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Structural Time Series Decomp Passengers

*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, 17 Dec 2010 16:42:30 +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/17/t12926040327vcnf0lrbl0ks1a.htm/, Retrieved Fri, 17 Dec 2010 17:40:33 +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/17/t12926040327vcnf0lrbl0ks1a.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 «

989236 1008380 1207763 1368839 1469798 1498721 1761769 1653214 1599104 1421179 1163995 1037735 1015407 1039210 1258049 1469445 1552346 1549144 1785895 1662335 1629440 1467430 1202209 1076982 1039367 1063449 1335135 1491602 1591972 1641248 1898849 1798580 1762444 1622044 1368955 1262973 1195650 1269530 1479279 1607819 1712466 1721766 1949843 1821326 1757802 1590367 1260647 1149235 1016367 1027885 1262159 1520854 1544144 1564709 1821776 1741365 1623386 1498658 1241822 1136029

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	989236	989236	0	0	0
2	1008380	1007464.82396763	18304.4583479359	915.176032371456	0.205158156588241
3	1207763	1190887.15417499	164849.202032658	16875.8458250149	1.68381616733103
4	1368839	1371096.55868827	178472.562432723	-2257.55868826592	0.14847010537782
5	1469798	1475942.25957356	113401.039471187	-6144.2595735563	-0.712754757498346
6	1498721	1503786.81736731	37693.4894229754	-5065.81736731116	-0.828882468346857
7	1761769	1741127.72496455	214372.611004934	20641.2750354532	1.93433688951141
8	1653214	1681601.15695943	-27997.9408651255	-28387.1569594327	-2.65354152616664
9	1599104	1596784.5114017	-78275.3155976183	2319.48859830071	-0.550450693824062
10	1421179	1427148.81367717	-159118.311904447	-5969.81367716915	-0.885091652012392
11	1163995	1169751.58806709	-246083.610723971	-5756.5880670883	-0.952120316062697
12	1037735	1025502.96921664	-155971.649565475	12232.0307833575	0.98657085251419
13	1015407	1006998.77809958	-34428.92199906	8408.22190042487	1.33218656308679
14	1039210	1050488.39296539	34586.3292676019	-11278.392965389	0.763051783989928
15	1258049	1233257.84531859	160152.958912378	24791.1546814107	1.38987413167301
16	1469445	1459806.03739443	216956.595676824	9638.96260557271	0.622455115941462
17	1552346	1555364.24688723	113678.637191466	-3018.24688723112	-1.12989323953066
18	1549144	1596435.21063852	51863.3106968983	-47291.2106385222	-0.676935426438004
19	1785895	1725616.81096116	117714.651268571	60278.1890388438	0.72094603575268
20	1662335	1706520.01100887	1195.99598397061	-44185.0110088708	-1.27568394604374
21	1629440	1628079.48332224	-66624.2140614589	1360.51667775942	-0.742514535171335
22	1467430	1465088.59365848	-148692.705242063	2341.40634152317	-0.898509045970153
23	1202209	1221073.46751818	-229874.489388055	-18864.4675181832	-0.888806448412663
24	1076982	1064615.55352724	-167362.50994988	12366.4464727641	0.684409797630143
25	1039367	1020007.1367768	-62890.7906012321	19359.8632231954	1.14547865516439
26	1063449	1083917.53658343	45164.8794267508	-20468.5365834302	1.185080709421
27	1335135	1309673.38194462	196678.198229775	25461.6180553813	1.66334635408133
28	1491602	1472031.75864276	167735.584703412	19570.2413572367	-0.317588360261953
29	1591972	1588490.14551138	124610.668068207	3481.85448862488	-0.471632508292719
30	1641248	1707721.93334476	120088.897975009	-66473.9333447636	-0.0495148007978715
31	1898849	1823942.98877171	116835.558845995	74906.0112282916	-0.0356191897324393
32	1798580	1848904.65893691	39552.8558076856	-50324.6589369119	-0.846106047608183
33	1762444	1764562.08133564	-64662.476808368	-2118.08133564485	-1.14098031432421
34	1622044	1609137.65111193	-141007.301035442	12906.3488880725	-0.83584892020799
35	1368955	1396424.86450519	-201320.55315407	-27469.8645051933	-0.660328170259007
36	1262973	1250238.41963702	-154962.61477317	12734.5803629803	0.507591915967803
37	1195650	1178211.66189516	-85223.3191993464	17438.3381048432	0.764564637363084
38	1269530	1299013.74935171	88010.0568999051	-29483.7493517064	1.89658182688081
39	1479279	1446327.56839184	137524.818977763	32951.4316081645	0.542615428927656
40	1607819	1581536.34651634	135585.953079742	26282.6534836635	-0.0212684448479848
41	1712466	1711511.77715323	130893.192539172	954.222846766093	-0.0513357024751949
42	1721766	1799806.99356781	95297.5878839816	-78040.9935678123	-0.389706535103795
43	1949843	1871248.31946547	75353.375776242	78594.6805345342	-0.21837085052715
44	1821326	1867719.92146283	9396.032132246	-46393.9214628335	-0.722108632902278
45	1757802	1761259.23649648	-87478.384271377	-3457.23649648099	-1.06061136852694
46	1590367	1572182.40923038	-172429.180155389	18184.5907696164	-0.930079379400444
47	1260647	1297721.38495309	-257731.673197424	-37074.3849530888	-0.933906473497344
48	1149235	1126798.59856733	-185181.564775639	22436.4014326662	0.794472369105847
49	1016367	1019680.90166342	-119917.971686716	-3313.90166341636	0.715242109788243
50	1027885	1050169.30788461	5746.21322480324	-22284.3078846106	1.37533144544749
51	1262159	1213280.5680722	136714.030597653	48878.4319278	1.434508435879
52	1520854	1481908.87526815	246666.669429353	38945.1247318533	1.20554623439595
53	1544144	1559351.85250321	105621.747152111	-15207.8525032085	-1.54342577943302
54	1564709	1647632.06503192	91182.5317806887	-82923.0650319214	-0.158059884367885
55	1821776	1739555.73745449	91799.8088902114	82220.2625455126	0.00675873584822836
56	1741365	1781923.57523916	50619.5636596885	-40558.575239164	-0.450848752998997
57	1623386	1634953.41940773	-113991.416630682	-11567.4194077305	-1.80221286015641
58	1498658	1463629.86899661	-161752.955039778	35028.1310033859	-0.522916605514228
59	1241822	1286066.64976003	-174921.488185682	-44244.6497600334	-0.144171435539331
60	1136029	1113060.38478289	-173326.690795354	22968.6152171129	0.0174653046580764

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t12926040327vcnf0lrbl0ks1a/1sugm1292604146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12926040327vcnf0lrbl0ks1a/1sugm1292604146.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12926040327vcnf0lrbl0ks1a/2k3f71292604146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12926040327vcnf0lrbl0ks1a/2k3f71292604146.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12926040327vcnf0lrbl0ks1a/3k3f71292604146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12926040327vcnf0lrbl0ks1a/3k3f71292604146.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12926040327vcnf0lrbl0ks1a/40y3g1292604146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12926040327vcnf0lrbl0ks1a/40y3g1292604146.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12926040327vcnf0lrbl0ks1a/564vv1292604146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12926040327vcnf0lrbl0ks1a/564vv1292604146.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

bitmap(file='test1.png')

plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time')

grid()

dev.off()

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='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')

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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