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Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationTue, 13 Dec 2016 21:40:57 +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/13/t14816616753a5alt6dfhvmepv.htm/, Retrieved Sun, 05 May 2024 01:17:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299226, Retrieved Sun, 05 May 2024 01:17:00 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
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...] [2016-12-13 20:40:57] [130d73899007e5ff8a4f636b9bcfb397] [Current]
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Dataseries X:
2650.84
2685.28
2706.04
2743.34
2768.48
2756.38
2788.68
2828.58
2853.18
2859
2900.32
2884.46
2884.3
2910.86
2916.62
2921.6
2926.58
2938.46
2942.92
2956.92
2946.78
2956.48
2968.1
2983.1
2993.04
3007.44
3024.64
3033.04
3047.94
3066.02
3096.46
3131.16
3133.54
3118.68
3133.5
3108.9
3136.04
3129.3
3136.1
3143.72
3199.24
3205.78
3191.44
3172.72
3211.92
3268.38
3289.52
3316.28
3348.6
3400.44
3425.68
3456.3
3454.46
3514.48
3546
3596.3
3616.2
3598.08
3595.28
3610.7
3628.74
3641.84
3637.66
3661.64
3686.56
3718.38
3728.88
3723.42
3726.34
3764.84
3782.26
3771.32
3766.66
3774.6
3795.42
3829.48
3873.62
3856.16
3875.42
3893.52
3918.86
3918.24
3942.22
3938.7
3997.98
3997.54
3973.24
3946.4
3937.48
3920.12
3940.74
3948.68
3935.74
3958.58
3975.44
4029.24
4013.44
4030.02
4032.04
4032.48
4020.54
4093.42
4098.18




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299226&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299226&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 time4 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
12650.842650.84000
22685.282682.705941510181.807607325838271.779155257140890.648883433859255
32706.042702.872055593562.038598447765691.922284400156740.615079940429743
42743.342738.941877193252.45142690711792.082408704070021.14027313661372
52768.482764.711120712182.786442321158742.1860863595980.780184420344653
62756.382755.08815768322.579170017078652.13199274661077-0.414612036737081
72788.682784.613138596163.090208683892812.247182379289620.899040139435979
82828.582823.753461708233.852230699485532.398005082715481.20118357144629
92853.182849.239659024664.354442981103022.486397873406220.719902637692031
1028592856.319965860284.423107594436822.497252786753750.0905937373344082
112900.322895.371621744415.360266059628762.63139415040711.14949599676841
122884.462883.074074297274.851153009187682.5649768443619-0.585481142103571
132884.32903.595523526314.68843160474579-20.33371794316960.626602799595264
142910.862908.962321537794.721345657062721.865358540779960.0190167915545479
152916.622914.685216636464.754551793935551.86842506812320.0330609258091417
162921.62919.713022049774.763723288631341.868868541547340.00901524638636851
172926.582924.696279073314.771375547153261.869193602003090.00723663636489267
182938.462936.140402973265.012365312566171.87867880080580.219782499671314
192942.922941.048354100695.008472080277071.87853597427611-0.00343656305892792
202956.922954.475557223825.331499882575161.889607778703330.27689186433656
212946.782945.828244791064.78114363960881.87195068467895-0.459466547477986
222956.482954.357071606484.932148202607741.876492949342260.123108164622251
232968.12965.788978304915.199553636539671.884045323573980.213393319188459
242983.12980.576048459185.601457516001761.894716598435310.314606363750249
252993.043007.3850371056.24515224299809-15.7213252148650.765784989833344
263007.443006.506774285335.886075428996971.31695459774881-0.212056029358025
273024.643022.636777079356.338175313113281.333045197190740.335650220261481
283033.043031.537658394226.451635347275321.334680685178360.0839333284960258
293047.943046.07233914916.813436116971771.339160352644070.264639199324635
303066.023063.951878968167.31391658262131.344975554024930.362193772550622
313096.463093.642290833618.335452608306241.356190403200190.732179141139968
323131.163128.086801816289.537505463717641.368670891647650.854094391460507
333133.543132.507566944849.300129563390871.36633891222724-0.16734274238546
343118.683118.822996852918.226465087537091.3563546459997-0.751553468646264
353133.53131.829932865198.451160646615731.358333262389730.156281391577358
363108.93109.556679392596.998922689457331.34621981049816-1.00425283443475
373136.043144.522585524638.19675104173547-10.28585678713120.975236806011448
383129.33129.922737650187.04052931673820.672933171792874-0.696649235644294
393136.13135.522268190976.971267257927460.671571990459087-0.0470865003443133
403143.723143.014375828236.996305307001180.671707050793780.0170134318215299
413199.243195.591350434019.194477267816180.681082223709551.48869913039059
423205.783205.079729734269.208694501308460.6811389646643430.00959809152316599
433191.443192.200477548198.137238413929840.677085973659302-0.721270945676944
443172.723173.776027052946.845532273543690.67245022162298-0.867287625259211
453211.923209.372111081418.24685092203190.6772225448808150.938687911238179
463268.383264.6365093492410.54319735791080.6846445119000421.53498983262749
473289.523287.9994985123211.17047316631530.6865688190481080.418504032029687
483316.283314.5883581972911.92615414017090.6887693604923970.503307213038325
493348.63351.5108128950713.103561917638-4.520860335103540.857032256713392
503400.443397.7856276719814.77594992890740.7114817909220381.02871140867378
513425.683424.2038969778515.34968114427320.7190391913970160.38008136762507
523456.33454.6009306732116.09093865826140.7206483249469540.4911025285434
533454.463454.7752992501715.30614184879310.719551536791787-0.519438282052465
543514.483511.0916304947917.33006056292330.7221513276239631.33832689701835
5535463544.2480219076118.11175815092370.7231027559382790.51646233428074
563596.33593.5476702068819.65334158244960.7248844065970181.01773224651673
573616.23615.3362019945719.75895245841720.7250003270749680.0696745587405355
583598.083599.6601876291718.00520627977220.723172087333311-1.15627385508407
593595.283595.9682147692116.9307840735060.722108263178394-0.707984551051291
603610.73610.1562909815616.79490107884960.721980472123255-0.0894937336801046
613628.743635.3195271484417.2020476001573-7.11884024570220.284097958576094
623641.843641.9060213553316.67007248135610.567723494809795-0.332296710280832
633637.663638.4127697029815.66930818346480.557805769041251-0.658058847630342
643661.643660.6547372331515.99543519401360.5580895958209150.214453232639686
653686.563685.4311189035516.43124779962270.558210782674350.286494830030973
663718.383716.8477421947517.17519498799110.5583810894782120.488920853465104
673728.883728.6695777972916.90936346167720.55832388198262-0.174660174269805
683723.423724.2481128527415.8499068504830.558107449162608-0.695940538136781
693726.343726.6555911371315.18211784672830.557977861033552-0.438570447293844
703764.843762.9122917415816.22924203337710.5581708950948280.687571847084745
713782.263781.5455819619116.3487102771080.5581918170978830.0784332081906119
723771.323772.4175984890315.08247139461840.557981155647733-0.831185198811925
733766.663774.679043335614.4509910052501-7.19204378161173-0.432437080463682
743774.63774.8978729417113.74051891614980.562986204574607-0.448368480289763
753795.423794.4753481051314.03080073743020.5653141909022480.190475030585031
763829.483827.6691201833514.98367028673190.5656147102704180.625194040185439
773873.623871.199623272616.40324991310740.5653744822653520.93131883622793
783856.163857.5473667590614.90852986234730.565659785805348-0.980534787345987
793875.423874.7080170099215.02054029608250.5656392577860430.0734733432061382
803893.523892.75756163515.17119921497160.5656130077464770.0988183181284377
813918.863917.662000875815.65534676539280.5655328635381280.317537071811014
823918.243918.6288113905114.92467602284970.565647773364586-0.479198029560763
833942.223941.1601311649515.30308109339690.5655912362987940.248158491302398
843938.73939.2526242022514.44687513334510.565712769901021-0.561476239687106
853997.983998.188879730916.649211782132-3.081004757214181.49361857917062
863997.543998.3580446258415.82824377051190.188331399200654-0.521609042495057
873973.243975.5739749974913.90696611297430.17527924830516-1.25995218256419
883946.43948.8641402534711.88604698375940.175131498343647-1.32508678542139
893937.483938.7350056774910.79064385792970.175504189694817-0.718210058691022
903920.123921.748896639519.408532916735040.17598730282746-0.906171039665926
913940.743939.990220555059.848042481793470.1758406044892840.28815538557534
923948.683948.585539335799.785707221754720.17586037812628-0.0408680774475675
933935.743936.95538230738.720040461226530.176181545905575-0.698658026327677
943958.583957.627372849289.314786037446650.1760112553648320.389913215475657
953975.443974.756343109749.703636034590070.1759054787065170.254925317895312
964029.244026.3431417609911.7878550645490.1753668372440081.36637193222906
974013.444017.9244704789610.785345346098-3.17904665312352-0.67601851417201
984030.024029.6673653887110.83299687021870.2937348923899070.0304148498888912
994032.044032.2827116308210.42404753068740.291308722410381-0.268140591105925
1004032.484032.83042743689.932552289649290.29132459618641-0.322203011279981
1014020.544021.621951958568.880464143459140.291739729105971-0.689686753687501
1024093.424089.3083629882911.80697287851950.2905742668052651.91843400916488
1034098.184098.0861945928711.65622525610640.29063152906519-0.0988201443441129

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 2650.84 & 2650.84 & 0 & 0 & 0 \tabularnewline
2 & 2685.28 & 2682.70594151018 & 1.80760732583827 & 1.77915525714089 & 0.648883433859255 \tabularnewline
3 & 2706.04 & 2702.87205559356 & 2.03859844776569 & 1.92228440015674 & 0.615079940429743 \tabularnewline
4 & 2743.34 & 2738.94187719325 & 2.4514269071179 & 2.08240870407002 & 1.14027313661372 \tabularnewline
5 & 2768.48 & 2764.71112071218 & 2.78644232115874 & 2.186086359598 & 0.780184420344653 \tabularnewline
6 & 2756.38 & 2755.0881576832 & 2.57917001707865 & 2.13199274661077 & -0.414612036737081 \tabularnewline
7 & 2788.68 & 2784.61313859616 & 3.09020868389281 & 2.24718237928962 & 0.899040139435979 \tabularnewline
8 & 2828.58 & 2823.75346170823 & 3.85223069948553 & 2.39800508271548 & 1.20118357144629 \tabularnewline
9 & 2853.18 & 2849.23965902466 & 4.35444298110302 & 2.48639787340622 & 0.719902637692031 \tabularnewline
10 & 2859 & 2856.31996586028 & 4.42310759443682 & 2.49725278675375 & 0.0905937373344082 \tabularnewline
11 & 2900.32 & 2895.37162174441 & 5.36026605962876 & 2.6313941504071 & 1.14949599676841 \tabularnewline
12 & 2884.46 & 2883.07407429727 & 4.85115300918768 & 2.5649768443619 & -0.585481142103571 \tabularnewline
13 & 2884.3 & 2903.59552352631 & 4.68843160474579 & -20.3337179431696 & 0.626602799595264 \tabularnewline
14 & 2910.86 & 2908.96232153779 & 4.72134565706272 & 1.86535854077996 & 0.0190167915545479 \tabularnewline
15 & 2916.62 & 2914.68521663646 & 4.75455179393555 & 1.8684250681232 & 0.0330609258091417 \tabularnewline
16 & 2921.6 & 2919.71302204977 & 4.76372328863134 & 1.86886854154734 & 0.00901524638636851 \tabularnewline
17 & 2926.58 & 2924.69627907331 & 4.77137554715326 & 1.86919360200309 & 0.00723663636489267 \tabularnewline
18 & 2938.46 & 2936.14040297326 & 5.01236531256617 & 1.8786788008058 & 0.219782499671314 \tabularnewline
19 & 2942.92 & 2941.04835410069 & 5.00847208027707 & 1.87853597427611 & -0.00343656305892792 \tabularnewline
20 & 2956.92 & 2954.47555722382 & 5.33149988257516 & 1.88960777870333 & 0.27689186433656 \tabularnewline
21 & 2946.78 & 2945.82824479106 & 4.7811436396088 & 1.87195068467895 & -0.459466547477986 \tabularnewline
22 & 2956.48 & 2954.35707160648 & 4.93214820260774 & 1.87649294934226 & 0.123108164622251 \tabularnewline
23 & 2968.1 & 2965.78897830491 & 5.19955363653967 & 1.88404532357398 & 0.213393319188459 \tabularnewline
24 & 2983.1 & 2980.57604845918 & 5.60145751600176 & 1.89471659843531 & 0.314606363750249 \tabularnewline
25 & 2993.04 & 3007.385037105 & 6.24515224299809 & -15.721325214865 & 0.765784989833344 \tabularnewline
26 & 3007.44 & 3006.50677428533 & 5.88607542899697 & 1.31695459774881 & -0.212056029358025 \tabularnewline
27 & 3024.64 & 3022.63677707935 & 6.33817531311328 & 1.33304519719074 & 0.335650220261481 \tabularnewline
28 & 3033.04 & 3031.53765839422 & 6.45163534727532 & 1.33468068517836 & 0.0839333284960258 \tabularnewline
29 & 3047.94 & 3046.0723391491 & 6.81343611697177 & 1.33916035264407 & 0.264639199324635 \tabularnewline
30 & 3066.02 & 3063.95187896816 & 7.3139165826213 & 1.34497555402493 & 0.362193772550622 \tabularnewline
31 & 3096.46 & 3093.64229083361 & 8.33545260830624 & 1.35619040320019 & 0.732179141139968 \tabularnewline
32 & 3131.16 & 3128.08680181628 & 9.53750546371764 & 1.36867089164765 & 0.854094391460507 \tabularnewline
33 & 3133.54 & 3132.50756694484 & 9.30012956339087 & 1.36633891222724 & -0.16734274238546 \tabularnewline
34 & 3118.68 & 3118.82299685291 & 8.22646508753709 & 1.3563546459997 & -0.751553468646264 \tabularnewline
35 & 3133.5 & 3131.82993286519 & 8.45116064661573 & 1.35833326238973 & 0.156281391577358 \tabularnewline
36 & 3108.9 & 3109.55667939259 & 6.99892268945733 & 1.34621981049816 & -1.00425283443475 \tabularnewline
37 & 3136.04 & 3144.52258552463 & 8.19675104173547 & -10.2858567871312 & 0.975236806011448 \tabularnewline
38 & 3129.3 & 3129.92273765018 & 7.0405293167382 & 0.672933171792874 & -0.696649235644294 \tabularnewline
39 & 3136.1 & 3135.52226819097 & 6.97126725792746 & 0.671571990459087 & -0.0470865003443133 \tabularnewline
40 & 3143.72 & 3143.01437582823 & 6.99630530700118 & 0.67170705079378 & 0.0170134318215299 \tabularnewline
41 & 3199.24 & 3195.59135043401 & 9.19447726781618 & 0.68108222370955 & 1.48869913039059 \tabularnewline
42 & 3205.78 & 3205.07972973426 & 9.20869450130846 & 0.681138964664343 & 0.00959809152316599 \tabularnewline
43 & 3191.44 & 3192.20047754819 & 8.13723841392984 & 0.677085973659302 & -0.721270945676944 \tabularnewline
44 & 3172.72 & 3173.77602705294 & 6.84553227354369 & 0.67245022162298 & -0.867287625259211 \tabularnewline
45 & 3211.92 & 3209.37211108141 & 8.2468509220319 & 0.677222544880815 & 0.938687911238179 \tabularnewline
46 & 3268.38 & 3264.63650934924 & 10.5431973579108 & 0.684644511900042 & 1.53498983262749 \tabularnewline
47 & 3289.52 & 3287.99949851232 & 11.1704731663153 & 0.686568819048108 & 0.418504032029687 \tabularnewline
48 & 3316.28 & 3314.58835819729 & 11.9261541401709 & 0.688769360492397 & 0.503307213038325 \tabularnewline
49 & 3348.6 & 3351.51081289507 & 13.103561917638 & -4.52086033510354 & 0.857032256713392 \tabularnewline
50 & 3400.44 & 3397.78562767198 & 14.7759499289074 & 0.711481790922038 & 1.02871140867378 \tabularnewline
51 & 3425.68 & 3424.20389697785 & 15.3496811442732 & 0.719039191397016 & 0.38008136762507 \tabularnewline
52 & 3456.3 & 3454.60093067321 & 16.0909386582614 & 0.720648324946954 & 0.4911025285434 \tabularnewline
53 & 3454.46 & 3454.77529925017 & 15.3061418487931 & 0.719551536791787 & -0.519438282052465 \tabularnewline
54 & 3514.48 & 3511.09163049479 & 17.3300605629233 & 0.722151327623963 & 1.33832689701835 \tabularnewline
55 & 3546 & 3544.24802190761 & 18.1117581509237 & 0.723102755938279 & 0.51646233428074 \tabularnewline
56 & 3596.3 & 3593.54767020688 & 19.6533415824496 & 0.724884406597018 & 1.01773224651673 \tabularnewline
57 & 3616.2 & 3615.33620199457 & 19.7589524584172 & 0.725000327074968 & 0.0696745587405355 \tabularnewline
58 & 3598.08 & 3599.66018762917 & 18.0052062797722 & 0.723172087333311 & -1.15627385508407 \tabularnewline
59 & 3595.28 & 3595.96821476921 & 16.930784073506 & 0.722108263178394 & -0.707984551051291 \tabularnewline
60 & 3610.7 & 3610.15629098156 & 16.7949010788496 & 0.721980472123255 & -0.0894937336801046 \tabularnewline
61 & 3628.74 & 3635.31952714844 & 17.2020476001573 & -7.1188402457022 & 0.284097958576094 \tabularnewline
62 & 3641.84 & 3641.90602135533 & 16.6700724813561 & 0.567723494809795 & -0.332296710280832 \tabularnewline
63 & 3637.66 & 3638.41276970298 & 15.6693081834648 & 0.557805769041251 & -0.658058847630342 \tabularnewline
64 & 3661.64 & 3660.65473723315 & 15.9954351940136 & 0.558089595820915 & 0.214453232639686 \tabularnewline
65 & 3686.56 & 3685.43111890355 & 16.4312477996227 & 0.55821078267435 & 0.286494830030973 \tabularnewline
66 & 3718.38 & 3716.84774219475 & 17.1751949879911 & 0.558381089478212 & 0.488920853465104 \tabularnewline
67 & 3728.88 & 3728.66957779729 & 16.9093634616772 & 0.55832388198262 & -0.174660174269805 \tabularnewline
68 & 3723.42 & 3724.24811285274 & 15.849906850483 & 0.558107449162608 & -0.695940538136781 \tabularnewline
69 & 3726.34 & 3726.65559113713 & 15.1821178467283 & 0.557977861033552 & -0.438570447293844 \tabularnewline
70 & 3764.84 & 3762.91229174158 & 16.2292420333771 & 0.558170895094828 & 0.687571847084745 \tabularnewline
71 & 3782.26 & 3781.54558196191 & 16.348710277108 & 0.558191817097883 & 0.0784332081906119 \tabularnewline
72 & 3771.32 & 3772.41759848903 & 15.0824713946184 & 0.557981155647733 & -0.831185198811925 \tabularnewline
73 & 3766.66 & 3774.6790433356 & 14.4509910052501 & -7.19204378161173 & -0.432437080463682 \tabularnewline
74 & 3774.6 & 3774.89787294171 & 13.7405189161498 & 0.562986204574607 & -0.448368480289763 \tabularnewline
75 & 3795.42 & 3794.47534810513 & 14.0308007374302 & 0.565314190902248 & 0.190475030585031 \tabularnewline
76 & 3829.48 & 3827.66912018335 & 14.9836702867319 & 0.565614710270418 & 0.625194040185439 \tabularnewline
77 & 3873.62 & 3871.1996232726 & 16.4032499131074 & 0.565374482265352 & 0.93131883622793 \tabularnewline
78 & 3856.16 & 3857.54736675906 & 14.9085298623473 & 0.565659785805348 & -0.980534787345987 \tabularnewline
79 & 3875.42 & 3874.70801700992 & 15.0205402960825 & 0.565639257786043 & 0.0734733432061382 \tabularnewline
80 & 3893.52 & 3892.757561635 & 15.1711992149716 & 0.565613007746477 & 0.0988183181284377 \tabularnewline
81 & 3918.86 & 3917.6620008758 & 15.6553467653928 & 0.565532863538128 & 0.317537071811014 \tabularnewline
82 & 3918.24 & 3918.62881139051 & 14.9246760228497 & 0.565647773364586 & -0.479198029560763 \tabularnewline
83 & 3942.22 & 3941.16013116495 & 15.3030810933969 & 0.565591236298794 & 0.248158491302398 \tabularnewline
84 & 3938.7 & 3939.25262420225 & 14.4468751333451 & 0.565712769901021 & -0.561476239687106 \tabularnewline
85 & 3997.98 & 3998.1888797309 & 16.649211782132 & -3.08100475721418 & 1.49361857917062 \tabularnewline
86 & 3997.54 & 3998.35804462584 & 15.8282437705119 & 0.188331399200654 & -0.521609042495057 \tabularnewline
87 & 3973.24 & 3975.57397499749 & 13.9069661129743 & 0.17527924830516 & -1.25995218256419 \tabularnewline
88 & 3946.4 & 3948.86414025347 & 11.8860469837594 & 0.175131498343647 & -1.32508678542139 \tabularnewline
89 & 3937.48 & 3938.73500567749 & 10.7906438579297 & 0.175504189694817 & -0.718210058691022 \tabularnewline
90 & 3920.12 & 3921.74889663951 & 9.40853291673504 & 0.17598730282746 & -0.906171039665926 \tabularnewline
91 & 3940.74 & 3939.99022055505 & 9.84804248179347 & 0.175840604489284 & 0.28815538557534 \tabularnewline
92 & 3948.68 & 3948.58553933579 & 9.78570722175472 & 0.17586037812628 & -0.0408680774475675 \tabularnewline
93 & 3935.74 & 3936.9553823073 & 8.72004046122653 & 0.176181545905575 & -0.698658026327677 \tabularnewline
94 & 3958.58 & 3957.62737284928 & 9.31478603744665 & 0.176011255364832 & 0.389913215475657 \tabularnewline
95 & 3975.44 & 3974.75634310974 & 9.70363603459007 & 0.175905478706517 & 0.254925317895312 \tabularnewline
96 & 4029.24 & 4026.34314176099 & 11.787855064549 & 0.175366837244008 & 1.36637193222906 \tabularnewline
97 & 4013.44 & 4017.92447047896 & 10.785345346098 & -3.17904665312352 & -0.67601851417201 \tabularnewline
98 & 4030.02 & 4029.66736538871 & 10.8329968702187 & 0.293734892389907 & 0.0304148498888912 \tabularnewline
99 & 4032.04 & 4032.28271163082 & 10.4240475306874 & 0.291308722410381 & -0.268140591105925 \tabularnewline
100 & 4032.48 & 4032.8304274368 & 9.93255228964929 & 0.29132459618641 & -0.322203011279981 \tabularnewline
101 & 4020.54 & 4021.62195195856 & 8.88046414345914 & 0.291739729105971 & -0.689686753687501 \tabularnewline
102 & 4093.42 & 4089.30836298829 & 11.8069728785195 & 0.290574266805265 & 1.91843400916488 \tabularnewline
103 & 4098.18 & 4098.08619459287 & 11.6562252561064 & 0.29063152906519 & -0.0988201443441129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299226&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]2650.84[/C][C]2650.84[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]2685.28[/C][C]2682.70594151018[/C][C]1.80760732583827[/C][C]1.77915525714089[/C][C]0.648883433859255[/C][/ROW]
[ROW][C]3[/C][C]2706.04[/C][C]2702.87205559356[/C][C]2.03859844776569[/C][C]1.92228440015674[/C][C]0.615079940429743[/C][/ROW]
[ROW][C]4[/C][C]2743.34[/C][C]2738.94187719325[/C][C]2.4514269071179[/C][C]2.08240870407002[/C][C]1.14027313661372[/C][/ROW]
[ROW][C]5[/C][C]2768.48[/C][C]2764.71112071218[/C][C]2.78644232115874[/C][C]2.186086359598[/C][C]0.780184420344653[/C][/ROW]
[ROW][C]6[/C][C]2756.38[/C][C]2755.0881576832[/C][C]2.57917001707865[/C][C]2.13199274661077[/C][C]-0.414612036737081[/C][/ROW]
[ROW][C]7[/C][C]2788.68[/C][C]2784.61313859616[/C][C]3.09020868389281[/C][C]2.24718237928962[/C][C]0.899040139435979[/C][/ROW]
[ROW][C]8[/C][C]2828.58[/C][C]2823.75346170823[/C][C]3.85223069948553[/C][C]2.39800508271548[/C][C]1.20118357144629[/C][/ROW]
[ROW][C]9[/C][C]2853.18[/C][C]2849.23965902466[/C][C]4.35444298110302[/C][C]2.48639787340622[/C][C]0.719902637692031[/C][/ROW]
[ROW][C]10[/C][C]2859[/C][C]2856.31996586028[/C][C]4.42310759443682[/C][C]2.49725278675375[/C][C]0.0905937373344082[/C][/ROW]
[ROW][C]11[/C][C]2900.32[/C][C]2895.37162174441[/C][C]5.36026605962876[/C][C]2.6313941504071[/C][C]1.14949599676841[/C][/ROW]
[ROW][C]12[/C][C]2884.46[/C][C]2883.07407429727[/C][C]4.85115300918768[/C][C]2.5649768443619[/C][C]-0.585481142103571[/C][/ROW]
[ROW][C]13[/C][C]2884.3[/C][C]2903.59552352631[/C][C]4.68843160474579[/C][C]-20.3337179431696[/C][C]0.626602799595264[/C][/ROW]
[ROW][C]14[/C][C]2910.86[/C][C]2908.96232153779[/C][C]4.72134565706272[/C][C]1.86535854077996[/C][C]0.0190167915545479[/C][/ROW]
[ROW][C]15[/C][C]2916.62[/C][C]2914.68521663646[/C][C]4.75455179393555[/C][C]1.8684250681232[/C][C]0.0330609258091417[/C][/ROW]
[ROW][C]16[/C][C]2921.6[/C][C]2919.71302204977[/C][C]4.76372328863134[/C][C]1.86886854154734[/C][C]0.00901524638636851[/C][/ROW]
[ROW][C]17[/C][C]2926.58[/C][C]2924.69627907331[/C][C]4.77137554715326[/C][C]1.86919360200309[/C][C]0.00723663636489267[/C][/ROW]
[ROW][C]18[/C][C]2938.46[/C][C]2936.14040297326[/C][C]5.01236531256617[/C][C]1.8786788008058[/C][C]0.219782499671314[/C][/ROW]
[ROW][C]19[/C][C]2942.92[/C][C]2941.04835410069[/C][C]5.00847208027707[/C][C]1.87853597427611[/C][C]-0.00343656305892792[/C][/ROW]
[ROW][C]20[/C][C]2956.92[/C][C]2954.47555722382[/C][C]5.33149988257516[/C][C]1.88960777870333[/C][C]0.27689186433656[/C][/ROW]
[ROW][C]21[/C][C]2946.78[/C][C]2945.82824479106[/C][C]4.7811436396088[/C][C]1.87195068467895[/C][C]-0.459466547477986[/C][/ROW]
[ROW][C]22[/C][C]2956.48[/C][C]2954.35707160648[/C][C]4.93214820260774[/C][C]1.87649294934226[/C][C]0.123108164622251[/C][/ROW]
[ROW][C]23[/C][C]2968.1[/C][C]2965.78897830491[/C][C]5.19955363653967[/C][C]1.88404532357398[/C][C]0.213393319188459[/C][/ROW]
[ROW][C]24[/C][C]2983.1[/C][C]2980.57604845918[/C][C]5.60145751600176[/C][C]1.89471659843531[/C][C]0.314606363750249[/C][/ROW]
[ROW][C]25[/C][C]2993.04[/C][C]3007.385037105[/C][C]6.24515224299809[/C][C]-15.721325214865[/C][C]0.765784989833344[/C][/ROW]
[ROW][C]26[/C][C]3007.44[/C][C]3006.50677428533[/C][C]5.88607542899697[/C][C]1.31695459774881[/C][C]-0.212056029358025[/C][/ROW]
[ROW][C]27[/C][C]3024.64[/C][C]3022.63677707935[/C][C]6.33817531311328[/C][C]1.33304519719074[/C][C]0.335650220261481[/C][/ROW]
[ROW][C]28[/C][C]3033.04[/C][C]3031.53765839422[/C][C]6.45163534727532[/C][C]1.33468068517836[/C][C]0.0839333284960258[/C][/ROW]
[ROW][C]29[/C][C]3047.94[/C][C]3046.0723391491[/C][C]6.81343611697177[/C][C]1.33916035264407[/C][C]0.264639199324635[/C][/ROW]
[ROW][C]30[/C][C]3066.02[/C][C]3063.95187896816[/C][C]7.3139165826213[/C][C]1.34497555402493[/C][C]0.362193772550622[/C][/ROW]
[ROW][C]31[/C][C]3096.46[/C][C]3093.64229083361[/C][C]8.33545260830624[/C][C]1.35619040320019[/C][C]0.732179141139968[/C][/ROW]
[ROW][C]32[/C][C]3131.16[/C][C]3128.08680181628[/C][C]9.53750546371764[/C][C]1.36867089164765[/C][C]0.854094391460507[/C][/ROW]
[ROW][C]33[/C][C]3133.54[/C][C]3132.50756694484[/C][C]9.30012956339087[/C][C]1.36633891222724[/C][C]-0.16734274238546[/C][/ROW]
[ROW][C]34[/C][C]3118.68[/C][C]3118.82299685291[/C][C]8.22646508753709[/C][C]1.3563546459997[/C][C]-0.751553468646264[/C][/ROW]
[ROW][C]35[/C][C]3133.5[/C][C]3131.82993286519[/C][C]8.45116064661573[/C][C]1.35833326238973[/C][C]0.156281391577358[/C][/ROW]
[ROW][C]36[/C][C]3108.9[/C][C]3109.55667939259[/C][C]6.99892268945733[/C][C]1.34621981049816[/C][C]-1.00425283443475[/C][/ROW]
[ROW][C]37[/C][C]3136.04[/C][C]3144.52258552463[/C][C]8.19675104173547[/C][C]-10.2858567871312[/C][C]0.975236806011448[/C][/ROW]
[ROW][C]38[/C][C]3129.3[/C][C]3129.92273765018[/C][C]7.0405293167382[/C][C]0.672933171792874[/C][C]-0.696649235644294[/C][/ROW]
[ROW][C]39[/C][C]3136.1[/C][C]3135.52226819097[/C][C]6.97126725792746[/C][C]0.671571990459087[/C][C]-0.0470865003443133[/C][/ROW]
[ROW][C]40[/C][C]3143.72[/C][C]3143.01437582823[/C][C]6.99630530700118[/C][C]0.67170705079378[/C][C]0.0170134318215299[/C][/ROW]
[ROW][C]41[/C][C]3199.24[/C][C]3195.59135043401[/C][C]9.19447726781618[/C][C]0.68108222370955[/C][C]1.48869913039059[/C][/ROW]
[ROW][C]42[/C][C]3205.78[/C][C]3205.07972973426[/C][C]9.20869450130846[/C][C]0.681138964664343[/C][C]0.00959809152316599[/C][/ROW]
[ROW][C]43[/C][C]3191.44[/C][C]3192.20047754819[/C][C]8.13723841392984[/C][C]0.677085973659302[/C][C]-0.721270945676944[/C][/ROW]
[ROW][C]44[/C][C]3172.72[/C][C]3173.77602705294[/C][C]6.84553227354369[/C][C]0.67245022162298[/C][C]-0.867287625259211[/C][/ROW]
[ROW][C]45[/C][C]3211.92[/C][C]3209.37211108141[/C][C]8.2468509220319[/C][C]0.677222544880815[/C][C]0.938687911238179[/C][/ROW]
[ROW][C]46[/C][C]3268.38[/C][C]3264.63650934924[/C][C]10.5431973579108[/C][C]0.684644511900042[/C][C]1.53498983262749[/C][/ROW]
[ROW][C]47[/C][C]3289.52[/C][C]3287.99949851232[/C][C]11.1704731663153[/C][C]0.686568819048108[/C][C]0.418504032029687[/C][/ROW]
[ROW][C]48[/C][C]3316.28[/C][C]3314.58835819729[/C][C]11.9261541401709[/C][C]0.688769360492397[/C][C]0.503307213038325[/C][/ROW]
[ROW][C]49[/C][C]3348.6[/C][C]3351.51081289507[/C][C]13.103561917638[/C][C]-4.52086033510354[/C][C]0.857032256713392[/C][/ROW]
[ROW][C]50[/C][C]3400.44[/C][C]3397.78562767198[/C][C]14.7759499289074[/C][C]0.711481790922038[/C][C]1.02871140867378[/C][/ROW]
[ROW][C]51[/C][C]3425.68[/C][C]3424.20389697785[/C][C]15.3496811442732[/C][C]0.719039191397016[/C][C]0.38008136762507[/C][/ROW]
[ROW][C]52[/C][C]3456.3[/C][C]3454.60093067321[/C][C]16.0909386582614[/C][C]0.720648324946954[/C][C]0.4911025285434[/C][/ROW]
[ROW][C]53[/C][C]3454.46[/C][C]3454.77529925017[/C][C]15.3061418487931[/C][C]0.719551536791787[/C][C]-0.519438282052465[/C][/ROW]
[ROW][C]54[/C][C]3514.48[/C][C]3511.09163049479[/C][C]17.3300605629233[/C][C]0.722151327623963[/C][C]1.33832689701835[/C][/ROW]
[ROW][C]55[/C][C]3546[/C][C]3544.24802190761[/C][C]18.1117581509237[/C][C]0.723102755938279[/C][C]0.51646233428074[/C][/ROW]
[ROW][C]56[/C][C]3596.3[/C][C]3593.54767020688[/C][C]19.6533415824496[/C][C]0.724884406597018[/C][C]1.01773224651673[/C][/ROW]
[ROW][C]57[/C][C]3616.2[/C][C]3615.33620199457[/C][C]19.7589524584172[/C][C]0.725000327074968[/C][C]0.0696745587405355[/C][/ROW]
[ROW][C]58[/C][C]3598.08[/C][C]3599.66018762917[/C][C]18.0052062797722[/C][C]0.723172087333311[/C][C]-1.15627385508407[/C][/ROW]
[ROW][C]59[/C][C]3595.28[/C][C]3595.96821476921[/C][C]16.930784073506[/C][C]0.722108263178394[/C][C]-0.707984551051291[/C][/ROW]
[ROW][C]60[/C][C]3610.7[/C][C]3610.15629098156[/C][C]16.7949010788496[/C][C]0.721980472123255[/C][C]-0.0894937336801046[/C][/ROW]
[ROW][C]61[/C][C]3628.74[/C][C]3635.31952714844[/C][C]17.2020476001573[/C][C]-7.1188402457022[/C][C]0.284097958576094[/C][/ROW]
[ROW][C]62[/C][C]3641.84[/C][C]3641.90602135533[/C][C]16.6700724813561[/C][C]0.567723494809795[/C][C]-0.332296710280832[/C][/ROW]
[ROW][C]63[/C][C]3637.66[/C][C]3638.41276970298[/C][C]15.6693081834648[/C][C]0.557805769041251[/C][C]-0.658058847630342[/C][/ROW]
[ROW][C]64[/C][C]3661.64[/C][C]3660.65473723315[/C][C]15.9954351940136[/C][C]0.558089595820915[/C][C]0.214453232639686[/C][/ROW]
[ROW][C]65[/C][C]3686.56[/C][C]3685.43111890355[/C][C]16.4312477996227[/C][C]0.55821078267435[/C][C]0.286494830030973[/C][/ROW]
[ROW][C]66[/C][C]3718.38[/C][C]3716.84774219475[/C][C]17.1751949879911[/C][C]0.558381089478212[/C][C]0.488920853465104[/C][/ROW]
[ROW][C]67[/C][C]3728.88[/C][C]3728.66957779729[/C][C]16.9093634616772[/C][C]0.55832388198262[/C][C]-0.174660174269805[/C][/ROW]
[ROW][C]68[/C][C]3723.42[/C][C]3724.24811285274[/C][C]15.849906850483[/C][C]0.558107449162608[/C][C]-0.695940538136781[/C][/ROW]
[ROW][C]69[/C][C]3726.34[/C][C]3726.65559113713[/C][C]15.1821178467283[/C][C]0.557977861033552[/C][C]-0.438570447293844[/C][/ROW]
[ROW][C]70[/C][C]3764.84[/C][C]3762.91229174158[/C][C]16.2292420333771[/C][C]0.558170895094828[/C][C]0.687571847084745[/C][/ROW]
[ROW][C]71[/C][C]3782.26[/C][C]3781.54558196191[/C][C]16.348710277108[/C][C]0.558191817097883[/C][C]0.0784332081906119[/C][/ROW]
[ROW][C]72[/C][C]3771.32[/C][C]3772.41759848903[/C][C]15.0824713946184[/C][C]0.557981155647733[/C][C]-0.831185198811925[/C][/ROW]
[ROW][C]73[/C][C]3766.66[/C][C]3774.6790433356[/C][C]14.4509910052501[/C][C]-7.19204378161173[/C][C]-0.432437080463682[/C][/ROW]
[ROW][C]74[/C][C]3774.6[/C][C]3774.89787294171[/C][C]13.7405189161498[/C][C]0.562986204574607[/C][C]-0.448368480289763[/C][/ROW]
[ROW][C]75[/C][C]3795.42[/C][C]3794.47534810513[/C][C]14.0308007374302[/C][C]0.565314190902248[/C][C]0.190475030585031[/C][/ROW]
[ROW][C]76[/C][C]3829.48[/C][C]3827.66912018335[/C][C]14.9836702867319[/C][C]0.565614710270418[/C][C]0.625194040185439[/C][/ROW]
[ROW][C]77[/C][C]3873.62[/C][C]3871.1996232726[/C][C]16.4032499131074[/C][C]0.565374482265352[/C][C]0.93131883622793[/C][/ROW]
[ROW][C]78[/C][C]3856.16[/C][C]3857.54736675906[/C][C]14.9085298623473[/C][C]0.565659785805348[/C][C]-0.980534787345987[/C][/ROW]
[ROW][C]79[/C][C]3875.42[/C][C]3874.70801700992[/C][C]15.0205402960825[/C][C]0.565639257786043[/C][C]0.0734733432061382[/C][/ROW]
[ROW][C]80[/C][C]3893.52[/C][C]3892.757561635[/C][C]15.1711992149716[/C][C]0.565613007746477[/C][C]0.0988183181284377[/C][/ROW]
[ROW][C]81[/C][C]3918.86[/C][C]3917.6620008758[/C][C]15.6553467653928[/C][C]0.565532863538128[/C][C]0.317537071811014[/C][/ROW]
[ROW][C]82[/C][C]3918.24[/C][C]3918.62881139051[/C][C]14.9246760228497[/C][C]0.565647773364586[/C][C]-0.479198029560763[/C][/ROW]
[ROW][C]83[/C][C]3942.22[/C][C]3941.16013116495[/C][C]15.3030810933969[/C][C]0.565591236298794[/C][C]0.248158491302398[/C][/ROW]
[ROW][C]84[/C][C]3938.7[/C][C]3939.25262420225[/C][C]14.4468751333451[/C][C]0.565712769901021[/C][C]-0.561476239687106[/C][/ROW]
[ROW][C]85[/C][C]3997.98[/C][C]3998.1888797309[/C][C]16.649211782132[/C][C]-3.08100475721418[/C][C]1.49361857917062[/C][/ROW]
[ROW][C]86[/C][C]3997.54[/C][C]3998.35804462584[/C][C]15.8282437705119[/C][C]0.188331399200654[/C][C]-0.521609042495057[/C][/ROW]
[ROW][C]87[/C][C]3973.24[/C][C]3975.57397499749[/C][C]13.9069661129743[/C][C]0.17527924830516[/C][C]-1.25995218256419[/C][/ROW]
[ROW][C]88[/C][C]3946.4[/C][C]3948.86414025347[/C][C]11.8860469837594[/C][C]0.175131498343647[/C][C]-1.32508678542139[/C][/ROW]
[ROW][C]89[/C][C]3937.48[/C][C]3938.73500567749[/C][C]10.7906438579297[/C][C]0.175504189694817[/C][C]-0.718210058691022[/C][/ROW]
[ROW][C]90[/C][C]3920.12[/C][C]3921.74889663951[/C][C]9.40853291673504[/C][C]0.17598730282746[/C][C]-0.906171039665926[/C][/ROW]
[ROW][C]91[/C][C]3940.74[/C][C]3939.99022055505[/C][C]9.84804248179347[/C][C]0.175840604489284[/C][C]0.28815538557534[/C][/ROW]
[ROW][C]92[/C][C]3948.68[/C][C]3948.58553933579[/C][C]9.78570722175472[/C][C]0.17586037812628[/C][C]-0.0408680774475675[/C][/ROW]
[ROW][C]93[/C][C]3935.74[/C][C]3936.9553823073[/C][C]8.72004046122653[/C][C]0.176181545905575[/C][C]-0.698658026327677[/C][/ROW]
[ROW][C]94[/C][C]3958.58[/C][C]3957.62737284928[/C][C]9.31478603744665[/C][C]0.176011255364832[/C][C]0.389913215475657[/C][/ROW]
[ROW][C]95[/C][C]3975.44[/C][C]3974.75634310974[/C][C]9.70363603459007[/C][C]0.175905478706517[/C][C]0.254925317895312[/C][/ROW]
[ROW][C]96[/C][C]4029.24[/C][C]4026.34314176099[/C][C]11.787855064549[/C][C]0.175366837244008[/C][C]1.36637193222906[/C][/ROW]
[ROW][C]97[/C][C]4013.44[/C][C]4017.92447047896[/C][C]10.785345346098[/C][C]-3.17904665312352[/C][C]-0.67601851417201[/C][/ROW]
[ROW][C]98[/C][C]4030.02[/C][C]4029.66736538871[/C][C]10.8329968702187[/C][C]0.293734892389907[/C][C]0.0304148498888912[/C][/ROW]
[ROW][C]99[/C][C]4032.04[/C][C]4032.28271163082[/C][C]10.4240475306874[/C][C]0.291308722410381[/C][C]-0.268140591105925[/C][/ROW]
[ROW][C]100[/C][C]4032.48[/C][C]4032.8304274368[/C][C]9.93255228964929[/C][C]0.29132459618641[/C][C]-0.322203011279981[/C][/ROW]
[ROW][C]101[/C][C]4020.54[/C][C]4021.62195195856[/C][C]8.88046414345914[/C][C]0.291739729105971[/C][C]-0.689686753687501[/C][/ROW]
[ROW][C]102[/C][C]4093.42[/C][C]4089.30836298829[/C][C]11.8069728785195[/C][C]0.290574266805265[/C][C]1.91843400916488[/C][/ROW]
[ROW][C]103[/C][C]4098.18[/C][C]4098.08619459287[/C][C]11.6562252561064[/C][C]0.29063152906519[/C][C]-0.0988201443441129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299226&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
12650.842650.84000
22685.282682.705941510181.807607325838271.779155257140890.648883433859255
32706.042702.872055593562.038598447765691.922284400156740.615079940429743
42743.342738.941877193252.45142690711792.082408704070021.14027313661372
52768.482764.711120712182.786442321158742.1860863595980.780184420344653
62756.382755.08815768322.579170017078652.13199274661077-0.414612036737081
72788.682784.613138596163.090208683892812.247182379289620.899040139435979
82828.582823.753461708233.852230699485532.398005082715481.20118357144629
92853.182849.239659024664.354442981103022.486397873406220.719902637692031
1028592856.319965860284.423107594436822.497252786753750.0905937373344082
112900.322895.371621744415.360266059628762.63139415040711.14949599676841
122884.462883.074074297274.851153009187682.5649768443619-0.585481142103571
132884.32903.595523526314.68843160474579-20.33371794316960.626602799595264
142910.862908.962321537794.721345657062721.865358540779960.0190167915545479
152916.622914.685216636464.754551793935551.86842506812320.0330609258091417
162921.62919.713022049774.763723288631341.868868541547340.00901524638636851
172926.582924.696279073314.771375547153261.869193602003090.00723663636489267
182938.462936.140402973265.012365312566171.87867880080580.219782499671314
192942.922941.048354100695.008472080277071.87853597427611-0.00343656305892792
202956.922954.475557223825.331499882575161.889607778703330.27689186433656
212946.782945.828244791064.78114363960881.87195068467895-0.459466547477986
222956.482954.357071606484.932148202607741.876492949342260.123108164622251
232968.12965.788978304915.199553636539671.884045323573980.213393319188459
242983.12980.576048459185.601457516001761.894716598435310.314606363750249
252993.043007.3850371056.24515224299809-15.7213252148650.765784989833344
263007.443006.506774285335.886075428996971.31695459774881-0.212056029358025
273024.643022.636777079356.338175313113281.333045197190740.335650220261481
283033.043031.537658394226.451635347275321.334680685178360.0839333284960258
293047.943046.07233914916.813436116971771.339160352644070.264639199324635
303066.023063.951878968167.31391658262131.344975554024930.362193772550622
313096.463093.642290833618.335452608306241.356190403200190.732179141139968
323131.163128.086801816289.537505463717641.368670891647650.854094391460507
333133.543132.507566944849.300129563390871.36633891222724-0.16734274238546
343118.683118.822996852918.226465087537091.3563546459997-0.751553468646264
353133.53131.829932865198.451160646615731.358333262389730.156281391577358
363108.93109.556679392596.998922689457331.34621981049816-1.00425283443475
373136.043144.522585524638.19675104173547-10.28585678713120.975236806011448
383129.33129.922737650187.04052931673820.672933171792874-0.696649235644294
393136.13135.522268190976.971267257927460.671571990459087-0.0470865003443133
403143.723143.014375828236.996305307001180.671707050793780.0170134318215299
413199.243195.591350434019.194477267816180.681082223709551.48869913039059
423205.783205.079729734269.208694501308460.6811389646643430.00959809152316599
433191.443192.200477548198.137238413929840.677085973659302-0.721270945676944
443172.723173.776027052946.845532273543690.67245022162298-0.867287625259211
453211.923209.372111081418.24685092203190.6772225448808150.938687911238179
463268.383264.6365093492410.54319735791080.6846445119000421.53498983262749
473289.523287.9994985123211.17047316631530.6865688190481080.418504032029687
483316.283314.5883581972911.92615414017090.6887693604923970.503307213038325
493348.63351.5108128950713.103561917638-4.520860335103540.857032256713392
503400.443397.7856276719814.77594992890740.7114817909220381.02871140867378
513425.683424.2038969778515.34968114427320.7190391913970160.38008136762507
523456.33454.6009306732116.09093865826140.7206483249469540.4911025285434
533454.463454.7752992501715.30614184879310.719551536791787-0.519438282052465
543514.483511.0916304947917.33006056292330.7221513276239631.33832689701835
5535463544.2480219076118.11175815092370.7231027559382790.51646233428074
563596.33593.5476702068819.65334158244960.7248844065970181.01773224651673
573616.23615.3362019945719.75895245841720.7250003270749680.0696745587405355
583598.083599.6601876291718.00520627977220.723172087333311-1.15627385508407
593595.283595.9682147692116.9307840735060.722108263178394-0.707984551051291
603610.73610.1562909815616.79490107884960.721980472123255-0.0894937336801046
613628.743635.3195271484417.2020476001573-7.11884024570220.284097958576094
623641.843641.9060213553316.67007248135610.567723494809795-0.332296710280832
633637.663638.4127697029815.66930818346480.557805769041251-0.658058847630342
643661.643660.6547372331515.99543519401360.5580895958209150.214453232639686
653686.563685.4311189035516.43124779962270.558210782674350.286494830030973
663718.383716.8477421947517.17519498799110.5583810894782120.488920853465104
673728.883728.6695777972916.90936346167720.55832388198262-0.174660174269805
683723.423724.2481128527415.8499068504830.558107449162608-0.695940538136781
693726.343726.6555911371315.18211784672830.557977861033552-0.438570447293844
703764.843762.9122917415816.22924203337710.5581708950948280.687571847084745
713782.263781.5455819619116.3487102771080.5581918170978830.0784332081906119
723771.323772.4175984890315.08247139461840.557981155647733-0.831185198811925
733766.663774.679043335614.4509910052501-7.19204378161173-0.432437080463682
743774.63774.8978729417113.74051891614980.562986204574607-0.448368480289763
753795.423794.4753481051314.03080073743020.5653141909022480.190475030585031
763829.483827.6691201833514.98367028673190.5656147102704180.625194040185439
773873.623871.199623272616.40324991310740.5653744822653520.93131883622793
783856.163857.5473667590614.90852986234730.565659785805348-0.980534787345987
793875.423874.7080170099215.02054029608250.5656392577860430.0734733432061382
803893.523892.75756163515.17119921497160.5656130077464770.0988183181284377
813918.863917.662000875815.65534676539280.5655328635381280.317537071811014
823918.243918.6288113905114.92467602284970.565647773364586-0.479198029560763
833942.223941.1601311649515.30308109339690.5655912362987940.248158491302398
843938.73939.2526242022514.44687513334510.565712769901021-0.561476239687106
853997.983998.188879730916.649211782132-3.081004757214181.49361857917062
863997.543998.3580446258415.82824377051190.188331399200654-0.521609042495057
873973.243975.5739749974913.90696611297430.17527924830516-1.25995218256419
883946.43948.8641402534711.88604698375940.175131498343647-1.32508678542139
893937.483938.7350056774910.79064385792970.175504189694817-0.718210058691022
903920.123921.748896639519.408532916735040.17598730282746-0.906171039665926
913940.743939.990220555059.848042481793470.1758406044892840.28815538557534
923948.683948.585539335799.785707221754720.17586037812628-0.0408680774475675
933935.743936.95538230738.720040461226530.176181545905575-0.698658026327677
943958.583957.627372849289.314786037446650.1760112553648320.389913215475657
953975.443974.756343109749.703636034590070.1759054787065170.254925317895312
964029.244026.3431417609911.7878550645490.1753668372440081.36637193222906
974013.444017.9244704789610.785345346098-3.17904665312352-0.67601851417201
984030.024029.6673653887110.83299687021870.2937348923899070.0304148498888912
994032.044032.2827116308210.42404753068740.291308722410381-0.268140591105925
1004032.484032.83042743689.932552289649290.29132459618641-0.322203011279981
1014020.544021.621951958568.880464143459140.291739729105971-0.689686753687501
1024093.424089.3083629882911.80697287851950.2905742668052651.91843400916488
1034098.184098.0861945928711.65622525610640.29063152906519-0.0988201443441129







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
14124.666325656184120.886186631683.780139024502
24143.416707780744141.878621674581.53808610616199
34163.311675591244162.871056717470.440618873766701
44188.87372930424183.863491760375.01023754383827
54203.485371112964204.85592680326-1.37055569030202
64226.795451481734225.848361846160.947089635576843
74250.300601009564246.840796889053.45980412051006
84264.154271087564267.83323193194-3.67896084438111
94283.689792938864288.82566697484-5.13587403598276
104306.22938849934309.81810201773-3.5887135184335
114329.668613582054330.81053706063-1.14192347857437
124351.543024366844351.80297210352-0.259947736682093

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 4124.66632565618 & 4120.88618663168 & 3.780139024502 \tabularnewline
2 & 4143.41670778074 & 4141.87862167458 & 1.53808610616199 \tabularnewline
3 & 4163.31167559124 & 4162.87105671747 & 0.440618873766701 \tabularnewline
4 & 4188.8737293042 & 4183.86349176037 & 5.01023754383827 \tabularnewline
5 & 4203.48537111296 & 4204.85592680326 & -1.37055569030202 \tabularnewline
6 & 4226.79545148173 & 4225.84836184616 & 0.947089635576843 \tabularnewline
7 & 4250.30060100956 & 4246.84079688905 & 3.45980412051006 \tabularnewline
8 & 4264.15427108756 & 4267.83323193194 & -3.67896084438111 \tabularnewline
9 & 4283.68979293886 & 4288.82566697484 & -5.13587403598276 \tabularnewline
10 & 4306.2293884993 & 4309.81810201773 & -3.5887135184335 \tabularnewline
11 & 4329.66861358205 & 4330.81053706063 & -1.14192347857437 \tabularnewline
12 & 4351.54302436684 & 4351.80297210352 & -0.259947736682093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299226&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]4124.66632565618[/C][C]4120.88618663168[/C][C]3.780139024502[/C][/ROW]
[ROW][C]2[/C][C]4143.41670778074[/C][C]4141.87862167458[/C][C]1.53808610616199[/C][/ROW]
[ROW][C]3[/C][C]4163.31167559124[/C][C]4162.87105671747[/C][C]0.440618873766701[/C][/ROW]
[ROW][C]4[/C][C]4188.8737293042[/C][C]4183.86349176037[/C][C]5.01023754383827[/C][/ROW]
[ROW][C]5[/C][C]4203.48537111296[/C][C]4204.85592680326[/C][C]-1.37055569030202[/C][/ROW]
[ROW][C]6[/C][C]4226.79545148173[/C][C]4225.84836184616[/C][C]0.947089635576843[/C][/ROW]
[ROW][C]7[/C][C]4250.30060100956[/C][C]4246.84079688905[/C][C]3.45980412051006[/C][/ROW]
[ROW][C]8[/C][C]4264.15427108756[/C][C]4267.83323193194[/C][C]-3.67896084438111[/C][/ROW]
[ROW][C]9[/C][C]4283.68979293886[/C][C]4288.82566697484[/C][C]-5.13587403598276[/C][/ROW]
[ROW][C]10[/C][C]4306.2293884993[/C][C]4309.81810201773[/C][C]-3.5887135184335[/C][/ROW]
[ROW][C]11[/C][C]4329.66861358205[/C][C]4330.81053706063[/C][C]-1.14192347857437[/C][/ROW]
[ROW][C]12[/C][C]4351.54302436684[/C][C]4351.80297210352[/C][C]-0.259947736682093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299226&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
14124.666325656184120.886186631683.780139024502
24143.416707780744141.878621674581.53808610616199
34163.311675591244162.871056717470.440618873766701
44188.87372930424183.863491760375.01023754383827
54203.485371112964204.85592680326-1.37055569030202
64226.795451481734225.848361846160.947089635576843
74250.300601009564246.840796889053.45980412051006
84264.154271087564267.83323193194-3.67896084438111
94283.689792938864288.82566697484-5.13587403598276
104306.22938849934309.81810201773-3.5887135184335
114329.668613582054330.81053706063-1.14192347857437
124351.543024366844351.80297210352-0.259947736682093



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')