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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: Mon, 21 Dec 2009 02:08:31 -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/21/t126138725591saxannm69576p.htm/, Retrieved Mon, 21 Dec 2009 10:21:02 +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/21/t126138725591saxannm69576p.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 «

43.9 51 51.9 54.3 50.3 57.2 48.8 41.1 58 63 53.8 54.7 55.5 56.1 69.6 69.4 57.2 68 53.3 47.9 60.8 61.7 57.8 51.4 50.5 48.1 58.7 54 56.1 60.4 51.2 50.7 56.4 53.3 52.6 47.7 49.5 48.5 55.3 49.8 57.4 64.6 53 41.5 55.9 58.4 53.5 50.6 58.5 49.1 61.1 52.3 58.4 65.5 61.7 45.1 52.1 59.3 57.9 45 64.9 63.8 69.4 71.1 62.9 73.5 62.7 51.9 73.3 66.7 62.5 70.3

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	43.9	43.9	0	0	0
2	51	47.0479387398247	0.24246683375215	1.36127753333564	1.26074627467546
3	51.9	49.5342044573152	0.412987969954243	0.764955558711433	0.838804156120813
4	54.3	51.7451352605692	0.516212506737741	1.06982193952045	0.750065638183191
5	50.3	51.4439479180592	0.480574326747510	-0.411927839400074	-0.361439218912688
6	57.2	53.7136744294499	0.543890285639209	1.82353776836626	0.812245665555612
7	48.8	52.1143454957541	0.47805805650679	-1.28726242350551	-0.985070826735972
8	41.1	47.760532949035	0.342811600505252	-2.04994527836049	-2.23456079808479
9	58	51.2873604747634	0.426533846893818	3.65991224604987	1.47734413378979
10	63	56.2145549394808	0.539688542622203	2.45830289517002	2.09221944455839
11	53.8	55.8733849364426	0.518301384147634	-1.22496659807875	-0.409975474867575
12	54.7	55.4524730780714	0.496155828427303	0.153305781609470	-0.437501565988379
13	55.5	57.2137936267642	0.403544336590115	-3.09934484575627	0.742458763455314
14	56.1	57.0771307197501	0.392992277629068	-0.525075027860392	-0.234573078051621
15	69.6	62.0735706490003	0.552314505873602	3.9823786694186	1.90134065412892
16	69.4	65.2130162649649	0.634058184746527	2.07758161621901	1.12295731789267
17	57.2	63.3156165040426	0.568944095229283	-3.94398964904352	-1.14258144736441
18	68	64.0569273753986	0.572579756536737	3.7911040639145	0.0793874532872976
19	53.3	60.4609247448855	0.496871557211125	-3.43639356611302	-1.93847418203173
20	47.9	56.8953227745794	0.429988951815727	-5.34213010193577	-1.89781595802939
21	60.8	57.2300038721172	0.428512357523582	3.65597926641452	-0.0446256332810679
22	61.7	58.078799393715	0.434733065915889	3.24132049544587	0.197037454541535
23	57.8	58.665479890017	0.436790180774811	-1.0031199612954	0.0713087354670697
24	51.4	56.5205861697773	0.415703256923539	-2.76442592757245	-1.21607328704858
25	50.5	55.6602877343843	0.441615487726866	-3.93064842701421	-0.647276116576455
26	48.1	54.017399115343	0.423337757501751	-4.09893107506617	-0.95745141010759
27	58.7	54.5918222914814	0.426558460246747	3.98489833801232	0.0661858454190987
28	54	53.5627312210493	0.393706123874252	1.63883702357988	-0.646869717969869
29	56.1	55.8723404210094	0.431978256949423	-1.39938091882231	0.871665033531613
30	60.4	55.9037541521121	0.425180674207333	4.84354048535129	-0.185180304537702
31	51.2	55.1256249163574	0.40753460907217	-2.86987058899475	-0.561221199723659
32	50.7	55.5916794889004	0.408304050185515	-4.94334935173621	0.0274188324302579
33	56.4	54.9460147901125	0.395512987722059	2.38777761910336	-0.495000302771469
34	53.3	53.3254751159663	0.373080785757881	1.76481470901880	-0.948101104512396
35	52.6	52.9628137655943	0.366331965554350	0.292384820102349	-0.346396265326864
36	47.7	51.9175948379928	0.360300557721662	-2.95175299722619	-0.667564961315599
37	49.5	52.0501093070393	0.361659253801339	-2.34098209502258	-0.110589336348128
38	48.5	52.3682319027137	0.361391120771481	-3.83003906323649	-0.0202617188999141
39	55.3	52.062220239986	0.351520656521622	3.79866147425206	-0.300867366572693
40	49.8	51.1198439336862	0.329266842405976	-0.235467901674758	-0.584259757644702
41	57.4	53.8016886513668	0.367756647942991	1.59671098904213	1.07693451108175
42	64.6	56.2007683888942	0.397261616130124	6.64476157929764	0.941276089190515
43	53	56.5644550195515	0.396833113957337	-3.53515562036393	-0.0156816421068382
44	41.5	53.1173281501338	0.353128277250413	-8.2418979766742	-1.80360053532200
45	55.9	52.6978891283608	0.345229832807771	3.8830523635093	-0.363403968629055
46	58.4	53.9697061289951	0.353516947382205	3.61147962849906	0.436450342765258
47	53.5	53.7834264408139	0.349783102788396	0.194895942929942	-0.254555779513232
48	50.6	53.809930073161	0.34866390722899	-2.92201788178038	-0.152980773781150
49	58.5	56.3294912998827	0.347653553262243	0.219858868129653	1.03626506214856
50	49.1	55.5076773649549	0.341245570942051	-5.38179407121510	-0.546431061873394
51	61.1	56.1979145777984	0.345160624848429	4.60411669204185	0.159767017226671
52	52.3	55.6408298362745	0.332837940992319	-2.57537673913724	-0.412051704598823
53	58.4	56.4410338984136	0.339238991834958	1.55942427093638	0.215107328161140
54	65.5	57.3610775175908	0.346582183426134	7.63712642411612	0.269732110002818
55	61.7	59.750761672456	0.369722564814509	0.168861027988275	0.955299266811731
56	45.1	57.9393276734584	0.347745408073652	-10.9275216672941	-1.02427063400410
57	52.1	54.7301677654341	0.316143752212948	0.499294035600076	-1.6745044760329
58	59.3	54.7786456372212	0.314125520537027	4.75747062226951	-0.126183068522801
59	57.9	55.9442343857171	0.319023954589263	1.20286214037656	0.401830949908647
60	45	53.7503789767764	0.310296283456105	-6.52122851060423	-1.18842426686792
61	64.9	57.202412029433	0.316417516307943	4.90375079310187	1.48885659181867
62	63.8	61.9043978034601	0.339482792982958	-1.94912412260782	2.05277376906402
63	69.4	63.5757642112196	0.351615772456315	4.67681014191960	0.615212032284827
64	71.1	67.6776069842966	0.393704615350883	0.212171503698324	1.72659235314474
65	62.9	66.3313211961322	0.373432710832944	-1.93647182756971	-0.804579225143055
66	73.5	66.4234058215092	0.370313306245914	7.32007982348669	-0.130947420279429
67	62.7	64.7718229996596	0.349867923716709	-0.309872141465174	-0.946344253981577
68	51.9	63.5243679145122	0.335455565307162	-10.2251337672085	-0.750541928905227
69	73.3	66.6708608101405	0.357613082724162	4.15787629510025	1.32396538337305
70	66.7	65.6339073344452	0.348388593795638	2.29513311893782	-0.657694490440457
71	62.5	64.079292453877	0.338603684591910	0.101185287133001	-0.898314217644751
72	70.3	69.2023457109599	0.356066973006593	-3.13519557616029	2.26093228719687

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t126138725591saxannm69576p/1hoow1261386508.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126138725591saxannm69576p/1hoow1261386508.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126138725591saxannm69576p/2844e1261386508.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126138725591saxannm69576p/2844e1261386508.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126138725591saxannm69576p/3s0xt1261386508.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126138725591saxannm69576p/3s0xt1261386508.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126138725591saxannm69576p/4mt4c1261386508.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126138725591saxannm69576p/4mt4c1261386508.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126138725591saxannm69576p/5vy3q1261386508.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126138725591saxannm69576p/5vy3q1261386508.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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