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WS9

*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: Sun, 06 Dec 2009 08:13:07 -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/06/t1260112435zt73r4i51ttopcz.htm/, Retrieved Sun, 06 Dec 2009 16:14:02 +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/06/t1260112435zt73r4i51ttopcz.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 «

10414,9 12476,8 12384,6 12266,7 12919,9 11497,3 12142 13919,4 12656,8 12034,1 13199,7 10881,3 11301,2 13643,9 12517 13981,1 14275,7 13435 13565,7 16216,3 12970 14079,9 14235 12213,4 12581 14130,4 14210,8 14378,5 13142,8 13714,7 13621,9 15379,8 13306,3 14391,2 14909,9 14025,4 12951,2 14344,3 16093,4 15413,6 14705,7 15972,8 16241,4 16626,4 17136,2 15622,9 18003,9 16136,1 14423,7 16789,4 16782,2 14133,8 12607 12004,5 12175,4 13268 12299,3 11800,6 13873,3 12269,6

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	10414.9	10414.9	0	0	0
2	12476.8	11986.7143157158	72.5907689086392	490.085684284226	1.88245541158710
3	12384.6	12380.8239443246	88.3566353659489	3.77605567544202	0.477124864408427
4	12266.7	12339.9153376747	84.8151765382335	-73.2153376746813	-0.223696855269900
5	12919.9	12644.2539301933	87.901746369392	275.646069806741	0.387151487804389
6	11497.3	11992.2101899245	80.275256871552	-494.910189924496	-1.30430890953452
7	12142	11941.5979054084	78.899919702437	200.402094591628	-0.230417083179349
8	13919.4	13068.4889582319	90.8541930763192	850.911041768102	1.84310385129774
9	12656.8	12986.5088436674	88.7717232752276	-329.708843667419	-0.303787261758424
10	12034.1	12382.2736311851	80.1613984544392	-348.173631185062	-1.21762916846940
11	13199.7	12732.6597471352	83.5895961605094	467.040252864830	0.47463707088919
12	10881.3	11673.1677306072	68.8171446801262	-791.867730607161	-2.00710807886463
13	11301.2	11845.0907584699	66.231334918307	-543.890758469913	0.197176874366809
14	13643.9	12708.0775645809	72.3358651041639	935.822435419067	1.38177730067491
15	12517	12741.0042166361	71.3305927723695	-224.004216636068	-0.0638419287637921
16	13981.1	13533.6764687296	89.53097523124	447.423531270369	1.22053362873885
17	14275.7	13752.1497805945	91.9948813251609	523.55021940551	0.224593727141872
18	13435	13938.6454514490	93.3697424019842	-503.645451448963	0.165577341149965
19	13565.7	13924.7973701326	91.9965374392374	-359.097370132605	-0.187841860858894
20	16216.3	14701.0829616665	100.759359214357	1515.21703833349	1.19798727220817
21	12970	13927.1113730342	89.0286972613423	-957.111373034246	-1.53061688811245
22	14079.9	14125.2933056096	90.5226842878062	-45.3933056095834	0.190925715701640
23	14235	13703.0748784593	84.1538649568585	531.925121540712	-0.895830588701286
24	12213.4	13329.3535634922	80.3432287081576	-1115.95356349221	-0.800748573406247
25	12581	13385.5066111323	80.2682096002647	-804.506611132293	-0.0430312598770271
26	14130.4	13349.4838781825	79.0380971620759	780.916121817504	-0.202217411286757
27	14210.8	14169.6884643440	93.3532157286406	41.1115356559795	1.24768770824706
28	14378.5	14204.8495557465	92.0660325364289	173.650444253494	-0.0987037239538626
29	13142.8	13396.4748715224	73.6069523699097	-253.674871522432	-1.55528192363082
30	13714.7	13804.0334237375	79.5750058156826	-89.3334237375037	0.581671395862051
31	13621.9	14104.3016204323	83.135461377311	-482.401620432338	0.385061806367694
32	15379.8	13837.9886272563	77.7282370435252	1541.81137274374	-0.609634025418624
33	13306.3	14057.393382634	79.8944191666793	-751.093382634006	0.247031098944685
34	14391.2	14162.3762643713	80.2658792324204	228.823735628661	0.043700264628799
35	14909.9	14201.5234934233	79.7120937970591	708.376506576667	-0.0715417360164041
36	14025.4	14746.5226639460	85.101425860396	-721.12266394596	0.810877852226727
37	12951.2	14325.9878497038	79.5118819278745	-1374.78784970377	-0.884126284977143
38	14344.3	14045.0763440678	74.3961269745379	299.22365593219	-0.623801523786547
39	16093.4	15076.1737637513	92.0044458484128	1017.22623624872	1.63101952750475
40	15413.6	15123.1538664184	91.0729228982325	290.446133581597	-0.076764230726259
41	14705.7	15158.3171836411	89.9184089430259	-452.617183641073	-0.0962566641610976
42	15972.8	15719.9381141668	99.0908809869327	252.861885833172	0.818087098189793
43	16241.4	16295.4495183719	107.76611090318	-54.0495183718894	0.828436312909904
44	16626.4	15768.6895384782	96.7491641021483	857.710461521787	-1.10354942394755
45	17136.2	16911.7955241907	114.280870189783	224.404475809268	1.81838504209820
46	15622.9	16268.3266729907	102.110495617744	-645.426672990685	-1.31530223531364
47	18003.9	16858.9634181646	109.519383428450	1144.93658183540	0.847482504137743
48	16136.1	16829.3958356651	107.508803639363	-693.295835665049	-0.241547565718181
49	14423.7	16274.8072965875	97.7434799940832	-1851.1072965875	-1.15008810602703
50	16789.4	16592.4406258495	101.36544608688	196.959374150487	0.379705018855491
51	16782.2	16189.0257140567	91.9210257845975	593.174285943283	-0.864714889736485
52	14133.8	14882.5931565347	63.6402016941964	-748.793156534742	-2.39275906912631
53	12607	13877.9817669784	41.6667644730760	-1270.98176697844	-1.83763748476646
54	12004.5	12686.8058298238	16.9183970773988	-682.305829823762	-2.13245739655853
55	12175.4	12214.4862802562	7.48460512561205	-39.0862802561969	-0.848444374173807
56	13268	12485.1645541865	12.3610931170309	782.835445813458	0.456544099362177
57	12299.3	12152.4565866256	6.1963179923449	146.843413374378	-0.598043717279071
58	11800.6	12391.6477978286	10.2124111880962	-591.04779782855	0.403398419545134
59	13873.3	12545.8566225337	12.6145196144026	1327.44337746630	0.249254179390781
60	12269.6	12653.7692725488	14.1809859140995	-384.169272548789	0.165072824014381

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260112435zt73r4i51ttopcz/1jbbh1260112384.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260112435zt73r4i51ttopcz/1jbbh1260112384.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260112435zt73r4i51ttopcz/2zoaz1260112384.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260112435zt73r4i51ttopcz/2zoaz1260112384.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260112435zt73r4i51ttopcz/3imt81260112384.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260112435zt73r4i51ttopcz/3imt81260112384.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260112435zt73r4i51ttopcz/44oxf1260112384.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260112435zt73r4i51ttopcz/44oxf1260112384.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260112435zt73r4i51ttopcz/5j0ns1260112384.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260112435zt73r4i51ttopcz/5j0ns1260112384.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = 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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