| 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 07:23:59 -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/t1259936717hpkxtpzjimk4ulh.htm/, Retrieved Fri, 04 Dec 2009 15:25:24 +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/t1259936717hpkxtpzjimk4ulh.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 « | | 98,8
100,5
110,4
96,4
101,9
106,2
81
94,7
101
109,4
102,3
90,7
96,2
96,1
106
103,1
102
104,7
86
92,1
106,9
112,6
101,7
92
97,4
97
105,4
102,7
98,1
104,5
87,4
89,9
109,8
111,7
98,6
96,9
95,1
97
112,7
102,9
97,4
111,4
87,4
96,8
114,1
110,3
103,9
101,6
94,6
95,9
104,7
102,8
98,1
113,9
80,9
95,7
113,2
105,9
108,8
102,3
99
100,7
115,5
100,7
109,9
114,6
85,4
100,5
114,8
116,5
112,9
102
106
105,3
118,8
106,1
109,3
117,2
92,5
104,2
112,5
122,4
113,3
100
110,7
112,8
109,8
117,3
109,1
115,9
96
99,8
116,8
115,7
99,4
94,3 | | | | Output produced by software: |
| Structural Time Series Model | | t | Observed | Level | Slope | Seasonal | Stand. Residuals | | 1 | 98.8 | 98.8 | 0 | 0 | 0 | | 2 | 100.5 | 99.0098361764009 | -0.0391919649449301 | 1.49016382359911 | 0.388717178313888 | | 3 | 110.4 | 103.557938672195 | 0.289117512396445 | 6.8420613278053 | 2.37894910697432 | | 4 | 96.4 | 102.916616104524 | 0.204866863319226 | -6.51661610452434 | -0.453472455807471 | | 5 | 101.9 | 102.467031750271 | 0.148646019839951 | -0.567031750271342 | -0.389935500093396 | | 6 | 106.2 | 103.314154106381 | 0.199016738617089 | 2.88584589361902 | 0.485265288551031 | | 7 | 81 | 98.1421630341768 | -0.107051973677707 | -17.1421630341768 | -4.03755497919976 | | 8 | 94.7 | 95.2415616478735 | -0.232145392064929 | -0.541561647873479 | -2.17500001561392 | | 9 | 101 | 95.4144494351909 | -0.217351445974806 | 5.58555056480914 | 0.320074983827219 | | 10 | 109.4 | 98.829318846847 | -0.102465549659385 | 10.5706811531531 | 2.88736399319624 | | 11 | 102.3 | 101.082184715780 | -0.0340545801841086 | 1.21781528422044 | 1.87555612160628 | | 12 | 90.7 | 99.5211029931645 | -0.0765164808777496 | -8.82110299316446 | -1.21573693447957 | | 13 | 96.2 | 98.4278335880762 | -0.0786365050015628 | -2.22783358807624 | -0.837114293790518 | | 14 | 96.1 | 97.6344558667332 | -0.0779097749925256 | -1.53445586673316 | -0.597327158208534 | | 15 | 106 | 97.2148151878089 | -0.0817089763567255 | 8.78518481219112 | -0.271968943399785 | | 16 | 103.1 | 99.6618169891172 | -0.0188244895863435 | 3.43818301088279 | 1.88477326938139 | | 17 | 102 | 100.698616455163 | 0.0166870899182674 | 1.30138354483683 | 0.764909178644743 | | 18 | 104.7 | 100.138930896851 | -0.00458268671612825 | 4.56106910314886 | -0.422243923205732 | | 19 | 86 | 100.426142359364 | 0.00592639577782337 | -14.4261423593644 | 0.219563317532909 | | 20 | 92.1 | 99.2041441317476 | -0.0341627032902864 | -7.10414413174765 | -0.947080104535874 | | 21 | 106.9 | 99.9994108213925 | -0.0107872688890624 | 6.90058917860749 | 0.650523709474136 | | 22 | 112.6 | 100.924674703424 | 0.0111798728709737 | 11.6753252965756 | 0.741231190687254 | | 23 | 101.7 | 100.742016487239 | 0.00751345736828228 | 0.957983512761186 | -0.154306910210952 | | 24 | 92 | 100.477357537409 | 0.00347865014955188 | -8.4773575374093 | -0.217427882668088 | | 25 | 97.4 | 100.199303446008 | 0.000152177320648185 | -2.79930344600771 | -0.225435315804073 | | 26 | 97 | 99.9893586502527 | -0.00221301989496133 | -2.98935865025267 | -0.167732327906410 | | 27 | 105.4 | 99.651326768601 | -0.00668046894272565 | 5.74867323139898 | -0.265059650259245 | | 28 | 102.7 | 99.5463226882764 | -0.00833114375838917 | 3.15367731172359 | -0.0764024285973884 | | 29 | 98.1 | 98.7266147144523 | -0.024716530736683 | -0.626614714452342 | -0.6233580183334 | | 30 | 104.5 | 98.7024140438546 | -0.0247049416873436 | 5.79758595614544 | 0.000395471388422841 | | 31 | 87.4 | 99.3706841150724 | -0.00862983931384387 | -11.9706841150723 | 0.534309673127569 | | 32 | 89.9 | 99.283120171661 | -0.0104047850297574 | -9.38312017166093 | -0.0614178309585382 | | 33 | 109.8 | 100.212333996473 | 0.00906179768284433 | 9.58766600352698 | 0.737438521284237 | | 34 | 111.7 | 100.410859326785 | 0.0125454074693188 | 11.2891406732150 | 0.149661901763741 | | 35 | 98.6 | 99.7158992477079 | 0.00123238558733513 | -1.11589924770786 | -0.561278537023017 | | 36 | 96.9 | 100.671893513954 | 0.0145715389641173 | -3.77189351395415 | 0.759306942950503 | | 37 | 95.1 | 100.277128388259 | 0.00937848982912856 | -5.17712838825894 | -0.325724349963536 | | 38 | 97 | 99.9465804259737 | 0.00518462919910609 | -2.94658042597369 | -0.270001948785785 | | 39 | 112.7 | 101.397265781672 | 0.0237964810241387 | 11.3027342183279 | 1.14338861161793 | | 40 | 102.9 | 101.469161565781 | 0.0244698132418411 | 1.43083843421895 | 0.0378481793485489 | | 41 | 97.4 | 100.783988791014 | 0.0136337196838558 | -3.38398879101382 | -0.556052023203621 | | 42 | 111.4 | 101.856806009154 | 0.0308758078933629 | 9.54319399084579 | 0.828606522996382 | | 43 | 87.4 | 101.769756044686 | 0.0288996685262079 | -14.3697560446857 | -0.0923682580025581 | | 44 | 96.8 | 102.950634583458 | 0.048045614227143 | -6.15063458345759 | 0.90515765807726 | | 45 | 114.1 | 103.762502462743 | 0.0602233629901246 | 10.3374975372574 | 0.602428981689017 | | 46 | 110.3 | 102.912604112212 | 0.0466477584092689 | 7.3873958877875 | -0.720272168885567 | | 47 | 103.9 | 103.246960282092 | 0.0506124271222886 | 0.65303971790838 | 0.228286603326934 | | 48 | 101.6 | 103.872953200617 | 0.0579596860053997 | -2.2729532006167 | 0.457284546526323 | | 49 | 94.6 | 103.2698439776 | 0.0499844650346042 | -8.66984397760002 | -0.525669500923169 | | 50 | 95.9 | 102.287356603882 | 0.0378471829486033 | -6.38735660388211 | -0.820531912534926 | | 51 | 104.7 | 99.8783734079314 | 0.0089006847313382 | 4.82162659206855 | -1.94164489347105 | | 52 | 102.8 | 99.4090151217027 | 0.00307500483439561 | 3.39098487829731 | -0.378787462775978 | | 53 | 98.1 | 100.038101379486 | 0.0109906154563009 | -1.9381013794865 | 0.494996185223788 | | 54 | 113.9 | 101.454173949532 | 0.0293281300903765 | 12.4458260504676 | 1.11014924342745 | | 55 | 80.9 | 100.773068316939 | 0.0199016027302481 | -19.8730683169387 | -0.561470987021063 | | 56 | 95.7 | 100.817171353148 | 0.0202218476453798 | -5.11717135314811 | 0.0191492475154115 | | 57 | 113.2 | 101.173950995573 | 0.0245797155182187 | 12.0260490044272 | 0.266736234786609 | | 58 | 105.9 | 100.683320882683 | 0.0181488837195439 | 5.2166791173168 | -0.409016963290624 | | 59 | 108.8 | 102.121932281781 | 0.0351014118717504 | 6.67806771821907 | 1.12930723947157 | | 60 | 102.3 | 102.829289190337 | 0.0427747121393249 | -0.529289190336752 | 0.534999421844736 | | 61 | 99 | 103.756183193088 | 0.0525091831587319 | -4.75618319308842 | 0.703946053253157 | | 62 | 100.7 | 104.466051032359 | 0.059591557389357 | -3.76605103235891 | 0.523373688636769 | | 63 | 115.5 | 106.246493475362 | 0.0780223816736628 | 9.2535065246378 | 1.369460830772 | | 64 | 100.7 | 105.049882692110 | 0.0642789463183618 | -4.3498826921101 | -1.01367015760388 | | 65 | 109.9 | 106.388711889583 | 0.0782030914301732 | 3.51128811041656 | 1.01297767969026 | | 66 | 114.6 | 105.828033352111 | 0.0711344405141959 | 8.77196664788895 | -0.507603384435839 | | 67 | 85.4 | 105.58935604499 | 0.0676839168247103 | -20.1893560449899 | -0.246175581026117 | | 68 | 100.5 | 105.683769024753 | 0.0679807938960927 | -5.18376902475264 | 0.0212493259229752 | | 69 | 114.8 | 105.244076340435 | 0.0624140869473795 | 9.55592365956484 | -0.403900964636287 | | 70 | 116.5 | 106.966901115996 | 0.08023597268656 | 9.53309888400403 | 1.32213392324065 | | 71 | 112.9 | 107.774670324942 | 0.0878406200810959 | 5.12532967505839 | 0.579769434185688 | | 72 | 102 | 107.182998145959 | 0.080929299987709 | -5.18299814595898 | -0.541834657596631 | | 73 | 106 | 108.082999950545 | 0.0890638668738728 | -2.08299995054509 | 0.653363831570579 | | 74 | 105.3 | 108.892783705605 | 0.096099529042043 | -3.59278370560491 | 0.574983331025758 | | 75 | 118.8 | 109.236252956376 | 0.0984917682877512 | 9.56374704362398 | 0.197334193980319 | | 76 | 106.1 | 109.807591688791 | 0.103052877421846 | -3.70759168879077 | 0.377132033601843 | | 77 | 109.3 | 108.972746541674 | 0.0939907637044517 | 0.327253458326185 | -0.747902412160804 | | 78 | 117.2 | 108.553794248145 | 0.0890219911352814 | 8.64620575185526 | -0.408996736360124 | | 79 | 92.5 | 109.494963525861 | 0.097279416064863 | -16.9949635258609 | 0.679515249683659 | | 80 | 104.2 | 110.010801913117 | 0.101319218354531 | -5.81080191311746 | 0.333849764300692 | | 81 | 112.5 | 108.962124807663 | 0.0903205405309879 | 3.5378751923371 | -0.917612323072251 | | 82 | 122.4 | 109.660001921748 | 0.0960517884015915 | 12.7399980782524 | 0.485005688976279 | | 83 | 113.3 | 109.650511643925 | 0.0950728527480774 | 3.64948835607482 | -0.0842908545868984 | | 84 | 100 | 108.888217294143 | 0.0872611125754726 | -8.88821729414274 | -0.684995664189131 | | 85 | 110.7 | 109.710018127783 | 0.0938437929149724 | 0.989981872217309 | 0.587025782419494 | | 86 | 112.8 | 111.648262460642 | 0.110150253502444 | 1.15173753935811 | 1.47423888983122 | | 87 | 109.8 | 109.698685786573 | 0.0921156500481193 | 0.10131421342673 | -1.64645292240216 | | 88 | 117.3 | 111.470844030213 | 0.106737286436953 | 5.82915596978738 | 1.34294879762472 | | 89 | 109.1 | 111.545343882623 | 0.106457692833247 | -2.44534388262266 | -0.0257687263146201 | | 90 | 115.9 | 110.738494474843 | 0.0985564180282694 | 5.1615055251569 | -0.73005761651245 | | 91 | 96 | 110.977032369369 | 0.0997636310885871 | -14.9770323693694 | 0.111904473912141 | | 92 | 99.8 | 109.710545515005 | 0.0880402166762467 | -9.91054551500455 | -1.09238868789963 | | 93 | 116.8 | 110.203282249717 | 0.091486633574169 | 6.59671775028267 | 0.323649442445218 | | 94 | 115.7 | 108.723423210693 | 0.0782384954601769 | 6.97657678930742 | -1.25699249627229 | | 95 | 99.4 | 105.210053304681 | 0.0483135624866218 | -5.81005330468101 | -2.87387823368404 | | 96 | 94.3 | 103.766406806112 | 0.0360382604140943 | -9.46640680611158 | -1.19411146143459 |
| | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936717hpkxtpzjimk4ulh/1ldtc1259936634.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936717hpkxtpzjimk4ulh/1ldtc1259936634.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936717hpkxtpzjimk4ulh/2gn7a1259936634.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936717hpkxtpzjimk4ulh/2gn7a1259936634.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936717hpkxtpzjimk4ulh/323jp1259936634.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936717hpkxtpzjimk4ulh/323jp1259936634.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936717hpkxtpzjimk4ulh/4e9g01259936634.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936717hpkxtpzjimk4ulh/4e9g01259936634.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936717hpkxtpzjimk4ulh/5wofk1259936634.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936717hpkxtpzjimk4ulh/5wofk1259936634.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')
| | |
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