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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, 29 Dec 2010 13:54:31 +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/Dec/29/t1293630769bkxzrmbp0e79zs4.htm/, Retrieved Wed, 29 Dec 2010 14:52:55 +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/Dec/29/t1293630769bkxzrmbp0e79zs4.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 «

1203.6 1180.59 1156.85 1191.5 1191.33 1234.18 1220.33 1228.81 1207.01 1249.48 1248.29 1280.08 1280.66 1294.87 1310.61 1270.09 1270.2 1276.66 1303.82 1335.85 1377.94 1400.63 1418.3 1438.24 1406.82 1420.86 1482.37 1530.62 1503.35 1455.27 1473.99 1526.75 1549.38 1481.14 1468.36 1378.55 1330.63 1322.7 1385.59 1400.38 1280 1267.38 1282.83 1166.36 968.75 896.24 903.25 825.88 735.09 797.87 872.81 919.14 919.32 987.48 1020.62 1057.08 1036.19 1095.63 1115.1 1073.87 1104.49 1169.43 1186.69 1089.41 1030.71 1101.6 1049.33 1141.2 1183.26 1180.55

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	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	1203.6	1203.6	0	0	0
2	1180.59	1181.83054196833	-1.47498088467055	-1.24054196832557	-0.284024198566593
3	1156.85	1158.40276492714	-3.12916107787666	-1.55276492713600	-0.462323929741867
4	1191.5	1192.01424019813	0.669401288963926	-0.514240198133606	0.760616874849795
5	1191.33	1192.70611934575	0.672235173313777	-1.37611934575391	0.000459285838405934
6	1234.18	1234.70291656316	6.58002256633772	-0.522916563157383	0.835829612692212
7	1220.33	1221.97292549325	3.58378469172501	-1.64292549324595	-0.387630878363085
8	1228.81	1229.81194943179	4.28068175819037	-1.00194943178630	0.0849579864893268
9	1207.01	1208.57725073455	-0.0503146153421739	-1.56725073455134	-0.507481825158163
10	1249.48	1249.90859443526	7.14287248709373	-0.428594435264753	0.82086059574743
11	1248.29	1249.74023734887	5.8517222871768	-1.45023734886888	-0.144761539281487
12	1280.08	1280.82290190401	10.3546672278062	-0.742901904006777	0.498938923335298
13	1280.66	1275.21063547458	7.64671773513533	5.44936452542237	-0.368327514523855
14	1294.87	1294.54749938523	9.71838081999919	0.322500614771585	0.196293489974706
15	1310.61	1311.55659085460	11.0353690801396	-0.946590854604094	0.143751476310473
16	1270.09	1270.90294479547	1.67084497884017	-0.812944795468013	-1.01702690110898
17	1270.2	1270.95184494053	1.37662636397690	-0.75184494052717	-0.0319219051988098
18	1276.66	1275.83873383233	2.0139550606445	0.82126616767429	0.0690879403785712
19	1303.82	1304.03784468268	6.77107288975171	-0.217844682676558	0.515363787841715
20	1335.85	1334.89445604312	11.1485680097861	0.955543956884228	0.474041356286752
21	1377.94	1378.55650846748	17.0595064661659	-0.616508467479832	0.639922229899437
22	1400.63	1400.07011461834	17.8694212537579	0.559885381663795	0.0876659464967215
23	1418.3	1419.29017889795	18.1150641760275	-0.990178897949044	0.0265860692238078
24	1438.24	1437.85538305442	18.1969030628394	0.384616945581490	0.0088557807557456
25	1406.82	1413.62079459185	10.5832916706126	-6.80079459184968	-0.901442063586917
26	1420.86	1420.59549304146	9.93827698556037	0.264506958542139	-0.0649279143585996
27	1482.37	1479.05048958830	18.7375528218357	3.31951041169606	0.954465066061165
28	1530.62	1529.91198003084	24.5750185281037	0.708019969155754	0.630843765579274
29	1503.35	1505.43376495054	15.6634808200939	-2.08376495053548	-0.963662637039344
30	1455.27	1456.10312923839	3.85712254199394	-0.833129238389272	-1.27705335854543
31	1473.99	1472.58249671507	6.14989163406348	1.40750328492636	0.248027542212725
32	1526.75	1524.27853444794	14.4229540707048	2.47146555206171	0.895025146735357
33	1549.38	1549.43836503032	16.3731993238712	-0.0583650303234399	0.210997924800498
34	1481.14	1483.12738189375	1.35429076178113	-1.9873818937538	-1.62496921053214
35	1468.36	1468.60415016739	-1.52994286708432	-0.244150167388990	-0.312080844887497
36	1378.55	1379.40970929419	-17.4434279596324	-0.859709294190633	-1.72170130499990
37	1330.63	1340.09292393723	-21.3880618538749	-9.46292393723279	-0.451118795166033
38	1322.7	1323.57543919964	-20.5138341225812	-0.875439199635194	0.0902442463882552
39	1385.59	1380.06514646780	-6.56943056665926	5.52485353219783	1.51256578428503
40	1400.38	1397.76117241646	-2.16523547337056	2.61882758354123	0.476059988298106
41	1280	1284.23960953062	-22.372626527401	-4.23960953062272	-2.18511249938945
42	1267.38	1266.07992115587	-21.6082043740081	1.30007884412644	0.0826867743341093
43	1282.83	1280.91134873228	-14.9966386807511	1.91865126772350	0.715244094821404
44	1166.36	1169.54167044699	-32.4820818206898	-3.1816704469876	-1.89169962196002
45	968.75	971.730025609308	-62.4784000181356	-2.98002560930846	-3.2453517183306
46	896.24	896.435677762127	-64.8036881421995	-0.195677762126545	-0.251588995916415
47	903.25	896.326794186749	-53.065015178427	6.92320581325083	1.27015766709631
48	825.88	827.117635861972	-55.9916476971527	-1.23763586197186	-0.316704900562764
49	735.09	748.617320251757	-60.0573085461071	-13.5273202517568	-0.456862317864839
50	797.87	797.734431881375	-40.4129240524773	0.135568118624634	2.05604575055323
51	872.81	864.005074905056	-21.1151238393168	8.80492509494428	2.09256909221330
52	919.14	908.016106417033	-9.30619823359594	11.1238935829666	1.27685535300450
53	919.32	922.265054996798	-5.03549660036184	-2.94505499679804	0.461805437371435
54	987.48	985.326941497581	7.30965135007947	2.15305850241862	1.33538037188976
55	1020.62	1014.81907655139	11.3308889362981	5.80092344861396	0.435030050251917
56	1057.08	1050.51773296625	15.7481921427191	6.56226703374715	0.477902688790586
57	1036.19	1038.47515658027	10.7104055367327	-2.28515658026792	-0.545053910784206
58	1095.63	1095.21953837437	19.0554864526338	0.410461625631616	0.902929730448005
59	1115.1	1106.91151977254	17.7206058843324	8.18848022746418	-0.144434962164476
60	1073.87	1075.52133933223	8.82681568371132	-1.65133933223487	-0.962748007605339
61	1104.49	1125.35890700867	16.2394810504188	-20.8689070086678	0.824107489298788
62	1169.43	1172.96189607397	21.8911302851220	-3.53189607397373	0.59671510432668
63	1186.69	1181.99745962783	19.5674769396398	4.69254037216617	-0.251846304781234
64	1089.41	1084.97465089641	-1.55693244978512	4.43534910359214	-2.28483253462047
65	1030.71	1037.89762562787	-9.80451386639556	-7.18762562786593	-0.891833279370407
66	1101.6	1095.78627262500	2.45916866098518	5.81372737499819	1.32656148890715
67	1049.33	1048.34263486264	-6.58118110520495	0.987365137363155	-0.978023875229743
68	1141.2	1127.55862208272	8.96150786880428	13.6413779172789	1.68156261293303
69	1183.26	1186.42609458333	18.0022741912657	-3.16609458333172	0.97816078291961
70	1180.55	1182.22475562239	13.9798161313664	-1.67475562239472	-0.435232562037672

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630769bkxzrmbp0e79zs4/16k9g1293630865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630769bkxzrmbp0e79zs4/16k9g1293630865.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630769bkxzrmbp0e79zs4/26k9g1293630865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630769bkxzrmbp0e79zs4/26k9g1293630865.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630769bkxzrmbp0e79zs4/3zc8j1293630865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630769bkxzrmbp0e79zs4/3zc8j1293630865.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630769bkxzrmbp0e79zs4/4r3qm1293630865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630769bkxzrmbp0e79zs4/4r3qm1293630865.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630769bkxzrmbp0e79zs4/5r3qm1293630865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630769bkxzrmbp0e79zs4/5r3qm1293630865.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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