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Structural decomposition

*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, 30 Nov 2010 15:46:51 +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/Nov/30/t129113193671gmvpyyqo9tu0s.htm/, Retrieved Tue, 30 Nov 2010 16:45:42 +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/Nov/30/t129113193671gmvpyyqo9tu0s.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 «

37 30 47 35 30 43 82 40 47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 3

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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	37	37	0	0	0
2	30	34.0671216941213	-0.315647564790337	-0.31564756420223	-0.291558207717331
3	47	39.2754159647873	0.113018493807602	0.113018493807602	0.578107943214642
4	35	37.5988237864005	0.00609133324206647	0.00609133324206532	-0.194826675503084
5	30	34.6320001040144	-0.138701975676196	-0.138701975676196	-0.332720022217105
6	43	37.8293262532751	0.000285907581016487	0.000285907581015099	0.380390337897555
7	82	54.7345055002265	0.62635014152385	0.626350141523854	1.95163954894543
8	40	49.2755246002829	0.420161822917526	0.420161822917527	-0.708354793270166
9	47	48.5140071337029	0.382767179877118	0.382767179877118	-0.138315627892971
10	19	37.4418734766951	0.0393381287320684	0.0393381287320691	-1.34590727617731
11	52	42.9493225713565	0.196172304749665	0.196172304749665	0.644218893332828
12	136	78.0933079792282	1.16141281737792	1.16141281737792	4.12555501966769
13	80	82.405037674586	0.803640669539752	-8.84004735984471	0.530702819484212
14	42	65.0516229548378	0.0542762836813006	0.0542762800922897	-1.77265834157425
15	54	60.6291616810058	-0.0882405583830091	-0.088240558383007	-0.486105172608378
16	66	62.6908790939866	-0.0332794524032328	-0.0332794524032380	0.244988724128414
17	81	69.6599622576009	0.117309882915424	0.117309882915424	0.817045414994713
18	63	67.1730843092634	0.0681303204142184	0.0681303204142267	-0.307662362506208
19	137	93.4363647150941	0.517998469675756	0.517998469675762	3.11621286205938
20	72	85.5313411834837	0.382951410803086	0.382951410803083	-1.00607462956371
21	107	93.6607944645395	0.501082284767511	0.501082284767512	0.927555972162997
22	58	80.4581507083647	0.299773952706316	0.299773952706319	-1.64344569595362
23	36	63.9282717919332	0.0595876339530189	0.0595876339530240	-2.02043376961061
24	52	59.4901342371581	-0.00312292677736641	-0.00312292677736388	-0.540352334075333
25	79	65.1690426899526	-0.296953819164317	3.26649201321126	0.816165646442566
26	77	69.9327223130034	-0.163312320080150	-0.163312322518920	0.539272135660072
27	54	63.696644480193	-0.286949059374766	-0.286949059374757	-0.689461813374959
28	84	71.36192367388	-0.156425160934276	-0.156425160934279	0.929873009781318
29	48	62.5185716246564	-0.277014316578656	-0.277014316578658	-1.03081504793801
30	96	74.9978916868859	-0.120642791282769	-0.120642791282758	1.52551438746289
31	83	77.957327068086	-0.0861183040178078	-0.0861183040177992	0.369943849126872
32	66	73.475654327657	-0.132359631914891	-0.132359631914895	-0.529282107445417
33	61	68.7937954814648	-0.178114250777881	-0.178114250777882	-0.548661028790547
34	53	62.8678560875564	-0.234074404504519	-0.234074404504517	-0.693846020030631
35	30	50.5756706788763	-0.348672470763643	-0.348672470763633	-1.45650350855119
36	74	59.201726585533	-0.264956524801259	-0.264956524801255	1.08452121249381
37	69	61.1893369280218	-0.340368376575945	3.74405214385024	0.306764690482265
38	59	60.2507129540982	-0.351984696680386	-0.351984698212666	-0.066248576140395
39	42	53.1654926142638	-0.452751478680410	-0.452751478680399	-0.780052519204419
40	65	57.5263519187164	-0.394566544141757	-0.394566544141754	0.569637095178366
41	70	62.1043985930574	-0.343602933535737	-0.343602933535741	0.594751043722194
42	100	76.1679614815683	-0.212865165055240	-0.212865165055235	1.73294071933137
43	63	71.2077381412589	-0.252361260117054	-0.252361260117045	-0.572833479964084
44	105	83.7167245568239	-0.152461310528321	-0.152461310528320	1.54266792276289
45	82	83.0393651242567	-0.156399367687836	-0.156399367687836	-0.0635234520492033
46	81	82.2413505760636	-0.161070698414878	-0.161070698414877	-0.0777025118569286
47	75	79.5098004563027	-0.179382579357404	-0.179382579357389	-0.311435709355405
48	102	87.8170695670264	-0.119905104111077	-0.119905104111073	1.02853626661158
49	121	98.1776365906012	-0.379305767555715	4.17236344605525	1.38956946142677
50	98	98.0252471038806	-0.375822002172828	-0.3758220051039	0.0256770062449916
51	76	89.551338558132	-0.471632224648908	-0.471632224648893	-0.949062463098624
52	77	84.7142848944818	-0.513393193667197	-0.513393193667215	-0.520173830686708
53	63	76.4680432022279	-0.576207605766888	-0.576207605766901	-0.929151736810298
54	37	61.6154720271693	-0.679047834469404	-0.67904783446939	-1.72303017901997
55	35	51.5422352461928	-0.741186105626393	-0.741186105626385	-1.13661230541679
56	23	40.7467671380797	-0.803858613012813	-0.803858613012816	-1.21823775261747
57	40	40.262604186947	-0.801945924159431	-0.80194592415943	0.0387700424106709
58	29	35.8754559445217	-0.822791267543264	-0.822791267543263	-0.435018971173871
59	37	36.0806574502545	-0.816934544693994	-0.816934544693976	0.124777017289439
60	51	41.4056556852203	-0.782462054720102	-0.782462054720095	0.745672735826488
61	20	30.8154211638528	-0.589907706695399	6.4889847728376	-1.27958777101575
62	28	29.5929232536214	-0.597938619671958	-0.597938618900505	-0.0725809712450768
63	13	23.1643585852979	-0.654976183051592	-0.654976183051577	-0.688446400776884
64	22	22.5639684032535	-0.654544118317453	-0.654544118317453	0.00653360043588675
65	25	23.3065448214487	-0.645144805925538	-0.645144805925545	0.168378293764226
66	13	19.3067416834582	-0.665179475688209	-0.665179475688207	-0.40577759389535
67	16	17.9072892961621	-0.669210268870825	-0.669210268870812	-0.0889989704429047
68	13	15.9132811790094	-0.676070590934731	-0.676070590934732	-0.160765922038189
69	16	15.7710589955398	-0.673414637318863	-0.673414637318866	0.0648296106054625
70	17	16.0530142911655	-0.668791046538752	-0.668791046538751	0.116069874743964
71	9	13.2647473091235	-0.678851458114668	-0.678851458114651	-0.257571998873056
72	17	14.4742974934467	-0.670012753262825	-0.670012753262816	0.229532537273078
73	25	15.108446727048	-0.691229840461706	7.60352824346882	0.168327091104721
74	14	14.5224697436582	-0.690090782816285	-0.690090781198667	0.0121934073330585
75	8	11.8921815668287	-0.706269006103503	-0.706269006103486	-0.230287521451263
76	7	9.88412868911363	-0.715056437033845	-0.715056437033845	-0.156307444342482
77	10	9.74499471328324	-0.711749866376998	-0.711749866377005	0.0695562316457681
78	7	8.54205488396047	-0.714255113106516	-0.714255113106513	-0.0595073600282687
79	10	8.89933859595211	-0.709227947786835	-0.709227947786822	0.130042020223480
80	3	6.52786932164335	-0.716589688967188	-0.71658968896719	-0.201933830992266

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t129113193671gmvpyyqo9tu0s/1bzj51291132007.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t129113193671gmvpyyqo9tu0s/1bzj51291132007.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t129113193671gmvpyyqo9tu0s/2m80p1291132007.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t129113193671gmvpyyqo9tu0s/2m80p1291132007.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t129113193671gmvpyyqo9tu0s/3m80p1291132007.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t129113193671gmvpyyqo9tu0s/3m80p1291132007.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t129113193671gmvpyyqo9tu0s/4xh0s1291132007.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t129113193671gmvpyyqo9tu0s/4xh0s1291132007.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t129113193671gmvpyyqo9tu0s/57qzw1291132007.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t129113193671gmvpyyqo9tu0s/57qzw1291132007.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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