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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, 14 Dec 2016 10:56:01 +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/14/t1481710405o4di3f2cwzz60o6.htm/, Retrieved Fri, 01 Nov 2024 03:39:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299278, Retrieved Fri, 01 Nov 2024 03:39:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsF1 competition
Estimated Impact150
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...] [2016-12-14 09:56:01] [00d6a26c230b6c589ee3bbc701d55499] [Current]
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Dataseries X:
3840
3140
4580
4740
3920
4900
3400
3440
2600
2220
2190
2550
2720
3720
4710
5070
6030
5280
4420
3940
2750
2980
2690
2650
4000
4150
6050
6280
5520
4800
4610
3530
2790
2750
2470
2610
3680
3820
4460
4760
3290
3610
3650
3130
2850
2720
2740
2760
3330
3850
5430
5180
4770
5360
4950
3720
3330
3000
2760
3040
3260
3780
4670
4320
4080
4210
3350
3390
2630
2350
2330
2230
2830
3230
4240
3750
4160
3960
3000
2890
2300
2320
2270
1970
2920
3310
4370
3990
3970
3850
3510
2840
2130
2280
1960
1740
2370
1980
2680
3510
3350
3290
3150
2490
2490
2930
3590
2040
2480
2760
3400
3470
3130
3670
3080
2430




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 time7 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299278&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]7 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299278&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 time7 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
138403840000
231403378.73928540231-441.002319034933-23.1554705374842-1.45346518058223
345804270.52925520006499.36252711018534.36579390268582.51622833975735
447404761.70873678208493.721001798134-20.0531965328994-0.0152425294007286
539204171.40440609373-260.295286436165-34.85538105162-2.00518176880343
649004717.5094153553301.76766369853622.26941545149191.48791598612571
734003708.05881447572-612.583997679904-47.5697489227614-2.41991635877642
834403374.32277598633-418.11209478343110.27415185209070.51469124202741
926002672.95298985716-615.651081667897-16.6774038282152-0.52280009260688
1022202194.18567878407-520.195633676746-1.379164865854970.252628138488499
1121902102.00198211865-221.7294283597492.970576097644560.789907217842839
1225502435.63167748696165.5385991360184.042901828281871.02492612486024
1327202617.43011301874176.5699244732899.4273403788740.0329022468943481
1437203632.43579873482692.025329166997-26.21654831143621.25463955131998
1547104603.92395309973883.21429073997652.47355602145170.510341599406078
1650705125.26924550336633.34131322445213.172140269952-0.653589977701227
1760306014.93759192899809.57894886147-33.71521646618420.464886574106217
1852805516.29999774136-91.145188919224614.2664129295434-2.38349957574579
1944204631.07590739199-638.463561301925-58.7625060709934-1.44851843775799
2039403909.3774918498-695.84461728756446.5906575905267-0.151859878759221
2127502835.97114443021-956.118607475318-13.5403914541-0.688827098449572
2229802755.07541773048-352.81025122500457.03094889242471.59668953544719
2326902636.33862216724-191.4669028135418.761411887472740.427004018237362
2426502594.9783113447-88.059817209669926.24509020875350.273695687685055
2540003680.76187881659712.24352937166195.5250218475832.24858944917219
2641504244.7087647147617.381400202226-71.7065566251277-0.239872091116836
2760505770.920590145771233.03844123724109.5208462022961.64335501445905
2862806464.61896096412863.894795370247-84.6109592400094-0.969408162445285
2955205863.33961106202-135.440797967285-71.1395228437983-2.63711075449169
3048004932.32917743157-678.53862897094316.2362195745503-1.43710935348022
3146104579.22435155323-456.172937071835-30.07892470576320.588509750782495
3235303598.46632297724-814.69231629061429.6461952002031-0.948826860872665
3327902833.80659422151-780.499094687744-53.16404230480940.0904939195485752
3427502576.54696500512-422.92132494048275.59608183399630.946351495535097
3524702408.64741473008-248.66250634906813.66402846828640.461184584408936
3626102554.0195307632520.3243166146576-17.63081085327260.712161185856549
3736803360.50172461623555.28600107227172.1127626273791.46628711419088
3838203977.03569184382595.181904067248-167.0956775296860.102639903676472
3944604391.98618426764473.87233891348101.007255731359-0.323528223957812
4047604778.8682838812414.703204920424-2.95595517938009-0.155772392296708
4132903692.11166009676-603.603577028766-127.658546061212-2.68756482936943
4236103496.91754109904-326.48417208094738.10750596809430.733254425318873
4336503551.67883990089-67.565862854864328.23353034686880.685253749173065
4431303182.45801371439-272.483011330353.00976614514414-0.542315290740357
4528502925.62232730795-261.853609658651-78.49956983143430.0281311889532525
4627202654.5771250362-268.0972610178667.1129742531981-0.0165242505925542
4727402671.30176991298-74.669113295762316.33992296099960.511916180103459
4827602788.3243611050955.3660641169996-63.52550144866490.344421006295209
4933303110.71547905422236.542342623121169.8997977341970.490028120882771
5038503898.55080849581599.119135847119-141.813327129650.94180067950228
5154305168.395368189041048.79443641972140.3204959127361.19786516689011
5251805298.8251041264426.87689473504547.6920161372126-1.64023785523859
5347705075.65654947159-12.3029880119862-188.058291023398-1.15924435720128
5453605281.77050792943135.2821607012438.5775056307350.390479187980275
5549505002.11297397465-145.33542699859823.3302353122844-0.742687858547684
5637203940.3505795277-765.293117548797-53.6833365056658-1.64072175863313
5733303337.34879227909-655.50102786687-36.86519937725890.290569742612641
5830002887.49036451048-516.3915884418375.1108718959280.368163169867688
5927602666.55478347024-316.59809704500539.73388435960010.528766704902433
6030402963.3530264340797.751149141162-34.77101632030171.09790564459537
6132603163.2673569198166.87683300286678.03459961463020.18549597877877
6237803872.93605361268525.844921534268-186.3070547524790.937892075935303
6346704452.00263305716561.443605228659208.4479016462560.0947190817479567
6443204386.60327907854138.28203797895346.4065957561254-1.11751185642857
6540804340.6299391594214.1208473138647-227.512797388954-0.327782785859868
6642104184.45339169096-100.61666905743356.2384460688332-0.303545784635347
6733503413.53517355982-552.59818609554357.4613220338201-1.19622683900889
6833903316.47818205706-245.315735548555-8.735701899685530.81322487521402
6926302756.11257750334-457.841147998416-69.2205488173186-0.562458448977055
7023502283.34155120012-467.91138037862369.3542596922807-0.0266515629357425
7123302223.08713847743-193.07273273791733.34199887930260.727398058820998
7222302227.01682791007-60.3710354716885-32.55511750217790.351718731301237
7328302686.62708010589290.62133333196748.94919647362050.937267427184289
7432303348.46986908434536.944550466266-182.9682106162040.645990762216787
7542403968.95635701592.749198830773256.1265331786330.148330160191332
7637503877.67740341752132.058816684907-4.83491890768045-1.21778164417322
7741604293.13768722283322.682572749897-183.8657831420820.503341901178464
7839604006.6925119694-86.87617092571362.5562325399833-1.08342584878908
7930003171.89242290222-590.130740580691-37.5344323521474-1.33192421535762
8028902796.36520467766-445.67036289323955.06761166842040.382316084856256
8123002356.18887426417-441.971798696255-57.17629684725340.0097884285146448
8223202198.20175965049-250.82330539463470.76541391165390.505886019426765
8322702183.45239525541-92.007496232743144.14900154315060.420346664522298
8419702059.57646802758-113.433352723006-83.8529388194332-0.056796361946719
8529202713.78188572726403.70756680775167.63690641688881.37661984655088
8633103437.45124770049616.457342742792-183.3884174474510.559326669361359
8743704066.01675342063624.539334265834301.8278344869620.0214639297991569
8839904174.50814352291277.597320910575-92.0881563307845-0.917720735071705
8939704170.4467585144188.3955472946109-150.164448070471-0.49970010084349
9038503825.03175108108-202.853394155083102.515808689728-0.770399370043574
9135103569.35686968892-238.33950682712-49.8996578249931-0.0939174086493037
9228402891.90375315104-533.47551245166726.7523740217043-0.781084001169778
9321302231.71376336314-618.649808927583-79.0141974658877-0.225417922147866
9422802088.14691077977-299.371568894743106.761766909980.844986586268361
9519601880.36348495552-237.85444151814363.24195447900670.162830104520873
9617401842.51924862471-103.562285644652-138.3348694866170.355997739214639
9723702221.27952644068220.84311479977662.02874144318090.861801862927948
9819802234.6798399080582.7298836819939-218.270966810069-0.363717037254999
9926802335.0970022357894.5309936807675341.7605541989390.0313197167560972
10035103346.59899300097710.169793389808-0.4824383100041131.62922849179125
10133503600.49463795572403.976464020836-169.183932954639-0.808878543083779
10232903353.00204110888-32.922601262746253.1830684308517-1.15560062269876
10331503182.15945479889-125.467797480166-7.52554956086523-0.244925804389593
10424902569.83544761996-452.3066202581047.16755612325855-0.864990450825186
10524902499.88855924299-195.593876215591-78.22383119088010.679402623152704
10629302719.2558272900882.9456341477656136.5979747910070.737168934485167
10735903392.41059583825478.8998096120792.18724146931241.04811784471595
10820402567.97476614943-395.345420524482-295.070215666665-2.31744050914963
10924802335.97641401419-285.624250355151114.7610103944250.291088648625699
11027602800.34452400303214.125338549627-172.3127536476241.31762204038507
11134003136.75671683939295.698522691995241.5443359700620.216375603040091
11234703435.83817844823297.96730660779733.55818386382150.00600599104207181
11331303341.6482921680635.0062449687202-141.849467523127-0.694834705578163
11436703545.44879095324148.11162722313894.49834421873290.299152303508781
11530803166.3582288251-205.3122862385277.63641801321179-0.935335180567832
11624302553.31674989925-478.775176021785-50.5816725106638-0.723732580348708

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 3840 & 3840 & 0 & 0 & 0 \tabularnewline
2 & 3140 & 3378.73928540231 & -441.002319034933 & -23.1554705374842 & -1.45346518058223 \tabularnewline
3 & 4580 & 4270.52925520006 & 499.362527110185 & 34.3657939026858 & 2.51622833975735 \tabularnewline
4 & 4740 & 4761.70873678208 & 493.721001798134 & -20.0531965328994 & -0.0152425294007286 \tabularnewline
5 & 3920 & 4171.40440609373 & -260.295286436165 & -34.85538105162 & -2.00518176880343 \tabularnewline
6 & 4900 & 4717.5094153553 & 301.767663698536 & 22.2694154514919 & 1.48791598612571 \tabularnewline
7 & 3400 & 3708.05881447572 & -612.583997679904 & -47.5697489227614 & -2.41991635877642 \tabularnewline
8 & 3440 & 3374.32277598633 & -418.112094783431 & 10.2741518520907 & 0.51469124202741 \tabularnewline
9 & 2600 & 2672.95298985716 & -615.651081667897 & -16.6774038282152 & -0.52280009260688 \tabularnewline
10 & 2220 & 2194.18567878407 & -520.195633676746 & -1.37916486585497 & 0.252628138488499 \tabularnewline
11 & 2190 & 2102.00198211865 & -221.729428359749 & 2.97057609764456 & 0.789907217842839 \tabularnewline
12 & 2550 & 2435.63167748696 & 165.538599136018 & 4.04290182828187 & 1.02492612486024 \tabularnewline
13 & 2720 & 2617.43011301874 & 176.56992447328 & 99.427340378874 & 0.0329022468943481 \tabularnewline
14 & 3720 & 3632.43579873482 & 692.025329166997 & -26.2165483114362 & 1.25463955131998 \tabularnewline
15 & 4710 & 4603.92395309973 & 883.214290739976 & 52.4735560214517 & 0.510341599406078 \tabularnewline
16 & 5070 & 5125.26924550336 & 633.341313224452 & 13.172140269952 & -0.653589977701227 \tabularnewline
17 & 6030 & 6014.93759192899 & 809.57894886147 & -33.7152164661842 & 0.464886574106217 \tabularnewline
18 & 5280 & 5516.29999774136 & -91.1451889192246 & 14.2664129295434 & -2.38349957574579 \tabularnewline
19 & 4420 & 4631.07590739199 & -638.463561301925 & -58.7625060709934 & -1.44851843775799 \tabularnewline
20 & 3940 & 3909.3774918498 & -695.844617287564 & 46.5906575905267 & -0.151859878759221 \tabularnewline
21 & 2750 & 2835.97114443021 & -956.118607475318 & -13.5403914541 & -0.688827098449572 \tabularnewline
22 & 2980 & 2755.07541773048 & -352.810251225004 & 57.0309488924247 & 1.59668953544719 \tabularnewline
23 & 2690 & 2636.33862216724 & -191.466902813541 & 8.76141188747274 & 0.427004018237362 \tabularnewline
24 & 2650 & 2594.9783113447 & -88.0598172096699 & 26.2450902087535 & 0.273695687685055 \tabularnewline
25 & 4000 & 3680.76187881659 & 712.243529371661 & 95.525021847583 & 2.24858944917219 \tabularnewline
26 & 4150 & 4244.7087647147 & 617.381400202226 & -71.7065566251277 & -0.239872091116836 \tabularnewline
27 & 6050 & 5770.92059014577 & 1233.03844123724 & 109.520846202296 & 1.64335501445905 \tabularnewline
28 & 6280 & 6464.61896096412 & 863.894795370247 & -84.6109592400094 & -0.969408162445285 \tabularnewline
29 & 5520 & 5863.33961106202 & -135.440797967285 & -71.1395228437983 & -2.63711075449169 \tabularnewline
30 & 4800 & 4932.32917743157 & -678.538628970943 & 16.2362195745503 & -1.43710935348022 \tabularnewline
31 & 4610 & 4579.22435155323 & -456.172937071835 & -30.0789247057632 & 0.588509750782495 \tabularnewline
32 & 3530 & 3598.46632297724 & -814.692316290614 & 29.6461952002031 & -0.948826860872665 \tabularnewline
33 & 2790 & 2833.80659422151 & -780.499094687744 & -53.1640423048094 & 0.0904939195485752 \tabularnewline
34 & 2750 & 2576.54696500512 & -422.921324940482 & 75.5960818339963 & 0.946351495535097 \tabularnewline
35 & 2470 & 2408.64741473008 & -248.662506349068 & 13.6640284682864 & 0.461184584408936 \tabularnewline
36 & 2610 & 2554.01953076325 & 20.3243166146576 & -17.6308108532726 & 0.712161185856549 \tabularnewline
37 & 3680 & 3360.50172461623 & 555.28600107227 & 172.112762627379 & 1.46628711419088 \tabularnewline
38 & 3820 & 3977.03569184382 & 595.181904067248 & -167.095677529686 & 0.102639903676472 \tabularnewline
39 & 4460 & 4391.98618426764 & 473.87233891348 & 101.007255731359 & -0.323528223957812 \tabularnewline
40 & 4760 & 4778.8682838812 & 414.703204920424 & -2.95595517938009 & -0.155772392296708 \tabularnewline
41 & 3290 & 3692.11166009676 & -603.603577028766 & -127.658546061212 & -2.68756482936943 \tabularnewline
42 & 3610 & 3496.91754109904 & -326.484172080947 & 38.1075059680943 & 0.733254425318873 \tabularnewline
43 & 3650 & 3551.67883990089 & -67.5658628548643 & 28.2335303468688 & 0.685253749173065 \tabularnewline
44 & 3130 & 3182.45801371439 & -272.48301133035 & 3.00976614514414 & -0.542315290740357 \tabularnewline
45 & 2850 & 2925.62232730795 & -261.853609658651 & -78.4995698314343 & 0.0281311889532525 \tabularnewline
46 & 2720 & 2654.5771250362 & -268.09726101786 & 67.1129742531981 & -0.0165242505925542 \tabularnewline
47 & 2740 & 2671.30176991298 & -74.6691132957623 & 16.3399229609996 & 0.511916180103459 \tabularnewline
48 & 2760 & 2788.32436110509 & 55.3660641169996 & -63.5255014486649 & 0.344421006295209 \tabularnewline
49 & 3330 & 3110.71547905422 & 236.542342623121 & 169.899797734197 & 0.490028120882771 \tabularnewline
50 & 3850 & 3898.55080849581 & 599.119135847119 & -141.81332712965 & 0.94180067950228 \tabularnewline
51 & 5430 & 5168.39536818904 & 1048.79443641972 & 140.320495912736 & 1.19786516689011 \tabularnewline
52 & 5180 & 5298.8251041264 & 426.876894735045 & 47.6920161372126 & -1.64023785523859 \tabularnewline
53 & 4770 & 5075.65654947159 & -12.3029880119862 & -188.058291023398 & -1.15924435720128 \tabularnewline
54 & 5360 & 5281.77050792943 & 135.28216070124 & 38.577505630735 & 0.390479187980275 \tabularnewline
55 & 4950 & 5002.11297397465 & -145.335426998598 & 23.3302353122844 & -0.742687858547684 \tabularnewline
56 & 3720 & 3940.3505795277 & -765.293117548797 & -53.6833365056658 & -1.64072175863313 \tabularnewline
57 & 3330 & 3337.34879227909 & -655.50102786687 & -36.8651993772589 & 0.290569742612641 \tabularnewline
58 & 3000 & 2887.49036451048 & -516.39158844183 & 75.110871895928 & 0.368163169867688 \tabularnewline
59 & 2760 & 2666.55478347024 & -316.598097045005 & 39.7338843596001 & 0.528766704902433 \tabularnewline
60 & 3040 & 2963.35302643407 & 97.751149141162 & -34.7710163203017 & 1.09790564459537 \tabularnewline
61 & 3260 & 3163.2673569198 & 166.876833002866 & 78.0345996146302 & 0.18549597877877 \tabularnewline
62 & 3780 & 3872.93605361268 & 525.844921534268 & -186.307054752479 & 0.937892075935303 \tabularnewline
63 & 4670 & 4452.00263305716 & 561.443605228659 & 208.447901646256 & 0.0947190817479567 \tabularnewline
64 & 4320 & 4386.60327907854 & 138.282037978953 & 46.4065957561254 & -1.11751185642857 \tabularnewline
65 & 4080 & 4340.62993915942 & 14.1208473138647 & -227.512797388954 & -0.327782785859868 \tabularnewline
66 & 4210 & 4184.45339169096 & -100.616669057433 & 56.2384460688332 & -0.303545784635347 \tabularnewline
67 & 3350 & 3413.53517355982 & -552.598186095543 & 57.4613220338201 & -1.19622683900889 \tabularnewline
68 & 3390 & 3316.47818205706 & -245.315735548555 & -8.73570189968553 & 0.81322487521402 \tabularnewline
69 & 2630 & 2756.11257750334 & -457.841147998416 & -69.2205488173186 & -0.562458448977055 \tabularnewline
70 & 2350 & 2283.34155120012 & -467.911380378623 & 69.3542596922807 & -0.0266515629357425 \tabularnewline
71 & 2330 & 2223.08713847743 & -193.072732737917 & 33.3419988793026 & 0.727398058820998 \tabularnewline
72 & 2230 & 2227.01682791007 & -60.3710354716885 & -32.5551175021779 & 0.351718731301237 \tabularnewline
73 & 2830 & 2686.62708010589 & 290.621333331967 & 48.9491964736205 & 0.937267427184289 \tabularnewline
74 & 3230 & 3348.46986908434 & 536.944550466266 & -182.968210616204 & 0.645990762216787 \tabularnewline
75 & 4240 & 3968.95635701 & 592.749198830773 & 256.126533178633 & 0.148330160191332 \tabularnewline
76 & 3750 & 3877.67740341752 & 132.058816684907 & -4.83491890768045 & -1.21778164417322 \tabularnewline
77 & 4160 & 4293.13768722283 & 322.682572749897 & -183.865783142082 & 0.503341901178464 \tabularnewline
78 & 3960 & 4006.6925119694 & -86.876170925713 & 62.5562325399833 & -1.08342584878908 \tabularnewline
79 & 3000 & 3171.89242290222 & -590.130740580691 & -37.5344323521474 & -1.33192421535762 \tabularnewline
80 & 2890 & 2796.36520467766 & -445.670362893239 & 55.0676116684204 & 0.382316084856256 \tabularnewline
81 & 2300 & 2356.18887426417 & -441.971798696255 & -57.1762968472534 & 0.0097884285146448 \tabularnewline
82 & 2320 & 2198.20175965049 & -250.823305394634 & 70.7654139116539 & 0.505886019426765 \tabularnewline
83 & 2270 & 2183.45239525541 & -92.0074962327431 & 44.1490015431506 & 0.420346664522298 \tabularnewline
84 & 1970 & 2059.57646802758 & -113.433352723006 & -83.8529388194332 & -0.056796361946719 \tabularnewline
85 & 2920 & 2713.78188572726 & 403.707566807751 & 67.6369064168888 & 1.37661984655088 \tabularnewline
86 & 3310 & 3437.45124770049 & 616.457342742792 & -183.388417447451 & 0.559326669361359 \tabularnewline
87 & 4370 & 4066.01675342063 & 624.539334265834 & 301.827834486962 & 0.0214639297991569 \tabularnewline
88 & 3990 & 4174.50814352291 & 277.597320910575 & -92.0881563307845 & -0.917720735071705 \tabularnewline
89 & 3970 & 4170.44675851441 & 88.3955472946109 & -150.164448070471 & -0.49970010084349 \tabularnewline
90 & 3850 & 3825.03175108108 & -202.853394155083 & 102.515808689728 & -0.770399370043574 \tabularnewline
91 & 3510 & 3569.35686968892 & -238.33950682712 & -49.8996578249931 & -0.0939174086493037 \tabularnewline
92 & 2840 & 2891.90375315104 & -533.475512451667 & 26.7523740217043 & -0.781084001169778 \tabularnewline
93 & 2130 & 2231.71376336314 & -618.649808927583 & -79.0141974658877 & -0.225417922147866 \tabularnewline
94 & 2280 & 2088.14691077977 & -299.371568894743 & 106.76176690998 & 0.844986586268361 \tabularnewline
95 & 1960 & 1880.36348495552 & -237.854441518143 & 63.2419544790067 & 0.162830104520873 \tabularnewline
96 & 1740 & 1842.51924862471 & -103.562285644652 & -138.334869486617 & 0.355997739214639 \tabularnewline
97 & 2370 & 2221.27952644068 & 220.843114799776 & 62.0287414431809 & 0.861801862927948 \tabularnewline
98 & 1980 & 2234.67983990805 & 82.7298836819939 & -218.270966810069 & -0.363717037254999 \tabularnewline
99 & 2680 & 2335.09700223578 & 94.5309936807675 & 341.760554198939 & 0.0313197167560972 \tabularnewline
100 & 3510 & 3346.59899300097 & 710.169793389808 & -0.482438310004113 & 1.62922849179125 \tabularnewline
101 & 3350 & 3600.49463795572 & 403.976464020836 & -169.183932954639 & -0.808878543083779 \tabularnewline
102 & 3290 & 3353.00204110888 & -32.9226012627462 & 53.1830684308517 & -1.15560062269876 \tabularnewline
103 & 3150 & 3182.15945479889 & -125.467797480166 & -7.52554956086523 & -0.244925804389593 \tabularnewline
104 & 2490 & 2569.83544761996 & -452.306620258104 & 7.16755612325855 & -0.864990450825186 \tabularnewline
105 & 2490 & 2499.88855924299 & -195.593876215591 & -78.2238311908801 & 0.679402623152704 \tabularnewline
106 & 2930 & 2719.25582729008 & 82.9456341477656 & 136.597974791007 & 0.737168934485167 \tabularnewline
107 & 3590 & 3392.41059583825 & 478.89980961207 & 92.1872414693124 & 1.04811784471595 \tabularnewline
108 & 2040 & 2567.97476614943 & -395.345420524482 & -295.070215666665 & -2.31744050914963 \tabularnewline
109 & 2480 & 2335.97641401419 & -285.624250355151 & 114.761010394425 & 0.291088648625699 \tabularnewline
110 & 2760 & 2800.34452400303 & 214.125338549627 & -172.312753647624 & 1.31762204038507 \tabularnewline
111 & 3400 & 3136.75671683939 & 295.698522691995 & 241.544335970062 & 0.216375603040091 \tabularnewline
112 & 3470 & 3435.83817844823 & 297.967306607797 & 33.5581838638215 & 0.00600599104207181 \tabularnewline
113 & 3130 & 3341.64829216806 & 35.0062449687202 & -141.849467523127 & -0.694834705578163 \tabularnewline
114 & 3670 & 3545.44879095324 & 148.111627223138 & 94.4983442187329 & 0.299152303508781 \tabularnewline
115 & 3080 & 3166.3582288251 & -205.312286238527 & 7.63641801321179 & -0.935335180567832 \tabularnewline
116 & 2430 & 2553.31674989925 & -478.775176021785 & -50.5816725106638 & -0.723732580348708 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299278&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]3840[/C][C]3840[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]3140[/C][C]3378.73928540231[/C][C]-441.002319034933[/C][C]-23.1554705374842[/C][C]-1.45346518058223[/C][/ROW]
[ROW][C]3[/C][C]4580[/C][C]4270.52925520006[/C][C]499.362527110185[/C][C]34.3657939026858[/C][C]2.51622833975735[/C][/ROW]
[ROW][C]4[/C][C]4740[/C][C]4761.70873678208[/C][C]493.721001798134[/C][C]-20.0531965328994[/C][C]-0.0152425294007286[/C][/ROW]
[ROW][C]5[/C][C]3920[/C][C]4171.40440609373[/C][C]-260.295286436165[/C][C]-34.85538105162[/C][C]-2.00518176880343[/C][/ROW]
[ROW][C]6[/C][C]4900[/C][C]4717.5094153553[/C][C]301.767663698536[/C][C]22.2694154514919[/C][C]1.48791598612571[/C][/ROW]
[ROW][C]7[/C][C]3400[/C][C]3708.05881447572[/C][C]-612.583997679904[/C][C]-47.5697489227614[/C][C]-2.41991635877642[/C][/ROW]
[ROW][C]8[/C][C]3440[/C][C]3374.32277598633[/C][C]-418.112094783431[/C][C]10.2741518520907[/C][C]0.51469124202741[/C][/ROW]
[ROW][C]9[/C][C]2600[/C][C]2672.95298985716[/C][C]-615.651081667897[/C][C]-16.6774038282152[/C][C]-0.52280009260688[/C][/ROW]
[ROW][C]10[/C][C]2220[/C][C]2194.18567878407[/C][C]-520.195633676746[/C][C]-1.37916486585497[/C][C]0.252628138488499[/C][/ROW]
[ROW][C]11[/C][C]2190[/C][C]2102.00198211865[/C][C]-221.729428359749[/C][C]2.97057609764456[/C][C]0.789907217842839[/C][/ROW]
[ROW][C]12[/C][C]2550[/C][C]2435.63167748696[/C][C]165.538599136018[/C][C]4.04290182828187[/C][C]1.02492612486024[/C][/ROW]
[ROW][C]13[/C][C]2720[/C][C]2617.43011301874[/C][C]176.56992447328[/C][C]99.427340378874[/C][C]0.0329022468943481[/C][/ROW]
[ROW][C]14[/C][C]3720[/C][C]3632.43579873482[/C][C]692.025329166997[/C][C]-26.2165483114362[/C][C]1.25463955131998[/C][/ROW]
[ROW][C]15[/C][C]4710[/C][C]4603.92395309973[/C][C]883.214290739976[/C][C]52.4735560214517[/C][C]0.510341599406078[/C][/ROW]
[ROW][C]16[/C][C]5070[/C][C]5125.26924550336[/C][C]633.341313224452[/C][C]13.172140269952[/C][C]-0.653589977701227[/C][/ROW]
[ROW][C]17[/C][C]6030[/C][C]6014.93759192899[/C][C]809.57894886147[/C][C]-33.7152164661842[/C][C]0.464886574106217[/C][/ROW]
[ROW][C]18[/C][C]5280[/C][C]5516.29999774136[/C][C]-91.1451889192246[/C][C]14.2664129295434[/C][C]-2.38349957574579[/C][/ROW]
[ROW][C]19[/C][C]4420[/C][C]4631.07590739199[/C][C]-638.463561301925[/C][C]-58.7625060709934[/C][C]-1.44851843775799[/C][/ROW]
[ROW][C]20[/C][C]3940[/C][C]3909.3774918498[/C][C]-695.844617287564[/C][C]46.5906575905267[/C][C]-0.151859878759221[/C][/ROW]
[ROW][C]21[/C][C]2750[/C][C]2835.97114443021[/C][C]-956.118607475318[/C][C]-13.5403914541[/C][C]-0.688827098449572[/C][/ROW]
[ROW][C]22[/C][C]2980[/C][C]2755.07541773048[/C][C]-352.810251225004[/C][C]57.0309488924247[/C][C]1.59668953544719[/C][/ROW]
[ROW][C]23[/C][C]2690[/C][C]2636.33862216724[/C][C]-191.466902813541[/C][C]8.76141188747274[/C][C]0.427004018237362[/C][/ROW]
[ROW][C]24[/C][C]2650[/C][C]2594.9783113447[/C][C]-88.0598172096699[/C][C]26.2450902087535[/C][C]0.273695687685055[/C][/ROW]
[ROW][C]25[/C][C]4000[/C][C]3680.76187881659[/C][C]712.243529371661[/C][C]95.525021847583[/C][C]2.24858944917219[/C][/ROW]
[ROW][C]26[/C][C]4150[/C][C]4244.7087647147[/C][C]617.381400202226[/C][C]-71.7065566251277[/C][C]-0.239872091116836[/C][/ROW]
[ROW][C]27[/C][C]6050[/C][C]5770.92059014577[/C][C]1233.03844123724[/C][C]109.520846202296[/C][C]1.64335501445905[/C][/ROW]
[ROW][C]28[/C][C]6280[/C][C]6464.61896096412[/C][C]863.894795370247[/C][C]-84.6109592400094[/C][C]-0.969408162445285[/C][/ROW]
[ROW][C]29[/C][C]5520[/C][C]5863.33961106202[/C][C]-135.440797967285[/C][C]-71.1395228437983[/C][C]-2.63711075449169[/C][/ROW]
[ROW][C]30[/C][C]4800[/C][C]4932.32917743157[/C][C]-678.538628970943[/C][C]16.2362195745503[/C][C]-1.43710935348022[/C][/ROW]
[ROW][C]31[/C][C]4610[/C][C]4579.22435155323[/C][C]-456.172937071835[/C][C]-30.0789247057632[/C][C]0.588509750782495[/C][/ROW]
[ROW][C]32[/C][C]3530[/C][C]3598.46632297724[/C][C]-814.692316290614[/C][C]29.6461952002031[/C][C]-0.948826860872665[/C][/ROW]
[ROW][C]33[/C][C]2790[/C][C]2833.80659422151[/C][C]-780.499094687744[/C][C]-53.1640423048094[/C][C]0.0904939195485752[/C][/ROW]
[ROW][C]34[/C][C]2750[/C][C]2576.54696500512[/C][C]-422.921324940482[/C][C]75.5960818339963[/C][C]0.946351495535097[/C][/ROW]
[ROW][C]35[/C][C]2470[/C][C]2408.64741473008[/C][C]-248.662506349068[/C][C]13.6640284682864[/C][C]0.461184584408936[/C][/ROW]
[ROW][C]36[/C][C]2610[/C][C]2554.01953076325[/C][C]20.3243166146576[/C][C]-17.6308108532726[/C][C]0.712161185856549[/C][/ROW]
[ROW][C]37[/C][C]3680[/C][C]3360.50172461623[/C][C]555.28600107227[/C][C]172.112762627379[/C][C]1.46628711419088[/C][/ROW]
[ROW][C]38[/C][C]3820[/C][C]3977.03569184382[/C][C]595.181904067248[/C][C]-167.095677529686[/C][C]0.102639903676472[/C][/ROW]
[ROW][C]39[/C][C]4460[/C][C]4391.98618426764[/C][C]473.87233891348[/C][C]101.007255731359[/C][C]-0.323528223957812[/C][/ROW]
[ROW][C]40[/C][C]4760[/C][C]4778.8682838812[/C][C]414.703204920424[/C][C]-2.95595517938009[/C][C]-0.155772392296708[/C][/ROW]
[ROW][C]41[/C][C]3290[/C][C]3692.11166009676[/C][C]-603.603577028766[/C][C]-127.658546061212[/C][C]-2.68756482936943[/C][/ROW]
[ROW][C]42[/C][C]3610[/C][C]3496.91754109904[/C][C]-326.484172080947[/C][C]38.1075059680943[/C][C]0.733254425318873[/C][/ROW]
[ROW][C]43[/C][C]3650[/C][C]3551.67883990089[/C][C]-67.5658628548643[/C][C]28.2335303468688[/C][C]0.685253749173065[/C][/ROW]
[ROW][C]44[/C][C]3130[/C][C]3182.45801371439[/C][C]-272.48301133035[/C][C]3.00976614514414[/C][C]-0.542315290740357[/C][/ROW]
[ROW][C]45[/C][C]2850[/C][C]2925.62232730795[/C][C]-261.853609658651[/C][C]-78.4995698314343[/C][C]0.0281311889532525[/C][/ROW]
[ROW][C]46[/C][C]2720[/C][C]2654.5771250362[/C][C]-268.09726101786[/C][C]67.1129742531981[/C][C]-0.0165242505925542[/C][/ROW]
[ROW][C]47[/C][C]2740[/C][C]2671.30176991298[/C][C]-74.6691132957623[/C][C]16.3399229609996[/C][C]0.511916180103459[/C][/ROW]
[ROW][C]48[/C][C]2760[/C][C]2788.32436110509[/C][C]55.3660641169996[/C][C]-63.5255014486649[/C][C]0.344421006295209[/C][/ROW]
[ROW][C]49[/C][C]3330[/C][C]3110.71547905422[/C][C]236.542342623121[/C][C]169.899797734197[/C][C]0.490028120882771[/C][/ROW]
[ROW][C]50[/C][C]3850[/C][C]3898.55080849581[/C][C]599.119135847119[/C][C]-141.81332712965[/C][C]0.94180067950228[/C][/ROW]
[ROW][C]51[/C][C]5430[/C][C]5168.39536818904[/C][C]1048.79443641972[/C][C]140.320495912736[/C][C]1.19786516689011[/C][/ROW]
[ROW][C]52[/C][C]5180[/C][C]5298.8251041264[/C][C]426.876894735045[/C][C]47.6920161372126[/C][C]-1.64023785523859[/C][/ROW]
[ROW][C]53[/C][C]4770[/C][C]5075.65654947159[/C][C]-12.3029880119862[/C][C]-188.058291023398[/C][C]-1.15924435720128[/C][/ROW]
[ROW][C]54[/C][C]5360[/C][C]5281.77050792943[/C][C]135.28216070124[/C][C]38.577505630735[/C][C]0.390479187980275[/C][/ROW]
[ROW][C]55[/C][C]4950[/C][C]5002.11297397465[/C][C]-145.335426998598[/C][C]23.3302353122844[/C][C]-0.742687858547684[/C][/ROW]
[ROW][C]56[/C][C]3720[/C][C]3940.3505795277[/C][C]-765.293117548797[/C][C]-53.6833365056658[/C][C]-1.64072175863313[/C][/ROW]
[ROW][C]57[/C][C]3330[/C][C]3337.34879227909[/C][C]-655.50102786687[/C][C]-36.8651993772589[/C][C]0.290569742612641[/C][/ROW]
[ROW][C]58[/C][C]3000[/C][C]2887.49036451048[/C][C]-516.39158844183[/C][C]75.110871895928[/C][C]0.368163169867688[/C][/ROW]
[ROW][C]59[/C][C]2760[/C][C]2666.55478347024[/C][C]-316.598097045005[/C][C]39.7338843596001[/C][C]0.528766704902433[/C][/ROW]
[ROW][C]60[/C][C]3040[/C][C]2963.35302643407[/C][C]97.751149141162[/C][C]-34.7710163203017[/C][C]1.09790564459537[/C][/ROW]
[ROW][C]61[/C][C]3260[/C][C]3163.2673569198[/C][C]166.876833002866[/C][C]78.0345996146302[/C][C]0.18549597877877[/C][/ROW]
[ROW][C]62[/C][C]3780[/C][C]3872.93605361268[/C][C]525.844921534268[/C][C]-186.307054752479[/C][C]0.937892075935303[/C][/ROW]
[ROW][C]63[/C][C]4670[/C][C]4452.00263305716[/C][C]561.443605228659[/C][C]208.447901646256[/C][C]0.0947190817479567[/C][/ROW]
[ROW][C]64[/C][C]4320[/C][C]4386.60327907854[/C][C]138.282037978953[/C][C]46.4065957561254[/C][C]-1.11751185642857[/C][/ROW]
[ROW][C]65[/C][C]4080[/C][C]4340.62993915942[/C][C]14.1208473138647[/C][C]-227.512797388954[/C][C]-0.327782785859868[/C][/ROW]
[ROW][C]66[/C][C]4210[/C][C]4184.45339169096[/C][C]-100.616669057433[/C][C]56.2384460688332[/C][C]-0.303545784635347[/C][/ROW]
[ROW][C]67[/C][C]3350[/C][C]3413.53517355982[/C][C]-552.598186095543[/C][C]57.4613220338201[/C][C]-1.19622683900889[/C][/ROW]
[ROW][C]68[/C][C]3390[/C][C]3316.47818205706[/C][C]-245.315735548555[/C][C]-8.73570189968553[/C][C]0.81322487521402[/C][/ROW]
[ROW][C]69[/C][C]2630[/C][C]2756.11257750334[/C][C]-457.841147998416[/C][C]-69.2205488173186[/C][C]-0.562458448977055[/C][/ROW]
[ROW][C]70[/C][C]2350[/C][C]2283.34155120012[/C][C]-467.911380378623[/C][C]69.3542596922807[/C][C]-0.0266515629357425[/C][/ROW]
[ROW][C]71[/C][C]2330[/C][C]2223.08713847743[/C][C]-193.072732737917[/C][C]33.3419988793026[/C][C]0.727398058820998[/C][/ROW]
[ROW][C]72[/C][C]2230[/C][C]2227.01682791007[/C][C]-60.3710354716885[/C][C]-32.5551175021779[/C][C]0.351718731301237[/C][/ROW]
[ROW][C]73[/C][C]2830[/C][C]2686.62708010589[/C][C]290.621333331967[/C][C]48.9491964736205[/C][C]0.937267427184289[/C][/ROW]
[ROW][C]74[/C][C]3230[/C][C]3348.46986908434[/C][C]536.944550466266[/C][C]-182.968210616204[/C][C]0.645990762216787[/C][/ROW]
[ROW][C]75[/C][C]4240[/C][C]3968.95635701[/C][C]592.749198830773[/C][C]256.126533178633[/C][C]0.148330160191332[/C][/ROW]
[ROW][C]76[/C][C]3750[/C][C]3877.67740341752[/C][C]132.058816684907[/C][C]-4.83491890768045[/C][C]-1.21778164417322[/C][/ROW]
[ROW][C]77[/C][C]4160[/C][C]4293.13768722283[/C][C]322.682572749897[/C][C]-183.865783142082[/C][C]0.503341901178464[/C][/ROW]
[ROW][C]78[/C][C]3960[/C][C]4006.6925119694[/C][C]-86.876170925713[/C][C]62.5562325399833[/C][C]-1.08342584878908[/C][/ROW]
[ROW][C]79[/C][C]3000[/C][C]3171.89242290222[/C][C]-590.130740580691[/C][C]-37.5344323521474[/C][C]-1.33192421535762[/C][/ROW]
[ROW][C]80[/C][C]2890[/C][C]2796.36520467766[/C][C]-445.670362893239[/C][C]55.0676116684204[/C][C]0.382316084856256[/C][/ROW]
[ROW][C]81[/C][C]2300[/C][C]2356.18887426417[/C][C]-441.971798696255[/C][C]-57.1762968472534[/C][C]0.0097884285146448[/C][/ROW]
[ROW][C]82[/C][C]2320[/C][C]2198.20175965049[/C][C]-250.823305394634[/C][C]70.7654139116539[/C][C]0.505886019426765[/C][/ROW]
[ROW][C]83[/C][C]2270[/C][C]2183.45239525541[/C][C]-92.0074962327431[/C][C]44.1490015431506[/C][C]0.420346664522298[/C][/ROW]
[ROW][C]84[/C][C]1970[/C][C]2059.57646802758[/C][C]-113.433352723006[/C][C]-83.8529388194332[/C][C]-0.056796361946719[/C][/ROW]
[ROW][C]85[/C][C]2920[/C][C]2713.78188572726[/C][C]403.707566807751[/C][C]67.6369064168888[/C][C]1.37661984655088[/C][/ROW]
[ROW][C]86[/C][C]3310[/C][C]3437.45124770049[/C][C]616.457342742792[/C][C]-183.388417447451[/C][C]0.559326669361359[/C][/ROW]
[ROW][C]87[/C][C]4370[/C][C]4066.01675342063[/C][C]624.539334265834[/C][C]301.827834486962[/C][C]0.0214639297991569[/C][/ROW]
[ROW][C]88[/C][C]3990[/C][C]4174.50814352291[/C][C]277.597320910575[/C][C]-92.0881563307845[/C][C]-0.917720735071705[/C][/ROW]
[ROW][C]89[/C][C]3970[/C][C]4170.44675851441[/C][C]88.3955472946109[/C][C]-150.164448070471[/C][C]-0.49970010084349[/C][/ROW]
[ROW][C]90[/C][C]3850[/C][C]3825.03175108108[/C][C]-202.853394155083[/C][C]102.515808689728[/C][C]-0.770399370043574[/C][/ROW]
[ROW][C]91[/C][C]3510[/C][C]3569.35686968892[/C][C]-238.33950682712[/C][C]-49.8996578249931[/C][C]-0.0939174086493037[/C][/ROW]
[ROW][C]92[/C][C]2840[/C][C]2891.90375315104[/C][C]-533.475512451667[/C][C]26.7523740217043[/C][C]-0.781084001169778[/C][/ROW]
[ROW][C]93[/C][C]2130[/C][C]2231.71376336314[/C][C]-618.649808927583[/C][C]-79.0141974658877[/C][C]-0.225417922147866[/C][/ROW]
[ROW][C]94[/C][C]2280[/C][C]2088.14691077977[/C][C]-299.371568894743[/C][C]106.76176690998[/C][C]0.844986586268361[/C][/ROW]
[ROW][C]95[/C][C]1960[/C][C]1880.36348495552[/C][C]-237.854441518143[/C][C]63.2419544790067[/C][C]0.162830104520873[/C][/ROW]
[ROW][C]96[/C][C]1740[/C][C]1842.51924862471[/C][C]-103.562285644652[/C][C]-138.334869486617[/C][C]0.355997739214639[/C][/ROW]
[ROW][C]97[/C][C]2370[/C][C]2221.27952644068[/C][C]220.843114799776[/C][C]62.0287414431809[/C][C]0.861801862927948[/C][/ROW]
[ROW][C]98[/C][C]1980[/C][C]2234.67983990805[/C][C]82.7298836819939[/C][C]-218.270966810069[/C][C]-0.363717037254999[/C][/ROW]
[ROW][C]99[/C][C]2680[/C][C]2335.09700223578[/C][C]94.5309936807675[/C][C]341.760554198939[/C][C]0.0313197167560972[/C][/ROW]
[ROW][C]100[/C][C]3510[/C][C]3346.59899300097[/C][C]710.169793389808[/C][C]-0.482438310004113[/C][C]1.62922849179125[/C][/ROW]
[ROW][C]101[/C][C]3350[/C][C]3600.49463795572[/C][C]403.976464020836[/C][C]-169.183932954639[/C][C]-0.808878543083779[/C][/ROW]
[ROW][C]102[/C][C]3290[/C][C]3353.00204110888[/C][C]-32.9226012627462[/C][C]53.1830684308517[/C][C]-1.15560062269876[/C][/ROW]
[ROW][C]103[/C][C]3150[/C][C]3182.15945479889[/C][C]-125.467797480166[/C][C]-7.52554956086523[/C][C]-0.244925804389593[/C][/ROW]
[ROW][C]104[/C][C]2490[/C][C]2569.83544761996[/C][C]-452.306620258104[/C][C]7.16755612325855[/C][C]-0.864990450825186[/C][/ROW]
[ROW][C]105[/C][C]2490[/C][C]2499.88855924299[/C][C]-195.593876215591[/C][C]-78.2238311908801[/C][C]0.679402623152704[/C][/ROW]
[ROW][C]106[/C][C]2930[/C][C]2719.25582729008[/C][C]82.9456341477656[/C][C]136.597974791007[/C][C]0.737168934485167[/C][/ROW]
[ROW][C]107[/C][C]3590[/C][C]3392.41059583825[/C][C]478.89980961207[/C][C]92.1872414693124[/C][C]1.04811784471595[/C][/ROW]
[ROW][C]108[/C][C]2040[/C][C]2567.97476614943[/C][C]-395.345420524482[/C][C]-295.070215666665[/C][C]-2.31744050914963[/C][/ROW]
[ROW][C]109[/C][C]2480[/C][C]2335.97641401419[/C][C]-285.624250355151[/C][C]114.761010394425[/C][C]0.291088648625699[/C][/ROW]
[ROW][C]110[/C][C]2760[/C][C]2800.34452400303[/C][C]214.125338549627[/C][C]-172.312753647624[/C][C]1.31762204038507[/C][/ROW]
[ROW][C]111[/C][C]3400[/C][C]3136.75671683939[/C][C]295.698522691995[/C][C]241.544335970062[/C][C]0.216375603040091[/C][/ROW]
[ROW][C]112[/C][C]3470[/C][C]3435.83817844823[/C][C]297.967306607797[/C][C]33.5581838638215[/C][C]0.00600599104207181[/C][/ROW]
[ROW][C]113[/C][C]3130[/C][C]3341.64829216806[/C][C]35.0062449687202[/C][C]-141.849467523127[/C][C]-0.694834705578163[/C][/ROW]
[ROW][C]114[/C][C]3670[/C][C]3545.44879095324[/C][C]148.111627223138[/C][C]94.4983442187329[/C][C]0.299152303508781[/C][/ROW]
[ROW][C]115[/C][C]3080[/C][C]3166.3582288251[/C][C]-205.312286238527[/C][C]7.63641801321179[/C][C]-0.935335180567832[/C][/ROW]
[ROW][C]116[/C][C]2430[/C][C]2553.31674989925[/C][C]-478.775176021785[/C][C]-50.5816725106638[/C][C]-0.723732580348708[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299278&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
138403840000
231403378.73928540231-441.002319034933-23.1554705374842-1.45346518058223
345804270.52925520006499.36252711018534.36579390268582.51622833975735
447404761.70873678208493.721001798134-20.0531965328994-0.0152425294007286
539204171.40440609373-260.295286436165-34.85538105162-2.00518176880343
649004717.5094153553301.76766369853622.26941545149191.48791598612571
734003708.05881447572-612.583997679904-47.5697489227614-2.41991635877642
834403374.32277598633-418.11209478343110.27415185209070.51469124202741
926002672.95298985716-615.651081667897-16.6774038282152-0.52280009260688
1022202194.18567878407-520.195633676746-1.379164865854970.252628138488499
1121902102.00198211865-221.7294283597492.970576097644560.789907217842839
1225502435.63167748696165.5385991360184.042901828281871.02492612486024
1327202617.43011301874176.5699244732899.4273403788740.0329022468943481
1437203632.43579873482692.025329166997-26.21654831143621.25463955131998
1547104603.92395309973883.21429073997652.47355602145170.510341599406078
1650705125.26924550336633.34131322445213.172140269952-0.653589977701227
1760306014.93759192899809.57894886147-33.71521646618420.464886574106217
1852805516.29999774136-91.145188919224614.2664129295434-2.38349957574579
1944204631.07590739199-638.463561301925-58.7625060709934-1.44851843775799
2039403909.3774918498-695.84461728756446.5906575905267-0.151859878759221
2127502835.97114443021-956.118607475318-13.5403914541-0.688827098449572
2229802755.07541773048-352.81025122500457.03094889242471.59668953544719
2326902636.33862216724-191.4669028135418.761411887472740.427004018237362
2426502594.9783113447-88.059817209669926.24509020875350.273695687685055
2540003680.76187881659712.24352937166195.5250218475832.24858944917219
2641504244.7087647147617.381400202226-71.7065566251277-0.239872091116836
2760505770.920590145771233.03844123724109.5208462022961.64335501445905
2862806464.61896096412863.894795370247-84.6109592400094-0.969408162445285
2955205863.33961106202-135.440797967285-71.1395228437983-2.63711075449169
3048004932.32917743157-678.53862897094316.2362195745503-1.43710935348022
3146104579.22435155323-456.172937071835-30.07892470576320.588509750782495
3235303598.46632297724-814.69231629061429.6461952002031-0.948826860872665
3327902833.80659422151-780.499094687744-53.16404230480940.0904939195485752
3427502576.54696500512-422.92132494048275.59608183399630.946351495535097
3524702408.64741473008-248.66250634906813.66402846828640.461184584408936
3626102554.0195307632520.3243166146576-17.63081085327260.712161185856549
3736803360.50172461623555.28600107227172.1127626273791.46628711419088
3838203977.03569184382595.181904067248-167.0956775296860.102639903676472
3944604391.98618426764473.87233891348101.007255731359-0.323528223957812
4047604778.8682838812414.703204920424-2.95595517938009-0.155772392296708
4132903692.11166009676-603.603577028766-127.658546061212-2.68756482936943
4236103496.91754109904-326.48417208094738.10750596809430.733254425318873
4336503551.67883990089-67.565862854864328.23353034686880.685253749173065
4431303182.45801371439-272.483011330353.00976614514414-0.542315290740357
4528502925.62232730795-261.853609658651-78.49956983143430.0281311889532525
4627202654.5771250362-268.0972610178667.1129742531981-0.0165242505925542
4727402671.30176991298-74.669113295762316.33992296099960.511916180103459
4827602788.3243611050955.3660641169996-63.52550144866490.344421006295209
4933303110.71547905422236.542342623121169.8997977341970.490028120882771
5038503898.55080849581599.119135847119-141.813327129650.94180067950228
5154305168.395368189041048.79443641972140.3204959127361.19786516689011
5251805298.8251041264426.87689473504547.6920161372126-1.64023785523859
5347705075.65654947159-12.3029880119862-188.058291023398-1.15924435720128
5453605281.77050792943135.2821607012438.5775056307350.390479187980275
5549505002.11297397465-145.33542699859823.3302353122844-0.742687858547684
5637203940.3505795277-765.293117548797-53.6833365056658-1.64072175863313
5733303337.34879227909-655.50102786687-36.86519937725890.290569742612641
5830002887.49036451048-516.3915884418375.1108718959280.368163169867688
5927602666.55478347024-316.59809704500539.73388435960010.528766704902433
6030402963.3530264340797.751149141162-34.77101632030171.09790564459537
6132603163.2673569198166.87683300286678.03459961463020.18549597877877
6237803872.93605361268525.844921534268-186.3070547524790.937892075935303
6346704452.00263305716561.443605228659208.4479016462560.0947190817479567
6443204386.60327907854138.28203797895346.4065957561254-1.11751185642857
6540804340.6299391594214.1208473138647-227.512797388954-0.327782785859868
6642104184.45339169096-100.61666905743356.2384460688332-0.303545784635347
6733503413.53517355982-552.59818609554357.4613220338201-1.19622683900889
6833903316.47818205706-245.315735548555-8.735701899685530.81322487521402
6926302756.11257750334-457.841147998416-69.2205488173186-0.562458448977055
7023502283.34155120012-467.91138037862369.3542596922807-0.0266515629357425
7123302223.08713847743-193.07273273791733.34199887930260.727398058820998
7222302227.01682791007-60.3710354716885-32.55511750217790.351718731301237
7328302686.62708010589290.62133333196748.94919647362050.937267427184289
7432303348.46986908434536.944550466266-182.9682106162040.645990762216787
7542403968.95635701592.749198830773256.1265331786330.148330160191332
7637503877.67740341752132.058816684907-4.83491890768045-1.21778164417322
7741604293.13768722283322.682572749897-183.8657831420820.503341901178464
7839604006.6925119694-86.87617092571362.5562325399833-1.08342584878908
7930003171.89242290222-590.130740580691-37.5344323521474-1.33192421535762
8028902796.36520467766-445.67036289323955.06761166842040.382316084856256
8123002356.18887426417-441.971798696255-57.17629684725340.0097884285146448
8223202198.20175965049-250.82330539463470.76541391165390.505886019426765
8322702183.45239525541-92.007496232743144.14900154315060.420346664522298
8419702059.57646802758-113.433352723006-83.8529388194332-0.056796361946719
8529202713.78188572726403.70756680775167.63690641688881.37661984655088
8633103437.45124770049616.457342742792-183.3884174474510.559326669361359
8743704066.01675342063624.539334265834301.8278344869620.0214639297991569
8839904174.50814352291277.597320910575-92.0881563307845-0.917720735071705
8939704170.4467585144188.3955472946109-150.164448070471-0.49970010084349
9038503825.03175108108-202.853394155083102.515808689728-0.770399370043574
9135103569.35686968892-238.33950682712-49.8996578249931-0.0939174086493037
9228402891.90375315104-533.47551245166726.7523740217043-0.781084001169778
9321302231.71376336314-618.649808927583-79.0141974658877-0.225417922147866
9422802088.14691077977-299.371568894743106.761766909980.844986586268361
9519601880.36348495552-237.85444151814363.24195447900670.162830104520873
9617401842.51924862471-103.562285644652-138.3348694866170.355997739214639
9723702221.27952644068220.84311479977662.02874144318090.861801862927948
9819802234.6798399080582.7298836819939-218.270966810069-0.363717037254999
9926802335.0970022357894.5309936807675341.7605541989390.0313197167560972
10035103346.59899300097710.169793389808-0.4824383100041131.62922849179125
10133503600.49463795572403.976464020836-169.183932954639-0.808878543083779
10232903353.00204110888-32.922601262746253.1830684308517-1.15560062269876
10331503182.15945479889-125.467797480166-7.52554956086523-0.244925804389593
10424902569.83544761996-452.3066202581047.16755612325855-0.864990450825186
10524902499.88855924299-195.593876215591-78.22383119088010.679402623152704
10629302719.2558272900882.9456341477656136.5979747910070.737168934485167
10735903392.41059583825478.8998096120792.18724146931241.04811784471595
10820402567.97476614943-395.345420524482-295.070215666665-2.31744050914963
10924802335.97641401419-285.624250355151114.7610103944250.291088648625699
11027602800.34452400303214.125338549627-172.3127536476241.31762204038507
11134003136.75671683939295.698522691995241.5443359700620.216375603040091
11234703435.83817844823297.96730660779733.55818386382150.00600599104207181
11331303341.6482921680635.0062449687202-141.849467523127-0.694834705578163
11436703545.44879095324148.11162722313894.49834421873290.299152303508781
11530803166.3582288251-205.3122862385277.63641801321179-0.935335180567832
11624302553.31674989925-478.775176021785-50.5816725106638-0.723732580348708







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
11917.979782596742708.80757790401-790.827795307263
21861.566759891822716.65868895232-855.0919290605
32119.655762781792724.50980000063-604.854037218837
41450.212983272262732.36091104894-1282.14792777668
52375.878671558522740.21202209725-364.333350538728
62759.749032374192748.0631331455611.6858992286309
73642.294521791152755.91424419387886.380277597283
83875.64392533762763.765355242181111.87857009542
93567.200841768722771.61646629049795.584375478237
103737.281465915072779.4675773388957.813888576268
113188.641330608322787.31868838711401.322642221209
122527.759186140382795.16979943542-267.410613295039
132012.193115176472803.02091048373-790.827795307262
141955.780092471542810.87202153204-855.0919290605
152213.869095361512818.72313258035-604.854037218837
161544.426315851982826.57424362866-1282.14792777668
172470.092004138242834.42535467697-364.333350538728
182853.962364953912842.2764657252811.6858992286307

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 1917.97978259674 & 2708.80757790401 & -790.827795307263 \tabularnewline
2 & 1861.56675989182 & 2716.65868895232 & -855.0919290605 \tabularnewline
3 & 2119.65576278179 & 2724.50980000063 & -604.854037218837 \tabularnewline
4 & 1450.21298327226 & 2732.36091104894 & -1282.14792777668 \tabularnewline
5 & 2375.87867155852 & 2740.21202209725 & -364.333350538728 \tabularnewline
6 & 2759.74903237419 & 2748.06313314556 & 11.6858992286309 \tabularnewline
7 & 3642.29452179115 & 2755.91424419387 & 886.380277597283 \tabularnewline
8 & 3875.6439253376 & 2763.76535524218 & 1111.87857009542 \tabularnewline
9 & 3567.20084176872 & 2771.61646629049 & 795.584375478237 \tabularnewline
10 & 3737.28146591507 & 2779.4675773388 & 957.813888576268 \tabularnewline
11 & 3188.64133060832 & 2787.31868838711 & 401.322642221209 \tabularnewline
12 & 2527.75918614038 & 2795.16979943542 & -267.410613295039 \tabularnewline
13 & 2012.19311517647 & 2803.02091048373 & -790.827795307262 \tabularnewline
14 & 1955.78009247154 & 2810.87202153204 & -855.0919290605 \tabularnewline
15 & 2213.86909536151 & 2818.72313258035 & -604.854037218837 \tabularnewline
16 & 1544.42631585198 & 2826.57424362866 & -1282.14792777668 \tabularnewline
17 & 2470.09200413824 & 2834.42535467697 & -364.333350538728 \tabularnewline
18 & 2853.96236495391 & 2842.27646572528 & 11.6858992286307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299278&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]1917.97978259674[/C][C]2708.80757790401[/C][C]-790.827795307263[/C][/ROW]
[ROW][C]2[/C][C]1861.56675989182[/C][C]2716.65868895232[/C][C]-855.0919290605[/C][/ROW]
[ROW][C]3[/C][C]2119.65576278179[/C][C]2724.50980000063[/C][C]-604.854037218837[/C][/ROW]
[ROW][C]4[/C][C]1450.21298327226[/C][C]2732.36091104894[/C][C]-1282.14792777668[/C][/ROW]
[ROW][C]5[/C][C]2375.87867155852[/C][C]2740.21202209725[/C][C]-364.333350538728[/C][/ROW]
[ROW][C]6[/C][C]2759.74903237419[/C][C]2748.06313314556[/C][C]11.6858992286309[/C][/ROW]
[ROW][C]7[/C][C]3642.29452179115[/C][C]2755.91424419387[/C][C]886.380277597283[/C][/ROW]
[ROW][C]8[/C][C]3875.6439253376[/C][C]2763.76535524218[/C][C]1111.87857009542[/C][/ROW]
[ROW][C]9[/C][C]3567.20084176872[/C][C]2771.61646629049[/C][C]795.584375478237[/C][/ROW]
[ROW][C]10[/C][C]3737.28146591507[/C][C]2779.4675773388[/C][C]957.813888576268[/C][/ROW]
[ROW][C]11[/C][C]3188.64133060832[/C][C]2787.31868838711[/C][C]401.322642221209[/C][/ROW]
[ROW][C]12[/C][C]2527.75918614038[/C][C]2795.16979943542[/C][C]-267.410613295039[/C][/ROW]
[ROW][C]13[/C][C]2012.19311517647[/C][C]2803.02091048373[/C][C]-790.827795307262[/C][/ROW]
[ROW][C]14[/C][C]1955.78009247154[/C][C]2810.87202153204[/C][C]-855.0919290605[/C][/ROW]
[ROW][C]15[/C][C]2213.86909536151[/C][C]2818.72313258035[/C][C]-604.854037218837[/C][/ROW]
[ROW][C]16[/C][C]1544.42631585198[/C][C]2826.57424362866[/C][C]-1282.14792777668[/C][/ROW]
[ROW][C]17[/C][C]2470.09200413824[/C][C]2834.42535467697[/C][C]-364.333350538728[/C][/ROW]
[ROW][C]18[/C][C]2853.96236495391[/C][C]2842.27646572528[/C][C]11.6858992286307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299278&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299278&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
11917.979782596742708.80757790401-790.827795307263
21861.566759891822716.65868895232-855.0919290605
32119.655762781792724.50980000063-604.854037218837
41450.212983272262732.36091104894-1282.14792777668
52375.878671558522740.21202209725-364.333350538728
62759.749032374192748.0631331455611.6858992286309
73642.294521791152755.91424419387886.380277597283
83875.64392533762763.765355242181111.87857009542
93567.200841768722771.61646629049795.584375478237
103737.281465915072779.4675773388957.813888576268
113188.641330608322787.31868838711401.322642221209
122527.759186140382795.16979943542-267.410613295039
132012.193115176472803.02091048373-790.827795307262
141955.780092471542810.87202153204-855.0919290605
152213.869095361512818.72313258035-604.854037218837
161544.426315851982826.57424362866-1282.14792777668
172470.092004138242834.42535467697-364.333350538728
182853.962364953912842.2764657252811.6858992286307



Parameters (Session):
par1 = 12 ; par2 = 18 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = 18 ; 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')