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*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 07:55:50 -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/t125993858367lszch4f8p906k.htm/, Retrieved Fri, 04 Dec 2009 15:56:29 +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/t125993858367lszch4f8p906k.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 «

611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	611	611	0	0	0
2	594	600.764715726819	-10.7943516711373	-6.76471572681921	-1.79417466550545
3	595	590.130715219314	-10.6922034506268	4.86928478068624	0.0135938238352938
4	591	587.228517321978	-5.5162059619089	3.77148267802237	0.724337656566066
5	589	587.518362551015	-1.66275031714706	1.48163744898465	0.499410966495785
6	584	584.81072081983	-2.34298130283852	-0.810720819829668	-0.0887250814437027
7	573	575.314563085944	-7.01140140169183	-2.31456308594446	-0.611703208028301
8	567	566.466885878727	-8.21292832342608	0.533114121273051	-0.157136433768578
9	569	565.563410628786	-3.42885730958781	3.43658937121447	0.62555036552411
10	621	604.874532001955	24.5391521874869	16.1254679980455	3.65735221006601
11	629	632.725732429867	26.7059716998185	-3.72573242986689	0.283344523304397
12	628	636.858544399272	11.9394895598296	-8.85854439927163	-1.93093038824835
13	612	620.927066934544	-6.2267084480038	-8.92706693454376	-2.38476752768488
14	595	603.453602299613	-13.5910085716291	-8.45360229961277	-0.97884873548042
15	597	592.9638286582	-11.6133764404110	4.03617134179969	0.256319207056960
16	593	589.204349054148	-6.68086790295861	3.79565094585194	0.654112630564915
17	590	586.779954141924	-3.97317185894816	3.22004585807604	0.356670496902642
18	580	578.073761001415	-6.96665484059367	1.92623899858534	-0.389762015972569
19	574	571.402373026475	-6.78088407564728	2.59762697352457	0.024279516547364
20	573	572.149021127488	-2.03709711090835	0.850978872512251	0.620873163415635
21	573	582.431369202074	5.73800974653048	-9.43136920207416	1.01671498597325
22	620	602.607283696578	14.8517376439537	17.3927163034216	1.19176013189274
23	626	622.023708786183	17.7315891334107	3.97629121381659	0.37660135848543
24	620	625.051542177408	8.46621582962653	-5.05154217740801	-1.21221175899113
25	588	603.571892883564	-10.4094328635746	-15.5718928835645	-2.4762133653004
26	566	579.24200625601	-19.1958760129663	-13.2420062560106	-1.15095315601659
27	557	556.703631738739	-21.2888491651675	0.296368261261291	-0.272843819168515
28	561	551.441627072655	-11.3123835046369	9.55837292734549	1.30914873959252
29	549	542.533782437369	-9.80819393816252	6.46621756263141	0.197665336189131
30	532	529.381383373013	-11.9012179129370	2.61861662698734	-0.273405424219038
31	526	522.632535179101	-8.68831446585023	3.36746482089860	0.419478618704594
32	511	515.466459881514	-7.73958239790163	-4.46645988151417	0.124076269173489
33	499	514.019104682471	-3.8133722778245	-15.0191046824708	0.513498786688406
34	555	533.16018774185	10.5158987360941	21.8398122581504	1.87377848599719
35	565	553.704835438537	16.7738909173384	11.2951645614632	0.818423415510956
36	542	545.648829238228	1.28521689417607	-3.64882923822804	-2.02704658924266
37	527	538.058014998981	-4.25600353352343	-11.0580149989809	-0.725774793671245
38	510	525.673371532448	-9.32959979527289	-15.6733715324482	-0.66340214563967
39	514	518.610647186793	-7.92043704187319	-4.6106471867933	0.183994200324925
40	517	508.63311278329	-9.19579345652974	8.36688721671029	-0.167015905203778
41	508	499.139423178701	-9.38090086953022	8.86057682129927	-0.0242750247298982
42	493	490.185988416559	-9.11494262783895	2.81401158344059	0.0347846894223537
43	490	484.442394824679	-7.02111352255654	5.55760517532102	0.273474028940806
44	469	477.444652784926	-7.00661571675337	-8.44465278492575	0.0018949568782837
45	478	494.633602251873	8.00675331544998	-16.6336022518727	1.96336642792224
46	528	509.373269698053	12.1860687054673	18.6267303019467	0.546590436834772
47	534	515.984789809338	8.72585072083472	18.0152101906616	-0.452632450021529
48	518	519.630323216397	5.57178393674495	-1.63032321639718	-0.412767216269535
49	506	517.277719177839	0.649183786890601	-11.2777191778392	-0.644180662158148
50	502	518.075157695488	0.741221283426512	-16.0751576954881	0.0120297749557840
51	516	519.494205550949	1.16096821078641	-3.49420555094931	0.0548397257549317
52	528	519.30712472379	0.327384945714345	8.69287527621017	-0.109095347491193
53	533	521.954158895163	1.76361255775956	11.0458411048365	0.188159321498297
54	536	530.330700742707	5.86276146142825	5.66929925729287	0.536318992376891
55	537	533.705006891428	4.32153770869993	3.29499310857175	-0.201389600791940
56	524	541.108992342443	6.22830744562767	-17.1089923424426	0.249182208264339
57	536	553.577796364227	10.0872894480547	-17.5777963642266	0.504581332978417
58	587	566.12601120269	11.6093156318716	20.8739887973100	0.199082830889453
59	597	577.154284927014	11.2498657079142	19.8457150729865	-0.0470290540356877
60	581	582.035188042145	7.30813064230398	-1.03518804214537	-0.515801062787485

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993858367lszch4f8p906k/1q03b1259938548.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993858367lszch4f8p906k/1q03b1259938548.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993858367lszch4f8p906k/2tu861259938548.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993858367lszch4f8p906k/2tu861259938548.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993858367lszch4f8p906k/3egtz1259938548.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993858367lszch4f8p906k/3egtz1259938548.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993858367lszch4f8p906k/4jso51259938548.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993858367lszch4f8p906k/4jso51259938548.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993858367lszch4f8p906k/58ipg1259938548.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993858367lszch4f8p906k/58ipg1259938548.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')

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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