759466745436 86 268347 264329.984513265 3684.96314141705 4017.01548673516 -0.221869429510257 87 273046 271645.457236562 5907.04618810927 1400.54276343817 0.734628693754829 88 273963 273610.286032283 3495.28633470969 352.713967717219 -0.797932356444467 89 267430 276480.296127308 3112.5612259563 -9050.29612730787 -0.126689952964128 90 271993 281671.656136184 4385.83631050951 -9678.65613618361 0.421347929455546 91 292710 284933.844870195 3697.65435529559 7776.15512980473 -0.227562193110791 92 295881 288619.79881185 3690.49431605292 7261.20118815018 -0.00236675304644896 93 293299 290654.719821155 2678.19392873028 2644.28017884468 -0.334710134743844 94 288576 291400.839718485 1497.06521423281 -2824.83971848502 -0.390756492252324

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/07/t12602261623sm3szhvivf8hxx/1kjsn1260226102.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/07/t12602261623sm3szhvivf8hxx/1kjsn1260226102.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/07/t12602261623sm3szhvivf8hxx/2us7m1260226102.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/07/t12602261623sm3szhvivf8hxx/2us7m1260226102.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/07/t12602261623sm3szhvivf8hxx/3amf21260226102.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/07/t12602261623sm3szhvivf8hxx/3amf21260226102.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/07/t12602261623sm3szhvivf8hxx/41f9b1260226102.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/07/t12602261623sm3szhvivf8hxx/41f9b1260226102.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/07/t12602261623sm3szhvivf8hxx/5ryo81260226102.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/07/t12602261623sm3szhvivf8hxx/5ryo81260226102.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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by