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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, 10 Dec 2010 19:58:02 +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/10/t1292011012tyf3zz8stc9jchp.htm/, Retrieved Fri, 10 Dec 2010 20:56:52 +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/10/t1292011012tyf3zz8stc9jchp.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 «

42.33600 42.14710 40.25640 39.18980 39.13170 38.15070 38.27070 39.13350 40.12190 41.28450 42.57490 43.90190 43.18350 43.61880 44.76240 45.19720 44.38810 43.55520 43.56780 44.21350 45.14510 45.80790 42.32820 37.89990 34.79640 35.21440 36.37270 36.25020 36.82610 36.77230 36.90420 37.04940 36.82590 36.13570 36.03000 35.79270 35.91740 35.40080 35.17230 34.92110 35.02920 34.77390 34.89990 34.90540 34.56800 34.40600 34.45780 34.73160 34.26020 33.88490 34.05490 34.27550 34.13930 34.15870 34.53860 33.79870 33.49730 33.68020 34.32840 34.15380 33.91840 34.32620 34.77500 35.01190 34.55130 34.69510 35.47300 35.97940 36.47890 36.39100 36.67040 37.41620 37.11850 36.30010 35.70020 35.58590 35.67770 35.24080 34.80160 34.43890 34.98810 36.06800 36.35660 36.12540 34.87100 35.21990 34.33900 33.82340 34.51990 35.53000 35.79660 33.84840 33.98710 34.11610 33.82350 32.45400 31.87740 31.11500 31.04360 30.88680 31.30010 30.05070 28.6 etc...

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	42.336	42.336	0	0	0
2	42.1471	42.1754349982682	-0.0283349982681699	-0.0283349982681699	-0.0690720062199077
3	40.2564	40.3301585321872	-0.0737585321871807	-0.0737585321871807	-2.12702631200036
4	39.1898	39.2871976133781	-0.0973976133781213	-0.0973976133781214	-1.13427192952268
5	39.1317	39.2281837154445	-0.0964837154445443	-0.0964837154445445	0.0449082970192552
6	38.1507	38.1354593226654	-0.00381016933365392	0.0152406773346167	-1.34935442656653
7	38.2707	38.2654873685552	0.00521263144479248	0.00521263144479224	0.130181099146390
8	39.1335	39.1193541670269	0.014145832973075	0.0141458329730749	0.98644881374596
9	40.1219	40.0977103098880	0.0241896901119562	0.0241896901119563	1.12070681919169
10	41.2845	41.2486938784443	0.0358061215557107	0.035806121555711	1.30960897473060
11	42.5749	42.5169140363312	-0.0144964909171888	0.0579859636687527	1.53697221355352
12	43.9019	43.8598373340189	0.0420626659810896	0.0420626659810905	1.42534413509020
13	43.1835	43.1464735105333	0.0370264894667286	0.0370264894667293	-0.876405403784229
14	43.6188	43.5791532901114	0.0396467098886186	0.0396467098886194	0.459005717086123
15	44.7624	44.7155379092456	0.0468620907544423	0.0468620907544434	1.27232121794807
16	45.1972	45.325737276247	0.0321343190617536	-0.12853727624702	0.684598777446415
17	44.3881	44.3852897561311	0.00281024386891927	0.00281024386892037	-1.05187311654929
18	43.5552	43.556446601927	-0.00124660192695745	-0.00124660192695665	-0.963982254050247
19	43.5678	43.568979710131	-0.00117971013099891	-0.00117971013099811	0.0159720859088201
20	44.2135	44.2115697115612	0.00193028843884514	0.00193028843884620	0.746185881750455
21	45.1451	45.0857267863623	-0.0148433034094282	0.0593732136377067	1.04662656695006
22	45.8079	45.8053926923313	0.00250730766872622	0.00250730766872800	0.806945502164552
23	42.3282	42.3390344826571	-0.010834482657136	-0.0108344826571358	-4.01875042277396
24	37.8999	37.9275950379095	-0.0276950379095074	-0.0276950379095093	-5.09815187636318
25	34.7964	34.8357901137023	-0.0393901137022745	-0.039390113702278	-3.54978097681965
26	35.2144	35.0419039441639	-0.0431240139590303	0.172496055836135	0.292383387894325
27	36.3727	36.3888326982875	-0.0161326982874871	-0.0161326982874899	1.54205611982829
28	36.2502	36.2666693036700	-0.0164693036700490	-0.0164693036700518	-0.122797597770205
29	36.8261	36.8407006308022	-0.0146006308022213	-0.0146006308022238	0.683874560576457
30	36.7723	36.7870238992579	-0.0147238992578703	-0.0147238992578729	-0.0452548513316112
31	36.9042	36.8418071860854	-0.0155982034786384	0.0623928139145636	0.082368161679674
32	37.0494	37.0611259458685	-0.0117259458684654	-0.0117259458684678	0.262335511197369
33	36.8259	36.8381967654176	-0.0122967654176189	-0.0122967654176214	-0.244543796890893
34	36.1357	36.1498190859287	-0.0141190859287129	-0.0141190859287159	-0.782804266559144
35	36.03	36.0443646111659	-0.0143646111659006	-0.0143646111659036	-0.105752835567033
36	35.7927	35.7473652959147	-0.0113336760213133	0.0453347040852663	-0.333745842672942
37	35.9174	35.9260131764210	-0.0086131764210399	-0.0086131764210431	0.213175199160961
38	35.4008	35.4106056337465	-0.00980563374654099	-0.00980563374654458	-0.58669462035019
39	35.1723	35.1826177985358	-0.0103177985357711	-0.0103177985357748	-0.252579704308682
40	34.9211	34.9319806074145	-0.0108806074144817	-0.0108806074144857	-0.278206170139057
41	35.0292	34.9833504507029	-0.0114623873242698	0.0458495492970949	0.073313186079764
42	34.7739	34.7876939582631	-0.0137939582630737	-0.0137939582630777	-0.207433780394040
43	34.8999	34.9134033263347	-0.0135033263346902	-0.0135033263346941	0.161475439642412
44	34.9054	34.9188639003467	-0.0134639003466439	-0.0134639003466478	0.0219507133518113
45	34.568	34.5821345754978	-0.0141345754978107	-0.0141345754978149	-0.374178901412724
46	34.406	34.3564689381184	-0.0123827654703913	0.0495310618815827	-0.248611291692362
47	34.4578	34.4687685980807	-0.0109685980807150	-0.0109685980807194	0.140814289058293
48	34.7316	34.7420373133852	-0.0104373133852268	-0.0104373133852309	0.32897022088489
49	34.2602	34.2714957168946	-0.0112957168945674	-0.0112957168945720	-0.532513984239502
50	33.8849	33.8968723047783	-0.0119723047783055	-0.0119723047783104	-0.42050628564687
51	34.0549	34.0034841157504	-0.0128539710624059	0.0514158842496424	0.139142645752838
52	34.2755	34.2853262711457	-0.0098262711457204	-0.0098262711457249	0.333589568509462
53	34.1393	34.1493401014813	-0.0100401014813066	-0.0100401014813112	-0.146002085277924
54	34.1587	34.1686903715804	-0.00999037158036111	-0.00999037158036572	0.0340127841374934
55	34.5386	34.547932883604	-0.00933288360401597	-0.00933288360402013	0.45044939718966
56	33.7987	33.7817883416114	-0.00422791459714528	0.0169116583886022	-0.886827406835394
57	33.4973	33.504095658889	-0.00679565888896662	-0.00679565888897212	-0.310140884005287
58	33.6802	33.6867020123593	-0.00650201235929028	-0.00650201235929555	0.219174984097073
59	34.3284	34.3338901081709	-0.00549010817090561	-0.00549010817091009	0.756445750594122
60	34.1538	34.1595510802252	-0.00575108022521263	-0.00575108022521731	-0.195390589058263
61	33.9184	33.9016222892184	-0.00419442769539634	0.0167777107816057	-0.295170688122443
62	34.3262	34.3266832857126	-0.000483285712594828	-0.000483285712599496	0.487595146530007
63	34.775	34.7748423680462	0.000157631953803572	0.000157631953799489	0.519134947841041
64	35.0119	35.0114051282069	0.000494871793150427	0.000494871793146656	0.273549820008466
65	34.5513	34.5514610241815	-0.000161024181514142	-0.00016102418151853	-0.532784005673423
66	34.6951	34.6912702364525	-0.000957440886867086	0.00382976354748494	0.163678814922834
67	35.473	35.4677298013416	0.00527019865843264	0.00527019865842931	0.88426031140884
68	35.9794	35.9734669312361	0.00593306876388299	0.00593306876388036	0.579072313984052
69	36.4789	36.4723149273661	0.00658507263395113	0.00658507263394921	0.570333662555418
70	36.391	36.3845395778572	0.00646042214275177	0.00646042214274971	-0.109180865127905
71	36.6704	36.6899317828840	0.00488294572101047	-0.0195317828840359	0.349283413677853
72	37.4162	37.4060096296604	0.0101903703396122	0.0101903703396115	0.809870478658174
73	37.1185	37.1086892725327	0.009810727467342	0.00981072746734083	-0.355793640670887
74	36.3001	36.2913092364797	0.00879076352033125	0.00879076352032881	-0.957069016655067
75	35.7002	35.6921579336035	0.00804206639648234	0.00804206639647896	-0.703395274827105
76	35.5859	35.6196534377774	0.00843835944435643	-0.0337534377774116	-0.0940478766329062
77	35.6777	35.6689760693888	0.00872393061118309	0.0087239306111796	0.0466034876406184
78	35.2408	35.2325906466744	0.0082093533255566	0.0082093533255524	-0.514976730637595
79	34.8016	34.7939066897564	0.00769331024359199	0.00769331024358705	-0.517040364796021
80	34.4389	34.4316334101587	0.00726658984128804	0.00726658984128249	-0.428038480215796
81	34.9881	35.0066999999486	0.00464999998714276	-0.0185999999485536	0.662569821814272
82	36.068	36.0564891304654	0.0115108695346299	0.0115108695346269	1.19238897480090
83	36.3566	36.344788273647	0.0118117263530114	0.0118117263530089	0.320223781243564
84	36.1254	36.1138518438484	0.0115481561515925	0.0115481561515895	-0.280841690321558
85	34.871	34.8608234019771	0.0101765980228857	0.0101765980228805	-1.46302087756877
86	35.2199	35.2539677315407	0.00851693288517614	-0.0340677315406872	0.446646691128553
87	34.339	34.3362184615454	0.00278153845456787	0.00278153845456227	-1.05758951860822
88	33.8234	33.8211495901696	0.00225040983043347	0.00225040983042692	-0.599096687508627
89	34.5199	34.5169389969368	0.00296100306321863	0.00296100306321336	0.80234888250385
90	35.53	35.526009202464	0.00399079753603803	0.00399079753603464	1.16395786680534
91	35.7966	35.8080148893079	0.00285372232698653	-0.0114148893079352	0.324087151269594
92	33.8484	33.8569947572612	-0.00859475726114858	-0.00859475726115417	-2.23243263379413
93	33.9871	33.9955518913476	-0.0084518913475583	-0.0084518913475636	0.170234101089905
94	34.1161	34.1244187015307	-0.00831870153067683	-0.00831870153068186	0.158858404795086
95	33.8235	33.8320939012381	-0.00859390123812694	-0.00859390123813253	-0.328554917264523
96	32.454	32.4410371782952	-0.00324070542618606	0.0129628217047803	-1.61087201631425
97	31.8774	31.8837217511378	-0.00632175113782064	-0.0063217511378305	-0.633460440698992
98	31.115	31.1220179557853	-0.00701795578529623	-0.00701795578530763	-0.873849604103909
99	31.0436	31.0506771848967	-0.00707718489667595	-0.00707718489668748	-0.0744106152827217
100	30.8868	30.8940147977779	-0.00721479777789522	-0.00721479777790706	-0.173044699715184
101	31.3001	31.2656692029748	-0.00860769925629113	0.0344307970252080	0.441295385732062
102	30.0507	30.0656116666347	-0.0149116666346762	-0.014911666634689	-1.36291779855194
103	28.6799	28.6959999999655	-0.0160999999654886	-0.0160999999655043	-1.56712457252792
104	27.6438	27.6607931698410	-0.0169931698410127	-0.0169931698410305	-1.17890805504039
105	27.2394	27.2567321084494	-0.0173321084493499	-0.0173321084493686	-0.4477619683689
106	26.8549	26.7918366696757	-0.0157658325810478	0.063063330324271	-0.5211264212921
107	27.0158	27.0302830125227	-0.0144830125226532	-0.0144830125226727	0.290944503000938
108	26.9188	26.9333520066592	-0.0145520066591987	-0.0145520066592184	-0.095374378357103
109	26.4966	26.5114925647148	-0.0148925647147603	-0.0148925647147809	-0.471165862111062
110	26.785	26.7996393989685	-0.0146393989684372	-0.0146393989684571	0.350550364352526
111	26.8398	26.7812919276302	-0.0146270180924363	0.0585080723698248	-0.00431617583572449
112	26.4478	26.4638873599685	-0.0160873599685169	-0.0160873599685374	-0.346687060303721
113	25.1728	25.1898936850186	-0.017093685018531	-0.0170936850185544	-1.45509697808214
114	24.8784	24.8957151756850	-0.017315175685016	-0.0173151756850401	-0.320520818536446
115	25.4015	25.4183838786582	-0.0168838786581772	-0.0168838786582000	0.624631897486044
116	25.7716	25.7002496455275	-0.0178375886180969	0.0713503544724752	0.347642342186239
117	26.1181	26.1338524137636	-0.0157524137635734	-0.0157524137635944	0.517127090355379
118	26.3969	26.4124268759281	-0.0155268759280364	-0.0155268759280568	0.340460118845051
119	26.6571	26.6724159142789	-0.0153159142789076	-0.0153159142789272	0.318700604984224
120	25.1839	25.2003305045564	-0.0164305045564241	-0.0164305045564473	-1.68510477822649
121	23.8394	23.7907199396669	-0.0121700150832423	0.0486800603330799	-1.62075497610086
122	23.8619	23.8736486029201	-0.0117486029200313	-0.0117486029200587	0.108978106233011
123	24.2581	24.2695488611110	-0.0114488611109307	-0.0114488611109571	0.471537063720573
124	25.1098	25.1206151247970	-0.0108151247970110	-0.0108151247970352	0.997691342666033
125	26.1617	26.1717354365191	-0.0100354365190306	-0.0100354365190521	1.22836513292013
126	26.8087	26.7615171139343	-0.0117957215164157	0.0471828860657409	0.697626631317971
127	25.6577	25.6740761837173	-0.0163761837172688	-0.0163761837172905	-1.23307189753489
128	27.0982	27.1135473163577	-0.0153473163576667	-0.0153473163576845	1.68398892136697
129	27.4665	27.4815765701928	-0.0150765701927448	-0.0150765701927615	0.443454288556823
130	28.289	28.3034858956027	-0.0144858956026562	-0.0144858956026707	0.968147042093065
131	28.6933	28.6314919108446	-0.0154520222888464	0.061808089155439	0.398250905421869
132	27.2401	27.2611050339787	-0.0210050339786566	-0.0210050339786728	-1.55374796972025
133	27.2798	27.3007637661106	-0.0209637661106230	-0.0209637661106390	0.0701692816639394
134	27.6404	27.6611045515960	-0.0207045515960337	-0.0207045515960486	0.441051751541412
135	26.831	26.852239986387	-0.0212399863869989	-0.0212399863870161	-0.91165781480543
136	26.2467	26.1689315649363	-0.0194421087659109	0.0777684350637214	-0.76969532962713
137	25.2212	25.2442179016024	-0.0230179016024234	-0.0230179016024448	-1.03842076522797
138	25.3653	25.3882083879056	-0.0229083879056121	-0.0229083879056331	0.193174867004826
139	26.2592	26.2815079894862	-0.0223079894862055	-0.0223079894862238	1.05975706211745
140	27.2279	27.2495594240491	-0.0216594240491006	-0.021659424049116	1.14552610396128
141	26.3315	26.2550492229190	-0.0191126942702373	0.0764507770810251	-1.13078019658552
142	25.8981	25.9184230379432	-0.0203230379432188	-0.0203230379432385	-0.364317169491147
143	26.6898	26.7096094243843	-0.0198094243842789	-0.0198094243842962	0.938644095027547

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292011012tyf3zz8stc9jchp/1m5fk1292011077.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292011012tyf3zz8stc9jchp/1m5fk1292011077.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292011012tyf3zz8stc9jchp/2m5fk1292011077.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292011012tyf3zz8stc9jchp/2m5fk1292011077.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292011012tyf3zz8stc9jchp/3eee51292011077.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292011012tyf3zz8stc9jchp/3eee51292011077.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292011012tyf3zz8stc9jchp/475e81292011077.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292011012tyf3zz8stc9jchp/475e81292011077.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292011012tyf3zz8stc9jchp/575e81292011077.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292011012tyf3zz8stc9jchp/575e81292011077.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 <- 5

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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