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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, 08 Dec 2010 15:45:34 +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/08/t12918247105ulu57gexvf37ma.htm/, Retrieved Wed, 08 Dec 2010 17:11:50 +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/08/t12918247105ulu57gexvf37ma.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 «

186448 190530 194207 190855 200779 204428 207617 212071 214239 215883 223484 221529 225247 226699 231406 232324 237192 236727 240698 240688 245283 243556 247826 245798 250479 249216 251896 247616 249994 246552 248771 247551 249745 245742 249019 245841 248771 244723 246878 246014 248496 244351 248016 246509 249426 247840 251035 250161 254278 250801 253985 249174 251287 247947 249992 243805 255812 250417 253033 248705 253950 251484 251093 245996 252721 248019 250464 245571 252690 250183 253639 254436 265280 268705 270643 271480

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	186448	186448	0	0	0
2	190530	189443.206478839	1029.33220419497	890.020785754805	0.78251421709684
3	194207	192177.612464863	1813.07690699738	1363.1120694777	1.19727220457306
4	190855	191178.419501414	367.997511965863	726.732141889124	-1.83451990864378
5	200779	198822.704943896	3969.89691894923	-55.6464701710378	4.36671979599958
6	204428	203897.816356982	4508.1880655856	175.677137713201	0.675983271386587
7	207617	207341.345219200	3983.15050013976	632.88765731804	-0.6728272749546
8	212071	212275.934028050	4455.45675943443	-520.644352182208	0.591445455685734
9	214239	215377.100018362	3803.47772783333	-719.381390605238	-0.837915511501245
10	215883	216768.759225760	2621.69110652560	-135.938302770319	-1.45949284190488
11	223484	221608.513391647	3705.8055919098	1168.66380656737	1.37130233416204
12	221529	223102.814910569	2619.75285702308	-864.77164899968	-1.36439297924419
13	225247	225552.572990365	2537.20477824852	-252.541586212481	-0.104653900094717
14	226699	227521.937355548	2259.83846030852	-645.369317087628	-0.346615296785494
15	231406	229793.594281474	2265.60041219141	1608.68688395317	0.00726734027529162
16	232324	232753.387869256	2604.87643280511	-648.505719889776	0.426438434304928
17	237192	236619.795158346	3218.62545272556	178.311181539268	0.774292654880965
18	236727	238311.655364733	2473.9431491454	-1106.97632942550	-0.934477533450907
19	240698	239785.874594382	1986.87614210077	1225.24823405856	-0.613374915908075
20	240688	241610.567188944	1907.76975114746	-871.686006225396	-0.0994716354603897
21	245283	244306.894357468	2291.68662417526	729.78505585676	0.483466684295873
22	243556	245259.737913689	1639.14749308027	-1285.03503799079	-0.820104953725054
23	247826	246673.115743389	1529.17384412359	1223.48490616425	-0.138401057719906
24	245798	247302.368437061	1090.58816800139	-1222.71708360598	-0.551613512587953
25	250479	249058.353286301	1414.63283324510	1212.76222069587	0.407789110503336
26	249216	250462.925800347	1409.73123856884	-1243.78079086457	-0.00616378383910533
27	251896	251009.246105002	989.178436121106	1156.60862949153	-0.52911761446074
28	247616	250057.034277564	43.3384024854603	-1834.01172556649	-1.18970800536626
29	249994	249202.121333231	-394.152839294672	1072.53393932131	-0.550412172644179
30	246552	248002.276334087	-786.640652953867	-1198.46315895828	-0.493658961900905
31	248771	247188.620236879	-799.799329111193	1590.82184838269	-0.0165537198694503
32	247551	248161.926435148	63.9342269878309	-1165.11644007902	1.08647689789481
33	249745	248447.646702927	171.959286965826	1228.05451706507	0.135894324816302
34	245742	247586.468276386	-331.291863425981	-1521.60846938944	-0.633021914959784
35	249019	247569.499834552	-178.191036843134	1351.28216248905	0.192593573910546
36	245841	247164.304510909	-288.765448731972	-1252.36481291801	-0.139092154373678
37	248771	247168.396470154	-146.121256568831	1511.09633103572	0.179438389264937
38	244723	246571.440245203	-365.720480239398	-1707.56106426357	-0.276233733695153
39	246878	245740.858205996	-592.146010876303	1282.39685633466	-0.284827692172930
40	246014	246510.948741242	71.3875458672191	-922.624812764308	0.834667887752284
41	248496	246803.954897304	179.333700453313	1622.79683230270	0.135788418324018
42	244351	246366.508090233	-121.092671984742	-1822.77901698428	-0.377909849215498
43	248016	246717.387888836	108.796791499752	1151.13567344921	0.289183194615556
44	246509	247238.546209631	309.652534835092	-858.39871949876	0.252659775382279
45	249426	247649.624733798	359.055322195566	1744.68297111943	0.0621448194348233
46	247840	249127.567820517	904.04897681852	-1637.18862554151	0.685556226531153
47	251035	250017.681803927	897.261481933603	1021.67243713773	-0.00853812376006289
48	250161	251013.288851379	945.1640859416	-883.018986641396	0.0602575310043426
49	254278	252466.984773163	1192.86115024498	1652.11540815545	0.311582885806666
50	250801	252896.363794556	820.98122842145	-1856.79866604542	-0.467794233086307
51	253985	253242.64776461	589.764290766845	890.680008172866	-0.290852093051691
52	249174	251477.009877241	-557.51372822705	-1567.01867943003	-1.44318164656761
53	251287	249945.056688277	-1032.14657073833	1646.42452347952	-0.597049396448244
54	247947	249354.437514557	-817.085868900304	-1545.40112576965	0.270528704125709
55	249992	248589.953246446	-791.464521535174	1385.61042567176	0.0322295602262429
56	243805	246144.332072334	-1597.17669878153	-1822.45975495488	-1.01351990485014
57	255812	250668.892794572	1384.61778873104	3230.2589882248	3.75085346636858
58	250417	252114.632730353	1414.38936376873	-1716.73148153832	0.0374502009720471
59	253033	252233.897197885	783.555943998521	1203.78821063228	-0.793536784997278
60	248705	252184.276552414	377.729613412756	-3218.93510955375	-0.510496279468551
61	253950	251358.965626028	-208.251080832099	2966.94634505119	-0.737115715825917
62	251484	252245.104472423	324.80784031473	-1103.06676907255	0.670544446038215
63	251093	250767.632863407	-553.052013473135	888.522283546821	-1.10427577596664
64	245996	249405.437847183	-947.171938567868	-3156.60623958339	-0.495770578870859
65	252721	249368.963667711	-503.586452088063	3067.47217395686	0.557994197731928
66	248019	248806.785549731	-532.125464540649	-769.477508439316	-0.0358997394529611
67	250464	249012.097698266	-172.932062943911	1221.47643513947	0.451835867931494
68	245571	248899.736682055	-143.42892803819	-3347.66321615164	0.0371125265973846
69	252690	249312.794423238	127.626326935952	3203.32114023652	0.340965300935715
70	250183	250507.159023587	647.216534960947	-657.480940509797	0.65360191076776
71	253639	251997.856169453	1058.06169205399	1377.58288505149	0.516809543397047
72	254436	256164.329535706	2572.11654074478	-2699.60968753725	1.90455695061375
73	265280	261077.432522839	3712.37149525787	3471.0834388372	1.43434730158373
74	268705	267906.382971511	5230.40447943665	-175.215121130486	1.90956111585694
75	270643	271186.914572118	4280.65433545365	65.3588808731411	-1.19470785988385
76	271480	274956.402375852	4031.67374985382	-3316.67903674716	-0.31319717664437

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918247105ulu57gexvf37ma/1flfu1291823130.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918247105ulu57gexvf37ma/1flfu1291823130.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918247105ulu57gexvf37ma/2pcwx1291823130.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918247105ulu57gexvf37ma/2pcwx1291823130.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918247105ulu57gexvf37ma/30mdi1291823130.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918247105ulu57gexvf37ma/30mdi1291823130.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918247105ulu57gexvf37ma/40mdi1291823130.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918247105ulu57gexvf37ma/40mdi1291823130.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918247105ulu57gexvf37ma/50mdi1291823130.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918247105ulu57gexvf37ma/50mdi1291823130.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 4 ;

Parameters (R input):

par1 = 4 ; par2 = 4 ;

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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