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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: Mon, 20 Dec 2010 10:31:38 +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/20/t1292840969j0s7i9048j0im4p.htm/, Retrieved Mon, 20 Dec 2010 11:29:30 +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/20/t1292840969j0s7i9048j0im4p.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 «

377 370 358 357 349 348 369 381 368 361 351 351 358 354 347 345 343 340 362 370 373 371 354 357 363 364 363 358 357 357 380 378 376 380 379 384 392 394 392 396 392 396 419 421 420 418 410 418 426 428 430 424 423 427 441 449 452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456 459 446 441 439 454 460 457 451 444 437 443 471 469 454 444 436

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	377	377	0	0	0
2	370	370.77182044338	-0.364085612821178	-0.771820443379732	-0.819667559650175
3	358	360.893609121638	-0.857495727577432	-2.89360912163831	-1.91355436444758
4	357	357.415620668051	-0.996056511308958	-0.415620668050982	-0.539604561315922
5	349	350.83970524568	-1.3543561783321	-1.83970524567983	-1.13564667380614
6	348	348.360025830901	-1.44026926413622	-0.360025830900925	-0.226985859116976
7	369	364.748223455095	0.100972828102177	4.25177654490494	3.56919909301561
8	381	379.392957053473	1.47621628208954	1.60704294652741	2.89325467655363
9	368	372.1521922671	0.595226720096757	-4.15219226710039	-1.72504910273599
10	361	363.204447308049	-0.418766238031085	-2.204447308049	-1.88047706531214
11	351	353.165321518602	-1.48041460255603	-2.16532151860176	-1.8892437940748
12	351	350.892383082871	-1.5704160522584	0.107616917128553	-0.155211143839857
13	358	351.32485023196	-1.36810728454446	6.6751497680399	0.438266450244164
14	354	352.076002270524	-1.11403525794026	1.92399772947648	0.380781257302718
15	347	349.954315608161	-1.23557568771516	-2.95431560816111	-0.188602799786637
16	345	345.006621479103	-1.68137150246395	-0.00662147910329645	-0.718323472570808
17	343	343.587009975268	-1.6498889856861	-0.587009975267622	0.0504900209587586
18	340	343.61466339716	-1.4471591093792	-3.61466339716023	0.323004817281015
19	362	356.689626999325	0.316440277731347	5.31037300067548	2.79584782160258
20	370	365.640608624883	1.36904494594614	4.35939137511712	1.66223839209093
21	373	374.099630470416	2.23583511633671	-1.09963047041557	1.36477277648142
22	371	373.135618014036	1.84376353855187	-2.13561801403576	-0.615951608616155
23	354	360.605870908242	0.081014947189498	-6.60587090824167	-2.76472101998357
24	357	357.189883569378	-0.346286523988329	-0.189883569377656	-0.67185312408269
25	363	356.594075456645	-0.376563014431525	6.40592454335518	-0.049795096296961
26	364	360.235572821524	0.117262999243606	3.76442717847578	0.757845195309938
27	363	363.81207438243	0.541118643961598	-0.812074382429971	0.649314572456457
28	358	359.50948449846	-0.052734660459822	-1.50948449846026	-0.929504086686762
29	357	357.956856502646	-0.236887098776109	-0.95685650264629	-0.287984504425376
30	357	362.487131605139	0.34855666508877	-5.48713160513888	0.913195549643585
31	380	373.776142096145	1.6921768028427	6.22385790385535	2.09542913377379
32	378	376.480947315876	1.81655964322943	1.51905268412368	0.194039986755237
33	376	376.967723036841	1.65318516910728	-0.967723036840695	-0.25491793623416
34	380	378.362262052233	1.62140672881612	1.63773794776696	-0.0495799181184586
35	379	383.358179387028	2.03569926364257	-4.35817938702818	0.646020970100626
36	384	384.697499505624	1.9503842862427	-0.697499505623628	-0.13362166335584
37	392	386.781978466361	1.96681310289619	5.2180215336394	0.0261408019573997
38	394	390.36670575119	2.16545893081636	3.63329424881044	0.308168360185925
39	392	391.584932670452	2.04951883693086	0.415067329547941	-0.178795550749138
40	396	396.048168878826	2.34498936057412	-0.0481688788260475	0.461538675977981
41	392	395.657231146316	2.00947837623672	-3.6572311463158	-0.524664089560504
42	396	402.584559281025	2.61296206357534	-6.58455928102522	0.941174230757757
43	419	411.188908857562	3.34815215429608	7.81109114243753	1.14575356941826
44	421	418.222645004876	3.8003680787981	2.77735499512411	0.704988509357126
45	420	421.540873965666	3.74121033224067	-1.54087396566616	-0.092251729837293
46	418	419.420345201303	3.02210563705586	-1.42034520130258	-1.12115410578939
47	410	416.046067170086	2.23801765568379	-6.04606717008585	-1.22241688976023
48	418	418.261113927705	2.23520472976684	-0.261113927705485	-0.00440541806308474
49	426	420.881039815343	2.28235304194304	5.11896018465727	0.0743092737279108
50	428	423.790014025864	2.35920128185588	4.20998597413607	0.119580913899457
51	430	428.966846271361	2.7040092842992	1.03315372863909	0.533780219947932
52	424	425.639202944556	1.96619549060588	-1.63920294455554	-1.15113009152482
53	423	427.79452998348	1.98936070280676	-4.79452998348016	0.0362267310518663
54	427	434.006882740956	2.5070123665471	-7.00688274095597	0.80792065169002
55	441	435.147992225412	2.33956653551413	5.85200777458842	-0.261032918501219
56	449	443.718024251251	3.10329000985807	5.28197574874892	1.19051788788743
57	452	450.746121382134	3.5843473656921	1.2538786178657	0.749950498681144
58	462	459.961521619288	4.27434909726769	2.03847838071157	1.0754619111606
59	455	462.247256496182	4.03083406243002	-7.24725649618191	-0.379776504009806
60	461	462.702322082168	3.59316567385327	-1.70232208216846	-0.685217858541987
61	461	458.776602822135	2.67214511906328	2.22339717786457	-1.44567609583215
62	463	459.489233361039	2.43203265984592	3.51076663896065	-0.374004328178865
63	462	459.696647794025	2.15983394638893	2.30335220597479	-0.422337765361319
64	456	458.5781390031	1.75894162609772	-2.57813900310029	-0.625057931716198
65	455	460.384308997977	1.76472168977558	-5.3843089979765	0.00903628424572416
66	456	462.514135227732	1.80943856374319	-6.51413522773187	0.069828509226207
67	472	467.040343251498	2.14224012333407	4.95965674850217	0.519007671322199
68	472	468.559850787133	2.06596183005033	3.4401492128667	-0.118904411124607
69	471	471.222839953936	2.1390804674289	-0.222839953936187	0.113962276449176
70	465	465.377943341081	1.16159236816581	-0.377943341080785	-1.52337964930848
71	459	465.110296898625	0.986698782633627	-6.11029689862496	-0.27284469344212
72	465	464.904156907295	0.840753771687547	0.095843092705268	-0.228380088120873
73	468	465.203070043426	0.774414519033658	2.79692995657397	-0.103908823073392
74	467	463.499704837149	0.470992029945105	3.50029516285095	-0.472817491477764
75	463	460.714984237736	0.0727165456493103	2.28501576226447	-0.618844746909385
76	460	461.96351166672	0.216469654198623	-1.96351166671955	0.224072916997709
77	462	466.231179631062	0.71200826329687	-4.23117963106189	0.774399137178819
78	461	468.149877667799	0.859704521590386	-7.14987766779867	0.230700766303188
79	476	470.534259119806	1.04636549355092	5.46574088019368	0.291194156305576
80	476	472.331446799772	1.13828070839912	3.66855320022848	0.143283764387947
81	471	470.227751216171	0.741477597215622	0.77224878382903	-0.618361931042568
82	453	457.613439884611	-0.89264850803403	-4.61343988461131	-2.54673025457714
83	443	450.294990766958	-1.67856596034968	-7.2949907669579	-1.22633383089189
84	442	443.169469633218	-2.34478253898502	-1.16946963321799	-1.04200783037378
85	444	440.150113751741	-2.42733543476285	3.84988624825905	-0.129145953899806
86	438	434.589412651668	-2.81083748131147	3.41058734833206	-0.597741884616217
87	427	426.756398117148	-3.42505248800154	0.243601882851705	-0.955282341767888
88	424	425.940663608999	-3.10610261904724	-1.94066360899923	0.497121782484273
89	416	421.427165284535	-3.27818470621251	-5.42716528453461	-0.26882400381483
90	406	414.923467592817	-3.67277887304397	-8.92346759281678	-0.616406772481001
91	431	421.831706341288	-2.37801479218281	9.16829365871218	2.02031356674395
92	434	426.947223948541	-1.46109379286945	7.05277605145949	1.42943278590965
93	418	416.869559562373	-2.51520017272952	1.13044043762744	-1.64257234565825
94	412	414.271739515864	-2.52530406171486	-2.27173951586367	-0.015747501774449
95	404	410.366231823789	-2.69404714138637	-6.36623182378885	-0.263332374531435
96	409	409.22075434622	-2.50469851032565	-0.220754346219617	0.29602569033092
97	412	406.982911665032	-2.47205423423226	5.01708833496764	0.0510294650765298
98	406	402.070506644262	-2.77060467450632	3.92949335573771	-0.465403965078753
99	398	398.457860671294	-2.87356026566692	-0.457860671294424	-0.160231321976855
100	397	397.556668923814	-2.63251292740968	-0.556668923813682	0.375710414754938
101	385	391.380899274974	-3.06561020495785	-6.38089927497433	-0.676378661957069
102	390	398.412677184335	-1.83085258605721	-8.41267718433503	1.9287900953799
103	413	403.634772097366	-0.968162947003074	9.36522790263373	1.34630156421877
104	413	403.594187556936	-0.854708116535778	9.40581244306416	0.176881487629252
105	401	400.659750006732	-1.10902864906465	0.340249993268361	-0.396299940547861
106	397	399.088927178462	-1.16548159281065	-2.08892717846199	-0.087992563025745
107	397	402.268280572463	-0.634446023318783	-5.2682805724629	0.8287398188054
108	409	407.333703137259	0.062308229469326	1.66629686274122	1.08889843578405
109	419	411.858101656168	0.607962200826045	7.14189834383201	0.852527948642628
110	424	418.024645779809	1.28774022105419	5.97535422019062	1.05981250206448
111	428	426.508902504229	2.16743454135471	1.49109749577141	1.36973309683167
112	430	429.944423103743	2.32238243640613	0.0555768962565404	0.241526792630361
113	424	433.281111843845	2.44633089993157	-9.2811118438452	0.193527956233552
114	433	441.435458174522	3.14409920473569	-8.43545817452165	1.08986481447066
115	456	446.384278634567	3.36476831812477	9.61572136543327	0.344395841259839
116	459	449.148678842959	3.29136049739322	9.8513211570414	-0.11445405523389
117	446	447.352827828116	2.66947573471673	-1.35282782811619	-0.96911579267617
118	441	445.679040622549	2.13868614165583	-4.67904062254922	-0.827410190793463
119	439	446.253148069245	1.94750731670341	-7.25314806924458	-0.298354125337589
120	454	452.205431961933	2.43693597390293	1.79456803806664	0.764651870631468
121	460	454.837097114599	2.4607415186913	5.16290288540134	0.0371803987763305
122	457	454.196684573684	2.08161187814039	2.80331542631626	-0.591138382960509
123	451	451.469164802083	1.49388222389752	-0.469164802083169	-0.915454023901634
124	444	446.570753653916	0.712934872938267	-2.57075365391579	-1.21740888983367
125	437	447.588643567013	0.750192576524574	-10.5886435670132	0.058161869203174
126	443	451.020510290082	1.07791880795666	-8.02051029008233	0.511819873914855
127	471	458.740941773673	1.88987724960722	12.2590582263268	1.26723397921852
128	469	458.613319582734	1.64326669138684	10.3866804172657	-0.384529323267877
129	454	455.650326329031	1.08033099232356	-1.65032632903076	-0.877323910597753
130	444	450.510386488516	0.320338132477274	-6.51038648851589	-1.18480272773939
131	436	445.92693724783	-0.278741832755345	-9.9269372478295	-0.93489805075211

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840969j0s7i9048j0im4p/1dikr1292841093.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840969j0s7i9048j0im4p/1dikr1292841093.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840969j0s7i9048j0im4p/26rkc1292841093.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840969j0s7i9048j0im4p/26rkc1292841093.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840969j0s7i9048j0im4p/36rkc1292841093.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840969j0s7i9048j0im4p/36rkc1292841093.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840969j0s7i9048j0im4p/4yi1f1292841093.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840969j0s7i9048j0im4p/4yi1f1292841093.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840969j0s7i9048j0im4p/5yi1f1292841093.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840969j0s7i9048j0im4p/5yi1f1292841093.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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We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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