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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: Tue, 01 Dec 2009 13:19:53 -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/01/t1259698850edk46c756iehgps.htm/, Retrieved Tue, 01 Dec 2009 21:20:57 +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/01/t1259698850edk46c756iehgps.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 «

105.7 105.7 111.1 82.4 60 107.3 99.3 113.5 108.9 100.2 103.9 138.7 120.2 100.2 143.2 70.9 85.2 133 136.6 117.9 106.3 122.3 125.5 148.4 126.3 99.6 140.4 80.3 92.6 138.5 110.9 119.6 105 109 129.4 148.6 101.4 134.8 143.7 81.6 90.3 141.5 140.7 140.2 100.2 125.7 119.6 134.7 109 116.3 146.9 97.4 89.4 132.1 139.8 129 112.5 121.9 121.7 123.1

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	105.7	105.7	0	0	0
2	105.7	105.7	0	0	0
3	111.1	107.344641890952	0.192645853206376	2.61208368861288	0.338190942124921
4	82.4	100.326895275061	-0.600075382294971	-13.3728498193399	-1.42240244421262
5	60	87.5174259941417	-1.75053664145693	-18.6911621834243	-2.69747621349687
6	107.3	89.0505718051163	-1.49024760263120	15.5605353932202	0.800690552131691
7	99.3	91.5510583669497	-1.22151612148269	4.19590289301452	1.03906782151807
8	113.5	97.0803743430234	-0.82649359825072	10.0842550171730	1.83162986128148
9	108.9	101.109892214078	-0.573229049764033	3.07978723134908	1.35201187170876
10	100.2	101.863925582374	-0.510117976845719	-2.97895841956451	0.375707424520647
11	103.9	102.401034270145	-0.463902980348401	0.446663665654385	0.299715812680959
12	138.7	110.632002148510	-0.103094587762238	19.2449523969423	2.50755696337587
13	120.2	114.059543859670	-0.190180560818469	1.92359980046363	1.23823994394763
14	100.2	111.897671017583	-0.207307663468807	-9.64748941798102	-0.605839568422443
15	143.2	115.869341409268	-0.0674033660246292	23.6302832681622	1.12517454127873
16	70.9	107.833054548370	-0.40881613499513	-30.2736412071263	-2.06384449651805
17	85.2	105.324844806329	-0.501441985889379	-18.3500702207372	-0.552217588272277
18	133	107.973186321593	-0.369766808282961	22.2707069497622	0.854582903422955
19	136.6	114.966678922867	-0.0879056676377233	14.9659936411966	2.05648191777593
20	117.9	116.096642695102	-0.0456632230693495	0.670232969393747	0.347822952829285
21	106.3	114.168671211143	-0.104755625208360	-6.08193441103327	-0.546295481200169
22	122.3	116.676648421222	-0.0309511972668592	3.10592737659815	0.76709068478743
23	125.5	120.692182095864	0.0685164307821748	0.858464331763287	1.19918274733023
24	148.4	124.142749663215	0.132392437914821	20.9029679856657	1.01425815229225
25	126.3	125.061029125421	0.138413570838339	0.43181112242668	0.243563898297384
26	99.6	122.452534870750	0.105562095003110	-20.1075419925221	-0.83038327942993
27	140.4	119.344557009627	0.04145299970288	24.1072260256246	-0.931303001259527
28	80.3	116.764696837760	-0.0253619980276945	-34.0559029742654	-0.74137934681779
29	92.6	115.889376630318	-0.0490861674383372	-22.5142869220263	-0.239630627759551
30	138.5	116.97627899392	-0.0171800397997237	20.4791333381957	0.323196170420406
31	110.9	113.048117077832	-0.122538944725756	1.50083197840010	-1.12744357000475
32	119.6	113.275214429285	-0.113758541897876	5.99364189556269	0.102086436374914
33	105	113.683652284626	-0.101778182958227	-9.18479299296355	0.15411037847406
34	109	113.091021042820	-0.111845557685268	-3.61473435456395	-0.146100933780694
35	129.4	116.490495667621	-0.0495630727102119	9.46964457735282	1.05258495626533
36	148.6	119.333678281753	-0.00740157810017592	26.4063684877909	0.873169678890295
37	101.4	115.550594678437	-0.0513249479897345	-10.3879756007015	-1.14689559312488
38	134.8	121.683903661659	0.0262799532029827	7.00925803213681	1.86291849004383
39	143.7	122.332912563487	0.0359178839176765	20.7638946239946	0.184605385249156
40	81.6	121.010149249715	0.0111010033999638	-38.1150948868998	-0.397874960559327
41	90.3	118.927498745418	-0.0307478101275528	-26.6455086896791	-0.610582232646936
42	141.5	118.219588831063	-0.0446698127104764	23.9223417303094	-0.197972368086141
43	140.7	122.442773121828	0.0416232181086506	14.1856430975425	1.25537409573191
44	140.2	126.116926947210	0.111547948973462	10.5889732034897	1.07616620875523
45	100.2	124.027500026556	0.0722118925801899	-21.6929123064011	-0.65647133991494
46	125.7	125.434265889989	0.0938822776085803	-1.03816030193676	0.400356465308575
47	119.6	123.205986542125	0.0602670909621095	-1.32286003963186	-0.6999493453182
48	134.7	119.542745794677	0.0126008804425881	18.8361764870504	-1.12641386259487
49	109	119.600851986044	0.013132936655692	-10.6459083574572	0.0137845121989755
50	116.3	117.467922575887	-0.0124766503112657	0.948410174632398	-0.647659949334143
51	146.9	118.325760144995	-0.00104840327659503	27.7230476952086	0.260848333349537
52	97.4	121.810536767577	0.0495449346456143	-27.792987438657	1.03843764354762
53	89.4	121.867909438974	0.0496666138056852	-32.4754721804237	0.00232530902919012
54	132.1	120.066957932737	0.0200292356458956	13.8206473446498	-0.550063539746591
55	139.8	121.161962578917	0.037155975146691	17.5966587690845	0.320454294340977
56	129	120.456755547761	0.0257230743440486	9.26568050088583	-0.222191854850823
57	112.5	122.934935433748	0.0614070846420884	-12.8335725962588	0.737088650664419
58	121.9	122.880465098057	0.0598412153965649	-0.866591868259193	-0.0349580802515319
59	121.7	122.282889722149	0.0516673438225211	0.0657419627520186	-0.198935307335135
60	123.1	118.515419077226	0.00776149285919243	8.36315541656304	-1.15800237558920

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698850edk46c756iehgps/1ka3f1259698791.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698850edk46c756iehgps/1ka3f1259698791.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698850edk46c756iehgps/2xaer1259698791.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698850edk46c756iehgps/2xaer1259698791.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698850edk46c756iehgps/3a86c1259698791.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698850edk46c756iehgps/3a86c1259698791.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698850edk46c756iehgps/404bl1259698791.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698850edk46c756iehgps/404bl1259698791.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698850edk46c756iehgps/5cd5v1259698791.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698850edk46c756iehgps/5cd5v1259698791.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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