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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: Sat, 04 Dec 2010 10:40:15 +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/04/t12914591447ahx02ycw53tijz.htm/, Retrieved Sat, 04 Dec 2010 11:39:04 +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/04/t12914591447ahx02ycw53tijz.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 «
115.65 116.00 115.92 116.10 116.44 116.65 117.45 117.58 117.43 117.24 117.25 117.29 117.83 118.22 118.11 118.23 118.15 118.23 119.03 119.38 118.97 118.78 118.97 118.94 119.86 120.09 120.13 120.15 119.90 120.00 120.84 121.17 120.81 121.00 121.12 121.29 122.09 121.88 121.31 121.33 121.45 121.67 122.78 122.84 122.34 122.37 122.72 122.68 122.78 123.08 122.92 123.51 124.18 124.05 124.36 123.87 123.84 123.85 123.83 123.84 124.27 124.56 124.57 124.87 125.08 124.86 124.89 124.58 124.83 124.97 125.19 125.42 125.74 126.07 126.35 126.69 126.85 127.12 127.43 127.49 128.05 127.85 128.35 128.29 128.38 128.80 129.18 130.14 130.77 131.19 131.32 131.41 131.61 131.69 131.94 131.70 132.54 132.74 133.02 132.76 133.05 132.74 133.16 133.10 133.37 133.15 133.18 133.29 133.76 134.51 134.82 134.71 134.52 134.86 135.11 135.28 135.61 135.22 135.47 135.42 135.85 136.27 136.30 136.85 137.05 137.03 137.45 137.49 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
1115.65115.65000
2116115.9818100077340.01838244387294140.01818999226618300.252527193595836
3115.92115.9021925436460.01767690104207580.0178074563544112-0.124291598722975
4116.1116.0815669389650.01910396289621690.01843306103450850.20490373351158
5116.44116.4203430213060.02243506859234660.01965697869378710.404748717088198
6116.65116.6296361746370.02467356633271390.02036382536270730.236391328182542
7117.45117.4267536195730.03510109521415040.02324638042697740.976408047601386
8117.58117.5564060632610.03651710379705090.02359393673896570.119421828044821
9117.43117.4070779936860.03346799981703230.0229220063143926-0.234545189472957
10117.24117.2178687701680.02950686231451470.0221312298322948-0.280814000851031
11117.25117.2279364830120.02913518460642860.0220635169875933-0.0244961071349183
12117.29117.2678995354430.02935606464303930.02210046455661890.0136348173689662
13117.83117.8279582196570.01962522382982660.002041780343459020.803900748313027
14118.22118.2114613286340.03427028511596110.00853867136635420.389491426506659
15118.11118.1016739144650.03103830529290370.0083260855349157-0.180860618150768
16118.23118.2215459139160.03313185300686370.008454086083693580.111459948438816
17118.15118.1417046851730.03034765228201690.00829531482719991-0.141664500410630
18118.23118.2216367884300.03162043469824960.008363211570402030.0621423839899646
19119.03119.0206140273810.05206298811542010.009385972619197270.96118603195028
20119.38119.3702283698520.0602633455174680.009771630148359450.372521192639426
21118.97118.9608198082210.04691155282318710.00918019177891073-0.587724329801521
22118.78118.7711090622070.03999107587183430.0088909377934619-0.295961791369892
23118.97118.9609314021620.04448872219020720.009068597838034070.187324210394114
24118.94118.9310169123670.04220134309405710.00898308763317918-0.0929832957740467
25119.86119.7827536894690.05671459533090680.07724631053075971.11098916188103
26120.09120.0931738321140.0670164992157165-0.003173832113745640.288532296011348
27120.13120.1331917438020.0661413364521953-0.00319174380164001-0.0336949910519468
28120.15120.1532213145480.064620159996269-0.00322131454750310-0.0575304381440674
29119.9119.9034161906410.0540790189144212-0.00341619064087193-0.392169249193262
30120120.0033887143620.0556405760975624-0.003388714362065180.0572249685848178
31120.84120.8429355805230.0826794537956774-0.002935580522555260.977202263837671
32121.17121.1727976881290.0913129084143743-0.002797688129150210.30805736763815
33120.81120.8130404296970.0753755543259667-0.00304042969727873-0.562027974971682
34121121.0029809785640.0794665466313658-0.002980978564148930.142715955284944
35121.12121.1229607131680.0809274096924518-0.002960713168277730.0504579892886297
36121.29121.2929177993220.0841666702323635-0.002917799321513450.110863109774528
37122.09121.9719771839250.1025267720854340.1180228160754370.788955963916515
38121.88121.8927353793540.0950497320658154-0.0127353793538752-0.212066910072116
39121.31121.3229377550530.0703380557593311-0.0129377550533776-0.827406152102633
40121.33121.3429524993350.068455292723622-0.0129524993352301-0.0626189620697052
41121.45121.4629379697320.070394873770151-0.01293796973230010.0641124470821511
42121.67121.6828973942330.0760557877496826-0.01289739423272660.186061867810581
43122.78122.7926276361140.115380146560984-0.01262763611376701.28577255198743
44122.84122.8526415327720.11326389820059-0.0126415327716493-0.0688621470640212
45122.34122.3527895142720.0897272016612077-0.0127895142717771-0.76249379721171
46122.37122.3828033711860.08742572613086-0.0128033711857806-0.0742551135930681
47122.72122.7327448090820.0975808412583762-0.01274480908211240.32641813516778
48122.68122.6927743030550.092241810079763-0.0127743030552919-0.171021380639404
49122.78122.6537732943520.08749291774053620.126226705647590-0.171143943204144
50123.08123.0884669394470.101765404160484-0.008466939447407260.410860105604533
51122.92122.9285031985060.0915226655140991-0.00850319850606015-0.325335684323825
52123.51123.5184368815980.11107593639987-0.008436881598148780.61950251326898
53124.18124.1883654463390.133050092921043-0.008365446339055940.694592876419209
54124.05124.0583977418430.122686621518244-0.00839774184295814-0.326886804312306
55124.36124.3683756525460.130080480197552-0.00837565254624170.232761193529043
56123.87123.8784458851860.105560516549692-0.00844588518562756-0.770502432817467
57123.84123.8484606311370.100191268242860-0.00846063113665434-0.168439743573861
58123.85123.8584700527610.0966136235887104-0.00847005276091639-0.112063036557741
59123.83123.8384817506490.0919814716297001-0.00848175064886684-0.144888783425414
60123.84123.8484896473890.0887208345018078-0.00848964738917044-0.101856731261566
61124.27124.1573388878740.09718349796606240.1126611121260030.284231596565138
62124.56124.5680052376850.110003866619804-0.008005237685350030.374316358589227
63124.57124.5780112431150.106013907309950-0.00801124311544532-0.124240285273038
64124.87124.8780000853960.113760733087220-0.00800008539563640.240994959771801
65125.08125.087994771140.117607316837244-0.007994771140079060.119558918572461
66124.86124.8680126678450.104102920415105-0.00801266784483552-0.419405800532859
67124.89124.8980164388280.101136640324124-0.00801643882782702-0.0920558457488502
68124.58124.5880365228830.0846682286066954-0.00803652288347129-0.51073569300864
69124.83124.8380287701220.0912947821437036-0.008028770121703420.205381252236177
70124.97124.9780265778200.0932480045928946-0.008026577820250950.060502713962426
71125.19125.1980211014240.0983337717978252-0.008021101424486060.157452463522122
72125.42125.4280156410680.103619242681835-0.008015641068284480.163555332894324
73125.74125.6436254944520.1080358803909790.09637450554763620.143671263824782
74126.07126.0767880345970.121267181667889-0.006788034596684660.390632183916148
75126.35126.3567845598210.127646746437791-0.006784559821500440.197172483521218
76126.69126.6967800789010.136184304135531-0.006780078900862160.263776018098636
77126.85126.8567795965710.137142107935406-0.00677959657060090.0295826286492075
78127.12127.1267770140950.142486868137002-0.006777014095471910.165028202896593
79127.43127.4367738890220.149227602600399-0.006773889021673170.208073708843153
80127.49127.4967754866240.145636186012625-0.00677548662419063-0.110832034594719
81128.05128.0567683662100.162318182330279-0.006768366210163880.514690098843767
82127.85127.8567743415640.147728424441733-0.00677434156386825-0.45004111924271
83128.35128.3567687658870.161916387730637-0.006768765886843410.437560284605828
84128.29128.2967721368390.152976961549658-0.0067721368393519-0.275643677825262
85128.38128.3140464944700.1475635068723870.0659535055295292-0.173296628838047
86128.8128.8041855398660.161455783925761-0.004185539866373710.413454540384058
87129.18129.1841847846200.170263320511135-0.004184784619601940.271452543890930
88130.14130.1441821162040.202094568361989-0.004182116203697870.980924766297536
89130.77130.7741807286510.219343847461841-0.004180728650811950.531496124132418
90131.19131.1941801042220.227433378181488-0.004180104222252540.249231987867644
91131.32131.3241803952030.223504916393713-0.00418039520331435-0.121020275885357
92131.41131.4141807778330.218121568065468-0.0041807778334815-0.165823771097982
93131.61131.6141808276760.217390785382992-0.00418082767613398-0.0225083946038305
94131.69131.6941811903240.211849833457394-0.00418119032385686-0.170649740070396
95131.94131.9441810936870.213388536469626-0.004181093686634840.0473853179836398
96131.7131.7041821958300.195100882659488-0.00418219582968136-0.563141178030224
97132.54132.4629133119510.2177075440939930.0770866880485680.717317894221467
98132.74132.7466985377610.220381147289899-0.006698537760615220.0800220164897185
99133.02133.0266988740160.222786318794830-0.006698874015797480.0740506542203427
100132.76132.7666963780850.203308597501148-0.00669637808475955-0.599652560183862
101133.05133.0566968081840.206806264328438-0.00669680818358190.107676359248572
102132.74132.7466943476240.185954256731259-0.00669434762422312-0.64190643719405
103133.16133.1666954169750.195397847270577-0.006695416974514240.29069955428044
104133.1133.1066942971520.185092357388909-0.00669429715246622-0.317219981840968
105133.37133.3766946544180.188518551878376-0.006694654417506380.105460492777396
106133.15133.1566930048620.172033521961578-0.00669300486197084-0.507404750865653
107133.18133.1866924544890.166301860484215-0.00669245448919807-0.176414125141703
108133.29133.2966922451260.164029782595622-0.00669224512650001-0.0699302399461945
109133.76133.6758315171580.1726808676905820.08416848284247490.273037510916112
110134.51134.5148507740960.199605902698991-0.004850774096089220.80911925827334
111134.82134.8248518408290.204061196973807-0.004851840829110660.137115817258155
112134.71134.7148489726290.191386069800438-0.00484897262872729-0.390081867956127
113134.52134.5248456301500.175993545885030-0.00484563015013189-0.473703029118262
114134.86134.8648470094960.182612850471515-0.004847009495681620.203705211402422
115135.11135.1148475533680.185332634510674-0.004847553368442860.0836985939822717
116135.28135.2848474346150.184713792827161-0.00484743461536893-0.0190439812556583
117135.61135.6148485144570.190577768666716-0.004848514457092920.180453472160793
118135.22135.2248443734730.167144503764707-0.00484437347294165-0.721109407741255
119135.47135.4748449405890.170488747883260-0.004844940588758150.102911046115494
120135.42135.4248434923370.161589219481035-0.0048434923373048-0.273859000704847
121135.85135.7878245322900.1696999229273530.06217546771036890.255081702787062
122136.27136.2744432673900.182496045813252-0.004443267389652610.385658136423935
123136.3136.3044415708190.176340702035974-0.00444157081918405-0.189408229389473
124136.85136.8544455995120.191423160219929-0.004445599512107870.464104788843426
125137.05137.0544456882530.191769359363634-0.004445688252636760.0106528915048918
126137.03137.0344435856170.183221369782278-0.00444358561666736-0.263028788016859
127137.45137.4544458416710.192778893025278-0.004445841671433570.29409160180962
128137.49137.4944444447350.186611976673231-0.00444444473519646-0.189759461520374
129137.55137.5544433337860.181501267335614-0.00444333378642823-0.157258755242033
130138.04138.0444459314240.193953904589672-0.004445931424138170.383171673817235
131138.03138.0344442834020.185721221199215-0.00444428340172875-0.253321473611620
132137.75137.7544406721070.166922134951341-0.00444067210683503-0.578450207779308
133138.27138.2095745620590.1785381068083570.06042543794149010.364410051749066
134138.99138.9933791408370.202966523397031-0.003379140837335080.737857287380823
135139.74139.7433855817750.225048172806429-0.003385581774628180.679444093618469
136139.7139.7033825955960.214349175454288-0.00338259559605109-0.329203625636553
137139.97139.9733831972800.216595593037474-0.003383197279490020.06912121847584
138140.21140.2133834401080.217540343469859-0.003383440107936940.0290694899016986
139140.78140.7833869493780.231767869815764-0.003386949377943240.437773201490415
140140.8140.8033849260190.223219554411299-0.00338492601931551-0.263026688153445
141140.64140.6433814123100.207750328641964-0.00338141230970242-0.47597857097088
142140.42140.4233776486190.190483535764326-0.00337764861881171-0.531288092584518
143140.85140.8533796710060.200151990721223-0.003379671006174570.297491865164447
144140.96140.9633789405240.196512862345127-0.00337894052394963-0.111973444082571
145141.04141.0084105355180.1904050312077670.0315894644815221-0.191250970842929
146141.71141.7112212400060.211081071047830-0.001221240006018960.625584883747847
147141.6141.6012175174440.198119991887893-0.00121751744393991-0.398799221112525
148142.11142.1112210032530.210709651578134-0.001221003252542950.387371048933425
149142.59142.5912238915500.221580093886486-0.001223891550312870.334472496338064
150142.56142.5612213021300.211424561921987-0.00122130212953237-0.312475447504409
151143143.0012235598030.220651464616771-0.001223559802812440.283902479235000
152143.18143.1812231744900.219010487381864-0.00122317449048027-0.050491215057801
153143.15143.1512209095360.208958684162314-0.00122090953573543-0.309283864685118
154143.1143.1012186491760.198505302635335-0.00121864917605908-0.321640038306946
155143.45143.4512199181410.204620686702851-0.001219918141179280.188164225732977
156143.59143.5912193987090.202012144548745-0.00121939870881676-0.0802622250161256
157143.92143.9028596054910.2064335283780880.01714039450923360.138238414707689
158144.66144.6599124867970.2286491502916228.75132031786096e-050.67309130735425
159144.34144.3399063219080.2065016656406899.36780923735011e-05-0.681450397201855
160144.82144.8199092803440.2175420480135199.07196564278975e-050.339698982433301
161144.49144.4899035966580.1954392811337259.64033417043948e-05-0.680075362604105
162144.41144.4099008529150.1843205609214449.91470851060573e-05-0.342109746387666
163144.99144.9899046353040.2002930348064009.53646962037927e-050.491454208906683
164144.95144.9499024310130.1905930806646439.75689874128691e-05-0.298456307895261
165145144.9999011933650.1849177357917789.8806634516933e-05-0.174623838713097
166145.66145.6599052067130.2040954549350309.47932866518e-050.590076616757458
167146.68146.6799118209910.2370311876097198.81790085578787e-051.01339543390291
168147.38147.3799154226290.2557199079560748.45773714590865e-050.575031094873836
169147.94147.9315876404580.2676577303104950.008412359541557380.372792194630364
170149.12149.1182027488940.3047328884215950.001797251105809471.12458424426375
171149.95149.9482084342700.3259365574679360.001791565730378210.652408723361886
172150.19150.1882075452990.3224675249470330.00179245470073418-0.106737614307209
173151.16151.1582139733000.3486066852723540.00178602670020670.804268576140127
174151.74151.7382161775970.3579474099752960.001783822402786400.287402380204505
175152.56152.5582204015190.3765992157878460.001779598481246400.573893053763314
176152.09152.0882129746230.342424329967260.00178702537744786-1.05151973175170
177152.46152.4582132067680.3435374834239830.001786793231751390.0342503996681979
178152.66152.6582120471770.3377432756059310.00178795282310546-0.178280934696552
179152.38152.3782072580900.3128067146433880.00179274191041355-0.76726891859786
180152.59152.5882064932480.3086566981566140.00179350675166802-0.127691228078682
181152.88152.8996465888730.308768983255411-0.01964658887331770.0035028307116053
182153.29153.2880060050790.3119800092226040.001993994921153280.0974923286469057
183152.35152.3479931904590.2614408015658590.00200680954142047-1.55502334137144
184152.49152.4879919955690.2565385535710770.00200800443116203-0.150835705711524
185152.2152.1979868351020.2344762377795130.00201316489839065-0.678828933903794
186151.57151.5679790021340.199579645192030.00202099786560996-1.07372387260869
187151.55151.5479770928510.1907158086703910.00202290714888067-0.272729197349074
188151.79151.7879775040870.1927052769233470.002022495913024580.0612134977903585
189151.52151.5179737990470.1740271392292600.0020262009526417-0.574703734331328
190151.76151.757974305990.1766902804652810.002025694010035950.0819416846464948
191151.92151.9179741829170.1760165405179000.00202581708286652-0.0207301865808285
192152.2152.1979749187310.1802140600351590.002025081269097000.129152804945906
193152.75152.7616837487130.195685697834622-0.01168374871320430.48222720801395
194153.49153.4876345831410.2170790594713030.002365416858865320.650078276006185
195153.78153.7776353211080.2200226907992060.002364678891698550.0905715825070175
196154.1154.0976362549890.224058513191550.002363745011431890.124176947377225
197154.62154.6176389077650.2360048869520030.002361092235179680.367574516253154
198154.65154.6476371357090.2276890217093320.00236286429069153-0.255868647151498
199154.81154.8076365769520.2249565991868170.00236342304781864-0.0840732417588463
200154.92154.9176356663180.2203161155110710.0023643336816947-0.142782002766105
201155.4155.3976376403770.2307988379222630.002362359623472000.322540731319622
202155.63155.6276376345490.2307665910553660.00236236545092473-0.000992197768050063
203155.76155.7576369291390.2266989258389270.00236307086103798-0.125157287854856
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/04/t12914591447ahx02ycw53tijz/1jw631291459208.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/04/t12914591447ahx02ycw53tijz/1jw631291459208.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/04/t12914591447ahx02ycw53tijz/2jw631291459208.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/04/t12914591447ahx02ycw53tijz/2jw631291459208.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/04/t12914591447ahx02ycw53tijz/3cnn61291459208.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/04/t12914591447ahx02ycw53tijz/3cnn61291459208.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/04/t12914591447ahx02ycw53tijz/4cnn61291459208.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/04/t12914591447ahx02ycw53tijz/4cnn61291459208.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/04/t12914591447ahx02ycw53tijz/5nwnr1291459208.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/04/t12914591447ahx02ycw53tijz/5nwnr1291459208.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')
 





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