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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationWed, 21 Dec 2016 14:19:15 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t1482326569dormfr61sdnb91j.htm/, Retrieved Tue, 07 May 2024 02:04:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302266, Retrieved Tue, 07 May 2024 02:04:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [Structural Time S...] [2016-12-21 13:19:15] [c6c2c19ee5e10dd65276916b11a37d00] [Current]
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Dataseries X:
2340
2377.5
2500
2395
2375
2395
2452.5
2462.5
2840
2750
2795
3035
2827.5
2850
3265
3220
3075
3325
3235
3320
3277.5
3050
3432.5
3575
3287.5
3297.5
3255
3135
3177.5
3172.5
3365
3775
3737.5
4060
4197.5
4195
4112.5
3977.5
3982.5
3985
4155
4295
4072.5
4017.5
3965
3847.5
3799.5
4215
4115
4210
4132.5
3955
4057.5
4152.5
4062.5
4092.5
4157.5
4325
4210
5107.5
4862.5
4920
5080
4615
4615
5057.5
4850
4720
5040
4815
5170
6420
5847.5
6177.5
6960
7170
6485
6785
7300
7105
7030
7222.5
7522.5
9500
8697.5
8662.5
8685
8642.5
8492.5
7702.5
7965
8097.5
7947.5
9227.5
7680
7820
7635
7347.5
7177.5
6982.5
7075
7230
7170
7022.5
7087.5
7440
7592.5
8297.5
7852.5
8097.5
8022.5
8062.5
7982.5
9540
8172.5
8007.5




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302266&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302266&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302266&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
123402340000
22377.52367.233405454171.819760648648482.238194981445370.0795006157569053
325002451.125259761144.834766652867348.355132237197250.331787105016021
423952416.009761202333.930388319921960.550061024324472-0.1705869403246
523752389.202212569383.375434950600572.67246784679053-0.132540709250695
623952391.577162893533.358481567344313.97399746849516-0.00432129172748133
72452.52428.491547334693.930372601243035.520895960358290.144903415894085
82462.52449.100253465594.22303463739844.219006779574710.0719677005249371
928402691.151713508188.5461142299665418.08890595154661.02531261468985
1027502729.615825288679.109578644219543.955894187038390.128859657939396
1127952769.739891516369.71379527138988.251287601532120.133457508801568
1230352934.2716961969912.827137317550515.9290229382380.66558279813771
132827.52938.2294839841113.3117645154502-105.686247698422-0.0474937873241679
1428502880.7680545659410.5576479878237-1.350583544412-0.256106773067522
1532653114.442970859216.985364120844138.37298325908970.91977797056215
1632203184.4546553851718.17957979921057.536272268487360.22542036127769
1730753118.5264788809816.45021977230481.29230537357024-0.359314648552381
1833253242.8918736466118.640615804902624.53393341790670.461221655110672
1932353238.9223995681118.17473149154198.13495309409837-0.0965894020315273
2033203293.2197622103618.93655258940267.533723647088250.154211702307976
213277.53277.6851658073218.191288764425718.1636780922675-0.14705788526295
2230503139.0611265407814.716958684781-5.66981927474918-0.668533020205088
233432.53317.8752701505718.43672765148427.44198400139870.69911768521765
2435753475.0635953578821.534621250609426.26664760943460.590470700260171
253287.53457.6250366950221.7133340492715-149.163061739282-0.18409020519121
263297.53371.7162411474718.0893062316505-24.9136021773597-0.417600273292963
2732553283.0433544827414.875441049801525.2311486269122-0.441446247057629
2831353188.6643266231811.97518149841732.7526496005543-0.46161293001099
293177.53188.2371904018511.661393385066-4.29328050327747-0.0525757686103256
303172.53168.3887104583710.869695616560220.4939730245123-0.133595123063294
3133653289.4124690594213.658695293349118.33686479401430.466858571894861
3237753588.0322399411120.959849805535938.94970683310831.20719507826729
333737.53677.4351380307222.735959003160524.53491240813890.289822093622384
3440603931.3816674345528.81254794775918.663187522696510.978667402774828
354197.54100.7046469591932.542534437449123.9364870844540.594499983240745
3641954157.7021073752833.172690139483824.62644934546580.103345208283392
374112.54216.8323433062633.5349900363939-117.8834598407860.116792508497025
383977.54090.9333118308328.3882075022114-37.5750181711095-0.638289399201538
393982.54010.898534087324.992358383519325.2954597939443-0.448684657873995
4039853999.403020709823.92444742521814.14001015941623-0.15353287953235
4141554101.6163729670826.147287106730913.39968725894470.33027860705445
4242954223.8926409652828.859114098467221.98842766266680.405551986901379
434072.54151.1930221422125.9860056052959-26.8117131653979-0.428346734696401
444017.54058.6967916020622.615170301563919.3096322612988-0.499593487528127
4539654006.4125988579820.4707357971163-3.1756968905518-0.315747957840474
463847.53920.7543560427517.4132149570119-19.0908461455259-0.447309927307919
473799.53840.8320023759814.60178836414458.32609874572846-0.41010345211154
4842154056.0729126967320.237627593269556.68342394988640.844456243060174
4941154144.4813263995421.7816049981624-64.45273161079120.29914435384386
5042104210.2636336552923.1815647085248-21.58314142987270.179195107096373
514132.54157.367559387820.761867691064212.6441218442029-0.31515152192724
5239554046.6455216427216.7324260952535-25.4988878945057-0.551986229765171
534057.54055.9029615391916.50791165255135.37365514912217-0.0314503667966252
544152.54102.412103232217.403738668888534.92479685517050.126220393459416
554062.54096.9665356511516.721168814512-22.9200136663469-0.096110567252689
564092.54085.5074117638315.877190066402721.2303748337544-0.118515870928345
574157.54129.8878129974316.733521154248813.21355675919370.119861129244165
5843254260.8266486406120.17430016346156.490293392622520.480203805696807
5942104250.7202190176619.2628724044372-25.4314988394169-0.127270966090229
605107.54742.4878667987533.1846066744802126.7941097065591.98454306838124
614862.54872.1779036195235.7819536792932-58.66741878455240.417422299588805
6249204925.6645013606136.3416489929837-14.32609628077050.0728442077689933
6350805018.6685475501938.147584197566333.44688145346210.235018764110266
6446154810.8310767364730.46449959125-72.8513467277084-1.03142622279947
6546154699.1104820828726.082014060966-12.7506004799732-0.597389088041919
665057.54896.8038351652631.345813410433474.54452096082310.720932715624712
6748504898.2955977910630.4306144958809-33.3106374637457-0.12538960350871
6847204793.5045936888826.28080505935-5.6389251522134-0.567886096502536
6950404946.3675775746330.171428221644630.10710241925650.531581536985529
7048154879.6582280210227.1905477108716-16.0433928555986-0.406816036611063
7151705110.3447819572833.4380135754134-42.41052740977410.854078644335017
7264205842.5309339655654.5744681143454227.5325067255332.93197824883405
735847.55917.7666371100755.1746111925073-80.68628834203470.0885751620888186
746177.56109.8131447911159.48647722974840.3624461841828430.566756487480733
7569606610.0302120652173.4937735857169133.1959910342451.83038474848596
7671707021.0338760759684.1050391392458-19.11769587863961.41427338476617
7764856766.8212022983473.5590059600665-112.730607297752-1.42038921125293
7867856750.6353771156270.771912074717479.228847932593-0.376721754905006
7973007111.263643614579.765988266641343.85893693920821.21645126814816
8071057155.4214018887378.6606647469661-32.6249771325416-0.149426429153028
8170307084.3339320600574.00901862042820.5055949500839-0.628392747593262
827222.57216.8587751684175.8270666484818-23.5998756870780.245523760105614
837522.57502.9883032265382.3458458757419-85.51482065546690.88188721059352
8495008598.21741136216113.438057371867396.6046476178284.24856048467419
858697.58794.23409625046115.926191701327-138.1992211497070.351963272810941
868662.58804.56251879973112.606425084409-89.9597101238461-0.439049847488828
8786858721.02748864729106.39602944279960.4602865675726-0.815572957822292
888642.58700.36619961777102.395797598065.25346796730905-0.532211547626269
898492.58679.1551564213798.5251161619856-125.041940696285-0.51873948723137
907702.58110.0745451812877.6759133498064-74.7274607143934-2.80126384317008
9179658006.0392658133472.005811418672249.5386178024729-0.762261426854444
928097.58088.7141728552472.33874776381853.468016236001590.0447520582235541
937947.58025.5332995040968.1085961044751-10.4878475147464-0.568431470235767
949227.58802.965384277990.245680358841271.05248065979532.97473293063835
9576808319.442493720272.3746581769191-353.716736192042-2.40479031200527
9678207809.1026354616754.3369926500251300.795565669235-2.44400115152435
9776357785.3441327248551.9402236030264-111.248080612252-0.331535872730529
987347.57580.4397504257643.8757058675172-105.982971849962-1.07074467601476
997177.57304.7387941301333.789816157607130.0441219651694-1.33025229068987
1006982.57099.2162065411426.25900038241781.97683280280159-1.00218631535104
10170757109.8430306833925.7687074473823-27.0650154706111-0.0655872938936936
10272307219.7714930483128.4033760680364-31.65668193554370.353056827842769
10371707174.7400511232626.106052574538731.7995891979927-0.307977653474792
1047022.57090.6254203770622.6582116138154-13.287289972498-0.462205031821818
1057087.57151.8947447938823.8660869245019-83.60403767727930.161906212837728
10674407246.1526059904726.0674786954105158.8349467694480.295104427622815
1077592.57633.3687065499437.3444335410613-220.3643004465041.51316791728332
1088297.57866.184914060443.4246016411119334.220292500450.819863543485335
1097852.57919.4654555884743.7299804210632-71.88869627867010.041723467775085
1108097.58079.4359387793847.3769793116031-39.45183525837690.485438363280367
1118022.58033.0081112039244.423638959127535.6852868918954-0.390829344851491
1128062.58066.1515713891844.06901048880311.93700401481591-0.0472314886892814
1137982.58055.9187097853542.3652645240366-46.4342380399158-0.227793343569029
11495408963.4739864593269.4770030109482146.4536329295173.62911712602861
1158172.58517.564336423753.335386006649-88.9320683611076-2.16118417368026
1168007.58237.3586884843542.8904317825085-64.1193288914091-1.39845768649353

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 2340 & 2340 & 0 & 0 & 0 \tabularnewline
2 & 2377.5 & 2367.23340545417 & 1.81976064864848 & 2.23819498144537 & 0.0795006157569053 \tabularnewline
3 & 2500 & 2451.12525976114 & 4.83476665286734 & 8.35513223719725 & 0.331787105016021 \tabularnewline
4 & 2395 & 2416.00976120233 & 3.93038831992196 & 0.550061024324472 & -0.1705869403246 \tabularnewline
5 & 2375 & 2389.20221256938 & 3.37543495060057 & 2.67246784679053 & -0.132540709250695 \tabularnewline
6 & 2395 & 2391.57716289353 & 3.35848156734431 & 3.97399746849516 & -0.00432129172748133 \tabularnewline
7 & 2452.5 & 2428.49154733469 & 3.93037260124303 & 5.52089596035829 & 0.144903415894085 \tabularnewline
8 & 2462.5 & 2449.10025346559 & 4.2230346373984 & 4.21900677957471 & 0.0719677005249371 \tabularnewline
9 & 2840 & 2691.15171350818 & 8.54611422996654 & 18.0889059515466 & 1.02531261468985 \tabularnewline
10 & 2750 & 2729.61582528867 & 9.10957864421954 & 3.95589418703839 & 0.128859657939396 \tabularnewline
11 & 2795 & 2769.73989151636 & 9.7137952713898 & 8.25128760153212 & 0.133457508801568 \tabularnewline
12 & 3035 & 2934.27169619699 & 12.8271373175505 & 15.929022938238 & 0.66558279813771 \tabularnewline
13 & 2827.5 & 2938.22948398411 & 13.3117645154502 & -105.686247698422 & -0.0474937873241679 \tabularnewline
14 & 2850 & 2880.76805456594 & 10.5576479878237 & -1.350583544412 & -0.256106773067522 \tabularnewline
15 & 3265 & 3114.4429708592 & 16.9853641208441 & 38.3729832590897 & 0.91977797056215 \tabularnewline
16 & 3220 & 3184.45465538517 & 18.1795797992105 & 7.53627226848736 & 0.22542036127769 \tabularnewline
17 & 3075 & 3118.52647888098 & 16.4502197723048 & 1.29230537357024 & -0.359314648552381 \tabularnewline
18 & 3325 & 3242.89187364661 & 18.6406158049026 & 24.5339334179067 & 0.461221655110672 \tabularnewline
19 & 3235 & 3238.92239956811 & 18.1747314915419 & 8.13495309409837 & -0.0965894020315273 \tabularnewline
20 & 3320 & 3293.21976221036 & 18.9365525894026 & 7.53372364708825 & 0.154211702307976 \tabularnewline
21 & 3277.5 & 3277.68516580732 & 18.1912887644257 & 18.1636780922675 & -0.14705788526295 \tabularnewline
22 & 3050 & 3139.06112654078 & 14.716958684781 & -5.66981927474918 & -0.668533020205088 \tabularnewline
23 & 3432.5 & 3317.87527015057 & 18.436727651484 & 27.4419840013987 & 0.69911768521765 \tabularnewline
24 & 3575 & 3475.06359535788 & 21.5346212506094 & 26.2666476094346 & 0.590470700260171 \tabularnewline
25 & 3287.5 & 3457.62503669502 & 21.7133340492715 & -149.163061739282 & -0.18409020519121 \tabularnewline
26 & 3297.5 & 3371.71624114747 & 18.0893062316505 & -24.9136021773597 & -0.417600273292963 \tabularnewline
27 & 3255 & 3283.04335448274 & 14.8754410498015 & 25.2311486269122 & -0.441446247057629 \tabularnewline
28 & 3135 & 3188.66432662318 & 11.9751814984173 & 2.7526496005543 & -0.46161293001099 \tabularnewline
29 & 3177.5 & 3188.23719040185 & 11.661393385066 & -4.29328050327747 & -0.0525757686103256 \tabularnewline
30 & 3172.5 & 3168.38871045837 & 10.8696956165602 & 20.4939730245123 & -0.133595123063294 \tabularnewline
31 & 3365 & 3289.41246905942 & 13.6586952933491 & 18.3368647940143 & 0.466858571894861 \tabularnewline
32 & 3775 & 3588.03223994111 & 20.9598498055359 & 38.9497068331083 & 1.20719507826729 \tabularnewline
33 & 3737.5 & 3677.43513803072 & 22.7359590031605 & 24.5349124081389 & 0.289822093622384 \tabularnewline
34 & 4060 & 3931.38166743455 & 28.8125479477591 & 8.66318752269651 & 0.978667402774828 \tabularnewline
35 & 4197.5 & 4100.70464695919 & 32.5425344374491 & 23.936487084454 & 0.594499983240745 \tabularnewline
36 & 4195 & 4157.70210737528 & 33.1726901394838 & 24.6264493454658 & 0.103345208283392 \tabularnewline
37 & 4112.5 & 4216.83234330626 & 33.5349900363939 & -117.883459840786 & 0.116792508497025 \tabularnewline
38 & 3977.5 & 4090.93331183083 & 28.3882075022114 & -37.5750181711095 & -0.638289399201538 \tabularnewline
39 & 3982.5 & 4010.8985340873 & 24.9923583835193 & 25.2954597939443 & -0.448684657873995 \tabularnewline
40 & 3985 & 3999.4030207098 & 23.9244474252181 & 4.14001015941623 & -0.15353287953235 \tabularnewline
41 & 4155 & 4101.61637296708 & 26.1472871067309 & 13.3996872589447 & 0.33027860705445 \tabularnewline
42 & 4295 & 4223.89264096528 & 28.8591140984672 & 21.9884276626668 & 0.405551986901379 \tabularnewline
43 & 4072.5 & 4151.19302214221 & 25.9860056052959 & -26.8117131653979 & -0.428346734696401 \tabularnewline
44 & 4017.5 & 4058.69679160206 & 22.6151703015639 & 19.3096322612988 & -0.499593487528127 \tabularnewline
45 & 3965 & 4006.41259885798 & 20.4707357971163 & -3.1756968905518 & -0.315747957840474 \tabularnewline
46 & 3847.5 & 3920.75435604275 & 17.4132149570119 & -19.0908461455259 & -0.447309927307919 \tabularnewline
47 & 3799.5 & 3840.83200237598 & 14.6017883641445 & 8.32609874572846 & -0.41010345211154 \tabularnewline
48 & 4215 & 4056.07291269673 & 20.2376275932695 & 56.6834239498864 & 0.844456243060174 \tabularnewline
49 & 4115 & 4144.48132639954 & 21.7816049981624 & -64.4527316107912 & 0.29914435384386 \tabularnewline
50 & 4210 & 4210.26363365529 & 23.1815647085248 & -21.5831414298727 & 0.179195107096373 \tabularnewline
51 & 4132.5 & 4157.3675593878 & 20.7618676910642 & 12.6441218442029 & -0.31515152192724 \tabularnewline
52 & 3955 & 4046.64552164272 & 16.7324260952535 & -25.4988878945057 & -0.551986229765171 \tabularnewline
53 & 4057.5 & 4055.90296153919 & 16.5079116525513 & 5.37365514912217 & -0.0314503667966252 \tabularnewline
54 & 4152.5 & 4102.4121032322 & 17.4037386688885 & 34.9247968551705 & 0.126220393459416 \tabularnewline
55 & 4062.5 & 4096.96653565115 & 16.721168814512 & -22.9200136663469 & -0.096110567252689 \tabularnewline
56 & 4092.5 & 4085.50741176383 & 15.8771900664027 & 21.2303748337544 & -0.118515870928345 \tabularnewline
57 & 4157.5 & 4129.88781299743 & 16.7335211542488 & 13.2135567591937 & 0.119861129244165 \tabularnewline
58 & 4325 & 4260.82664864061 & 20.1743001634615 & 6.49029339262252 & 0.480203805696807 \tabularnewline
59 & 4210 & 4250.72021901766 & 19.2628724044372 & -25.4314988394169 & -0.127270966090229 \tabularnewline
60 & 5107.5 & 4742.48786679875 & 33.1846066744802 & 126.794109706559 & 1.98454306838124 \tabularnewline
61 & 4862.5 & 4872.17790361952 & 35.7819536792932 & -58.6674187845524 & 0.417422299588805 \tabularnewline
62 & 4920 & 4925.66450136061 & 36.3416489929837 & -14.3260962807705 & 0.0728442077689933 \tabularnewline
63 & 5080 & 5018.66854755019 & 38.1475841975663 & 33.4468814534621 & 0.235018764110266 \tabularnewline
64 & 4615 & 4810.83107673647 & 30.46449959125 & -72.8513467277084 & -1.03142622279947 \tabularnewline
65 & 4615 & 4699.11048208287 & 26.082014060966 & -12.7506004799732 & -0.597389088041919 \tabularnewline
66 & 5057.5 & 4896.80383516526 & 31.3458134104334 & 74.5445209608231 & 0.720932715624712 \tabularnewline
67 & 4850 & 4898.29559779106 & 30.4306144958809 & -33.3106374637457 & -0.12538960350871 \tabularnewline
68 & 4720 & 4793.50459368888 & 26.28080505935 & -5.6389251522134 & -0.567886096502536 \tabularnewline
69 & 5040 & 4946.36757757463 & 30.1714282216446 & 30.1071024192565 & 0.531581536985529 \tabularnewline
70 & 4815 & 4879.65822802102 & 27.1905477108716 & -16.0433928555986 & -0.406816036611063 \tabularnewline
71 & 5170 & 5110.34478195728 & 33.4380135754134 & -42.4105274097741 & 0.854078644335017 \tabularnewline
72 & 6420 & 5842.53093396556 & 54.5744681143454 & 227.532506725533 & 2.93197824883405 \tabularnewline
73 & 5847.5 & 5917.76663711007 & 55.1746111925073 & -80.6862883420347 & 0.0885751620888186 \tabularnewline
74 & 6177.5 & 6109.81314479111 & 59.4864772297484 & 0.362446184182843 & 0.566756487480733 \tabularnewline
75 & 6960 & 6610.03021206521 & 73.4937735857169 & 133.195991034245 & 1.83038474848596 \tabularnewline
76 & 7170 & 7021.03387607596 & 84.1050391392458 & -19.1176958786396 & 1.41427338476617 \tabularnewline
77 & 6485 & 6766.82120229834 & 73.5590059600665 & -112.730607297752 & -1.42038921125293 \tabularnewline
78 & 6785 & 6750.63537711562 & 70.7719120747174 & 79.228847932593 & -0.376721754905006 \tabularnewline
79 & 7300 & 7111.2636436145 & 79.7659882666413 & 43.8589369392082 & 1.21645126814816 \tabularnewline
80 & 7105 & 7155.42140188873 & 78.6606647469661 & -32.6249771325416 & -0.149426429153028 \tabularnewline
81 & 7030 & 7084.33393206005 & 74.009018620428 & 20.5055949500839 & -0.628392747593262 \tabularnewline
82 & 7222.5 & 7216.85877516841 & 75.8270666484818 & -23.599875687078 & 0.245523760105614 \tabularnewline
83 & 7522.5 & 7502.98830322653 & 82.3458458757419 & -85.5148206554669 & 0.88188721059352 \tabularnewline
84 & 9500 & 8598.21741136216 & 113.438057371867 & 396.604647617828 & 4.24856048467419 \tabularnewline
85 & 8697.5 & 8794.23409625046 & 115.926191701327 & -138.199221149707 & 0.351963272810941 \tabularnewline
86 & 8662.5 & 8804.56251879973 & 112.606425084409 & -89.9597101238461 & -0.439049847488828 \tabularnewline
87 & 8685 & 8721.02748864729 & 106.396029442799 & 60.4602865675726 & -0.815572957822292 \tabularnewline
88 & 8642.5 & 8700.36619961777 & 102.39579759806 & 5.25346796730905 & -0.532211547626269 \tabularnewline
89 & 8492.5 & 8679.15515642137 & 98.5251161619856 & -125.041940696285 & -0.51873948723137 \tabularnewline
90 & 7702.5 & 8110.07454518128 & 77.6759133498064 & -74.7274607143934 & -2.80126384317008 \tabularnewline
91 & 7965 & 8006.03926581334 & 72.0058114186722 & 49.5386178024729 & -0.762261426854444 \tabularnewline
92 & 8097.5 & 8088.71417285524 & 72.3387477638185 & 3.46801623600159 & 0.0447520582235541 \tabularnewline
93 & 7947.5 & 8025.53329950409 & 68.1085961044751 & -10.4878475147464 & -0.568431470235767 \tabularnewline
94 & 9227.5 & 8802.9653842779 & 90.2456803588412 & 71.0524806597953 & 2.97473293063835 \tabularnewline
95 & 7680 & 8319.4424937202 & 72.3746581769191 & -353.716736192042 & -2.40479031200527 \tabularnewline
96 & 7820 & 7809.10263546167 & 54.3369926500251 & 300.795565669235 & -2.44400115152435 \tabularnewline
97 & 7635 & 7785.34413272485 & 51.9402236030264 & -111.248080612252 & -0.331535872730529 \tabularnewline
98 & 7347.5 & 7580.43975042576 & 43.8757058675172 & -105.982971849962 & -1.07074467601476 \tabularnewline
99 & 7177.5 & 7304.73879413013 & 33.7898161576071 & 30.0441219651694 & -1.33025229068987 \tabularnewline
100 & 6982.5 & 7099.21620654114 & 26.2590003824178 & 1.97683280280159 & -1.00218631535104 \tabularnewline
101 & 7075 & 7109.84303068339 & 25.7687074473823 & -27.0650154706111 & -0.0655872938936936 \tabularnewline
102 & 7230 & 7219.77149304831 & 28.4033760680364 & -31.6566819355437 & 0.353056827842769 \tabularnewline
103 & 7170 & 7174.74005112326 & 26.1060525745387 & 31.7995891979927 & -0.307977653474792 \tabularnewline
104 & 7022.5 & 7090.62542037706 & 22.6582116138154 & -13.287289972498 & -0.462205031821818 \tabularnewline
105 & 7087.5 & 7151.89474479388 & 23.8660869245019 & -83.6040376772793 & 0.161906212837728 \tabularnewline
106 & 7440 & 7246.15260599047 & 26.0674786954105 & 158.834946769448 & 0.295104427622815 \tabularnewline
107 & 7592.5 & 7633.36870654994 & 37.3444335410613 & -220.364300446504 & 1.51316791728332 \tabularnewline
108 & 8297.5 & 7866.1849140604 & 43.4246016411119 & 334.22029250045 & 0.819863543485335 \tabularnewline
109 & 7852.5 & 7919.46545558847 & 43.7299804210632 & -71.8886962786701 & 0.041723467775085 \tabularnewline
110 & 8097.5 & 8079.43593877938 & 47.3769793116031 & -39.4518352583769 & 0.485438363280367 \tabularnewline
111 & 8022.5 & 8033.00811120392 & 44.4236389591275 & 35.6852868918954 & -0.390829344851491 \tabularnewline
112 & 8062.5 & 8066.15157138918 & 44.0690104888031 & 1.93700401481591 & -0.0472314886892814 \tabularnewline
113 & 7982.5 & 8055.91870978535 & 42.3652645240366 & -46.4342380399158 & -0.227793343569029 \tabularnewline
114 & 9540 & 8963.47398645932 & 69.4770030109482 & 146.453632929517 & 3.62911712602861 \tabularnewline
115 & 8172.5 & 8517.5643364237 & 53.335386006649 & -88.9320683611076 & -2.16118417368026 \tabularnewline
116 & 8007.5 & 8237.35868848435 & 42.8904317825085 & -64.1193288914091 & -1.39845768649353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302266&T=1

[TABLE]
[ROW][C]Structural Time Series Model -- Interpolation[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Slope[/C][C]Seasonal[/C][C]Stand. Residuals[/C][/ROW]
[ROW][C]1[/C][C]2340[/C][C]2340[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]2377.5[/C][C]2367.23340545417[/C][C]1.81976064864848[/C][C]2.23819498144537[/C][C]0.0795006157569053[/C][/ROW]
[ROW][C]3[/C][C]2500[/C][C]2451.12525976114[/C][C]4.83476665286734[/C][C]8.35513223719725[/C][C]0.331787105016021[/C][/ROW]
[ROW][C]4[/C][C]2395[/C][C]2416.00976120233[/C][C]3.93038831992196[/C][C]0.550061024324472[/C][C]-0.1705869403246[/C][/ROW]
[ROW][C]5[/C][C]2375[/C][C]2389.20221256938[/C][C]3.37543495060057[/C][C]2.67246784679053[/C][C]-0.132540709250695[/C][/ROW]
[ROW][C]6[/C][C]2395[/C][C]2391.57716289353[/C][C]3.35848156734431[/C][C]3.97399746849516[/C][C]-0.00432129172748133[/C][/ROW]
[ROW][C]7[/C][C]2452.5[/C][C]2428.49154733469[/C][C]3.93037260124303[/C][C]5.52089596035829[/C][C]0.144903415894085[/C][/ROW]
[ROW][C]8[/C][C]2462.5[/C][C]2449.10025346559[/C][C]4.2230346373984[/C][C]4.21900677957471[/C][C]0.0719677005249371[/C][/ROW]
[ROW][C]9[/C][C]2840[/C][C]2691.15171350818[/C][C]8.54611422996654[/C][C]18.0889059515466[/C][C]1.02531261468985[/C][/ROW]
[ROW][C]10[/C][C]2750[/C][C]2729.61582528867[/C][C]9.10957864421954[/C][C]3.95589418703839[/C][C]0.128859657939396[/C][/ROW]
[ROW][C]11[/C][C]2795[/C][C]2769.73989151636[/C][C]9.7137952713898[/C][C]8.25128760153212[/C][C]0.133457508801568[/C][/ROW]
[ROW][C]12[/C][C]3035[/C][C]2934.27169619699[/C][C]12.8271373175505[/C][C]15.929022938238[/C][C]0.66558279813771[/C][/ROW]
[ROW][C]13[/C][C]2827.5[/C][C]2938.22948398411[/C][C]13.3117645154502[/C][C]-105.686247698422[/C][C]-0.0474937873241679[/C][/ROW]
[ROW][C]14[/C][C]2850[/C][C]2880.76805456594[/C][C]10.5576479878237[/C][C]-1.350583544412[/C][C]-0.256106773067522[/C][/ROW]
[ROW][C]15[/C][C]3265[/C][C]3114.4429708592[/C][C]16.9853641208441[/C][C]38.3729832590897[/C][C]0.91977797056215[/C][/ROW]
[ROW][C]16[/C][C]3220[/C][C]3184.45465538517[/C][C]18.1795797992105[/C][C]7.53627226848736[/C][C]0.22542036127769[/C][/ROW]
[ROW][C]17[/C][C]3075[/C][C]3118.52647888098[/C][C]16.4502197723048[/C][C]1.29230537357024[/C][C]-0.359314648552381[/C][/ROW]
[ROW][C]18[/C][C]3325[/C][C]3242.89187364661[/C][C]18.6406158049026[/C][C]24.5339334179067[/C][C]0.461221655110672[/C][/ROW]
[ROW][C]19[/C][C]3235[/C][C]3238.92239956811[/C][C]18.1747314915419[/C][C]8.13495309409837[/C][C]-0.0965894020315273[/C][/ROW]
[ROW][C]20[/C][C]3320[/C][C]3293.21976221036[/C][C]18.9365525894026[/C][C]7.53372364708825[/C][C]0.154211702307976[/C][/ROW]
[ROW][C]21[/C][C]3277.5[/C][C]3277.68516580732[/C][C]18.1912887644257[/C][C]18.1636780922675[/C][C]-0.14705788526295[/C][/ROW]
[ROW][C]22[/C][C]3050[/C][C]3139.06112654078[/C][C]14.716958684781[/C][C]-5.66981927474918[/C][C]-0.668533020205088[/C][/ROW]
[ROW][C]23[/C][C]3432.5[/C][C]3317.87527015057[/C][C]18.436727651484[/C][C]27.4419840013987[/C][C]0.69911768521765[/C][/ROW]
[ROW][C]24[/C][C]3575[/C][C]3475.06359535788[/C][C]21.5346212506094[/C][C]26.2666476094346[/C][C]0.590470700260171[/C][/ROW]
[ROW][C]25[/C][C]3287.5[/C][C]3457.62503669502[/C][C]21.7133340492715[/C][C]-149.163061739282[/C][C]-0.18409020519121[/C][/ROW]
[ROW][C]26[/C][C]3297.5[/C][C]3371.71624114747[/C][C]18.0893062316505[/C][C]-24.9136021773597[/C][C]-0.417600273292963[/C][/ROW]
[ROW][C]27[/C][C]3255[/C][C]3283.04335448274[/C][C]14.8754410498015[/C][C]25.2311486269122[/C][C]-0.441446247057629[/C][/ROW]
[ROW][C]28[/C][C]3135[/C][C]3188.66432662318[/C][C]11.9751814984173[/C][C]2.7526496005543[/C][C]-0.46161293001099[/C][/ROW]
[ROW][C]29[/C][C]3177.5[/C][C]3188.23719040185[/C][C]11.661393385066[/C][C]-4.29328050327747[/C][C]-0.0525757686103256[/C][/ROW]
[ROW][C]30[/C][C]3172.5[/C][C]3168.38871045837[/C][C]10.8696956165602[/C][C]20.4939730245123[/C][C]-0.133595123063294[/C][/ROW]
[ROW][C]31[/C][C]3365[/C][C]3289.41246905942[/C][C]13.6586952933491[/C][C]18.3368647940143[/C][C]0.466858571894861[/C][/ROW]
[ROW][C]32[/C][C]3775[/C][C]3588.03223994111[/C][C]20.9598498055359[/C][C]38.9497068331083[/C][C]1.20719507826729[/C][/ROW]
[ROW][C]33[/C][C]3737.5[/C][C]3677.43513803072[/C][C]22.7359590031605[/C][C]24.5349124081389[/C][C]0.289822093622384[/C][/ROW]
[ROW][C]34[/C][C]4060[/C][C]3931.38166743455[/C][C]28.8125479477591[/C][C]8.66318752269651[/C][C]0.978667402774828[/C][/ROW]
[ROW][C]35[/C][C]4197.5[/C][C]4100.70464695919[/C][C]32.5425344374491[/C][C]23.936487084454[/C][C]0.594499983240745[/C][/ROW]
[ROW][C]36[/C][C]4195[/C][C]4157.70210737528[/C][C]33.1726901394838[/C][C]24.6264493454658[/C][C]0.103345208283392[/C][/ROW]
[ROW][C]37[/C][C]4112.5[/C][C]4216.83234330626[/C][C]33.5349900363939[/C][C]-117.883459840786[/C][C]0.116792508497025[/C][/ROW]
[ROW][C]38[/C][C]3977.5[/C][C]4090.93331183083[/C][C]28.3882075022114[/C][C]-37.5750181711095[/C][C]-0.638289399201538[/C][/ROW]
[ROW][C]39[/C][C]3982.5[/C][C]4010.8985340873[/C][C]24.9923583835193[/C][C]25.2954597939443[/C][C]-0.448684657873995[/C][/ROW]
[ROW][C]40[/C][C]3985[/C][C]3999.4030207098[/C][C]23.9244474252181[/C][C]4.14001015941623[/C][C]-0.15353287953235[/C][/ROW]
[ROW][C]41[/C][C]4155[/C][C]4101.61637296708[/C][C]26.1472871067309[/C][C]13.3996872589447[/C][C]0.33027860705445[/C][/ROW]
[ROW][C]42[/C][C]4295[/C][C]4223.89264096528[/C][C]28.8591140984672[/C][C]21.9884276626668[/C][C]0.405551986901379[/C][/ROW]
[ROW][C]43[/C][C]4072.5[/C][C]4151.19302214221[/C][C]25.9860056052959[/C][C]-26.8117131653979[/C][C]-0.428346734696401[/C][/ROW]
[ROW][C]44[/C][C]4017.5[/C][C]4058.69679160206[/C][C]22.6151703015639[/C][C]19.3096322612988[/C][C]-0.499593487528127[/C][/ROW]
[ROW][C]45[/C][C]3965[/C][C]4006.41259885798[/C][C]20.4707357971163[/C][C]-3.1756968905518[/C][C]-0.315747957840474[/C][/ROW]
[ROW][C]46[/C][C]3847.5[/C][C]3920.75435604275[/C][C]17.4132149570119[/C][C]-19.0908461455259[/C][C]-0.447309927307919[/C][/ROW]
[ROW][C]47[/C][C]3799.5[/C][C]3840.83200237598[/C][C]14.6017883641445[/C][C]8.32609874572846[/C][C]-0.41010345211154[/C][/ROW]
[ROW][C]48[/C][C]4215[/C][C]4056.07291269673[/C][C]20.2376275932695[/C][C]56.6834239498864[/C][C]0.844456243060174[/C][/ROW]
[ROW][C]49[/C][C]4115[/C][C]4144.48132639954[/C][C]21.7816049981624[/C][C]-64.4527316107912[/C][C]0.29914435384386[/C][/ROW]
[ROW][C]50[/C][C]4210[/C][C]4210.26363365529[/C][C]23.1815647085248[/C][C]-21.5831414298727[/C][C]0.179195107096373[/C][/ROW]
[ROW][C]51[/C][C]4132.5[/C][C]4157.3675593878[/C][C]20.7618676910642[/C][C]12.6441218442029[/C][C]-0.31515152192724[/C][/ROW]
[ROW][C]52[/C][C]3955[/C][C]4046.64552164272[/C][C]16.7324260952535[/C][C]-25.4988878945057[/C][C]-0.551986229765171[/C][/ROW]
[ROW][C]53[/C][C]4057.5[/C][C]4055.90296153919[/C][C]16.5079116525513[/C][C]5.37365514912217[/C][C]-0.0314503667966252[/C][/ROW]
[ROW][C]54[/C][C]4152.5[/C][C]4102.4121032322[/C][C]17.4037386688885[/C][C]34.9247968551705[/C][C]0.126220393459416[/C][/ROW]
[ROW][C]55[/C][C]4062.5[/C][C]4096.96653565115[/C][C]16.721168814512[/C][C]-22.9200136663469[/C][C]-0.096110567252689[/C][/ROW]
[ROW][C]56[/C][C]4092.5[/C][C]4085.50741176383[/C][C]15.8771900664027[/C][C]21.2303748337544[/C][C]-0.118515870928345[/C][/ROW]
[ROW][C]57[/C][C]4157.5[/C][C]4129.88781299743[/C][C]16.7335211542488[/C][C]13.2135567591937[/C][C]0.119861129244165[/C][/ROW]
[ROW][C]58[/C][C]4325[/C][C]4260.82664864061[/C][C]20.1743001634615[/C][C]6.49029339262252[/C][C]0.480203805696807[/C][/ROW]
[ROW][C]59[/C][C]4210[/C][C]4250.72021901766[/C][C]19.2628724044372[/C][C]-25.4314988394169[/C][C]-0.127270966090229[/C][/ROW]
[ROW][C]60[/C][C]5107.5[/C][C]4742.48786679875[/C][C]33.1846066744802[/C][C]126.794109706559[/C][C]1.98454306838124[/C][/ROW]
[ROW][C]61[/C][C]4862.5[/C][C]4872.17790361952[/C][C]35.7819536792932[/C][C]-58.6674187845524[/C][C]0.417422299588805[/C][/ROW]
[ROW][C]62[/C][C]4920[/C][C]4925.66450136061[/C][C]36.3416489929837[/C][C]-14.3260962807705[/C][C]0.0728442077689933[/C][/ROW]
[ROW][C]63[/C][C]5080[/C][C]5018.66854755019[/C][C]38.1475841975663[/C][C]33.4468814534621[/C][C]0.235018764110266[/C][/ROW]
[ROW][C]64[/C][C]4615[/C][C]4810.83107673647[/C][C]30.46449959125[/C][C]-72.8513467277084[/C][C]-1.03142622279947[/C][/ROW]
[ROW][C]65[/C][C]4615[/C][C]4699.11048208287[/C][C]26.082014060966[/C][C]-12.7506004799732[/C][C]-0.597389088041919[/C][/ROW]
[ROW][C]66[/C][C]5057.5[/C][C]4896.80383516526[/C][C]31.3458134104334[/C][C]74.5445209608231[/C][C]0.720932715624712[/C][/ROW]
[ROW][C]67[/C][C]4850[/C][C]4898.29559779106[/C][C]30.4306144958809[/C][C]-33.3106374637457[/C][C]-0.12538960350871[/C][/ROW]
[ROW][C]68[/C][C]4720[/C][C]4793.50459368888[/C][C]26.28080505935[/C][C]-5.6389251522134[/C][C]-0.567886096502536[/C][/ROW]
[ROW][C]69[/C][C]5040[/C][C]4946.36757757463[/C][C]30.1714282216446[/C][C]30.1071024192565[/C][C]0.531581536985529[/C][/ROW]
[ROW][C]70[/C][C]4815[/C][C]4879.65822802102[/C][C]27.1905477108716[/C][C]-16.0433928555986[/C][C]-0.406816036611063[/C][/ROW]
[ROW][C]71[/C][C]5170[/C][C]5110.34478195728[/C][C]33.4380135754134[/C][C]-42.4105274097741[/C][C]0.854078644335017[/C][/ROW]
[ROW][C]72[/C][C]6420[/C][C]5842.53093396556[/C][C]54.5744681143454[/C][C]227.532506725533[/C][C]2.93197824883405[/C][/ROW]
[ROW][C]73[/C][C]5847.5[/C][C]5917.76663711007[/C][C]55.1746111925073[/C][C]-80.6862883420347[/C][C]0.0885751620888186[/C][/ROW]
[ROW][C]74[/C][C]6177.5[/C][C]6109.81314479111[/C][C]59.4864772297484[/C][C]0.362446184182843[/C][C]0.566756487480733[/C][/ROW]
[ROW][C]75[/C][C]6960[/C][C]6610.03021206521[/C][C]73.4937735857169[/C][C]133.195991034245[/C][C]1.83038474848596[/C][/ROW]
[ROW][C]76[/C][C]7170[/C][C]7021.03387607596[/C][C]84.1050391392458[/C][C]-19.1176958786396[/C][C]1.41427338476617[/C][/ROW]
[ROW][C]77[/C][C]6485[/C][C]6766.82120229834[/C][C]73.5590059600665[/C][C]-112.730607297752[/C][C]-1.42038921125293[/C][/ROW]
[ROW][C]78[/C][C]6785[/C][C]6750.63537711562[/C][C]70.7719120747174[/C][C]79.228847932593[/C][C]-0.376721754905006[/C][/ROW]
[ROW][C]79[/C][C]7300[/C][C]7111.2636436145[/C][C]79.7659882666413[/C][C]43.8589369392082[/C][C]1.21645126814816[/C][/ROW]
[ROW][C]80[/C][C]7105[/C][C]7155.42140188873[/C][C]78.6606647469661[/C][C]-32.6249771325416[/C][C]-0.149426429153028[/C][/ROW]
[ROW][C]81[/C][C]7030[/C][C]7084.33393206005[/C][C]74.009018620428[/C][C]20.5055949500839[/C][C]-0.628392747593262[/C][/ROW]
[ROW][C]82[/C][C]7222.5[/C][C]7216.85877516841[/C][C]75.8270666484818[/C][C]-23.599875687078[/C][C]0.245523760105614[/C][/ROW]
[ROW][C]83[/C][C]7522.5[/C][C]7502.98830322653[/C][C]82.3458458757419[/C][C]-85.5148206554669[/C][C]0.88188721059352[/C][/ROW]
[ROW][C]84[/C][C]9500[/C][C]8598.21741136216[/C][C]113.438057371867[/C][C]396.604647617828[/C][C]4.24856048467419[/C][/ROW]
[ROW][C]85[/C][C]8697.5[/C][C]8794.23409625046[/C][C]115.926191701327[/C][C]-138.199221149707[/C][C]0.351963272810941[/C][/ROW]
[ROW][C]86[/C][C]8662.5[/C][C]8804.56251879973[/C][C]112.606425084409[/C][C]-89.9597101238461[/C][C]-0.439049847488828[/C][/ROW]
[ROW][C]87[/C][C]8685[/C][C]8721.02748864729[/C][C]106.396029442799[/C][C]60.4602865675726[/C][C]-0.815572957822292[/C][/ROW]
[ROW][C]88[/C][C]8642.5[/C][C]8700.36619961777[/C][C]102.39579759806[/C][C]5.25346796730905[/C][C]-0.532211547626269[/C][/ROW]
[ROW][C]89[/C][C]8492.5[/C][C]8679.15515642137[/C][C]98.5251161619856[/C][C]-125.041940696285[/C][C]-0.51873948723137[/C][/ROW]
[ROW][C]90[/C][C]7702.5[/C][C]8110.07454518128[/C][C]77.6759133498064[/C][C]-74.7274607143934[/C][C]-2.80126384317008[/C][/ROW]
[ROW][C]91[/C][C]7965[/C][C]8006.03926581334[/C][C]72.0058114186722[/C][C]49.5386178024729[/C][C]-0.762261426854444[/C][/ROW]
[ROW][C]92[/C][C]8097.5[/C][C]8088.71417285524[/C][C]72.3387477638185[/C][C]3.46801623600159[/C][C]0.0447520582235541[/C][/ROW]
[ROW][C]93[/C][C]7947.5[/C][C]8025.53329950409[/C][C]68.1085961044751[/C][C]-10.4878475147464[/C][C]-0.568431470235767[/C][/ROW]
[ROW][C]94[/C][C]9227.5[/C][C]8802.9653842779[/C][C]90.2456803588412[/C][C]71.0524806597953[/C][C]2.97473293063835[/C][/ROW]
[ROW][C]95[/C][C]7680[/C][C]8319.4424937202[/C][C]72.3746581769191[/C][C]-353.716736192042[/C][C]-2.40479031200527[/C][/ROW]
[ROW][C]96[/C][C]7820[/C][C]7809.10263546167[/C][C]54.3369926500251[/C][C]300.795565669235[/C][C]-2.44400115152435[/C][/ROW]
[ROW][C]97[/C][C]7635[/C][C]7785.34413272485[/C][C]51.9402236030264[/C][C]-111.248080612252[/C][C]-0.331535872730529[/C][/ROW]
[ROW][C]98[/C][C]7347.5[/C][C]7580.43975042576[/C][C]43.8757058675172[/C][C]-105.982971849962[/C][C]-1.07074467601476[/C][/ROW]
[ROW][C]99[/C][C]7177.5[/C][C]7304.73879413013[/C][C]33.7898161576071[/C][C]30.0441219651694[/C][C]-1.33025229068987[/C][/ROW]
[ROW][C]100[/C][C]6982.5[/C][C]7099.21620654114[/C][C]26.2590003824178[/C][C]1.97683280280159[/C][C]-1.00218631535104[/C][/ROW]
[ROW][C]101[/C][C]7075[/C][C]7109.84303068339[/C][C]25.7687074473823[/C][C]-27.0650154706111[/C][C]-0.0655872938936936[/C][/ROW]
[ROW][C]102[/C][C]7230[/C][C]7219.77149304831[/C][C]28.4033760680364[/C][C]-31.6566819355437[/C][C]0.353056827842769[/C][/ROW]
[ROW][C]103[/C][C]7170[/C][C]7174.74005112326[/C][C]26.1060525745387[/C][C]31.7995891979927[/C][C]-0.307977653474792[/C][/ROW]
[ROW][C]104[/C][C]7022.5[/C][C]7090.62542037706[/C][C]22.6582116138154[/C][C]-13.287289972498[/C][C]-0.462205031821818[/C][/ROW]
[ROW][C]105[/C][C]7087.5[/C][C]7151.89474479388[/C][C]23.8660869245019[/C][C]-83.6040376772793[/C][C]0.161906212837728[/C][/ROW]
[ROW][C]106[/C][C]7440[/C][C]7246.15260599047[/C][C]26.0674786954105[/C][C]158.834946769448[/C][C]0.295104427622815[/C][/ROW]
[ROW][C]107[/C][C]7592.5[/C][C]7633.36870654994[/C][C]37.3444335410613[/C][C]-220.364300446504[/C][C]1.51316791728332[/C][/ROW]
[ROW][C]108[/C][C]8297.5[/C][C]7866.1849140604[/C][C]43.4246016411119[/C][C]334.22029250045[/C][C]0.819863543485335[/C][/ROW]
[ROW][C]109[/C][C]7852.5[/C][C]7919.46545558847[/C][C]43.7299804210632[/C][C]-71.8886962786701[/C][C]0.041723467775085[/C][/ROW]
[ROW][C]110[/C][C]8097.5[/C][C]8079.43593877938[/C][C]47.3769793116031[/C][C]-39.4518352583769[/C][C]0.485438363280367[/C][/ROW]
[ROW][C]111[/C][C]8022.5[/C][C]8033.00811120392[/C][C]44.4236389591275[/C][C]35.6852868918954[/C][C]-0.390829344851491[/C][/ROW]
[ROW][C]112[/C][C]8062.5[/C][C]8066.15157138918[/C][C]44.0690104888031[/C][C]1.93700401481591[/C][C]-0.0472314886892814[/C][/ROW]
[ROW][C]113[/C][C]7982.5[/C][C]8055.91870978535[/C][C]42.3652645240366[/C][C]-46.4342380399158[/C][C]-0.227793343569029[/C][/ROW]
[ROW][C]114[/C][C]9540[/C][C]8963.47398645932[/C][C]69.4770030109482[/C][C]146.453632929517[/C][C]3.62911712602861[/C][/ROW]
[ROW][C]115[/C][C]8172.5[/C][C]8517.5643364237[/C][C]53.335386006649[/C][C]-88.9320683611076[/C][C]-2.16118417368026[/C][/ROW]
[ROW][C]116[/C][C]8007.5[/C][C]8237.35868848435[/C][C]42.8904317825085[/C][C]-64.1193288914091[/C][C]-1.39845768649353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302266&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302266&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
123402340000
22377.52367.233405454171.819760648648482.238194981445370.0795006157569053
325002451.125259761144.834766652867348.355132237197250.331787105016021
423952416.009761202333.930388319921960.550061024324472-0.1705869403246
523752389.202212569383.375434950600572.67246784679053-0.132540709250695
623952391.577162893533.358481567344313.97399746849516-0.00432129172748133
72452.52428.491547334693.930372601243035.520895960358290.144903415894085
82462.52449.100253465594.22303463739844.219006779574710.0719677005249371
928402691.151713508188.5461142299665418.08890595154661.02531261468985
1027502729.615825288679.109578644219543.955894187038390.128859657939396
1127952769.739891516369.71379527138988.251287601532120.133457508801568
1230352934.2716961969912.827137317550515.9290229382380.66558279813771
132827.52938.2294839841113.3117645154502-105.686247698422-0.0474937873241679
1428502880.7680545659410.5576479878237-1.350583544412-0.256106773067522
1532653114.442970859216.985364120844138.37298325908970.91977797056215
1632203184.4546553851718.17957979921057.536272268487360.22542036127769
1730753118.5264788809816.45021977230481.29230537357024-0.359314648552381
1833253242.8918736466118.640615804902624.53393341790670.461221655110672
1932353238.9223995681118.17473149154198.13495309409837-0.0965894020315273
2033203293.2197622103618.93655258940267.533723647088250.154211702307976
213277.53277.6851658073218.191288764425718.1636780922675-0.14705788526295
2230503139.0611265407814.716958684781-5.66981927474918-0.668533020205088
233432.53317.8752701505718.43672765148427.44198400139870.69911768521765
2435753475.0635953578821.534621250609426.26664760943460.590470700260171
253287.53457.6250366950221.7133340492715-149.163061739282-0.18409020519121
263297.53371.7162411474718.0893062316505-24.9136021773597-0.417600273292963
2732553283.0433544827414.875441049801525.2311486269122-0.441446247057629
2831353188.6643266231811.97518149841732.7526496005543-0.46161293001099
293177.53188.2371904018511.661393385066-4.29328050327747-0.0525757686103256
303172.53168.3887104583710.869695616560220.4939730245123-0.133595123063294
3133653289.4124690594213.658695293349118.33686479401430.466858571894861
3237753588.0322399411120.959849805535938.94970683310831.20719507826729
333737.53677.4351380307222.735959003160524.53491240813890.289822093622384
3440603931.3816674345528.81254794775918.663187522696510.978667402774828
354197.54100.7046469591932.542534437449123.9364870844540.594499983240745
3641954157.7021073752833.172690139483824.62644934546580.103345208283392
374112.54216.8323433062633.5349900363939-117.8834598407860.116792508497025
383977.54090.9333118308328.3882075022114-37.5750181711095-0.638289399201538
393982.54010.898534087324.992358383519325.2954597939443-0.448684657873995
4039853999.403020709823.92444742521814.14001015941623-0.15353287953235
4141554101.6163729670826.147287106730913.39968725894470.33027860705445
4242954223.8926409652828.859114098467221.98842766266680.405551986901379
434072.54151.1930221422125.9860056052959-26.8117131653979-0.428346734696401
444017.54058.6967916020622.615170301563919.3096322612988-0.499593487528127
4539654006.4125988579820.4707357971163-3.1756968905518-0.315747957840474
463847.53920.7543560427517.4132149570119-19.0908461455259-0.447309927307919
473799.53840.8320023759814.60178836414458.32609874572846-0.41010345211154
4842154056.0729126967320.237627593269556.68342394988640.844456243060174
4941154144.4813263995421.7816049981624-64.45273161079120.29914435384386
5042104210.2636336552923.1815647085248-21.58314142987270.179195107096373
514132.54157.367559387820.761867691064212.6441218442029-0.31515152192724
5239554046.6455216427216.7324260952535-25.4988878945057-0.551986229765171
534057.54055.9029615391916.50791165255135.37365514912217-0.0314503667966252
544152.54102.412103232217.403738668888534.92479685517050.126220393459416
554062.54096.9665356511516.721168814512-22.9200136663469-0.096110567252689
564092.54085.5074117638315.877190066402721.2303748337544-0.118515870928345
574157.54129.8878129974316.733521154248813.21355675919370.119861129244165
5843254260.8266486406120.17430016346156.490293392622520.480203805696807
5942104250.7202190176619.2628724044372-25.4314988394169-0.127270966090229
605107.54742.4878667987533.1846066744802126.7941097065591.98454306838124
614862.54872.1779036195235.7819536792932-58.66741878455240.417422299588805
6249204925.6645013606136.3416489929837-14.32609628077050.0728442077689933
6350805018.6685475501938.147584197566333.44688145346210.235018764110266
6446154810.8310767364730.46449959125-72.8513467277084-1.03142622279947
6546154699.1104820828726.082014060966-12.7506004799732-0.597389088041919
665057.54896.8038351652631.345813410433474.54452096082310.720932715624712
6748504898.2955977910630.4306144958809-33.3106374637457-0.12538960350871
6847204793.5045936888826.28080505935-5.6389251522134-0.567886096502536
6950404946.3675775746330.171428221644630.10710241925650.531581536985529
7048154879.6582280210227.1905477108716-16.0433928555986-0.406816036611063
7151705110.3447819572833.4380135754134-42.41052740977410.854078644335017
7264205842.5309339655654.5744681143454227.5325067255332.93197824883405
735847.55917.7666371100755.1746111925073-80.68628834203470.0885751620888186
746177.56109.8131447911159.48647722974840.3624461841828430.566756487480733
7569606610.0302120652173.4937735857169133.1959910342451.83038474848596
7671707021.0338760759684.1050391392458-19.11769587863961.41427338476617
7764856766.8212022983473.5590059600665-112.730607297752-1.42038921125293
7867856750.6353771156270.771912074717479.228847932593-0.376721754905006
7973007111.263643614579.765988266641343.85893693920821.21645126814816
8071057155.4214018887378.6606647469661-32.6249771325416-0.149426429153028
8170307084.3339320600574.00901862042820.5055949500839-0.628392747593262
827222.57216.8587751684175.8270666484818-23.5998756870780.245523760105614
837522.57502.9883032265382.3458458757419-85.51482065546690.88188721059352
8495008598.21741136216113.438057371867396.6046476178284.24856048467419
858697.58794.23409625046115.926191701327-138.1992211497070.351963272810941
868662.58804.56251879973112.606425084409-89.9597101238461-0.439049847488828
8786858721.02748864729106.39602944279960.4602865675726-0.815572957822292
888642.58700.36619961777102.395797598065.25346796730905-0.532211547626269
898492.58679.1551564213798.5251161619856-125.041940696285-0.51873948723137
907702.58110.0745451812877.6759133498064-74.7274607143934-2.80126384317008
9179658006.0392658133472.005811418672249.5386178024729-0.762261426854444
928097.58088.7141728552472.33874776381853.468016236001590.0447520582235541
937947.58025.5332995040968.1085961044751-10.4878475147464-0.568431470235767
949227.58802.965384277990.245680358841271.05248065979532.97473293063835
9576808319.442493720272.3746581769191-353.716736192042-2.40479031200527
9678207809.1026354616754.3369926500251300.795565669235-2.44400115152435
9776357785.3441327248551.9402236030264-111.248080612252-0.331535872730529
987347.57580.4397504257643.8757058675172-105.982971849962-1.07074467601476
997177.57304.7387941301333.789816157607130.0441219651694-1.33025229068987
1006982.57099.2162065411426.25900038241781.97683280280159-1.00218631535104
10170757109.8430306833925.7687074473823-27.0650154706111-0.0655872938936936
10272307219.7714930483128.4033760680364-31.65668193554370.353056827842769
10371707174.7400511232626.106052574538731.7995891979927-0.307977653474792
1047022.57090.6254203770622.6582116138154-13.287289972498-0.462205031821818
1057087.57151.8947447938823.8660869245019-83.60403767727930.161906212837728
10674407246.1526059904726.0674786954105158.8349467694480.295104427622815
1077592.57633.3687065499437.3444335410613-220.3643004465041.51316791728332
1088297.57866.184914060443.4246016411119334.220292500450.819863543485335
1097852.57919.4654555884743.7299804210632-71.88869627867010.041723467775085
1108097.58079.4359387793847.3769793116031-39.45183525837690.485438363280367
1118022.58033.0081112039244.423638959127535.6852868918954-0.390829344851491
1128062.58066.1515713891844.06901048880311.93700401481591-0.0472314886892814
1137982.58055.9187097853542.3652645240366-46.4342380399158-0.227793343569029
11495408963.4739864593269.4770030109482146.4536329295173.62911712602861
1158172.58517.564336423753.335386006649-88.9320683611076-2.16118417368026
1168007.58237.3586884843542.8904317825085-64.1193288914091-1.39845768649353







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
18195.545116986678417.39256720261-221.847450215942
28559.152324601468468.7203330141490.4319915873277
38306.897649730858520.04809882566-213.150449094807
49093.676588289888571.37586463718522.300723652701
58688.638455591528622.703630448765.9348251428217
68768.044616988048674.0313962602294.0132207278185
78821.221812301138725.3591620717595.8626502293833
88771.764807941748776.68692788327-4.92211994152535
98592.712279994378828.01469369479-235.302413700421
109102.693348441348879.34245950631223.350888935024
118739.769822113578930.67022531784-190.900403204269
128756.226527011258981.99799112936-225.771464118112

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 8195.54511698667 & 8417.39256720261 & -221.847450215942 \tabularnewline
2 & 8559.15232460146 & 8468.72033301414 & 90.4319915873277 \tabularnewline
3 & 8306.89764973085 & 8520.04809882566 & -213.150449094807 \tabularnewline
4 & 9093.67658828988 & 8571.37586463718 & 522.300723652701 \tabularnewline
5 & 8688.63845559152 & 8622.7036304487 & 65.9348251428217 \tabularnewline
6 & 8768.04461698804 & 8674.03139626022 & 94.0132207278185 \tabularnewline
7 & 8821.22181230113 & 8725.35916207175 & 95.8626502293833 \tabularnewline
8 & 8771.76480794174 & 8776.68692788327 & -4.92211994152535 \tabularnewline
9 & 8592.71227999437 & 8828.01469369479 & -235.302413700421 \tabularnewline
10 & 9102.69334844134 & 8879.34245950631 & 223.350888935024 \tabularnewline
11 & 8739.76982211357 & 8930.67022531784 & -190.900403204269 \tabularnewline
12 & 8756.22652701125 & 8981.99799112936 & -225.771464118112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302266&T=2

[TABLE]
[ROW][C]Structural Time Series Model -- Extrapolation[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Seasonal[/C][/ROW]
[ROW][C]1[/C][C]8195.54511698667[/C][C]8417.39256720261[/C][C]-221.847450215942[/C][/ROW]
[ROW][C]2[/C][C]8559.15232460146[/C][C]8468.72033301414[/C][C]90.4319915873277[/C][/ROW]
[ROW][C]3[/C][C]8306.89764973085[/C][C]8520.04809882566[/C][C]-213.150449094807[/C][/ROW]
[ROW][C]4[/C][C]9093.67658828988[/C][C]8571.37586463718[/C][C]522.300723652701[/C][/ROW]
[ROW][C]5[/C][C]8688.63845559152[/C][C]8622.7036304487[/C][C]65.9348251428217[/C][/ROW]
[ROW][C]6[/C][C]8768.04461698804[/C][C]8674.03139626022[/C][C]94.0132207278185[/C][/ROW]
[ROW][C]7[/C][C]8821.22181230113[/C][C]8725.35916207175[/C][C]95.8626502293833[/C][/ROW]
[ROW][C]8[/C][C]8771.76480794174[/C][C]8776.68692788327[/C][C]-4.92211994152535[/C][/ROW]
[ROW][C]9[/C][C]8592.71227999437[/C][C]8828.01469369479[/C][C]-235.302413700421[/C][/ROW]
[ROW][C]10[/C][C]9102.69334844134[/C][C]8879.34245950631[/C][C]223.350888935024[/C][/ROW]
[ROW][C]11[/C][C]8739.76982211357[/C][C]8930.67022531784[/C][C]-190.900403204269[/C][/ROW]
[ROW][C]12[/C][C]8756.22652701125[/C][C]8981.99799112936[/C][C]-225.771464118112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302266&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302266&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
18195.545116986678417.39256720261-221.847450215942
28559.152324601468468.7203330141490.4319915873277
38306.897649730858520.04809882566-213.150449094807
49093.676588289888571.37586463718522.300723652701
58688.638455591528622.703630448765.9348251428217
68768.044616988048674.0313962602294.0132207278185
78821.221812301138725.3591620717595.8626502293833
88771.764807941748776.68692788327-4.92211994152535
98592.712279994378828.01469369479-235.302413700421
109102.693348441348879.34245950631223.350888935024
118739.769822113578930.67022531784-190.900403204269
128756.226527011258981.99799112936-225.771464118112



Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
R code (references can be found in the software module):
require('stsm')
require('stsm.class')
require('KFKSDS')
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
print(m$coef)
print(m$fitted)
print(m$resid)
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mm <- stsm.model(model = 'BSM', y = x, transPars = 'StructTS')
fit2 <- stsmFit(mm, stsm.method = 'maxlik.td.optim', method = par3, KF.args = list(P0cov = TRUE))
(fit2.comps <- tsSmooth(fit2, P0cov = FALSE)$states)
m2 <- set.pars(mm, pmax(fit2$par, .Machine$double.eps))
(ss <- char2numeric(m2))
(pred <- predict(ss, x, n.ahead = par2))
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()
bitmap(file='test6.png')
par(mfrow = c(3,1), mar = c(3,3,3,3))
plot(cbind(x, pred$pred), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred + 2 * pred$se, rev(pred$pred)), col = 'gray85', border = NA)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred - 2 * pred$se, rev(pred$pred)), col = ' gray85', border = NA)
lines(pred$pred, col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the observed series', side = 3, adj = 0)
plot(cbind(x, pred$a[,1]), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] + 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] - 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = ' gray85', border = NA)
lines(pred$a[,1], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the level component', side = 3, adj = 0)
plot(cbind(fit2.comps[,3], pred$a[,3]), type = 'n', plot.type = 'single', ylab = '')
lines(fit2.comps[,3])
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] + 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] - 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = ' gray85', border = NA)
lines(pred$a[,3], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the seasonal component', side = 3, adj = 0)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Interpolation',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')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Extrapolation',4,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,'Seasonal',header=TRUE)
a<-table.row.end(a)
for (i in 1:par2) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,pred$pred[i])
a<-table.element(a,pred$a[i,1])
a<-table.element(a,pred$a[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')