Workshop 9: Structural time series model

*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 09:57:36 -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/t1259945985evxh8y9k85cdr8g.htm/, Retrieved Fri, 04 Dec 2009 17:59:52 +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/t1259945985evxh8y9k85cdr8g.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:

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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

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Structural Time Series Model t Observed Level Slope Seasonal Stand. Residuals 1 267413 267413 0 0 0 2 267366 267384.357654688 -30.1595068318717 -18.3576546875851 -0.0120573306031779 3 264777 265475.763074761 -1230.64730462337 -698.763074761267 -0.387207780916152 4 258863 260376.173861343 -3814.08699359233 -1513.17386134343 -0.872939958251469 5 254844 254967.296867130 -4876.39017440018 -123.296867129658 -0.332923013120594 6 254868 253450.915489083 -2679.70950965243 1417.08451091689 0.693250988131664 7 277267 270270.991467447 10102.8845048435 6996.00853255312 4.05104096080793 8 285351 285788.003521678 13660.7770413176 -437.003521678314 1.12545651843299 9 286602 290736.276374637 7934.00112730939 -4134.27637463657 -1.81127216020215 10 283042 286687.500765639 59.2377145686369 -3645.50076563855 -2.49085226920937 11 276687 278491.420276328 -5364.70454217156 -1804.42027632774 -1.71558560645971 12 277915 275926.488391431 -3525.34750976614 1988.51160856897 0.581783458681778 13 277128 275888.618919733 -1242.35391333100 1239.38108026734 0.724897532317247 14 277103 276119.640050427 -273.442006580221 983.359949572523 0.311502990853579 15 275037 274310.546622751 -1256.50466219448 726.453377248726 -0.308218470510597 16 270150 270425.803219630 -2914.36198059900 -275.803219630438 -0.531896063830159 17 267140 267870.660803246 -2684.87710598065 -730.660803245781 0.073090659271585 18 264993 269620.758930962 131.330768791653 -4627.758930962 0.886951137946173 19 287259 279812.723471286 6487.8919808944 7446.276528714 2.00973341430148 20 291186 289067.085977756 8238.78670676581 2118.91402224363 0.554283770795183 21 292300 293757.165361327 5989.62411900662 -1457.16536132667 -0.711398811597042 22 288186 291683.116036667 878.090627124425 -3497.11603666658 -1.61678482966945 23 281477 286133.284538209 -3194.37722816267 -4656.28453820917 -1.28817389796142 24 282656 281944.939650254 -3823.35446379716 711.060349745754 -0.199045423403195 25 280190 279026.569949849 -3250.51792353097 1163.43005015073 0.181769936433091 26 280408 277630.461624367 -2075.11210274765 2777.53837563298 0.372419943967702 27 276836 274670.010576067 -2631.76032878241 2165.98942393288 -0.175527054931249 28 275216 273993.861055428 -1409.30215085815 1222.13894457248 0.388059482722576 29 274352 275843.892322561 638.320053464804 -1491.89232256089 0.650790183526992 30 271311 279467.553593881 2514.41172645266 -8156.55359388106 0.592726949539441 31 289802 283709.146279641 3595.88142113060 6092.85372035882 0.341553139415206 32 290726 287633.87658938 3801.70084968363 3092.1234106198 0.0651105199350271 33 292300 290947.529694055 3495.88292360939 1352.47030594478 -0.0967453124667064 34 278506 283703.845381414 -3236.44053030738 -5197.8453814141 -2.12942823619126 35 269826 275263.654781419 -6497.21044619752 -5437.65478141853 -1.03149128100706 36 265861 266174.582475066 -8120.73639557832 -313.58247506571 -0.513937878309871 37 269034 265211.732959609 -3633.50684142821 3822.2670403909 1.42162440072165 38 264176 261286.649501754 -3816.25618789996 2889.35049824554 -0.057799338075365 39 255198 254427.318593741 -5715.73511057414 770.681406259409 -0.59991216601527 40 253353 251794.842969670 -3796.22281900901 1558.15703032966 0.608055454268744 41 246057 248859.105094192 -3259.28166814887 -2802.10509419200 0.170316022397996 42 235372 245091.625017296 -3576.77771057387 -9719.62501729559 -0.100435874232346 43 258556 250185.433321911 1830.32169825703 8370.56667808898 1.70823975157416 44 260993 256661.473756067 4724.16034894314 4331.52624393292 0.914941079265525 45 254663 252630.03949029 -731.561202361268 2032.96050971022 -1.72577205456562 46 250643 252529.07339128 -338.486833767182 -1886.07339128014 0.124346023835854 47 243422 249524.259015868 -2000.44577866795 -6102.25901586832 -0.525848546663348 48 247105 249320.305104821 -880.464671722156 -2215.30510482084 0.354524958695860 49 248541 245548.325514164 -2684.14785318996 2992.67448583648 -0.570929765356757 50 245039 241221.400684498 -3708.24407242044 3817.5993155022 -0.323773745385182 51 237080 237068.307936376 -3984.86209867995 11.6920636239260 -0.0874174362504562 52 237085 234614.621625068 -3034.09109358949 2470.37837493234 0.300987728283051 53 225554 229476.274529091 -4342.42688382378 -3922.27452909119 -0.414592290697748 54 226839 236099.637483597 2483.23188002607 -9260.63748359721 2.16002895079982 55 247934 240991.185621812 3980.9826979265 6942.81437818779 0.47338301735257 56 248333 242009.140377945 2140.45408994991 6323.85962205526 -0.581806500273487 57 246969 244702.522303296 2483.81188586549 2266.47769670426 0.108596769884744 58 245098 246686.357752478 2173.28267813475 -1588.35775247784 -0.0982459658341283 59 246263 251949.608541643 4092.8627024764 -5686.60854164295 0.607477935434488 60 255765 256802.826340855 4565.41443157929 -1037.82634085482 0.149570211298826 61 264319 260744.512846186 4177.64727925764 3574.48715381359 -0.122688892520152 62 268347 264204.204960062 3731.62971125095 4142.79503993849 -0.140999503967521 63 273046 271478.899652959 5928.85174997248 1567.10034704079 0.694566262438454 64 273963 273042.358456985 3224.03588936383 920.641543015415 -0.856043335704996 65 267430 275607.501021547 2815.42548075274 -8177.50102154707 -0.129417363409643 66 271993 281017.300658991 4425.81672752953 -9024.30065899091 0.509664428701021 67 292710 284951.684445151 4120.90337429693 7758.31555484861 -0.096399711316369 68 295881 289357.08737976 4297.23224828357 6523.91262023977 0.0557380803996539 69 293299 291689.913715015 3080.48099843533 1609.08628498541 -0.384794295264137

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259945985evxh8y9k85cdr8g/1v3491259945854.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259945985evxh8y9k85cdr8g/1v3491259945854.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259945985evxh8y9k85cdr8g/2utzm1259945854.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259945985evxh8y9k85cdr8g/2utzm1259945854.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259945985evxh8y9k85cdr8g/3vgfx1259945854.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259945985evxh8y9k85cdr8g/3vgfx1259945854.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259945985evxh8y9k85cdr8g/4945l1259945854.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259945985evxh8y9k85cdr8g/4945l1259945854.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259945985evxh8y9k85cdr8g/5neg91259945854.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259945985evxh8y9k85cdr8g/5neg91259945854.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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