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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: Fri, 04 Dec 2009 08:18:11 -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/04/t12599399363im4a2kr5rgpw1u.htm/, Retrieved Fri, 04 Dec 2009 16:19:03 +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/04/t12599399363im4a2kr5rgpw1u.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 «

274412 272433 268361 268586 264768 269974 304744 309365 308347 298427 289231 291975 294912 293488 290555 284736 281818 287854 316263 325412 326011 328282 317480 317539 313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 301631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860

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	274412	274412	0	0	0
2	272433	272915.331243222	-1536.53084384839	-482.331243222391	-0.338623654549409
3	268361	268799.122134470	-3330.92334833379	-438.122134470516	-0.366553965051034
4	268586	267702.224607973	-1681.87956001712	883.775392027405	0.327333273611194
5	264768	265200.843148832	-2274.29443580010	-432.843148832322	-0.113348645025418
6	269974	268402.895045034	1663.72406398967	1571.10495496574	0.760817481143181
7	304744	297595.168170275	21522.7182083970	7148.83182972453	3.83338305917547
8	309365	313331.834411319	17346.1506062469	-3966.83441131916	-0.80577986934487
9	308347	312843.304041416	4473.9524022405	-4496.30404141599	-2.48363393347098
10	298427	301377.69301121	-7028.25884105017	-2950.69301120984	-2.21925759154732
11	289231	289315.814875962	-10660.3341628797	-84.8148759619235	-0.700776746326481
12	291975	288777.280434597	-3356.68394254999	3197.71956540326	1.40917605416842
13	294912	293435.987409544	2412.34308825241	1476.01259045597	1.11643885302276
14	293488	294349.808137479	1329.74388416496	-861.808137479141	-0.212154989716284
15	290555	291817.282139443	-1360.26157505993	-1262.28213944288	-0.516326195110005
16	284736	283538.793642386	-6168.46664626259	1197.20635761359	-0.94228338928797
17	281818	281539.16125601	-3253.0152011637	278.838743990042	0.562316101522241
18	287854	291768.18904268	6101.27162921385	-3914.18904268028	1.80073141511293
19	316263	307372.745272802	12693.2656434027	8890.25472719815	1.27283035286210
20	325412	324635.162316395	15867.7251346493	776.837683604883	0.612594340477746
21	326011	329293.453699349	8077.09122190138	-3282.45369934933	-1.50303440573641
22	328282	330488.168014075	3293.99277009526	-2206.16801407532	-0.92291927674726
23	317480	323033.844223356	-4173.15771833449	-5553.84422335603	-1.44073534577277
24	317539	316907.866059615	-5528.44574163976	631.133940384718	-0.261574900572907
25	313737	311841.338563644	-5207.8367779806	1895.661436356	0.0620445930500974
26	312276	310242.176924113	-2699.96131823118	2033.82307588703	0.48457626913015
27	309391	307433.771479096	-2774.54819742377	1957.22852090356	-0.0143576268861385
28	302950	302579.582375682	-4200.99390913032	370.417624318211	-0.276731279725493
29	300316	302623.141363542	-1275.18837928434	-2307.14136354206	0.565653289124374
30	304035	309533.626229561	4350.95791795764	-5498.62622956149	1.08344699943344
31	333476	324302.064447665	11496.3892111362	9173.93555233481	1.37844749665445
32	337698	335079.825922182	11002.9818491948	2618.17407781818	-0.0952285138832852
33	335932	339343.367579933	6372.3738702567	-3411.36757993327	-0.893408862725439
34	323931	327750.312711212	-5971.75098031309	-3819.3127112124	-2.38177187122071
35	313927	318827.285108482	-7998.57151110695	-4900.28510848161	-0.391063486422027
36	314485	313287.526171904	-6311.0201917799	1197.47382809586	0.325809075495368
37	313218	311163.057735359	-3435.59492878518	2054.94226464092	0.555785712657227
38	309664	307129.721157627	-3846.00214363422	2534.27884237343	-0.0791743990660157
39	302963	300096.480708253	-6023.43039165672	2866.5192917471	-0.419638235748755
40	298989	297944.395443389	-3382.54092587179	1044.60455661127	0.510806462926683
41	298423	301737.421643017	1526.54342605722	-3314.42164301650	0.948859165191138
42	301631	309852.917813861	6031.32613545839	-8221.91781386106	0.86831949760896
43	329765	320537.686576292	9207.06523899988	9227.3134237077	0.612377861916892
44	335083	330546.984688084	9754.65915616535	4536.01531191641	0.105666367668587
45	327616	328591.391099118	1755.99730782869	-975.39109911816	-1.54332240936234
46	309119	315616.708271650	-8306.8081279278	-6497.70827165035	-1.94153739068852
47	295916	302611.768810427	-11515.0378159255	-6695.76881042693	-0.619061199676495
48	291413	291415.209160826	-11297.5891894284	-2.20916082606256	0.0419824445006785
49	291542	286805.098485379	-6728.78645748018	4736.90151462053	0.882345691589225
50	284678	280371.265399233	-6527.41805721285	4306.73460076687	0.0388369324957708
51	276475	273925.579591636	-6471.78230516247	2549.42040836392	0.0107275180853488
52	272566	272134.750884506	-3288.09072248932	431.249115493753	0.615117379832908
53	264981	270572.314117175	-2112.31218835307	-5591.31411717515	0.227162822934790
54	263290	273017.474821697	993.23971692474	-9727.47482169688	0.598958672270499
55	296806	285819.163101555	9029.59102431937	10986.8368984454	1.54959489239122
56	303598	295852.386645859	9712.43503725265	7745.61335414147	0.131737935167007
57	286994	288017.905979002	-2230.76950886559	-1023.90597900196	-2.30443859788108
58	276427	281589.037515802	-5088.57497282072	-5162.0375158016	-0.551414775741474
59	266424	274020.912884393	-6776.25253728809	-7596.91288439303	-0.325687245836188
60	267153	268704.926201171	-5782.21809663462	-1551.92620117143	0.191897923184899
61	268381	263247.580490331	-5560.98386969369	5133.41950966913	0.0427053105037236
62	262522	257671.846846112	-5571.02086396402	4850.15315388839	-0.00193572589164921
63	255542	253324.760672138	-4739.7565715873	2217.23932786216	0.160319977754258
64	253158	251823.021642463	-2541.7159136013	1334.97835753746	0.42447042335363
65	243803	251048.122718691	-1340.92573154174	-7245.1227186907	0.231922251871647
66	250741	262013.223162209	7025.47664613629	-11272.2231622094	1.61409515775317
67	280445	270261.652827258	7856.21387119896	10183.3471727417	0.160200631772948
68	285257	273298.769406940	4584.27896123552	11958.2305930596	-0.631159446778872
69	270976	272059.522662531	629.96068160073	-1083.52266253091	-0.762968725238057
70	261076	266969.333068304	-3254.64318426131	-5893.3330683036	-0.749588609510796
71	255603	263581.089840154	-3345.37531792361	-7978.08984015428	-0.0175108783568468
72	260376	261541.563047107	-2458.31745417709	-1165.56304710658	0.171228690293025
73	263903	258529.380506851	-2834.63705512840	5373.61949314855	-0.0726227965228684
74	264291	258408.663443331	-991.983851739562	5882.33655666882	0.355379863651439
75	263276	260583.593108152	1155.29633683121	2692.40689184802	0.414183124611897
76	262572	261992.552286078	1327.23020441511	579.447713922341	0.0331942251311679
77	256167	266871.473009207	3736.65873814838	-10704.4730092072	0.465263807487358
78	264221	275268.620019142	6899.5263959274	-11047.6200191421	0.610293302613554
79	293860	282526.991580211	7142.91895769037	11333.0084197893	0.0469412918028616

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599399363im4a2kr5rgpw1u/1ski51259939888.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599399363im4a2kr5rgpw1u/1ski51259939888.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599399363im4a2kr5rgpw1u/2lhio1259939888.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599399363im4a2kr5rgpw1u/2lhio1259939888.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599399363im4a2kr5rgpw1u/3vhjg1259939888.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599399363im4a2kr5rgpw1u/3vhjg1259939888.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599399363im4a2kr5rgpw1u/48ed71259939888.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599399363im4a2kr5rgpw1u/48ed71259939888.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599399363im4a2kr5rgpw1u/5dn1x1259939888.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599399363im4a2kr5rgpw1u/5dn1x1259939888.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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