| paper - STSM | | *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: Tue, 14 Dec 2010 09:54:17 +0000 | | | | Cite this page as follows: | | Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8.htm/, Retrieved Tue, 14 Dec 2010 10:53:16 +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/2010/Dec/14/t129232039447lvhkh119whqk8.htm/},
year = {2010},
}
@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 = {2010},
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 « | | 235.1
280.7
264.6
240.7
201.4
240.8
241.1
223.8
206.1
174.7
203.3
220.5
299.5
347.4
338.3
327.7
351.6
396.6
438.8
395.6
363.5
378.8
357
369
464.8
479.1
431.3
366.5
326.3
355.1
331.6
261.3
249
205.5
235.6
240.9
264.9
253.8
232.3
193.8
177
213.2
207.2
180.6
188.6
175.4
199
179.6
225.8
234
200.2
183.6
178.2
203.2
208.5
191.8
172.8
148
159.4
154.5
213.2
196.4
182.8
176.4
153.6
173.2
171
151.2
161.9
157.2
201.7
236.4
356.1
398.3
403.7
384.6
365.8
368.1
367.9
347
343.3
292.9
311.5
300.9
366.9
356.9
329.7
316.2
269
289.3
266.2
253.6
233.8
228.4
253.6
260.1
306.6
309.2
309.5
271
279.9
317.9
298.4
246.7
227.3
209.1 | | | | Output produced by software: |
| Structural Time Series Model | | t | Observed | Level | Slope | Seasonal | Stand. Residuals | | 1 | 235.1 | 235.1 | 0 | 0 | 0 | | 2 | 280.7 | 277.878649536573 | 2.33022608678283 | 2.82135046342714 | 0.970748348648947 | | 3 | 264.6 | 263.743201274697 | 2.18084966922926 | 0.85679872530267 | -0.619229234750829 | | 4 | 240.7 | 239.843378150505 | 2.0815634288272 | 0.856621849495357 | -0.981939970825554 | | 5 | 201.4 | 201.376289167257 | 1.90925115385391 | 0.0237108327428216 | -1.52650067638383 | | 6 | 240.8 | 235.974497326326 | 2.05192202951772 | 4.82550267367366 | 1.23060003543256 | | 7 | 241.1 | 239.611900809375 | 2.05881381332922 | 1.48809919062534 | 0.0596862597994536 | | 8 | 223.8 | 222.969036673038 | 1.97791860145171 | 0.83096332696227 | -0.704028345304963 | | 9 | 206.1 | 205.015335290125 | 1.89207865600455 | 1.08466470987538 | -0.750323320077933 | | 10 | 174.7 | 174.474496218974 | 1.75299707805328 | 0.225503781025959 | -1.22092274127319 | | 11 | 203.3 | 199.406487485646 | 1.85197091703577 | 3.89351251435443 | 0.872555580311552 | | 12 | 220.5 | 218.047660285345 | 1.92335565800283 | 2.45233971465474 | 0.632011451096794 | | 13 | 299.5 | 287.629602259823 | -0.867602489607616 | 11.8703977401772 | 3.03148776271513 | | 14 | 347.4 | 342.965472625557 | 0.379012023382487 | 4.43452737444339 | 1.83263819796448 | | 15 | 338.3 | 340.469015585803 | 0.356887296458952 | -2.16901558580277 | -0.107635272395743 | | 16 | 327.7 | 327.227278125238 | 0.327181955037726 | 0.472721874762107 | -0.511563789044118 | | 17 | 351.6 | 352.007723883346 | 0.377447255130508 | -0.407723883345728 | 0.9196677598882 | | 18 | 396.6 | 390.645102098502 | 0.464642618464707 | 5.95489790149776 | 1.43887172529361 | | 19 | 438.8 | 434.95530607745 | 0.566195806126585 | 3.84469392254984 | 1.64893554230362 | | 20 | 395.6 | 400.644505699201 | 0.485738158637949 | -5.04450569920147 | -1.31164670295768 | | 21 | 363.5 | 364.386511530268 | 0.401243320369816 | -0.886511530267548 | -1.38184677146244 | | 22 | 378.8 | 378.138358893504 | 0.432566081018395 | 0.661641106496241 | 0.502108429645941 | | 23 | 357 | 356.83455297695 | 0.377587347438291 | 0.16544702304971 | -0.817690266447621 | | 24 | 369 | 369.985331560909 | 0.384746367573487 | -0.985331560909166 | 0.479963011744462 | | 25 | 464.8 | 448.359782102865 | -0.952611107170525 | 16.4402178971346 | 3.16072755887902 | | 26 | 479.1 | 473.976014820179 | -0.617455535088952 | 5.12398517982118 | 0.929711541026138 | | 27 | 431.3 | 438.537263291325 | -0.866908056398829 | -7.23726329132483 | -1.29881299324509 | | 28 | 366.5 | 375.533102786943 | -1.00552791824276 | -9.0331027869426 | -2.33722465655691 | | 29 | 326.3 | 333.857846689265 | -1.066383287159 | -7.55784668926473 | -1.52925385263982 | | 30 | 355.1 | 351.448844508518 | -1.03502990168687 | 3.65115549148218 | 0.701489228820092 | | 31 | 331.6 | 329.787635939933 | -1.07166722425051 | 1.8123640600669 | -0.775501364074007 | | 32 | 261.3 | 271.108918949166 | -1.1744235245023 | -9.80891894916622 | -2.16590539741366 | | 33 | 249 | 253.018497675771 | -1.20483220310683 | -4.01849767577088 | -0.636017003299866 | | 34 | 205.5 | 208.403384406243 | -1.28805219859473 | -2.90338440624275 | -1.63238768937127 | | 35 | 235.6 | 231.999772538107 | -1.24067804178706 | 3.60022746189321 | 0.935879152931365 | | 36 | 240.9 | 247.823166255779 | -1.25510060519951 | -6.92316625577877 | 0.641295741386453 | | 37 | 264.9 | 250.284097820484 | -1.29051061456061 | 14.615902179516 | 0.145382946982042 | | 38 | 253.8 | 245.692123336567 | -1.31726964778724 | 8.10787666343303 | -0.119002213600224 | | 39 | 232.3 | 234.817945248688 | -1.37958959139681 | -2.51794524868753 | -0.355772478318949 | | 40 | 193.8 | 202.73398965515 | -1.45637101285456 | -8.93398965515026 | -1.15465544133388 | | 41 | 177 | 188.624602298952 | -1.47351848902422 | -11.6246022989522 | -0.475763129355498 | | 42 | 213.2 | 205.590093773085 | -1.44780599933543 | 7.6099062269151 | 0.693221143161009 | | 43 | 207.2 | 200.916254522455 | -1.45270184190174 | 6.28374547754533 | -0.121278642607948 | | 44 | 180.6 | 190.481928935706 | -1.46672383207795 | -9.88192893570593 | -0.337652686755762 | | 45 | 188.6 | 187.405599926681 | -1.46932769193819 | 1.19440007331936 | -0.0605145835274915 | | 46 | 175.4 | 181.478623112595 | -1.47708960647708 | -6.0786231125948 | -0.167622094603992 | | 47 | 199 | 195.241497517955 | -1.45565689979554 | 3.75850248204536 | 0.572988137806708 | | 48 | 179.6 | 188.219680779707 | -1.44789933366152 | -8.61968077970726 | -0.209318719590888 | | 49 | 225.8 | 206.751333517532 | -1.56449601737826 | 19.0486664824682 | 0.76848762703954 | | 50 | 234 | 223.065580606754 | -1.46393011603634 | 10.9344193932461 | 0.654219739057499 | | 51 | 200.2 | 202.505629378843 | -1.5752420285696 | -2.30562937884331 | -0.710437435101487 | | 52 | 183.6 | 191.981438357092 | -1.59960093301114 | -8.38143835709222 | -0.336396421379105 | | 53 | 178.2 | 191.742035793182 | -1.59772695531059 | -13.5420357931817 | 0.0511454674329914 | | 54 | 203.2 | 194.723135870074 | -1.5920310205765 | 8.47686412992587 | 0.172138421528538 | | 55 | 208.5 | 200.365893371415 | -1.58221727827831 | 8.1341066285847 | 0.271968796776699 | | 56 | 191.8 | 201.385859883033 | -1.57846597785625 | -9.58585988303333 | 0.0978210181111924 | | 57 | 172.8 | 174.801385503025 | -1.61687907579335 | -2.0013855030251 | -0.94011818207454 | | 58 | 148 | 157.444426450243 | -1.64202614145225 | -9.44442645024321 | -0.591867426850214 | | 59 | 159.4 | 154.281024677452 | -1.64353955016627 | 5.11897532254839 | -0.05718434529103 | | 60 | 154.5 | 163.548671082677 | -1.66014566532345 | -9.04867108267693 | 0.410530171528305 | | 61 | 213.2 | 191.453647226868 | -1.77065708224 | 21.7463527731316 | 1.12670176747893 | | 62 | 196.4 | 184.13384785248 | -1.79371329765566 | 12.2661521475203 | -0.204759501229022 | | 63 | 182.8 | 183.950128304675 | -1.78538970014308 | -1.15012830467451 | 0.0599079372382813 | | 64 | 176.4 | 184.777272933263 | -1.77795238124193 | -8.37727293326292 | 0.098158498217201 | | 65 | 153.6 | 169.995333661313 | -1.79693020877862 | -16.3953336613133 | -0.488973239178999 | | 66 | 173.2 | 166.174348658389 | -1.79930520880372 | 7.02565134161057 | -0.0760932744058476 | | 67 | 171 | 163.703920548511 | -1.80014433729132 | 7.29607945148886 | -0.0252282899401596 | | 68 | 151.2 | 158.363313219096 | -1.8049783523128 | -7.16331321909565 | -0.133091170537747 | | 69 | 161.9 | 161.084654800455 | -1.79829505457864 | 0.815345199544675 | 0.170172419764591 | | 70 | 157.2 | 165.404042147141 | -1.7894361735729 | -8.2040421471406 | 0.230027221234123 | | 71 | 201.7 | 193.64076153313 | -1.76905073540438 | 8.05923846686976 | 1.12837708005752 | | 72 | 236.4 | 242.357316357528 | -1.84218716255518 | -5.9573163575282 | 1.89996872062642 | | 73 | 356.1 | 321.962822594572 | -2.04124571259702 | 34.1371774054281 | 3.0871749406237 | | 74 | 398.3 | 380.247061482248 | -1.8457739322112 | 18.0529385177524 | 2.23698639182873 | | 75 | 403.7 | 404.093269659919 | -1.72805764323721 | -0.393269659918639 | 0.956553297653652 | | 76 | 384.6 | 394.192245057296 | -1.75164779243467 | -9.59224505729585 | -0.306924442566173 | | 77 | 365.8 | 383.64743087803 | -1.7652989272544 | -17.8474308780302 | -0.330630189545905 | | 78 | 368.1 | 363.499426790646 | -1.78649870763394 | 4.60057320935429 | -0.691096792250607 | | 79 | 367.9 | 359.562989573822 | -1.7890423886293 | 8.33701042617826 | -0.0808190585594544 | | 80 | 347 | 354.186281296983 | -1.79373729535243 | -7.18628129698305 | -0.134867054357131 | | 81 | 343.3 | 343.178264442168 | -1.80676276256205 | 0.1217355578317 | -0.346425836382056 | | 82 | 292.9 | 308.174409905557 | -1.84979303894569 | -15.2744099055567 | -1.24811184619951 | | 83 | 311.5 | 307.705355012032 | -1.84916979451824 | 3.79464498796783 | 0.051881815665856 | | 84 | 300.9 | 315.245207649637 | -1.8612639467077 | -14.3452076496372 | 0.35335393291527 | | 85 | 366.9 | 337.609473280529 | -1.900080853347 | 29.2905267194715 | 0.915205323162074 | | 86 | 356.9 | 342.01444749463 | -1.88338332594053 | 14.8855525053701 | 0.234522439617019 | | 87 | 329.7 | 331.051109104116 | -1.92038162825464 | -1.35110910411592 | -0.338309090180236 | | 88 | 316.2 | 325.503761752541 | -1.93076967531457 | -9.30376175254145 | -0.136146005445651 | | 89 | 269 | 289.897988238813 | -1.98587549698718 | -20.8979882388133 | -1.26612605691273 | | 90 | 289.3 | 284.622530832517 | -1.9897040217129 | 4.67746916748271 | -0.12367364430659 | | 91 | 266.2 | 260.825155134065 | -2.01465127045557 | 5.37484486593492 | -0.819794525928847 | | 92 | 253.6 | 259.007992389454 | -2.01440222402308 | -5.40799238945414 | 0.00742412733846554 | | 93 | 233.8 | 232.74850371286 | -2.04695796123112 | 1.05149628713982 | -0.911534056284188 | | 94 | 228.4 | 241.458219853056 | -2.03457831649602 | -13.0582198530556 | 0.404377419767221 | | 95 | 253.6 | 249.498750452866 | -2.03160172875014 | 4.10124954713387 | 0.378554512134653 | | 96 | 260.1 | 273.67771583308 | -2.06040113380946 | -13.57771583308 | 0.986316516776123 | | 97 | 306.6 | 277.599488427056 | -2.06657678634736 | 29.0005115729439 | 0.225522500113115 | | 98 | 309.2 | 291.290720004724 | -2.03110641772116 | 17.9092799952763 | 0.587299970662815 | | 99 | 309.5 | 308.27352349758 | -1.96179904329962 | 1.22647650242031 | 0.708971826909975 | | 100 | 271 | 280.763372675471 | -2.03337485435866 | -9.76337267547105 | -0.958668298741562 | | 101 | 279.9 | 297.412273662904 | -2.001546887085 | -17.512273662904 | 0.70235667542396 | | 102 | 317.9 | 308.755261491531 | -1.9856489468385 | 9.14473850846849 | 0.501702270033072 | | 103 | 298.4 | 294.937184155733 | -1.99894854781884 | 3.46281584426708 | -0.444816503816065 | | 104 | 246.7 | 254.435782600903 | -2.04585833959804 | -7.73578260090311 | -1.44744849988057 | | 105 | 227.3 | 229.938047964283 | -2.07429386159314 | -2.63804796428298 | -0.844105406239112 | | 106 | 209.1 | 223.194361511141 | -2.07904842165478 | -14.0943615111413 | -0.175519482986977 |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8/1wcdb1292320452.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8/1wcdb1292320452.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8/26lvw1292320452.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8/26lvw1292320452.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8/3huuz1292320452.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8/3huuz1292320452.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8/4huuz1292320452.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8/4huuz1292320452.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8/5a4t11292320452.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/14/t129232039447lvhkh119whqk8/5a4t11292320452.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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