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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, 07 Dec 2016 11:21:02 +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/07/t14811064383xmosc87ppwu8o9.htm/, Retrieved Tue, 07 May 2024 11:07:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297974, Retrieved Tue, 07 May 2024 11:07:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
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...] [2016-12-07 10:21:02] [aed32bb2e1132335210cb15bafce0db8] [Current]
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Dataseries X:
1418.7
1344.1
1574.6
1621.6
1887.2
2055.3
1606.8
1494.8
1636
1485.7
1369.7
1333.8
1614.9
1297.3
1226.2
1098.5
1258.5
1065.2
1000.4
1820.2
1224.8
1428.4
1144
1166.9
1902.3
1949.4
1784.5
1671.5
1923.8
1882.8
2165
1826.9
1511.2
2063.1
2169.6
2495.3
2936.9
3076.9
3365.7
3846
3436.2
3561.1
3328
2762.9
2923
2731.1
2571.5
3282.4
4606.5
4698.7
5093.3
4477.3
3850.1
4275.2
3975
4495.9
4042.4
5221.3
2555
2694.6
2757.7
2760.9
3872.9
2888.7
2529.2
3458.3
2882.8
2958.5
2652.4
2869.8
2501.7
2576.1
3347.5
3036.1
3345.2
3223.2
4087
4157.2
3368
3957.5
3469
4501.6
3181.4
3464.5
4186.9
3064.7
4011.7
3537.1
4879.5
4488.7
4632.9
4405.8
2615.2
3338
2825.2
3012.7
4537.5
5676.7
5575.4
6643.4
5590.6
4697.6
5078.1
5769.9
5561.4
7268.8
6496.7
6489.3
10883.5
7998.6
7340
7814.4
5729.6
6463.5
6315.4
5357.1




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time8 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 time8 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297974&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]8 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297974&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297974&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 time8 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
11418.71418.7000
21344.11366.5713061792-3.56948543355039-4.55760419584237-0.0864028988960897
31574.61493.890813050091.544630883862299.239876029571040.292661484873991
41621.61571.089414060243.33192369930565.002242271569590.179825504957966
51887.21758.633959082816.5758525411408315.27141071214060.443760355708614
62055.31935.432109470929.1890909715013614.52293341342130.411518741141517
71606.81741.816218725136.24370225181014-9.2660820280699-0.490782217369603
81494.81591.981376686044.02174804146672-0.353140070032033-0.377784622654411
916361615.191869630484.293342111779258.903340285665980.0464428241088417
101485.71537.989773860083.14030125063569-1.73671541869426-0.197211977415325
111369.71436.611691991461.65909397165056-2.0903800652583-0.252874723759127
121333.81373.816261318880.743515679184307-0.0512402184725609-0.155910038391936
131614.91473.21323634632-6.2319608127911777.14280073034290.300334584064159
141297.31368.58703836833-9.42463389418662-24.7100252891915-0.200427887667687
151226.21280.79679310012-11.1681172021514-10.3453109220686-0.180783879335554
161098.51177.8368014445-12.5180224999796-24.5256385822624-0.219545081172962
171258.51223.83325043745-11.8350439981604-0.7198676344310480.141037677287757
181065.21126.54425967152-12.7424615853127-9.50062997275184-0.206342194410759
191000.41057.90714095379-13.3192437158924-23.569595065082-0.135019358418252
201820.21504.58144237659-8.582179956377436.30242412461611.11114395722603
211224.81350.17640973425-10.0960250439965-36.8444588055465-0.352193304487407
221428.41394.5378922872-9.523742363462410.807860099494290.131502886341638
2311441252.6322835628-10.9313856574085-28.2995931173173-0.31961458756517
241166.91203.89290916498-11.2962333416289-14.0403337730155-0.091233893957251
251902.31470.17087786351-18.5387613285876258.9196169442270.748463477188882
261949.41775.94697922808-11.28027698301283.614002435060070.71192781463576
271784.51789.51160200354-10.8189757839612-19.06163829436070.057887167407426
281671.51736.20602152654-11.399660581985-39.7037595517603-0.10162181804225
291923.81835.34365093241-10.132315719473522.76775449277260.265963678678396
301882.81864.82499288566-9.70811793723327-5.620931369345780.0954360971629886
3121652069.05038763994-7.45624888032936-31.54280677778740.515511689272018
321826.91908.29446103292-9.074080351606839.96115284133208-0.369378219275656
331511.21697.63611144059-11.2228108802556-66.3285488248884-0.485651350361482
342063.11891.33004860054-9.0101091875570649.70437549516260.493606614469561
352169.62067.63458798602-7.00025478233772-8.405658923922380.446310328514476
362495.32338.81983318372-4.4293363464502-9.307980420402880.669603365991278
372936.92570.79795110762-6.76848680518416222.4243057639720.60824541177533
383076.92874.46721607565-1.1242268784439633.2138314290940.704979510351887
393365.73174.721533272844.1006713538813221.04803856038320.705225106060743
4038463594.855973930449.926054687628039.279886303211880.993878597118153
413436.23509.512199148548.75996676531936-17.4522470986889-0.228775520902446
423561.13552.882039238879.16129130515632-12.11545049468450.0831980464275699
4333283435.154031546747.70922465968954-32.5780688576702-0.305069417862847
442762.93030.459257101412.97624484483925-25.1917699131318-0.991433196978584
4529233001.218574162362.60322205245789-59.2880362402049-0.0774414214185602
462731.12824.678990022550.50828553868050711.6659724590207-0.430565988830071
472571.52692.02592431402-1.0376752237442-42.3014484985263-0.319980392760999
483282.43041.567809168782.4056316216462334.7874814923260.842104177678407
494606.53809.822442364131.55831701711635339.629659845011.92110010713322
504698.74354.0398220035410.385134715247643.09521700786481.25527712658536
515093.34821.3296961795718.059930723971414.84351596067921.07212225330036
524477.34645.5512621558115.2388145401662-56.5427701059689-0.462465500273286
533850.14215.835076684799.39846813715694-107.329251713026-1.06660817603107
544275.24240.484743304359.5898110931522725.84198191472210.0365933747200572
5539754088.974211509667.59282566260467-20.2135549960825-0.386581118706613
564495.94330.4660700164210.497742428380429.31046221618240.561233178730934
574042.44200.823909939528.74515577165167-76.8767813250841-0.336231671629836
585221.34760.7823895641115.6789351998338139.8078546058311.32237988555296
5925553587.18488828050.962533963155867-340.28980062923-2.85224479792544
602694.63076.35754446314-4.51063179558055-83.9375240895632-1.22733971380313
612757.72756.47918170796-5.87704987118231186.996957781357-0.778875788211247
622760.92753.41183346211-5.833758700754335.910820721733170.00657037545960296
633872.93360.900951720394.27849551725115167.0228502265211.44237209160838
642888.73113.851447983510.503327957107125-81.1664322190081-0.598991219400021
652529.22836.46520774413-3.35433028316659-146.950334416703-0.66517952676575
663458.33147.67833198220.848564043221975128.8350808106060.753630401106775
672882.83034.1093931557-0.662467926269903-85.1676670459878-0.27414063915581
682958.52967.3831004057-1.535481410513129.3056196595539-0.15827817960257
692652.42864.08211513295-2.88679556425808-152.861345038195-0.243798430713991
702869.82695.52657743497-5.09079384337516270.02150149602-0.396851010628548
712501.72728.3868673458-4.59656642122729-248.6174272370540.0908734887580663
722576.12667.1823112695-5.25268156404715-58.3684691211311-0.135585290178379
733347.52944.6362291617-3.02564905839483237.8736050088440.691171239612016
743036.13046.0599488083-1.45220758906176-68.92685484323660.245888627186747
753345.23105.55201068114-0.460707048550066205.3538099529240.143603960725709
763223.23203.677327030441.05195696337254-36.73827646855730.234782213034533
7740873809.994585476419.80182479817792-70.57935665568521.44720979664391
784157.23949.474288752911.617077772041133.1346298167510.310317293260462
7933683678.378488638167.70371066114417-147.713453600218-0.676571455912599
803957.53805.070117813859.3497968177717483.96818506922480.284741769007284
8134693695.730259548487.70324853973406-158.444605986448-0.28401393061614
824501.63996.5831004376211.7648581410714336.3749366339450.701388291906766
833181.43688.659129634587.43465927718693-323.395991811846-0.764524753635127
843464.53610.759614148986.37681651814135-97.1809598360405-0.204198145188561
854186.93810.391775466848.35601049210202264.4764312408440.469261097061251
863064.73441.654796076952.71190826380343-163.390564496996-0.891496401624712
874011.73650.150086584336.02451927344858245.6475659282660.485723625903981
883537.13661.53140453136.10775594043336-127.4808206702980.0127508983383975
894879.54394.9513326383616.917454241489468.1935713375571.73758491368367
904488.74383.3016642559416.5040689711985121.776965882253-0.068301105611117
914632.94624.4582841379919.7208575533197-120.39563760810.537145571503131
924405.84465.8679622054117.171755142173742.1929372671517-0.426323563183069
932615.23539.907851550993.67540347615874-383.851883276928-2.25480998965566
9433383184.09715810441-1.4512676931549360.031790131274-0.85929233883555
952825.23140.83115298632-2.03488158639316-291.663121416006-0.0999009150948592
963012.73125.99349138606-2.20224723746266-105.954653975797-0.03061452406771
974537.53728.329806012594.95352846018361460.4073333701361.46103289974089
985676.74953.6114085853123.2360635326130.71197504699772.89292973634157
995575.45226.1360288268627.2143123439022208.7073931158490.589293915910753
1006643.46178.204803268641.6788250258397-60.46548396243892.20081783062137
1015590.65865.4770724691236.3149356392055-72.4402132810799-0.846177462036207
1024697.65172.9955438971225.5229514265488-58.5008845431084-1.74135863562718
1035078.15152.9251607877524.8542961574024-48.7377051450747-0.108941701554742
1045769.95400.8526397292828.1180041211806241.410007504340.532985570821992
1055561.45688.2639918033731.910036422433-275.2176824080220.619480402401029
1067268.86383.0824489546541.5593786077061506.5005785190881.58338942640373
1076496.76650.7958533013544.7886689618624-283.4115636041830.539914046896129
1086489.36711.075402427544.9996036998466-230.6344610682380.0370227326226909
10910883.58899.8931943262972.7023475219054751.1744661299315.16397954543848
1107998.68501.8786565432965.6233208983671-235.934433195257-1.11790566265187
11173407826.9853505291953.8898795851172-69.0131168169493-1.75276965257393
1127814.47827.4177057423853.051704017499617.3368204335279-0.127191896323315
1135729.66660.6249982571534.3778169257674-235.328783824769-2.91118924922466
1146463.56563.0844556542632.3935782048071-24.2455237841868-0.315052973895156
1156315.46478.7895171399730.6535220246295-96.7328447618162-0.278682339021362
1165357.15753.8483489320219.418607272646634.8690636441552-1.80441482488135

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 1418.7 & 1418.7 & 0 & 0 & 0 \tabularnewline
2 & 1344.1 & 1366.5713061792 & -3.56948543355039 & -4.55760419584237 & -0.0864028988960897 \tabularnewline
3 & 1574.6 & 1493.89081305009 & 1.54463088386229 & 9.23987602957104 & 0.292661484873991 \tabularnewline
4 & 1621.6 & 1571.08941406024 & 3.3319236993056 & 5.00224227156959 & 0.179825504957966 \tabularnewline
5 & 1887.2 & 1758.63395908281 & 6.57585254114083 & 15.2714107121406 & 0.443760355708614 \tabularnewline
6 & 2055.3 & 1935.43210947092 & 9.18909097150136 & 14.5229334134213 & 0.411518741141517 \tabularnewline
7 & 1606.8 & 1741.81621872513 & 6.24370225181014 & -9.2660820280699 & -0.490782217369603 \tabularnewline
8 & 1494.8 & 1591.98137668604 & 4.02174804146672 & -0.353140070032033 & -0.377784622654411 \tabularnewline
9 & 1636 & 1615.19186963048 & 4.29334211177925 & 8.90334028566598 & 0.0464428241088417 \tabularnewline
10 & 1485.7 & 1537.98977386008 & 3.14030125063569 & -1.73671541869426 & -0.197211977415325 \tabularnewline
11 & 1369.7 & 1436.61169199146 & 1.65909397165056 & -2.0903800652583 & -0.252874723759127 \tabularnewline
12 & 1333.8 & 1373.81626131888 & 0.743515679184307 & -0.0512402184725609 & -0.155910038391936 \tabularnewline
13 & 1614.9 & 1473.21323634632 & -6.23196081279117 & 77.1428007303429 & 0.300334584064159 \tabularnewline
14 & 1297.3 & 1368.58703836833 & -9.42463389418662 & -24.7100252891915 & -0.200427887667687 \tabularnewline
15 & 1226.2 & 1280.79679310012 & -11.1681172021514 & -10.3453109220686 & -0.180783879335554 \tabularnewline
16 & 1098.5 & 1177.8368014445 & -12.5180224999796 & -24.5256385822624 & -0.219545081172962 \tabularnewline
17 & 1258.5 & 1223.83325043745 & -11.8350439981604 & -0.719867634431048 & 0.141037677287757 \tabularnewline
18 & 1065.2 & 1126.54425967152 & -12.7424615853127 & -9.50062997275184 & -0.206342194410759 \tabularnewline
19 & 1000.4 & 1057.90714095379 & -13.3192437158924 & -23.569595065082 & -0.135019358418252 \tabularnewline
20 & 1820.2 & 1504.58144237659 & -8.5821799563774 & 36.3024241246161 & 1.11114395722603 \tabularnewline
21 & 1224.8 & 1350.17640973425 & -10.0960250439965 & -36.8444588055465 & -0.352193304487407 \tabularnewline
22 & 1428.4 & 1394.5378922872 & -9.52374236346241 & 0.80786009949429 & 0.131502886341638 \tabularnewline
23 & 1144 & 1252.6322835628 & -10.9313856574085 & -28.2995931173173 & -0.31961458756517 \tabularnewline
24 & 1166.9 & 1203.89290916498 & -11.2962333416289 & -14.0403337730155 & -0.091233893957251 \tabularnewline
25 & 1902.3 & 1470.17087786351 & -18.5387613285876 & 258.919616944227 & 0.748463477188882 \tabularnewline
26 & 1949.4 & 1775.94697922808 & -11.2802769830128 & 3.61400243506007 & 0.71192781463576 \tabularnewline
27 & 1784.5 & 1789.51160200354 & -10.8189757839612 & -19.0616382943607 & 0.057887167407426 \tabularnewline
28 & 1671.5 & 1736.20602152654 & -11.399660581985 & -39.7037595517603 & -0.10162181804225 \tabularnewline
29 & 1923.8 & 1835.34365093241 & -10.1323157194735 & 22.7677544927726 & 0.265963678678396 \tabularnewline
30 & 1882.8 & 1864.82499288566 & -9.70811793723327 & -5.62093136934578 & 0.0954360971629886 \tabularnewline
31 & 2165 & 2069.05038763994 & -7.45624888032936 & -31.5428067777874 & 0.515511689272018 \tabularnewline
32 & 1826.9 & 1908.29446103292 & -9.07408035160683 & 9.96115284133208 & -0.369378219275656 \tabularnewline
33 & 1511.2 & 1697.63611144059 & -11.2228108802556 & -66.3285488248884 & -0.485651350361482 \tabularnewline
34 & 2063.1 & 1891.33004860054 & -9.01010918755706 & 49.7043754951626 & 0.493606614469561 \tabularnewline
35 & 2169.6 & 2067.63458798602 & -7.00025478233772 & -8.40565892392238 & 0.446310328514476 \tabularnewline
36 & 2495.3 & 2338.81983318372 & -4.4293363464502 & -9.30798042040288 & 0.669603365991278 \tabularnewline
37 & 2936.9 & 2570.79795110762 & -6.76848680518416 & 222.424305763972 & 0.60824541177533 \tabularnewline
38 & 3076.9 & 2874.46721607565 & -1.12422687844396 & 33.213831429094 & 0.704979510351887 \tabularnewline
39 & 3365.7 & 3174.72153327284 & 4.10067135388132 & 21.0480385603832 & 0.705225106060743 \tabularnewline
40 & 3846 & 3594.85597393044 & 9.92605468762803 & 9.27988630321188 & 0.993878597118153 \tabularnewline
41 & 3436.2 & 3509.51219914854 & 8.75996676531936 & -17.4522470986889 & -0.228775520902446 \tabularnewline
42 & 3561.1 & 3552.88203923887 & 9.16129130515632 & -12.1154504946845 & 0.0831980464275699 \tabularnewline
43 & 3328 & 3435.15403154674 & 7.70922465968954 & -32.5780688576702 & -0.305069417862847 \tabularnewline
44 & 2762.9 & 3030.45925710141 & 2.97624484483925 & -25.1917699131318 & -0.991433196978584 \tabularnewline
45 & 2923 & 3001.21857416236 & 2.60322205245789 & -59.2880362402049 & -0.0774414214185602 \tabularnewline
46 & 2731.1 & 2824.67899002255 & 0.508285538680507 & 11.6659724590207 & -0.430565988830071 \tabularnewline
47 & 2571.5 & 2692.02592431402 & -1.0376752237442 & -42.3014484985263 & -0.319980392760999 \tabularnewline
48 & 3282.4 & 3041.56780916878 & 2.40563162164623 & 34.787481492326 & 0.842104177678407 \tabularnewline
49 & 4606.5 & 3809.82244236413 & 1.55831701711635 & 339.62965984501 & 1.92110010713322 \tabularnewline
50 & 4698.7 & 4354.03982200354 & 10.3851347152476 & 43.0952170078648 & 1.25527712658536 \tabularnewline
51 & 5093.3 & 4821.32969617957 & 18.0599307239714 & 14.8435159606792 & 1.07212225330036 \tabularnewline
52 & 4477.3 & 4645.55126215581 & 15.2388145401662 & -56.5427701059689 & -0.462465500273286 \tabularnewline
53 & 3850.1 & 4215.83507668479 & 9.39846813715694 & -107.329251713026 & -1.06660817603107 \tabularnewline
54 & 4275.2 & 4240.48474330435 & 9.58981109315227 & 25.8419819147221 & 0.0365933747200572 \tabularnewline
55 & 3975 & 4088.97421150966 & 7.59282566260467 & -20.2135549960825 & -0.386581118706613 \tabularnewline
56 & 4495.9 & 4330.46607001642 & 10.4977424283804 & 29.3104622161824 & 0.561233178730934 \tabularnewline
57 & 4042.4 & 4200.82390993952 & 8.74515577165167 & -76.8767813250841 & -0.336231671629836 \tabularnewline
58 & 5221.3 & 4760.78238956411 & 15.6789351998338 & 139.807854605831 & 1.32237988555296 \tabularnewline
59 & 2555 & 3587.1848882805 & 0.962533963155867 & -340.28980062923 & -2.85224479792544 \tabularnewline
60 & 2694.6 & 3076.35754446314 & -4.51063179558055 & -83.9375240895632 & -1.22733971380313 \tabularnewline
61 & 2757.7 & 2756.47918170796 & -5.87704987118231 & 186.996957781357 & -0.778875788211247 \tabularnewline
62 & 2760.9 & 2753.41183346211 & -5.83375870075433 & 5.91082072173317 & 0.00657037545960296 \tabularnewline
63 & 3872.9 & 3360.90095172039 & 4.27849551725115 & 167.022850226521 & 1.44237209160838 \tabularnewline
64 & 2888.7 & 3113.85144798351 & 0.503327957107125 & -81.1664322190081 & -0.598991219400021 \tabularnewline
65 & 2529.2 & 2836.46520774413 & -3.35433028316659 & -146.950334416703 & -0.66517952676575 \tabularnewline
66 & 3458.3 & 3147.6783319822 & 0.848564043221975 & 128.835080810606 & 0.753630401106775 \tabularnewline
67 & 2882.8 & 3034.1093931557 & -0.662467926269903 & -85.1676670459878 & -0.27414063915581 \tabularnewline
68 & 2958.5 & 2967.3831004057 & -1.5354814105131 & 29.3056196595539 & -0.15827817960257 \tabularnewline
69 & 2652.4 & 2864.08211513295 & -2.88679556425808 & -152.861345038195 & -0.243798430713991 \tabularnewline
70 & 2869.8 & 2695.52657743497 & -5.09079384337516 & 270.02150149602 & -0.396851010628548 \tabularnewline
71 & 2501.7 & 2728.3868673458 & -4.59656642122729 & -248.617427237054 & 0.0908734887580663 \tabularnewline
72 & 2576.1 & 2667.1823112695 & -5.25268156404715 & -58.3684691211311 & -0.135585290178379 \tabularnewline
73 & 3347.5 & 2944.6362291617 & -3.02564905839483 & 237.873605008844 & 0.691171239612016 \tabularnewline
74 & 3036.1 & 3046.0599488083 & -1.45220758906176 & -68.9268548432366 & 0.245888627186747 \tabularnewline
75 & 3345.2 & 3105.55201068114 & -0.460707048550066 & 205.353809952924 & 0.143603960725709 \tabularnewline
76 & 3223.2 & 3203.67732703044 & 1.05195696337254 & -36.7382764685573 & 0.234782213034533 \tabularnewline
77 & 4087 & 3809.99458547641 & 9.80182479817792 & -70.5793566556852 & 1.44720979664391 \tabularnewline
78 & 4157.2 & 3949.4742887529 & 11.617077772041 & 133.134629816751 & 0.310317293260462 \tabularnewline
79 & 3368 & 3678.37848863816 & 7.70371066114417 & -147.713453600218 & -0.676571455912599 \tabularnewline
80 & 3957.5 & 3805.07011781385 & 9.34979681777174 & 83.9681850692248 & 0.284741769007284 \tabularnewline
81 & 3469 & 3695.73025954848 & 7.70324853973406 & -158.444605986448 & -0.28401393061614 \tabularnewline
82 & 4501.6 & 3996.58310043762 & 11.7648581410714 & 336.374936633945 & 0.701388291906766 \tabularnewline
83 & 3181.4 & 3688.65912963458 & 7.43465927718693 & -323.395991811846 & -0.764524753635127 \tabularnewline
84 & 3464.5 & 3610.75961414898 & 6.37681651814135 & -97.1809598360405 & -0.204198145188561 \tabularnewline
85 & 4186.9 & 3810.39177546684 & 8.35601049210202 & 264.476431240844 & 0.469261097061251 \tabularnewline
86 & 3064.7 & 3441.65479607695 & 2.71190826380343 & -163.390564496996 & -0.891496401624712 \tabularnewline
87 & 4011.7 & 3650.15008658433 & 6.02451927344858 & 245.647565928266 & 0.485723625903981 \tabularnewline
88 & 3537.1 & 3661.5314045313 & 6.10775594043336 & -127.480820670298 & 0.0127508983383975 \tabularnewline
89 & 4879.5 & 4394.95133263836 & 16.9174542414894 & 68.193571337557 & 1.73758491368367 \tabularnewline
90 & 4488.7 & 4383.30166425594 & 16.5040689711985 & 121.776965882253 & -0.068301105611117 \tabularnewline
91 & 4632.9 & 4624.45828413799 & 19.7208575533197 & -120.3956376081 & 0.537145571503131 \tabularnewline
92 & 4405.8 & 4465.86796220541 & 17.1717551421737 & 42.1929372671517 & -0.426323563183069 \tabularnewline
93 & 2615.2 & 3539.90785155099 & 3.67540347615874 & -383.851883276928 & -2.25480998965566 \tabularnewline
94 & 3338 & 3184.09715810441 & -1.4512676931549 & 360.031790131274 & -0.85929233883555 \tabularnewline
95 & 2825.2 & 3140.83115298632 & -2.03488158639316 & -291.663121416006 & -0.0999009150948592 \tabularnewline
96 & 3012.7 & 3125.99349138606 & -2.20224723746266 & -105.954653975797 & -0.03061452406771 \tabularnewline
97 & 4537.5 & 3728.32980601259 & 4.95352846018361 & 460.407333370136 & 1.46103289974089 \tabularnewline
98 & 5676.7 & 4953.61140858531 & 23.23606353261 & 30.7119750469977 & 2.89292973634157 \tabularnewline
99 & 5575.4 & 5226.13602882686 & 27.2143123439022 & 208.707393115849 & 0.589293915910753 \tabularnewline
100 & 6643.4 & 6178.2048032686 & 41.6788250258397 & -60.4654839624389 & 2.20081783062137 \tabularnewline
101 & 5590.6 & 5865.47707246912 & 36.3149356392055 & -72.4402132810799 & -0.846177462036207 \tabularnewline
102 & 4697.6 & 5172.99554389712 & 25.5229514265488 & -58.5008845431084 & -1.74135863562718 \tabularnewline
103 & 5078.1 & 5152.92516078775 & 24.8542961574024 & -48.7377051450747 & -0.108941701554742 \tabularnewline
104 & 5769.9 & 5400.85263972928 & 28.1180041211806 & 241.41000750434 & 0.532985570821992 \tabularnewline
105 & 5561.4 & 5688.26399180337 & 31.910036422433 & -275.217682408022 & 0.619480402401029 \tabularnewline
106 & 7268.8 & 6383.08244895465 & 41.5593786077061 & 506.500578519088 & 1.58338942640373 \tabularnewline
107 & 6496.7 & 6650.79585330135 & 44.7886689618624 & -283.411563604183 & 0.539914046896129 \tabularnewline
108 & 6489.3 & 6711.0754024275 & 44.9996036998466 & -230.634461068238 & 0.0370227326226909 \tabularnewline
109 & 10883.5 & 8899.89319432629 & 72.7023475219054 & 751.174466129931 & 5.16397954543848 \tabularnewline
110 & 7998.6 & 8501.87865654329 & 65.6233208983671 & -235.934433195257 & -1.11790566265187 \tabularnewline
111 & 7340 & 7826.98535052919 & 53.8898795851172 & -69.0131168169493 & -1.75276965257393 \tabularnewline
112 & 7814.4 & 7827.41770574238 & 53.0517040174996 & 17.3368204335279 & -0.127191896323315 \tabularnewline
113 & 5729.6 & 6660.62499825715 & 34.3778169257674 & -235.328783824769 & -2.91118924922466 \tabularnewline
114 & 6463.5 & 6563.08445565426 & 32.3935782048071 & -24.2455237841868 & -0.315052973895156 \tabularnewline
115 & 6315.4 & 6478.78951713997 & 30.6535220246295 & -96.7328447618162 & -0.278682339021362 \tabularnewline
116 & 5357.1 & 5753.84834893202 & 19.4186072726466 & 34.8690636441552 & -1.80441482488135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297974&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]1418.7[/C][C]1418.7[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]1344.1[/C][C]1366.5713061792[/C][C]-3.56948543355039[/C][C]-4.55760419584237[/C][C]-0.0864028988960897[/C][/ROW]
[ROW][C]3[/C][C]1574.6[/C][C]1493.89081305009[/C][C]1.54463088386229[/C][C]9.23987602957104[/C][C]0.292661484873991[/C][/ROW]
[ROW][C]4[/C][C]1621.6[/C][C]1571.08941406024[/C][C]3.3319236993056[/C][C]5.00224227156959[/C][C]0.179825504957966[/C][/ROW]
[ROW][C]5[/C][C]1887.2[/C][C]1758.63395908281[/C][C]6.57585254114083[/C][C]15.2714107121406[/C][C]0.443760355708614[/C][/ROW]
[ROW][C]6[/C][C]2055.3[/C][C]1935.43210947092[/C][C]9.18909097150136[/C][C]14.5229334134213[/C][C]0.411518741141517[/C][/ROW]
[ROW][C]7[/C][C]1606.8[/C][C]1741.81621872513[/C][C]6.24370225181014[/C][C]-9.2660820280699[/C][C]-0.490782217369603[/C][/ROW]
[ROW][C]8[/C][C]1494.8[/C][C]1591.98137668604[/C][C]4.02174804146672[/C][C]-0.353140070032033[/C][C]-0.377784622654411[/C][/ROW]
[ROW][C]9[/C][C]1636[/C][C]1615.19186963048[/C][C]4.29334211177925[/C][C]8.90334028566598[/C][C]0.0464428241088417[/C][/ROW]
[ROW][C]10[/C][C]1485.7[/C][C]1537.98977386008[/C][C]3.14030125063569[/C][C]-1.73671541869426[/C][C]-0.197211977415325[/C][/ROW]
[ROW][C]11[/C][C]1369.7[/C][C]1436.61169199146[/C][C]1.65909397165056[/C][C]-2.0903800652583[/C][C]-0.252874723759127[/C][/ROW]
[ROW][C]12[/C][C]1333.8[/C][C]1373.81626131888[/C][C]0.743515679184307[/C][C]-0.0512402184725609[/C][C]-0.155910038391936[/C][/ROW]
[ROW][C]13[/C][C]1614.9[/C][C]1473.21323634632[/C][C]-6.23196081279117[/C][C]77.1428007303429[/C][C]0.300334584064159[/C][/ROW]
[ROW][C]14[/C][C]1297.3[/C][C]1368.58703836833[/C][C]-9.42463389418662[/C][C]-24.7100252891915[/C][C]-0.200427887667687[/C][/ROW]
[ROW][C]15[/C][C]1226.2[/C][C]1280.79679310012[/C][C]-11.1681172021514[/C][C]-10.3453109220686[/C][C]-0.180783879335554[/C][/ROW]
[ROW][C]16[/C][C]1098.5[/C][C]1177.8368014445[/C][C]-12.5180224999796[/C][C]-24.5256385822624[/C][C]-0.219545081172962[/C][/ROW]
[ROW][C]17[/C][C]1258.5[/C][C]1223.83325043745[/C][C]-11.8350439981604[/C][C]-0.719867634431048[/C][C]0.141037677287757[/C][/ROW]
[ROW][C]18[/C][C]1065.2[/C][C]1126.54425967152[/C][C]-12.7424615853127[/C][C]-9.50062997275184[/C][C]-0.206342194410759[/C][/ROW]
[ROW][C]19[/C][C]1000.4[/C][C]1057.90714095379[/C][C]-13.3192437158924[/C][C]-23.569595065082[/C][C]-0.135019358418252[/C][/ROW]
[ROW][C]20[/C][C]1820.2[/C][C]1504.58144237659[/C][C]-8.5821799563774[/C][C]36.3024241246161[/C][C]1.11114395722603[/C][/ROW]
[ROW][C]21[/C][C]1224.8[/C][C]1350.17640973425[/C][C]-10.0960250439965[/C][C]-36.8444588055465[/C][C]-0.352193304487407[/C][/ROW]
[ROW][C]22[/C][C]1428.4[/C][C]1394.5378922872[/C][C]-9.52374236346241[/C][C]0.80786009949429[/C][C]0.131502886341638[/C][/ROW]
[ROW][C]23[/C][C]1144[/C][C]1252.6322835628[/C][C]-10.9313856574085[/C][C]-28.2995931173173[/C][C]-0.31961458756517[/C][/ROW]
[ROW][C]24[/C][C]1166.9[/C][C]1203.89290916498[/C][C]-11.2962333416289[/C][C]-14.0403337730155[/C][C]-0.091233893957251[/C][/ROW]
[ROW][C]25[/C][C]1902.3[/C][C]1470.17087786351[/C][C]-18.5387613285876[/C][C]258.919616944227[/C][C]0.748463477188882[/C][/ROW]
[ROW][C]26[/C][C]1949.4[/C][C]1775.94697922808[/C][C]-11.2802769830128[/C][C]3.61400243506007[/C][C]0.71192781463576[/C][/ROW]
[ROW][C]27[/C][C]1784.5[/C][C]1789.51160200354[/C][C]-10.8189757839612[/C][C]-19.0616382943607[/C][C]0.057887167407426[/C][/ROW]
[ROW][C]28[/C][C]1671.5[/C][C]1736.20602152654[/C][C]-11.399660581985[/C][C]-39.7037595517603[/C][C]-0.10162181804225[/C][/ROW]
[ROW][C]29[/C][C]1923.8[/C][C]1835.34365093241[/C][C]-10.1323157194735[/C][C]22.7677544927726[/C][C]0.265963678678396[/C][/ROW]
[ROW][C]30[/C][C]1882.8[/C][C]1864.82499288566[/C][C]-9.70811793723327[/C][C]-5.62093136934578[/C][C]0.0954360971629886[/C][/ROW]
[ROW][C]31[/C][C]2165[/C][C]2069.05038763994[/C][C]-7.45624888032936[/C][C]-31.5428067777874[/C][C]0.515511689272018[/C][/ROW]
[ROW][C]32[/C][C]1826.9[/C][C]1908.29446103292[/C][C]-9.07408035160683[/C][C]9.96115284133208[/C][C]-0.369378219275656[/C][/ROW]
[ROW][C]33[/C][C]1511.2[/C][C]1697.63611144059[/C][C]-11.2228108802556[/C][C]-66.3285488248884[/C][C]-0.485651350361482[/C][/ROW]
[ROW][C]34[/C][C]2063.1[/C][C]1891.33004860054[/C][C]-9.01010918755706[/C][C]49.7043754951626[/C][C]0.493606614469561[/C][/ROW]
[ROW][C]35[/C][C]2169.6[/C][C]2067.63458798602[/C][C]-7.00025478233772[/C][C]-8.40565892392238[/C][C]0.446310328514476[/C][/ROW]
[ROW][C]36[/C][C]2495.3[/C][C]2338.81983318372[/C][C]-4.4293363464502[/C][C]-9.30798042040288[/C][C]0.669603365991278[/C][/ROW]
[ROW][C]37[/C][C]2936.9[/C][C]2570.79795110762[/C][C]-6.76848680518416[/C][C]222.424305763972[/C][C]0.60824541177533[/C][/ROW]
[ROW][C]38[/C][C]3076.9[/C][C]2874.46721607565[/C][C]-1.12422687844396[/C][C]33.213831429094[/C][C]0.704979510351887[/C][/ROW]
[ROW][C]39[/C][C]3365.7[/C][C]3174.72153327284[/C][C]4.10067135388132[/C][C]21.0480385603832[/C][C]0.705225106060743[/C][/ROW]
[ROW][C]40[/C][C]3846[/C][C]3594.85597393044[/C][C]9.92605468762803[/C][C]9.27988630321188[/C][C]0.993878597118153[/C][/ROW]
[ROW][C]41[/C][C]3436.2[/C][C]3509.51219914854[/C][C]8.75996676531936[/C][C]-17.4522470986889[/C][C]-0.228775520902446[/C][/ROW]
[ROW][C]42[/C][C]3561.1[/C][C]3552.88203923887[/C][C]9.16129130515632[/C][C]-12.1154504946845[/C][C]0.0831980464275699[/C][/ROW]
[ROW][C]43[/C][C]3328[/C][C]3435.15403154674[/C][C]7.70922465968954[/C][C]-32.5780688576702[/C][C]-0.305069417862847[/C][/ROW]
[ROW][C]44[/C][C]2762.9[/C][C]3030.45925710141[/C][C]2.97624484483925[/C][C]-25.1917699131318[/C][C]-0.991433196978584[/C][/ROW]
[ROW][C]45[/C][C]2923[/C][C]3001.21857416236[/C][C]2.60322205245789[/C][C]-59.2880362402049[/C][C]-0.0774414214185602[/C][/ROW]
[ROW][C]46[/C][C]2731.1[/C][C]2824.67899002255[/C][C]0.508285538680507[/C][C]11.6659724590207[/C][C]-0.430565988830071[/C][/ROW]
[ROW][C]47[/C][C]2571.5[/C][C]2692.02592431402[/C][C]-1.0376752237442[/C][C]-42.3014484985263[/C][C]-0.319980392760999[/C][/ROW]
[ROW][C]48[/C][C]3282.4[/C][C]3041.56780916878[/C][C]2.40563162164623[/C][C]34.787481492326[/C][C]0.842104177678407[/C][/ROW]
[ROW][C]49[/C][C]4606.5[/C][C]3809.82244236413[/C][C]1.55831701711635[/C][C]339.62965984501[/C][C]1.92110010713322[/C][/ROW]
[ROW][C]50[/C][C]4698.7[/C][C]4354.03982200354[/C][C]10.3851347152476[/C][C]43.0952170078648[/C][C]1.25527712658536[/C][/ROW]
[ROW][C]51[/C][C]5093.3[/C][C]4821.32969617957[/C][C]18.0599307239714[/C][C]14.8435159606792[/C][C]1.07212225330036[/C][/ROW]
[ROW][C]52[/C][C]4477.3[/C][C]4645.55126215581[/C][C]15.2388145401662[/C][C]-56.5427701059689[/C][C]-0.462465500273286[/C][/ROW]
[ROW][C]53[/C][C]3850.1[/C][C]4215.83507668479[/C][C]9.39846813715694[/C][C]-107.329251713026[/C][C]-1.06660817603107[/C][/ROW]
[ROW][C]54[/C][C]4275.2[/C][C]4240.48474330435[/C][C]9.58981109315227[/C][C]25.8419819147221[/C][C]0.0365933747200572[/C][/ROW]
[ROW][C]55[/C][C]3975[/C][C]4088.97421150966[/C][C]7.59282566260467[/C][C]-20.2135549960825[/C][C]-0.386581118706613[/C][/ROW]
[ROW][C]56[/C][C]4495.9[/C][C]4330.46607001642[/C][C]10.4977424283804[/C][C]29.3104622161824[/C][C]0.561233178730934[/C][/ROW]
[ROW][C]57[/C][C]4042.4[/C][C]4200.82390993952[/C][C]8.74515577165167[/C][C]-76.8767813250841[/C][C]-0.336231671629836[/C][/ROW]
[ROW][C]58[/C][C]5221.3[/C][C]4760.78238956411[/C][C]15.6789351998338[/C][C]139.807854605831[/C][C]1.32237988555296[/C][/ROW]
[ROW][C]59[/C][C]2555[/C][C]3587.1848882805[/C][C]0.962533963155867[/C][C]-340.28980062923[/C][C]-2.85224479792544[/C][/ROW]
[ROW][C]60[/C][C]2694.6[/C][C]3076.35754446314[/C][C]-4.51063179558055[/C][C]-83.9375240895632[/C][C]-1.22733971380313[/C][/ROW]
[ROW][C]61[/C][C]2757.7[/C][C]2756.47918170796[/C][C]-5.87704987118231[/C][C]186.996957781357[/C][C]-0.778875788211247[/C][/ROW]
[ROW][C]62[/C][C]2760.9[/C][C]2753.41183346211[/C][C]-5.83375870075433[/C][C]5.91082072173317[/C][C]0.00657037545960296[/C][/ROW]
[ROW][C]63[/C][C]3872.9[/C][C]3360.90095172039[/C][C]4.27849551725115[/C][C]167.022850226521[/C][C]1.44237209160838[/C][/ROW]
[ROW][C]64[/C][C]2888.7[/C][C]3113.85144798351[/C][C]0.503327957107125[/C][C]-81.1664322190081[/C][C]-0.598991219400021[/C][/ROW]
[ROW][C]65[/C][C]2529.2[/C][C]2836.46520774413[/C][C]-3.35433028316659[/C][C]-146.950334416703[/C][C]-0.66517952676575[/C][/ROW]
[ROW][C]66[/C][C]3458.3[/C][C]3147.6783319822[/C][C]0.848564043221975[/C][C]128.835080810606[/C][C]0.753630401106775[/C][/ROW]
[ROW][C]67[/C][C]2882.8[/C][C]3034.1093931557[/C][C]-0.662467926269903[/C][C]-85.1676670459878[/C][C]-0.27414063915581[/C][/ROW]
[ROW][C]68[/C][C]2958.5[/C][C]2967.3831004057[/C][C]-1.5354814105131[/C][C]29.3056196595539[/C][C]-0.15827817960257[/C][/ROW]
[ROW][C]69[/C][C]2652.4[/C][C]2864.08211513295[/C][C]-2.88679556425808[/C][C]-152.861345038195[/C][C]-0.243798430713991[/C][/ROW]
[ROW][C]70[/C][C]2869.8[/C][C]2695.52657743497[/C][C]-5.09079384337516[/C][C]270.02150149602[/C][C]-0.396851010628548[/C][/ROW]
[ROW][C]71[/C][C]2501.7[/C][C]2728.3868673458[/C][C]-4.59656642122729[/C][C]-248.617427237054[/C][C]0.0908734887580663[/C][/ROW]
[ROW][C]72[/C][C]2576.1[/C][C]2667.1823112695[/C][C]-5.25268156404715[/C][C]-58.3684691211311[/C][C]-0.135585290178379[/C][/ROW]
[ROW][C]73[/C][C]3347.5[/C][C]2944.6362291617[/C][C]-3.02564905839483[/C][C]237.873605008844[/C][C]0.691171239612016[/C][/ROW]
[ROW][C]74[/C][C]3036.1[/C][C]3046.0599488083[/C][C]-1.45220758906176[/C][C]-68.9268548432366[/C][C]0.245888627186747[/C][/ROW]
[ROW][C]75[/C][C]3345.2[/C][C]3105.55201068114[/C][C]-0.460707048550066[/C][C]205.353809952924[/C][C]0.143603960725709[/C][/ROW]
[ROW][C]76[/C][C]3223.2[/C][C]3203.67732703044[/C][C]1.05195696337254[/C][C]-36.7382764685573[/C][C]0.234782213034533[/C][/ROW]
[ROW][C]77[/C][C]4087[/C][C]3809.99458547641[/C][C]9.80182479817792[/C][C]-70.5793566556852[/C][C]1.44720979664391[/C][/ROW]
[ROW][C]78[/C][C]4157.2[/C][C]3949.4742887529[/C][C]11.617077772041[/C][C]133.134629816751[/C][C]0.310317293260462[/C][/ROW]
[ROW][C]79[/C][C]3368[/C][C]3678.37848863816[/C][C]7.70371066114417[/C][C]-147.713453600218[/C][C]-0.676571455912599[/C][/ROW]
[ROW][C]80[/C][C]3957.5[/C][C]3805.07011781385[/C][C]9.34979681777174[/C][C]83.9681850692248[/C][C]0.284741769007284[/C][/ROW]
[ROW][C]81[/C][C]3469[/C][C]3695.73025954848[/C][C]7.70324853973406[/C][C]-158.444605986448[/C][C]-0.28401393061614[/C][/ROW]
[ROW][C]82[/C][C]4501.6[/C][C]3996.58310043762[/C][C]11.7648581410714[/C][C]336.374936633945[/C][C]0.701388291906766[/C][/ROW]
[ROW][C]83[/C][C]3181.4[/C][C]3688.65912963458[/C][C]7.43465927718693[/C][C]-323.395991811846[/C][C]-0.764524753635127[/C][/ROW]
[ROW][C]84[/C][C]3464.5[/C][C]3610.75961414898[/C][C]6.37681651814135[/C][C]-97.1809598360405[/C][C]-0.204198145188561[/C][/ROW]
[ROW][C]85[/C][C]4186.9[/C][C]3810.39177546684[/C][C]8.35601049210202[/C][C]264.476431240844[/C][C]0.469261097061251[/C][/ROW]
[ROW][C]86[/C][C]3064.7[/C][C]3441.65479607695[/C][C]2.71190826380343[/C][C]-163.390564496996[/C][C]-0.891496401624712[/C][/ROW]
[ROW][C]87[/C][C]4011.7[/C][C]3650.15008658433[/C][C]6.02451927344858[/C][C]245.647565928266[/C][C]0.485723625903981[/C][/ROW]
[ROW][C]88[/C][C]3537.1[/C][C]3661.5314045313[/C][C]6.10775594043336[/C][C]-127.480820670298[/C][C]0.0127508983383975[/C][/ROW]
[ROW][C]89[/C][C]4879.5[/C][C]4394.95133263836[/C][C]16.9174542414894[/C][C]68.193571337557[/C][C]1.73758491368367[/C][/ROW]
[ROW][C]90[/C][C]4488.7[/C][C]4383.30166425594[/C][C]16.5040689711985[/C][C]121.776965882253[/C][C]-0.068301105611117[/C][/ROW]
[ROW][C]91[/C][C]4632.9[/C][C]4624.45828413799[/C][C]19.7208575533197[/C][C]-120.3956376081[/C][C]0.537145571503131[/C][/ROW]
[ROW][C]92[/C][C]4405.8[/C][C]4465.86796220541[/C][C]17.1717551421737[/C][C]42.1929372671517[/C][C]-0.426323563183069[/C][/ROW]
[ROW][C]93[/C][C]2615.2[/C][C]3539.90785155099[/C][C]3.67540347615874[/C][C]-383.851883276928[/C][C]-2.25480998965566[/C][/ROW]
[ROW][C]94[/C][C]3338[/C][C]3184.09715810441[/C][C]-1.4512676931549[/C][C]360.031790131274[/C][C]-0.85929233883555[/C][/ROW]
[ROW][C]95[/C][C]2825.2[/C][C]3140.83115298632[/C][C]-2.03488158639316[/C][C]-291.663121416006[/C][C]-0.0999009150948592[/C][/ROW]
[ROW][C]96[/C][C]3012.7[/C][C]3125.99349138606[/C][C]-2.20224723746266[/C][C]-105.954653975797[/C][C]-0.03061452406771[/C][/ROW]
[ROW][C]97[/C][C]4537.5[/C][C]3728.32980601259[/C][C]4.95352846018361[/C][C]460.407333370136[/C][C]1.46103289974089[/C][/ROW]
[ROW][C]98[/C][C]5676.7[/C][C]4953.61140858531[/C][C]23.23606353261[/C][C]30.7119750469977[/C][C]2.89292973634157[/C][/ROW]
[ROW][C]99[/C][C]5575.4[/C][C]5226.13602882686[/C][C]27.2143123439022[/C][C]208.707393115849[/C][C]0.589293915910753[/C][/ROW]
[ROW][C]100[/C][C]6643.4[/C][C]6178.2048032686[/C][C]41.6788250258397[/C][C]-60.4654839624389[/C][C]2.20081783062137[/C][/ROW]
[ROW][C]101[/C][C]5590.6[/C][C]5865.47707246912[/C][C]36.3149356392055[/C][C]-72.4402132810799[/C][C]-0.846177462036207[/C][/ROW]
[ROW][C]102[/C][C]4697.6[/C][C]5172.99554389712[/C][C]25.5229514265488[/C][C]-58.5008845431084[/C][C]-1.74135863562718[/C][/ROW]
[ROW][C]103[/C][C]5078.1[/C][C]5152.92516078775[/C][C]24.8542961574024[/C][C]-48.7377051450747[/C][C]-0.108941701554742[/C][/ROW]
[ROW][C]104[/C][C]5769.9[/C][C]5400.85263972928[/C][C]28.1180041211806[/C][C]241.41000750434[/C][C]0.532985570821992[/C][/ROW]
[ROW][C]105[/C][C]5561.4[/C][C]5688.26399180337[/C][C]31.910036422433[/C][C]-275.217682408022[/C][C]0.619480402401029[/C][/ROW]
[ROW][C]106[/C][C]7268.8[/C][C]6383.08244895465[/C][C]41.5593786077061[/C][C]506.500578519088[/C][C]1.58338942640373[/C][/ROW]
[ROW][C]107[/C][C]6496.7[/C][C]6650.79585330135[/C][C]44.7886689618624[/C][C]-283.411563604183[/C][C]0.539914046896129[/C][/ROW]
[ROW][C]108[/C][C]6489.3[/C][C]6711.0754024275[/C][C]44.9996036998466[/C][C]-230.634461068238[/C][C]0.0370227326226909[/C][/ROW]
[ROW][C]109[/C][C]10883.5[/C][C]8899.89319432629[/C][C]72.7023475219054[/C][C]751.174466129931[/C][C]5.16397954543848[/C][/ROW]
[ROW][C]110[/C][C]7998.6[/C][C]8501.87865654329[/C][C]65.6233208983671[/C][C]-235.934433195257[/C][C]-1.11790566265187[/C][/ROW]
[ROW][C]111[/C][C]7340[/C][C]7826.98535052919[/C][C]53.8898795851172[/C][C]-69.0131168169493[/C][C]-1.75276965257393[/C][/ROW]
[ROW][C]112[/C][C]7814.4[/C][C]7827.41770574238[/C][C]53.0517040174996[/C][C]17.3368204335279[/C][C]-0.127191896323315[/C][/ROW]
[ROW][C]113[/C][C]5729.6[/C][C]6660.62499825715[/C][C]34.3778169257674[/C][C]-235.328783824769[/C][C]-2.91118924922466[/C][/ROW]
[ROW][C]114[/C][C]6463.5[/C][C]6563.08445565426[/C][C]32.3935782048071[/C][C]-24.2455237841868[/C][C]-0.315052973895156[/C][/ROW]
[ROW][C]115[/C][C]6315.4[/C][C]6478.78951713997[/C][C]30.6535220246295[/C][C]-96.7328447618162[/C][C]-0.278682339021362[/C][/ROW]
[ROW][C]116[/C][C]5357.1[/C][C]5753.84834893202[/C][C]19.4186072726466[/C][C]34.8690636441552[/C][C]-1.80441482488135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297974&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297974&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
11418.71418.7000
21344.11366.5713061792-3.56948543355039-4.55760419584237-0.0864028988960897
31574.61493.890813050091.544630883862299.239876029571040.292661484873991
41621.61571.089414060243.33192369930565.002242271569590.179825504957966
51887.21758.633959082816.5758525411408315.27141071214060.443760355708614
62055.31935.432109470929.1890909715013614.52293341342130.411518741141517
71606.81741.816218725136.24370225181014-9.2660820280699-0.490782217369603
81494.81591.981376686044.02174804146672-0.353140070032033-0.377784622654411
916361615.191869630484.293342111779258.903340285665980.0464428241088417
101485.71537.989773860083.14030125063569-1.73671541869426-0.197211977415325
111369.71436.611691991461.65909397165056-2.0903800652583-0.252874723759127
121333.81373.816261318880.743515679184307-0.0512402184725609-0.155910038391936
131614.91473.21323634632-6.2319608127911777.14280073034290.300334584064159
141297.31368.58703836833-9.42463389418662-24.7100252891915-0.200427887667687
151226.21280.79679310012-11.1681172021514-10.3453109220686-0.180783879335554
161098.51177.8368014445-12.5180224999796-24.5256385822624-0.219545081172962
171258.51223.83325043745-11.8350439981604-0.7198676344310480.141037677287757
181065.21126.54425967152-12.7424615853127-9.50062997275184-0.206342194410759
191000.41057.90714095379-13.3192437158924-23.569595065082-0.135019358418252
201820.21504.58144237659-8.582179956377436.30242412461611.11114395722603
211224.81350.17640973425-10.0960250439965-36.8444588055465-0.352193304487407
221428.41394.5378922872-9.523742363462410.807860099494290.131502886341638
2311441252.6322835628-10.9313856574085-28.2995931173173-0.31961458756517
241166.91203.89290916498-11.2962333416289-14.0403337730155-0.091233893957251
251902.31470.17087786351-18.5387613285876258.9196169442270.748463477188882
261949.41775.94697922808-11.28027698301283.614002435060070.71192781463576
271784.51789.51160200354-10.8189757839612-19.06163829436070.057887167407426
281671.51736.20602152654-11.399660581985-39.7037595517603-0.10162181804225
291923.81835.34365093241-10.132315719473522.76775449277260.265963678678396
301882.81864.82499288566-9.70811793723327-5.620931369345780.0954360971629886
3121652069.05038763994-7.45624888032936-31.54280677778740.515511689272018
321826.91908.29446103292-9.074080351606839.96115284133208-0.369378219275656
331511.21697.63611144059-11.2228108802556-66.3285488248884-0.485651350361482
342063.11891.33004860054-9.0101091875570649.70437549516260.493606614469561
352169.62067.63458798602-7.00025478233772-8.405658923922380.446310328514476
362495.32338.81983318372-4.4293363464502-9.307980420402880.669603365991278
372936.92570.79795110762-6.76848680518416222.4243057639720.60824541177533
383076.92874.46721607565-1.1242268784439633.2138314290940.704979510351887
393365.73174.721533272844.1006713538813221.04803856038320.705225106060743
4038463594.855973930449.926054687628039.279886303211880.993878597118153
413436.23509.512199148548.75996676531936-17.4522470986889-0.228775520902446
423561.13552.882039238879.16129130515632-12.11545049468450.0831980464275699
4333283435.154031546747.70922465968954-32.5780688576702-0.305069417862847
442762.93030.459257101412.97624484483925-25.1917699131318-0.991433196978584
4529233001.218574162362.60322205245789-59.2880362402049-0.0774414214185602
462731.12824.678990022550.50828553868050711.6659724590207-0.430565988830071
472571.52692.02592431402-1.0376752237442-42.3014484985263-0.319980392760999
483282.43041.567809168782.4056316216462334.7874814923260.842104177678407
494606.53809.822442364131.55831701711635339.629659845011.92110010713322
504698.74354.0398220035410.385134715247643.09521700786481.25527712658536
515093.34821.3296961795718.059930723971414.84351596067921.07212225330036
524477.34645.5512621558115.2388145401662-56.5427701059689-0.462465500273286
533850.14215.835076684799.39846813715694-107.329251713026-1.06660817603107
544275.24240.484743304359.5898110931522725.84198191472210.0365933747200572
5539754088.974211509667.59282566260467-20.2135549960825-0.386581118706613
564495.94330.4660700164210.497742428380429.31046221618240.561233178730934
574042.44200.823909939528.74515577165167-76.8767813250841-0.336231671629836
585221.34760.7823895641115.6789351998338139.8078546058311.32237988555296
5925553587.18488828050.962533963155867-340.28980062923-2.85224479792544
602694.63076.35754446314-4.51063179558055-83.9375240895632-1.22733971380313
612757.72756.47918170796-5.87704987118231186.996957781357-0.778875788211247
622760.92753.41183346211-5.833758700754335.910820721733170.00657037545960296
633872.93360.900951720394.27849551725115167.0228502265211.44237209160838
642888.73113.851447983510.503327957107125-81.1664322190081-0.598991219400021
652529.22836.46520774413-3.35433028316659-146.950334416703-0.66517952676575
663458.33147.67833198220.848564043221975128.8350808106060.753630401106775
672882.83034.1093931557-0.662467926269903-85.1676670459878-0.27414063915581
682958.52967.3831004057-1.535481410513129.3056196595539-0.15827817960257
692652.42864.08211513295-2.88679556425808-152.861345038195-0.243798430713991
702869.82695.52657743497-5.09079384337516270.02150149602-0.396851010628548
712501.72728.3868673458-4.59656642122729-248.6174272370540.0908734887580663
722576.12667.1823112695-5.25268156404715-58.3684691211311-0.135585290178379
733347.52944.6362291617-3.02564905839483237.8736050088440.691171239612016
743036.13046.0599488083-1.45220758906176-68.92685484323660.245888627186747
753345.23105.55201068114-0.460707048550066205.3538099529240.143603960725709
763223.23203.677327030441.05195696337254-36.73827646855730.234782213034533
7740873809.994585476419.80182479817792-70.57935665568521.44720979664391
784157.23949.474288752911.617077772041133.1346298167510.310317293260462
7933683678.378488638167.70371066114417-147.713453600218-0.676571455912599
803957.53805.070117813859.3497968177717483.96818506922480.284741769007284
8134693695.730259548487.70324853973406-158.444605986448-0.28401393061614
824501.63996.5831004376211.7648581410714336.3749366339450.701388291906766
833181.43688.659129634587.43465927718693-323.395991811846-0.764524753635127
843464.53610.759614148986.37681651814135-97.1809598360405-0.204198145188561
854186.93810.391775466848.35601049210202264.4764312408440.469261097061251
863064.73441.654796076952.71190826380343-163.390564496996-0.891496401624712
874011.73650.150086584336.02451927344858245.6475659282660.485723625903981
883537.13661.53140453136.10775594043336-127.4808206702980.0127508983383975
894879.54394.9513326383616.917454241489468.1935713375571.73758491368367
904488.74383.3016642559416.5040689711985121.776965882253-0.068301105611117
914632.94624.4582841379919.7208575533197-120.39563760810.537145571503131
924405.84465.8679622054117.171755142173742.1929372671517-0.426323563183069
932615.23539.907851550993.67540347615874-383.851883276928-2.25480998965566
9433383184.09715810441-1.4512676931549360.031790131274-0.85929233883555
952825.23140.83115298632-2.03488158639316-291.663121416006-0.0999009150948592
963012.73125.99349138606-2.20224723746266-105.954653975797-0.03061452406771
974537.53728.329806012594.95352846018361460.4073333701361.46103289974089
985676.74953.6114085853123.2360635326130.71197504699772.89292973634157
995575.45226.1360288268627.2143123439022208.7073931158490.589293915910753
1006643.46178.204803268641.6788250258397-60.46548396243892.20081783062137
1015590.65865.4770724691236.3149356392055-72.4402132810799-0.846177462036207
1024697.65172.9955438971225.5229514265488-58.5008845431084-1.74135863562718
1035078.15152.9251607877524.8542961574024-48.7377051450747-0.108941701554742
1045769.95400.8526397292828.1180041211806241.410007504340.532985570821992
1055561.45688.2639918033731.910036422433-275.2176824080220.619480402401029
1067268.86383.0824489546541.5593786077061506.5005785190881.58338942640373
1076496.76650.7958533013544.7886689618624-283.4115636041830.539914046896129
1086489.36711.075402427544.9996036998466-230.6344610682380.0370227326226909
10910883.58899.8931943262972.7023475219054751.1744661299315.16397954543848
1107998.68501.8786565432965.6233208983671-235.934433195257-1.11790566265187
11173407826.9853505291953.8898795851172-69.0131168169493-1.75276965257393
1127814.47827.4177057423853.051704017499617.3368204335279-0.127191896323315
1135729.66660.6249982571534.3778169257674-235.328783824769-2.91118924922466
1146463.56563.0844556542632.3935782048071-24.2455237841868-0.315052973895156
1156315.46478.7895171399730.6535220246295-96.7328447618162-0.278682339021362
1165357.15753.8483489320219.418607272646634.8690636441552-1.80441482488135







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15007.692171754975642.17361289807-634.481441143098
25922.419359477785681.50342943569240.915930042087
35035.913602567155720.83324597331-684.91964340616
44896.978467829145760.16306251093-863.184594681794
56856.834408613265799.492879048551057.34152956471
65894.597129798755838.8226955861855.7744342125713
76084.026943720925878.1525121238205.874431597118
86495.654722467275917.48232866142578.172393805847
95895.093986979155956.81214519904-61.71815821989
106121.045629075445996.14196173666124.903667338779
116087.146269120896035.4717782742851.6744908466065
126004.448554855136074.80159481191-70.3530399567754

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 5007.69217175497 & 5642.17361289807 & -634.481441143098 \tabularnewline
2 & 5922.41935947778 & 5681.50342943569 & 240.915930042087 \tabularnewline
3 & 5035.91360256715 & 5720.83324597331 & -684.91964340616 \tabularnewline
4 & 4896.97846782914 & 5760.16306251093 & -863.184594681794 \tabularnewline
5 & 6856.83440861326 & 5799.49287904855 & 1057.34152956471 \tabularnewline
6 & 5894.59712979875 & 5838.82269558618 & 55.7744342125713 \tabularnewline
7 & 6084.02694372092 & 5878.1525121238 & 205.874431597118 \tabularnewline
8 & 6495.65472246727 & 5917.48232866142 & 578.172393805847 \tabularnewline
9 & 5895.09398697915 & 5956.81214519904 & -61.71815821989 \tabularnewline
10 & 6121.04562907544 & 5996.14196173666 & 124.903667338779 \tabularnewline
11 & 6087.14626912089 & 6035.47177827428 & 51.6744908466065 \tabularnewline
12 & 6004.44855485513 & 6074.80159481191 & -70.3530399567754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297974&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]5007.69217175497[/C][C]5642.17361289807[/C][C]-634.481441143098[/C][/ROW]
[ROW][C]2[/C][C]5922.41935947778[/C][C]5681.50342943569[/C][C]240.915930042087[/C][/ROW]
[ROW][C]3[/C][C]5035.91360256715[/C][C]5720.83324597331[/C][C]-684.91964340616[/C][/ROW]
[ROW][C]4[/C][C]4896.97846782914[/C][C]5760.16306251093[/C][C]-863.184594681794[/C][/ROW]
[ROW][C]5[/C][C]6856.83440861326[/C][C]5799.49287904855[/C][C]1057.34152956471[/C][/ROW]
[ROW][C]6[/C][C]5894.59712979875[/C][C]5838.82269558618[/C][C]55.7744342125713[/C][/ROW]
[ROW][C]7[/C][C]6084.02694372092[/C][C]5878.1525121238[/C][C]205.874431597118[/C][/ROW]
[ROW][C]8[/C][C]6495.65472246727[/C][C]5917.48232866142[/C][C]578.172393805847[/C][/ROW]
[ROW][C]9[/C][C]5895.09398697915[/C][C]5956.81214519904[/C][C]-61.71815821989[/C][/ROW]
[ROW][C]10[/C][C]6121.04562907544[/C][C]5996.14196173666[/C][C]124.903667338779[/C][/ROW]
[ROW][C]11[/C][C]6087.14626912089[/C][C]6035.47177827428[/C][C]51.6744908466065[/C][/ROW]
[ROW][C]12[/C][C]6004.44855485513[/C][C]6074.80159481191[/C][C]-70.3530399567754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297974&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297974&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
15007.692171754975642.17361289807-634.481441143098
25922.419359477785681.50342943569240.915930042087
35035.913602567155720.83324597331-684.91964340616
44896.978467829145760.16306251093-863.184594681794
56856.834408613265799.492879048551057.34152956471
65894.597129798755838.8226955861855.7744342125713
76084.026943720925878.1525121238205.874431597118
86495.654722467275917.48232866142578.172393805847
95895.093986979155956.81214519904-61.71815821989
106121.045629075445996.14196173666124.903667338779
116087.146269120896035.4717782742851.6744908466065
126004.448554855136074.80159481191-70.3530399567754



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')