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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 15:45:35 -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/t12599667697p4lsr6xcxhkbej.htm/, Retrieved Fri, 04 Dec 2009 23:46:16 +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/2009/Dec/04/t12599667697p4lsr6xcxhkbej.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 «

102.80 118.72 119.01 118.61 120.43 111.83 116.79 131.71 120.57 117.83 130.80 107.46 112.09 129.47 119.72 134.81 135.80 129.27 126.94 153.45 121.86 133.47 135.34 117.10 120.65 132.49 137.60 138.69 125.53 133.09 129.08 145.94 129.07 139.69 142.09 137.29 127.03 137.25 156.87 150.89 139.14 158.30 149.00 158.36 168.06 153.38 173.86 162.47 145.17 168.89 166.64 140.07 128.84 123.40 120.30 129.66 118.12 113.91 131.09 119.14 115.33

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	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	102.8	102.8	0	0	0
2	118.72	114.782034532604	0.544748731207629	3.93796546739591	1.5016766394609
3	119.01	118.574136808636	0.705907420710852	0.435863191363683	0.495975304070011
4	118.61	118.900091317516	0.695319232732628	-0.290091317515946	-0.0681451771864634
5	120.43	119.61353873612	0.695564438762509	0.816461263880088	0.00332412911584292
6	111.83	115.016064112754	0.648418697856438	-3.18606411275436	-0.970778696005901
7	116.79	115.025431281053	0.642950185206062	1.7645687189466	-0.117094027564651
8	131.71	124.459379632054	0.72280486464318	7.25062036794618	1.60967624902769
9	120.57	123.615059663230	0.708074067210482	-3.04505966323035	-0.286868722278071
10	117.83	119.890720101432	0.666215185027466	-2.06072010143239	-0.81133923800776
11	130.8	125.328282554335	0.710897548542552	5.47171744566472	0.87339948572819
12	107.46	115.711606789359	0.615255630219125	-8.2516067893593	-1.89050218102496
13	112.09	116.583058423700	0.607490411114577	-4.49305842369981	0.0510342840132408
14	129.47	122.765932073876	0.619269424941919	6.70406792612378	1.01190798118922
15	119.72	121.910722827836	0.588250625414513	-2.19072282783557	-0.248991663922578
16	134.81	129.065963525772	0.727275473894457	5.74403647422832	1.15623667828975
17	135.8	132.212530701997	0.762697306458408	3.58746929800272	0.439502884174452
18	129.27	133.346772874874	0.76617471395629	-4.07677287487419	0.0680170372315233
19	126.94	131.325846629645	0.746672121187336	-4.38584662964456	-0.510570456047832
20	153.45	138.919542601982	0.791673885292347	14.5304573980182	1.25387560409885
21	121.86	131.891386598153	0.737887976018393	-10.0313865981526	-1.43166863199556
22	133.47	133.631571263271	0.74475163822905	-0.161571263271032	0.183481242284209
23	135.34	129.545307906726	0.720059102333632	5.79469209327393	-0.883680351298068
24	117.1	127.094528915416	0.719273405955426	-9.9945289154161	-0.580831637602893
25	120.65	127.195322353099	0.722912945226276	-6.5453223530992	-0.115157656244479
26	132.49	126.765055045864	0.7208614723226	5.72494495413641	-0.209927933061647
27	137.6	135.995517894505	0.818417505620169	1.60448210549522	1.49852549191873
28	138.69	136.394304406191	0.812193234305878	2.29569559380864	-0.0743664294146008
29	125.53	128.959181582118	0.704504396803709	-3.42918158211757	-1.48991514546401
30	133.09	132.572836360736	0.733146994555963	0.51716363926417	0.531001088891679
31	129.08	135.046368511377	0.746179540549839	-5.96636851137686	0.318647598837167
32	145.94	131.849628276973	0.721148338054773	14.0903717230267	-0.722314456937508
33	129.07	135.476291672758	0.737955989005935	-6.40629167275833	0.532171132341931
34	139.69	137.108438593937	0.742318659106817	2.58156140606299	0.163656817599235
35	142.09	136.243780080347	0.73758371769658	5.84621991965328	-0.293861994751582
36	137.29	142.234627515824	0.739370102049005	-4.94462751582387	0.962092945867542
37	127.03	138.998604105968	0.741899592003961	-11.9686041059682	-0.729692373070082
38	137.25	136.752444021369	0.733227850801848	0.497555978630793	-0.542397067167401
39	156.87	146.144420236687	0.80286926808999	10.7255797633132	1.54729566526100
40	150.89	147.100710435579	0.80455780725181	3.78928956442145	0.0274038640410396
41	139.14	145.785147864767	0.78117756767927	-6.64514786476734	-0.382662049098098
42	158.3	152.507477798969	0.837045113527888	5.7925222010311	1.08207086121228
43	149	154.179602808230	0.84337304623839	-5.17960280823045	0.152748209699735
44	158.36	150.057862866459	0.812725931245071	8.30213713354111	-0.909344153241108
45	168.06	163.093776383657	0.874502032812853	4.96622361634313	2.23825741702652
46	153.38	158.326042372378	0.85298069557824	-4.94604237237773	-1.03229841976618
47	173.86	164.159688482321	0.864440664831046	9.70031151767864	0.910697185743786
48	162.47	165.933317744839	0.865389121029962	-3.46331774483859	0.166306046825845
49	145.17	161.696463300159	0.859302748582286	-16.5264633001589	-0.932198631889592
50	168.89	167.283253040011	0.875447901593302	1.60674695998922	0.85760666420435
51	166.64	162.033988696205	0.835433678880579	4.60601130379523	-1.10152246408654
52	140.07	147.458818288567	0.700375631719434	-7.3888182885675	-2.76787906597551
53	128.84	140.821467372655	0.631944763271959	-11.9814673726553	-1.32571240749699
54	123.4	127.710199795470	0.514198440616602	-4.31019979547042	-2.50033714604736
55	120.3	124.722661006933	0.488827737971778	-4.42266100693287	-0.639845405386887
56	129.66	125.444525422225	0.490198216503249	4.21547457777513	0.0426505253904493
57	118.12	118.183707720328	0.454524092001214	-0.0637077203279084	-1.41857192826512
58	113.91	119.142552679375	0.456216491416185	-5.23255267937484	0.092236304904101
59	131.09	120.647576061941	0.458547401336228	10.4424239380592	0.191717538727549
60	119.14	121.038743752205	0.458439809244851	-1.89874375220497	-0.0123122287647229
61	115.33	127.448529087400	0.470400364217843	-12.1185290874005	1.08536045198542

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599667697p4lsr6xcxhkbej/1e76l1259966732.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599667697p4lsr6xcxhkbej/1e76l1259966732.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599667697p4lsr6xcxhkbej/2a77t1259966732.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599667697p4lsr6xcxhkbej/2a77t1259966732.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599667697p4lsr6xcxhkbej/3gqzi1259966732.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599667697p4lsr6xcxhkbej/3gqzi1259966732.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599667697p4lsr6xcxhkbej/44sft1259966732.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599667697p4lsr6xcxhkbej/44sft1259966732.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599667697p4lsr6xcxhkbej/5a6qo1259966732.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599667697p4lsr6xcxhkbej/5a6qo1259966732.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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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