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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: Wed, 16 Dec 2009 07:18:57 -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/16/t1260973190zmhjwsrg6x6sogq.htm/, Retrieved Wed, 16 Dec 2009 15:19:57 +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/16/t1260973190zmhjwsrg6x6sogq.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 «

19915 19843 19761 20858 21968 23061 22661 22269 21857 21568 21274 20987 19683 19381 19071 20772 22485 24181 23479 22782 22067 21489 20903 20330 19736 19483 19242 20334 21423 22523 21986 21462 20908 20575 20237 19904 19610 19251 18941 20450 21946 23409 22741 22069 21539 21189 20960 20704 19697 19598 19456 20316 21083 22158 21469 20892 20578 20233 19947 20049

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	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	19915	19915	0	0	0
2	19843	19843.9943178957	-71.0878571363803	-0.994317895669007	-0.118782435020626
3	19761	19760.7309832625	-82.7960266846761	0.26901673746091	-0.0197979137823644
4	20858	20822.0785203464	1008.51469063160	35.9214796535916	1.80930311820643
5	21968	21973.665317112	1145.05557553730	-5.66531711198193	0.226651828859217
6	23061	23064.7500111397	1093.53921294631	-3.75001113973822	-0.0855081607236897
7	22661	22707.9502449778	-290.808999241377	-46.9502449778206	-2.29777874350131
8	22269	22262.8157970249	-438.11153945891	6.18420297505747	-0.244496714917772
9	21857	21855.5771135006	-408.643565299405	1.42288649942803	0.0489117356031883
10	21568	21565.2986171617	-295.664706117176	2.70138283831989	0.187525347244533
11	21274	21275.6281967602	-289.943191324189	-1.62819676019485	0.00949672404276561
12	20987	20987.8237163819	-287.901802787922	-0.823716381864051	0.00338835156325109
13	19683	19713.5671243585	-1229.09328510059	-30.5671243585169	-1.56288797494588
14	19381	19310.5884745786	-440.188265186597	70.4115254213785	1.31544285068647
15	19071	19115.7896343943	-211.956638228701	-44.7896343942592	0.382814742405743
16	20772	20656.3772658778	1417.39023402376	115.622734122209	2.70100817048867
17	22485	22522.4357334842	1834.19199958307	-37.4357334841831	0.691915353464615
18	24181	24141.5093033162	1634.28478145999	39.4906966838404	-0.331810701648741
19	23479	23624.4298294729	-364.968905476902	-145.429829472927	-3.31841868158201
20	22782	22775.8528421517	-814.37349815881	6.14715784833346	-0.74593380816506
21	22067	22056.2694797685	-726.287662105801	10.7305202315412	0.146207240116577
22	21489	21478.6668899565	-588.118382226589	10.3331100434600	0.2293370881841
23	20903	20933.5700212574	-548.139154619983	-30.5700212574086	0.0663586319469552
24	20330	20275.3975838953	-650.388126238181	54.6024161047364	-0.169715975389280
25	19736	19789.5287823	-497.55170229978	-53.528782300006	0.253817091961421
26	19483	19358.6951226839	-435.517830545865	124.304877316061	0.103160025034256
27	19242	19360.8158324495	-34.3595406185888	-118.815832449519	0.669222744032911
28	20334	20212.0385840219	779.028274343585	121.961415978093	1.34931367886376
29	21423	21503.3169349686	1248.84227704478	-80.3169349686257	0.779813140841009
30	22523	22377.3750178998	904.978549369957	145.624982100197	-0.570766242281175
31	21986	22155.8645338846	-128.625359802679	-169.864533884586	-1.71560132897775
32	21462	21477.5015573102	-633.022576485718	-15.5015573102070	-0.837212478640571
33	20908	20895.7119109632	-586.015725582298	12.2880890368417	0.0780232366798802
34	20575	20556.1559478777	-359.884050177029	18.8440521223227	0.375339451984497
35	20237	20254.9294447219	-306.063858675002	-17.9294447218936	0.0893324737880168
36	19904	19868.3104800743	-379.969738580598	35.6895199256944	-0.122671609575035
37	19610	19643.4889262014	-237.656303722162	-33.4889262014213	0.236367687042846
38	19251	19137.8444870749	-483.583490040556	113.155512925058	-0.408410334452181
39	18941	19081.9069836659	-94.1583856891801	-140.906983665920	0.648006001669356
40	20450	20312.1968177511	1114.45402029051	137.803182248911	2.00602414980104
41	21946	22015.432028425	1651.00213349906	-69.4320284250129	0.890443159575436
42	23409	23226.2270462425	1249.74236237062	182.772953757488	-0.666052638284688
43	22741	22952.3107253375	-139.244469042447	-211.310725337477	-2.30546715178198
44	22069	22111.0188322956	-779.231719801418	-42.0188322955578	-1.06226889600168
45	21539	21523.7632597185	-604.22883162796	15.2367402815033	0.290474498005167
46	21189	21158.6678057946	-386.235921657021	30.3321942054257	0.361830646819602
47	20960	20961.7651676648	-213.639583325585	-1.76516766481449	0.286481276815693
48	20704	20701.5272083712	-256.113325669308	2.47279162876521	-0.0705004529366505
49	19697	19728.6285921275	-909.418221897572	-31.6285921275245	-1.08506379752044
50	19598	19424.1086607690	-358.094964831915	173.891339230955	0.915106239945355
51	19456	19651.4821299626	173.136185246543	-195.482129962565	0.882959553042894
52	20316	20235.6739290013	546.746310628885	80.3260709987073	0.620273994884358
53	21083	21160.3438615304	889.878027274081	-77.3438615303965	0.569405803683436
54	22158	21880.0884890089	735.391152201141	277.911510991058	-0.256435028722037
55	21469	21665.6914020749	-127.163385140742	-196.691402074868	-1.43168603319950
56	20892	20968.7377564075	-644.621381960067	-76.7377564074897	-0.858890526294234
57	20578	20556.6979809134	-433.403931988053	21.3020190865555	0.350584443613076
58	20233	20221.433729847	-344.278388730544	11.5662701530151	0.147933217242533
59	19947	19964.3764038498	-265.069359148595	-17.3764038497780	0.131473536489530
60	20049	19945.1468305703	-41.8454646103689	103.8531694297	0.370530374304483

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260973190zmhjwsrg6x6sogq/1rpu21260973133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260973190zmhjwsrg6x6sogq/1rpu21260973133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260973190zmhjwsrg6x6sogq/28d6o1260973133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260973190zmhjwsrg6x6sogq/28d6o1260973133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260973190zmhjwsrg6x6sogq/3r8y91260973133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260973190zmhjwsrg6x6sogq/3r8y91260973133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260973190zmhjwsrg6x6sogq/4n6b41260973133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260973190zmhjwsrg6x6sogq/4n6b41260973133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260973190zmhjwsrg6x6sogq/5ghj71260973133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260973190zmhjwsrg6x6sogq/5ghj71260973133.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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