| WS 9 Estimation of Box-Jenkins ARIMA 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 08:05:58 -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/t125993924898g41sltvia5jis.htm/, Retrieved Fri, 04 Dec 2009 16:07:35 +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/t125993924898g41sltvia5jis.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: | | WS 9 Estimation of Box-Jenkins ARIMA models | | | | IsPrivate? | | No (this computation is public) | | | | User-defined keywords: | | | | | Dataseries X: | | » Textbox « » Textfile « » CSV « | | 14,5
14,3
15,3
14,4
13,7
14,2
13,5
11,9
14,6
15,6
14,1
14,9
14,2
14,6
17,2
15,4
14,3
17,5
14,5
14,4
16,6
16,7
16,6
16,9
15,7
16,4
18,4
16,9
16,5
18,3
15,1
15,7
18,1
16,8
18,9
19
18,1
17,8
21,5
17,1
18,7
19
16,4
16,9
18,6
19,3
19,4
17,6
18,6
18,1
20,4
18,1
19,6
19,9
19,2
17,8
19,2
22
21,1
19,5
22,2
20,9
22,2
23,5
21,5
24,3
22,8
20,3
23,7
23,3
19,6
18
17,3
16,8
18,2
16,5
16
18,4
| | | | Output produced by software: |
| Structural Time Series Model | | t | Observed | Level | Slope | Seasonal | Stand. Residuals | | 1 | 14.5 | 14.5 | 0 | 0 | 0 | | 2 | 14.3 | 14.3532218182990 | -0.00650225312906405 | -0.0532218182989612 | -0.151829303867976 | | 3 | 15.3 | 14.9042468127159 | 0.0221512184686178 | 0.395753187284099 | 0.680304199751437 | | 4 | 14.4 | 14.6934835096618 | 0.0150706721362367 | -0.293483509661792 | -0.337630616060789 | | 5 | 13.7 | 14.0989306329845 | 0.00584767975717651 | -0.398930632984534 | -0.90856652746136 | | 6 | 14.2 | 14.0448094080469 | 0.00526892341835372 | 0.155190591953142 | -0.0894615253839601 | | 7 | 13.5 | 13.7278684502808 | 0.00238740292848135 | -0.227868450280822 | -0.480207980211774 | | 8 | 11.9 | 12.6440390367895 | -0.0078565033500251 | -0.74403903678947 | -1.61756646487085 | | 9 | 14.6 | 13.5443622179084 | 0.00104458290109341 | 1.0556377820916 | 1.35193602981695 | | 10 | 15.6 | 14.8616318798438 | 0.0140556822103159 | 0.738368120156154 | 1.95920789642376 | | 11 | 14.1 | 14.6717808787331 | 0.01205412414273 | -0.571780878733093 | -0.303522151587398 | | 12 | 14.9 | 14.7612690248497 | 0.0128056502406377 | 0.138730975150275 | 0.115265945672613 | | 13 | 14.2 | 14.5505149719730 | 0.0193929732869372 | -0.350514971973031 | -0.360797676478492 | | 14 | 14.6 | 14.7394672222748 | 0.0195642190422452 | -0.139467222274828 | 0.251732325083284 | | 15 | 17.2 | 15.8595821180274 | 0.042461483965316 | 1.34041788197258 | 1.51102678726127 | | 16 | 15.4 | 15.8020613150722 | 0.0402579077027993 | -0.402061315072151 | -0.142486226205362 | | 17 | 14.3 | 15.1757455510875 | 0.0296765015125833 | -0.875745551087479 | -0.982445746081785 | | 18 | 17.5 | 16.0677923826787 | 0.0385983579899382 | 1.4322076173213 | 1.28323239136818 | | 19 | 14.5 | 15.2616428316980 | 0.0321521798218614 | -0.761642831698038 | -1.25856164838959 | | 20 | 14.4 | 15.3386659103121 | 0.0324655419080657 | -0.938665910312065 | 0.0668356042082085 | | 21 | 16.6 | 15.7416778414265 | 0.0351287782094691 | 0.858322158573519 | 0.551782821700158 | | 22 | 16.7 | 15.8647353203460 | 0.0357516574602543 | 0.835264679654023 | 0.13090789383413 | | 23 | 16.6 | 16.5749556669574 | 0.0393142507167759 | 0.0250443330426124 | 1.00331810435859 | | 24 | 16.9 | 16.76615084066 | 0.0393901374549768 | 0.133849159340004 | 0.226268981842783 | | 25 | 15.7 | 16.5898405928147 | 0.0405413055923513 | -0.889840592814692 | -0.326194337796170 | | 26 | 16.4 | 16.8379800330433 | 0.0408874335213664 | -0.437980033043308 | 0.307617912360923 | | 27 | 18.4 | 16.9475124945745 | 0.0416588342943506 | 1.4524875054255 | 0.0983964622634089 | | 28 | 16.9 | 17.0523186369762 | 0.0426108584669144 | -0.152318636976206 | 0.0908400463021881 | | 29 | 16.5 | 17.3896860995715 | 0.0466630120987782 | -0.889686099571456 | 0.432104020782224 | | 30 | 18.3 | 16.9607051215087 | 0.0415969334380195 | 1.33929487849132 | -0.705324316528581 | | 31 | 15.1 | 16.3608499895819 | 0.0363632815578634 | -1.26084998958185 | -0.954898009220748 | | 32 | 15.7 | 16.5261959018995 | 0.0372418509196335 | -0.82619590189947 | 0.192173761268289 | | 33 | 18.1 | 16.9973193674175 | 0.0398732773335018 | 1.10268063258254 | 0.646351461294702 | | 34 | 16.8 | 16.6983749639089 | 0.0381654497863639 | 0.101625036091081 | -0.504334933047932 | | 35 | 18.9 | 17.8347830546934 | 0.0415688789169400 | 1.06521694530657 | 1.63337616668555 | | 36 | 19 | 18.5204423605592 | 0.0419639633318892 | 0.479557639440806 | 0.959233167815239 | | 37 | 18.1 | 18.9519756382336 | 0.0418571561531171 | -0.851975638233591 | 0.581186433947571 | | 38 | 17.8 | 18.7006636190141 | 0.0409743418313897 | -0.900663619014137 | -0.432837243733768 | | 39 | 21.5 | 19.4512550753658 | 0.0466396815812547 | 2.04874492463417 | 1.03175368849035 | | 40 | 17.1 | 18.4323237136876 | 0.0348119442346677 | -1.33232371368758 | -1.54675674779101 | | 41 | 18.7 | 18.7468442202362 | 0.0380031856588257 | -0.0468442202362262 | 0.409968934751498 | | 42 | 19 | 18.0757165571750 | 0.0309373212186635 | 0.924283442824951 | -1.04921918481289 | | 43 | 16.4 | 17.8185541078603 | 0.0285942280798430 | -1.41855410786029 | -0.428367511942265 | | 44 | 16.9 | 17.8260446084405 | 0.0284548936807973 | -0.926044608440547 | -0.0314293942089173 | | 45 | 18.6 | 17.6662617069595 | 0.0274504521770733 | 0.933738293040485 | -0.280321827806223 | | 46 | 19.3 | 18.7806352783862 | 0.0318024844573274 | 0.519364721613836 | 1.61730217470358 | | 47 | 19.4 | 18.8986393765442 | 0.0320175585937234 | 0.50136062345577 | 0.128186919162402 | | 48 | 17.6 | 18.0816056319130 | 0.0309064284464227 | -0.481605631912962 | -1.26286987421494 | | 49 | 18.6 | 18.6754807804339 | 0.0317361484265937 | -0.0754807804339405 | 0.836215106867895 | | 50 | 18.1 | 19.0382459477397 | 0.0329165860636176 | -0.938245947739723 | 0.488374871941854 | | 51 | 20.4 | 18.4722753592372 | 0.0289860915915749 | 1.92772464076283 | -0.876166727396246 | | 52 | 18.1 | 18.9202244690803 | 0.0326861257621256 | -0.820224469080279 | 0.611785974620364 | | 53 | 19.6 | 19.1689471734590 | 0.0347497108593148 | 0.431052826540968 | 0.317135766264417 | | 54 | 19.9 | 19.0294631028693 | 0.0331919999304526 | 0.870536897130678 | -0.257552919549820 | | 55 | 19.2 | 19.8471734825025 | 0.0392044550188137 | -0.647173482502464 | 1.16511728205475 | | 56 | 17.8 | 19.4208104028436 | 0.0362949361160086 | -1.62081040284357 | -0.692773534588495 | | 57 | 19.2 | 19.0312195574406 | 0.0342141799336740 | 0.168780442559367 | -0.633818145267439 | | 58 | 22 | 20.2376482368600 | 0.0384144868396215 | 1.76235176313997 | 1.74347338170622 | | 59 | 21.1 | 20.4401322403705 | 0.0388167140884143 | 0.659867759629505 | 0.243898459514867 | | 60 | 19.5 | 20.394964725237 | 0.0386609491135392 | -0.894964725237015 | -0.124787568852385 | | 61 | 22.2 | 21.4369025094406 | 0.0409214615431257 | 0.763097490559361 | 1.48771109188717 | | 62 | 20.9 | 21.6985276655376 | 0.0417476902809566 | -0.798527665537587 | 0.325708355771775 | | 63 | 22.2 | 21.1204839693465 | 0.0381808792588933 | 1.07951603065353 | -0.90993732336224 | | 64 | 23.5 | 22.8049983601181 | 0.0503878153577447 | 0.695001639881928 | 2.41351501765741 | | 65 | 21.5 | 22.1385222746870 | 0.0445442367829420 | -0.638522274687041 | -1.05422109455686 | | 66 | 24.3 | 22.8813269991486 | 0.0500757768112967 | 1.41867300085143 | 1.03198623927225 | | 67 | 22.8 | 23.1546643815529 | 0.0516455052942918 | -0.354664381552921 | 0.331273151295866 | | 68 | 20.3 | 22.5418608010356 | 0.0477669899088914 | -2.24186080103563 | -0.987815705053212 | | 69 | 23.7 | 23.2900740674559 | 0.0509801363543038 | 0.409925932544065 | 1.04170245144483 | | 70 | 23.3 | 22.5377815915662 | 0.0482167783924409 | 0.762218408433842 | -1.19418333655362 | | 71 | 19.6 | 20.6285373143518 | 0.0431727674353351 | -1.02853731435178 | -2.90863295597613 | | 72 | 18 | 19.7426512718360 | 0.0410861558289649 | -1.74265127183596 | -1.37943338834347 | | 73 | 17.3 | 17.9895305123466 | 0.036322510472855 | -0.68953051234658 | -2.65871347167898 | | 74 | 16.8 | 17.5240270957728 | 0.0344329381781700 | -0.72402709577282 | -0.741025416888488 | | 75 | 18.2 | 17.6215394311672 | 0.0347612324495996 | 0.578460568832749 | 0.0928257205832044 | | 76 | 16.5 | 16.5622898879485 | 0.0277117694342975 | -0.0622898879484602 | -1.60820758490952 | | 77 | 16 | 16.6613997601635 | 0.0282177641002253 | -0.661399760163488 | 0.105166035732995 | | 78 | 18.4 | 16.8868131282224 | 0.0296029686147793 | 1.51318687177761 | 0.291496508415680 |
| | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2009/Dec/04/t125993924898g41sltvia5jis/1g3jb1259939155.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t125993924898g41sltvia5jis/1g3jb1259939155.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t125993924898g41sltvia5jis/2vzdf1259939155.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t125993924898g41sltvia5jis/2vzdf1259939155.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t125993924898g41sltvia5jis/3n2p81259939155.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t125993924898g41sltvia5jis/3n2p81259939155.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t125993924898g41sltvia5jis/4iqok1259939155.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t125993924898g41sltvia5jis/4iqok1259939155.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t125993924898g41sltvia5jis/5quc91259939155.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t125993924898g41sltvia5jis/5quc91259939155.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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