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Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationWed, 14 Dec 2016 15:11:08 +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/t1481725399p3vz6nvy9kui3jk.htm/, Retrieved Fri, 01 Nov 2024 03:44:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299487, Retrieved Fri, 01 Nov 2024 03:44:57 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
4622.90
4378.70
4487.10
4381.00
5057.90
4766.20
4902.30
4798.10
5587.30
5217.10
5366.10
5259.80
5886.90
5544.70
5676.40
5581.10
6201.00
5812.10
5963.10
5799.70
6647.10
6266.30
6382.30
6204.20
7039.90
6604.80
6815.60
6605.20
7402.60
6879.80
7012.50
6748.70
7501.40
7026.10
7245.90
7061.80
7865.70
7449.60
7605.60
7366.60
8301.30
7821.70
8052.30
7817.50




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299487&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299487&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299487&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
14622.94622.9000
24378.74419.10914854643-58.9609185078669-40.4091485464351-1.22890897893268
34487.14469.88546882567-10.175805668452117.21453117433531.7306692649036
443814442.02766222773-19.0466859919566-61.0276622277286-0.250734328107812
55057.94755.59728533528133.747182278812302.3027146647164.44873902381376
64766.24869.58465826783124.074986662622-103.384658267831-0.274612152360142
74902.34937.330998634997.0671212030757-35.0309986348985-0.775584574301283
84798.15006.0390951352683.2967221146504-207.939095135259-0.397734520911458
95587.35215.57066036121144.185491413088371.7293396387871.74654708699991
105217.15321.55813603507125.690967985869-104.458136035073-0.533276215238207
115366.15410.86595288626108.099292896574-44.7659528862613-0.505573912977092
125259.85513.56294244317105.48557548124-253.762942443167-0.0752902148008226
135886.95536.9687635301765.7805026450071349.931236469834-1.14215204394469
145544.75622.4549273012975.3133683384217-77.75492730129390.274445111914531
155676.45710.8767703811281.6550023149874-34.47677038111770.182493285032891
165581.15801.9450890897986.2088314465093-220.8450890897940.131076048705412
1762015868.3498807182276.6279870125426332.650119281777-0.275741170734308
185812.15910.024516686959.7185510795571-97.9245166869043-0.486687914772327
195963.15989.4420229064269.2485030557711-26.34202290642440.274285353809371
205799.76027.2521562171354.0394009733936-227.552156217127-0.437742977104376
216647.16231.9463582387126.922876887151415.15364176132.09770249528298
226266.36371.85337174215133.20429793794-105.5533717421540.180789260422819
236382.36435.643188497799.6231412080932-53.3431884977015-0.966519927616493
246204.26500.0467815758582.5847330954499-295.846781575853-0.490392464828712
257039.96611.6370618968396.6169560669927428.2629381031710.403869970344837
266604.86692.2795409430188.888869166022-87.4795409430082-0.222426679798152
276815.66832.79700032171113.86560291513-17.19700032171360.718870494541553
286605.26924.00119970183102.902533166176-318.801199701826-0.315534692201029
297402.66987.4695866999583.8251933699846415.130413300052-0.549076425610768
306879.87010.8975800404954.6064064044811-131.097580040492-0.840963490206819
317012.57032.0451101573138.4197657563907-19.5451101573139-0.465877457914403
326748.77055.6795371526431.2669563027393-306.979537152642-0.205869316194618
337501.47069.8605740748423.001178475807431.539425925157-0.237902330613114
347026.17127.5933278734939.8035219395206-101.4933278734950.483598367168725
357245.97231.6890072888870.906600352327214.21099271111730.89519643370529
367061.87346.9142333812592.3469399935959-285.1142333812520.617087329040971
377865.77447.817119734696.4861115670918417.8828802653990.119131990126667
387449.67566.6481543252107.296075342104-117.0481543252030.311128078424258
397605.67629.4496975845985.7706362322349-23.8496975845878-0.619536628058519
407366.67672.8711369461765.2830613334002-306.271136946169-0.589665233141102
418301.37840.73286543048114.908279319523460.5671345695191.42829328879236
427821.77935.25480900191105.045835367545-113.554809001909-0.28385693967523
438052.38056.40193474565112.835272167363-4.101934745648320.224192472221623
447817.58163.80954588616110.209493639576-346.309545886161-0.0755741133520917

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 4622.9 & 4622.9 & 0 & 0 & 0 \tabularnewline
2 & 4378.7 & 4419.10914854643 & -58.9609185078669 & -40.4091485464351 & -1.22890897893268 \tabularnewline
3 & 4487.1 & 4469.88546882567 & -10.1758056684521 & 17.2145311743353 & 1.7306692649036 \tabularnewline
4 & 4381 & 4442.02766222773 & -19.0466859919566 & -61.0276622277286 & -0.250734328107812 \tabularnewline
5 & 5057.9 & 4755.59728533528 & 133.747182278812 & 302.302714664716 & 4.44873902381376 \tabularnewline
6 & 4766.2 & 4869.58465826783 & 124.074986662622 & -103.384658267831 & -0.274612152360142 \tabularnewline
7 & 4902.3 & 4937.3309986349 & 97.0671212030757 & -35.0309986348985 & -0.775584574301283 \tabularnewline
8 & 4798.1 & 5006.03909513526 & 83.2967221146504 & -207.939095135259 & -0.397734520911458 \tabularnewline
9 & 5587.3 & 5215.57066036121 & 144.185491413088 & 371.729339638787 & 1.74654708699991 \tabularnewline
10 & 5217.1 & 5321.55813603507 & 125.690967985869 & -104.458136035073 & -0.533276215238207 \tabularnewline
11 & 5366.1 & 5410.86595288626 & 108.099292896574 & -44.7659528862613 & -0.505573912977092 \tabularnewline
12 & 5259.8 & 5513.56294244317 & 105.48557548124 & -253.762942443167 & -0.0752902148008226 \tabularnewline
13 & 5886.9 & 5536.96876353017 & 65.7805026450071 & 349.931236469834 & -1.14215204394469 \tabularnewline
14 & 5544.7 & 5622.45492730129 & 75.3133683384217 & -77.7549273012939 & 0.274445111914531 \tabularnewline
15 & 5676.4 & 5710.87677038112 & 81.6550023149874 & -34.4767703811177 & 0.182493285032891 \tabularnewline
16 & 5581.1 & 5801.94508908979 & 86.2088314465093 & -220.845089089794 & 0.131076048705412 \tabularnewline
17 & 6201 & 5868.34988071822 & 76.6279870125426 & 332.650119281777 & -0.275741170734308 \tabularnewline
18 & 5812.1 & 5910.0245166869 & 59.7185510795571 & -97.9245166869043 & -0.486687914772327 \tabularnewline
19 & 5963.1 & 5989.44202290642 & 69.2485030557711 & -26.3420229064244 & 0.274285353809371 \tabularnewline
20 & 5799.7 & 6027.25215621713 & 54.0394009733936 & -227.552156217127 & -0.437742977104376 \tabularnewline
21 & 6647.1 & 6231.9463582387 & 126.922876887151 & 415.1536417613 & 2.09770249528298 \tabularnewline
22 & 6266.3 & 6371.85337174215 & 133.20429793794 & -105.553371742154 & 0.180789260422819 \tabularnewline
23 & 6382.3 & 6435.6431884977 & 99.6231412080932 & -53.3431884977015 & -0.966519927616493 \tabularnewline
24 & 6204.2 & 6500.04678157585 & 82.5847330954499 & -295.846781575853 & -0.490392464828712 \tabularnewline
25 & 7039.9 & 6611.63706189683 & 96.6169560669927 & 428.262938103171 & 0.403869970344837 \tabularnewline
26 & 6604.8 & 6692.27954094301 & 88.888869166022 & -87.4795409430082 & -0.222426679798152 \tabularnewline
27 & 6815.6 & 6832.79700032171 & 113.86560291513 & -17.1970003217136 & 0.718870494541553 \tabularnewline
28 & 6605.2 & 6924.00119970183 & 102.902533166176 & -318.801199701826 & -0.315534692201029 \tabularnewline
29 & 7402.6 & 6987.46958669995 & 83.8251933699846 & 415.130413300052 & -0.549076425610768 \tabularnewline
30 & 6879.8 & 7010.89758004049 & 54.6064064044811 & -131.097580040492 & -0.840963490206819 \tabularnewline
31 & 7012.5 & 7032.04511015731 & 38.4197657563907 & -19.5451101573139 & -0.465877457914403 \tabularnewline
32 & 6748.7 & 7055.67953715264 & 31.2669563027393 & -306.979537152642 & -0.205869316194618 \tabularnewline
33 & 7501.4 & 7069.86057407484 & 23.001178475807 & 431.539425925157 & -0.237902330613114 \tabularnewline
34 & 7026.1 & 7127.59332787349 & 39.8035219395206 & -101.493327873495 & 0.483598367168725 \tabularnewline
35 & 7245.9 & 7231.68900728888 & 70.9066003523272 & 14.2109927111173 & 0.89519643370529 \tabularnewline
36 & 7061.8 & 7346.91423338125 & 92.3469399935959 & -285.114233381252 & 0.617087329040971 \tabularnewline
37 & 7865.7 & 7447.8171197346 & 96.4861115670918 & 417.882880265399 & 0.119131990126667 \tabularnewline
38 & 7449.6 & 7566.6481543252 & 107.296075342104 & -117.048154325203 & 0.311128078424258 \tabularnewline
39 & 7605.6 & 7629.44969758459 & 85.7706362322349 & -23.8496975845878 & -0.619536628058519 \tabularnewline
40 & 7366.6 & 7672.87113694617 & 65.2830613334002 & -306.271136946169 & -0.589665233141102 \tabularnewline
41 & 8301.3 & 7840.73286543048 & 114.908279319523 & 460.567134569519 & 1.42829328879236 \tabularnewline
42 & 7821.7 & 7935.25480900191 & 105.045835367545 & -113.554809001909 & -0.28385693967523 \tabularnewline
43 & 8052.3 & 8056.40193474565 & 112.835272167363 & -4.10193474564832 & 0.224192472221623 \tabularnewline
44 & 7817.5 & 8163.80954588616 & 110.209493639576 & -346.309545886161 & -0.0755741133520917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299487&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]4622.9[/C][C]4622.9[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]4378.7[/C][C]4419.10914854643[/C][C]-58.9609185078669[/C][C]-40.4091485464351[/C][C]-1.22890897893268[/C][/ROW]
[ROW][C]3[/C][C]4487.1[/C][C]4469.88546882567[/C][C]-10.1758056684521[/C][C]17.2145311743353[/C][C]1.7306692649036[/C][/ROW]
[ROW][C]4[/C][C]4381[/C][C]4442.02766222773[/C][C]-19.0466859919566[/C][C]-61.0276622277286[/C][C]-0.250734328107812[/C][/ROW]
[ROW][C]5[/C][C]5057.9[/C][C]4755.59728533528[/C][C]133.747182278812[/C][C]302.302714664716[/C][C]4.44873902381376[/C][/ROW]
[ROW][C]6[/C][C]4766.2[/C][C]4869.58465826783[/C][C]124.074986662622[/C][C]-103.384658267831[/C][C]-0.274612152360142[/C][/ROW]
[ROW][C]7[/C][C]4902.3[/C][C]4937.3309986349[/C][C]97.0671212030757[/C][C]-35.0309986348985[/C][C]-0.775584574301283[/C][/ROW]
[ROW][C]8[/C][C]4798.1[/C][C]5006.03909513526[/C][C]83.2967221146504[/C][C]-207.939095135259[/C][C]-0.397734520911458[/C][/ROW]
[ROW][C]9[/C][C]5587.3[/C][C]5215.57066036121[/C][C]144.185491413088[/C][C]371.729339638787[/C][C]1.74654708699991[/C][/ROW]
[ROW][C]10[/C][C]5217.1[/C][C]5321.55813603507[/C][C]125.690967985869[/C][C]-104.458136035073[/C][C]-0.533276215238207[/C][/ROW]
[ROW][C]11[/C][C]5366.1[/C][C]5410.86595288626[/C][C]108.099292896574[/C][C]-44.7659528862613[/C][C]-0.505573912977092[/C][/ROW]
[ROW][C]12[/C][C]5259.8[/C][C]5513.56294244317[/C][C]105.48557548124[/C][C]-253.762942443167[/C][C]-0.0752902148008226[/C][/ROW]
[ROW][C]13[/C][C]5886.9[/C][C]5536.96876353017[/C][C]65.7805026450071[/C][C]349.931236469834[/C][C]-1.14215204394469[/C][/ROW]
[ROW][C]14[/C][C]5544.7[/C][C]5622.45492730129[/C][C]75.3133683384217[/C][C]-77.7549273012939[/C][C]0.274445111914531[/C][/ROW]
[ROW][C]15[/C][C]5676.4[/C][C]5710.87677038112[/C][C]81.6550023149874[/C][C]-34.4767703811177[/C][C]0.182493285032891[/C][/ROW]
[ROW][C]16[/C][C]5581.1[/C][C]5801.94508908979[/C][C]86.2088314465093[/C][C]-220.845089089794[/C][C]0.131076048705412[/C][/ROW]
[ROW][C]17[/C][C]6201[/C][C]5868.34988071822[/C][C]76.6279870125426[/C][C]332.650119281777[/C][C]-0.275741170734308[/C][/ROW]
[ROW][C]18[/C][C]5812.1[/C][C]5910.0245166869[/C][C]59.7185510795571[/C][C]-97.9245166869043[/C][C]-0.486687914772327[/C][/ROW]
[ROW][C]19[/C][C]5963.1[/C][C]5989.44202290642[/C][C]69.2485030557711[/C][C]-26.3420229064244[/C][C]0.274285353809371[/C][/ROW]
[ROW][C]20[/C][C]5799.7[/C][C]6027.25215621713[/C][C]54.0394009733936[/C][C]-227.552156217127[/C][C]-0.437742977104376[/C][/ROW]
[ROW][C]21[/C][C]6647.1[/C][C]6231.9463582387[/C][C]126.922876887151[/C][C]415.1536417613[/C][C]2.09770249528298[/C][/ROW]
[ROW][C]22[/C][C]6266.3[/C][C]6371.85337174215[/C][C]133.20429793794[/C][C]-105.553371742154[/C][C]0.180789260422819[/C][/ROW]
[ROW][C]23[/C][C]6382.3[/C][C]6435.6431884977[/C][C]99.6231412080932[/C][C]-53.3431884977015[/C][C]-0.966519927616493[/C][/ROW]
[ROW][C]24[/C][C]6204.2[/C][C]6500.04678157585[/C][C]82.5847330954499[/C][C]-295.846781575853[/C][C]-0.490392464828712[/C][/ROW]
[ROW][C]25[/C][C]7039.9[/C][C]6611.63706189683[/C][C]96.6169560669927[/C][C]428.262938103171[/C][C]0.403869970344837[/C][/ROW]
[ROW][C]26[/C][C]6604.8[/C][C]6692.27954094301[/C][C]88.888869166022[/C][C]-87.4795409430082[/C][C]-0.222426679798152[/C][/ROW]
[ROW][C]27[/C][C]6815.6[/C][C]6832.79700032171[/C][C]113.86560291513[/C][C]-17.1970003217136[/C][C]0.718870494541553[/C][/ROW]
[ROW][C]28[/C][C]6605.2[/C][C]6924.00119970183[/C][C]102.902533166176[/C][C]-318.801199701826[/C][C]-0.315534692201029[/C][/ROW]
[ROW][C]29[/C][C]7402.6[/C][C]6987.46958669995[/C][C]83.8251933699846[/C][C]415.130413300052[/C][C]-0.549076425610768[/C][/ROW]
[ROW][C]30[/C][C]6879.8[/C][C]7010.89758004049[/C][C]54.6064064044811[/C][C]-131.097580040492[/C][C]-0.840963490206819[/C][/ROW]
[ROW][C]31[/C][C]7012.5[/C][C]7032.04511015731[/C][C]38.4197657563907[/C][C]-19.5451101573139[/C][C]-0.465877457914403[/C][/ROW]
[ROW][C]32[/C][C]6748.7[/C][C]7055.67953715264[/C][C]31.2669563027393[/C][C]-306.979537152642[/C][C]-0.205869316194618[/C][/ROW]
[ROW][C]33[/C][C]7501.4[/C][C]7069.86057407484[/C][C]23.001178475807[/C][C]431.539425925157[/C][C]-0.237902330613114[/C][/ROW]
[ROW][C]34[/C][C]7026.1[/C][C]7127.59332787349[/C][C]39.8035219395206[/C][C]-101.493327873495[/C][C]0.483598367168725[/C][/ROW]
[ROW][C]35[/C][C]7245.9[/C][C]7231.68900728888[/C][C]70.9066003523272[/C][C]14.2109927111173[/C][C]0.89519643370529[/C][/ROW]
[ROW][C]36[/C][C]7061.8[/C][C]7346.91423338125[/C][C]92.3469399935959[/C][C]-285.114233381252[/C][C]0.617087329040971[/C][/ROW]
[ROW][C]37[/C][C]7865.7[/C][C]7447.8171197346[/C][C]96.4861115670918[/C][C]417.882880265399[/C][C]0.119131990126667[/C][/ROW]
[ROW][C]38[/C][C]7449.6[/C][C]7566.6481543252[/C][C]107.296075342104[/C][C]-117.048154325203[/C][C]0.311128078424258[/C][/ROW]
[ROW][C]39[/C][C]7605.6[/C][C]7629.44969758459[/C][C]85.7706362322349[/C][C]-23.8496975845878[/C][C]-0.619536628058519[/C][/ROW]
[ROW][C]40[/C][C]7366.6[/C][C]7672.87113694617[/C][C]65.2830613334002[/C][C]-306.271136946169[/C][C]-0.589665233141102[/C][/ROW]
[ROW][C]41[/C][C]8301.3[/C][C]7840.73286543048[/C][C]114.908279319523[/C][C]460.567134569519[/C][C]1.42829328879236[/C][/ROW]
[ROW][C]42[/C][C]7821.7[/C][C]7935.25480900191[/C][C]105.045835367545[/C][C]-113.554809001909[/C][C]-0.28385693967523[/C][/ROW]
[ROW][C]43[/C][C]8052.3[/C][C]8056.40193474565[/C][C]112.835272167363[/C][C]-4.10193474564832[/C][C]0.224192472221623[/C][/ROW]
[ROW][C]44[/C][C]7817.5[/C][C]8163.80954588616[/C][C]110.209493639576[/C][C]-346.309545886161[/C][C]-0.0755741133520917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299487&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299487&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
14622.94622.9000
24378.74419.10914854643-58.9609185078669-40.4091485464351-1.22890897893268
34487.14469.88546882567-10.175805668452117.21453117433531.7306692649036
443814442.02766222773-19.0466859919566-61.0276622277286-0.250734328107812
55057.94755.59728533528133.747182278812302.3027146647164.44873902381376
64766.24869.58465826783124.074986662622-103.384658267831-0.274612152360142
74902.34937.330998634997.0671212030757-35.0309986348985-0.775584574301283
84798.15006.0390951352683.2967221146504-207.939095135259-0.397734520911458
95587.35215.57066036121144.185491413088371.7293396387871.74654708699991
105217.15321.55813603507125.690967985869-104.458136035073-0.533276215238207
115366.15410.86595288626108.099292896574-44.7659528862613-0.505573912977092
125259.85513.56294244317105.48557548124-253.762942443167-0.0752902148008226
135886.95536.9687635301765.7805026450071349.931236469834-1.14215204394469
145544.75622.4549273012975.3133683384217-77.75492730129390.274445111914531
155676.45710.8767703811281.6550023149874-34.47677038111770.182493285032891
165581.15801.9450890897986.2088314465093-220.8450890897940.131076048705412
1762015868.3498807182276.6279870125426332.650119281777-0.275741170734308
185812.15910.024516686959.7185510795571-97.9245166869043-0.486687914772327
195963.15989.4420229064269.2485030557711-26.34202290642440.274285353809371
205799.76027.2521562171354.0394009733936-227.552156217127-0.437742977104376
216647.16231.9463582387126.922876887151415.15364176132.09770249528298
226266.36371.85337174215133.20429793794-105.5533717421540.180789260422819
236382.36435.643188497799.6231412080932-53.3431884977015-0.966519927616493
246204.26500.0467815758582.5847330954499-295.846781575853-0.490392464828712
257039.96611.6370618968396.6169560669927428.2629381031710.403869970344837
266604.86692.2795409430188.888869166022-87.4795409430082-0.222426679798152
276815.66832.79700032171113.86560291513-17.19700032171360.718870494541553
286605.26924.00119970183102.902533166176-318.801199701826-0.315534692201029
297402.66987.4695866999583.8251933699846415.130413300052-0.549076425610768
306879.87010.8975800404954.6064064044811-131.097580040492-0.840963490206819
317012.57032.0451101573138.4197657563907-19.5451101573139-0.465877457914403
326748.77055.6795371526431.2669563027393-306.979537152642-0.205869316194618
337501.47069.8605740748423.001178475807431.539425925157-0.237902330613114
347026.17127.5933278734939.8035219395206-101.4933278734950.483598367168725
357245.97231.6890072888870.906600352327214.21099271111730.89519643370529
367061.87346.9142333812592.3469399935959-285.1142333812520.617087329040971
377865.77447.817119734696.4861115670918417.8828802653990.119131990126667
387449.67566.6481543252107.296075342104-117.0481543252030.311128078424258
397605.67629.4496975845985.7706362322349-23.8496975845878-0.619536628058519
407366.67672.8711369461765.2830613334002-306.271136946169-0.589665233141102
418301.37840.73286543048114.908279319523460.5671345695191.42829328879236
427821.77935.25480900191105.045835367545-113.554809001909-0.28385693967523
438052.38056.40193474565112.835272167363-4.101934745648320.224192472221623
447817.58163.80954588616110.209493639576-346.309545886161-0.0755741133520917







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
18731.238434495798267.59271962597463.645714869813
28255.672584786538374.76165251573-119.089067729197
38480.297725001098481.93058540549-1.63286040440295
48246.175731559048589.09951829525-342.923786736213
59159.914166054828696.26845118501463.645714869813
68684.348316345578803.43738407477-119.089067729197
78908.973456560128910.60631696453-1.63286040440295
88674.851463118079017.77524985429-342.923786736213
99588.589897613869124.94418274405463.645714869813
109113.024047904619232.11311563381-119.089067729197
119337.649188119169339.28204852356-1.63286040440295
129103.527194677119446.45098141332-342.923786736213
1310017.26562917299553.61991430308463.645714869813
149541.699779463649660.78884719284-119.089067729197
159766.32491967829767.9577800826-1.63286040440295
169532.202926236159875.12671297236-342.923786736213
1710445.94136073199982.29564586212463.645714869813
189970.3755110226810089.4645787519-119.089067729197

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 8731.23843449579 & 8267.59271962597 & 463.645714869813 \tabularnewline
2 & 8255.67258478653 & 8374.76165251573 & -119.089067729197 \tabularnewline
3 & 8480.29772500109 & 8481.93058540549 & -1.63286040440295 \tabularnewline
4 & 8246.17573155904 & 8589.09951829525 & -342.923786736213 \tabularnewline
5 & 9159.91416605482 & 8696.26845118501 & 463.645714869813 \tabularnewline
6 & 8684.34831634557 & 8803.43738407477 & -119.089067729197 \tabularnewline
7 & 8908.97345656012 & 8910.60631696453 & -1.63286040440295 \tabularnewline
8 & 8674.85146311807 & 9017.77524985429 & -342.923786736213 \tabularnewline
9 & 9588.58989761386 & 9124.94418274405 & 463.645714869813 \tabularnewline
10 & 9113.02404790461 & 9232.11311563381 & -119.089067729197 \tabularnewline
11 & 9337.64918811916 & 9339.28204852356 & -1.63286040440295 \tabularnewline
12 & 9103.52719467711 & 9446.45098141332 & -342.923786736213 \tabularnewline
13 & 10017.2656291729 & 9553.61991430308 & 463.645714869813 \tabularnewline
14 & 9541.69977946364 & 9660.78884719284 & -119.089067729197 \tabularnewline
15 & 9766.3249196782 & 9767.9577800826 & -1.63286040440295 \tabularnewline
16 & 9532.20292623615 & 9875.12671297236 & -342.923786736213 \tabularnewline
17 & 10445.9413607319 & 9982.29564586212 & 463.645714869813 \tabularnewline
18 & 9970.37551102268 & 10089.4645787519 & -119.089067729197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299487&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]8731.23843449579[/C][C]8267.59271962597[/C][C]463.645714869813[/C][/ROW]
[ROW][C]2[/C][C]8255.67258478653[/C][C]8374.76165251573[/C][C]-119.089067729197[/C][/ROW]
[ROW][C]3[/C][C]8480.29772500109[/C][C]8481.93058540549[/C][C]-1.63286040440295[/C][/ROW]
[ROW][C]4[/C][C]8246.17573155904[/C][C]8589.09951829525[/C][C]-342.923786736213[/C][/ROW]
[ROW][C]5[/C][C]9159.91416605482[/C][C]8696.26845118501[/C][C]463.645714869813[/C][/ROW]
[ROW][C]6[/C][C]8684.34831634557[/C][C]8803.43738407477[/C][C]-119.089067729197[/C][/ROW]
[ROW][C]7[/C][C]8908.97345656012[/C][C]8910.60631696453[/C][C]-1.63286040440295[/C][/ROW]
[ROW][C]8[/C][C]8674.85146311807[/C][C]9017.77524985429[/C][C]-342.923786736213[/C][/ROW]
[ROW][C]9[/C][C]9588.58989761386[/C][C]9124.94418274405[/C][C]463.645714869813[/C][/ROW]
[ROW][C]10[/C][C]9113.02404790461[/C][C]9232.11311563381[/C][C]-119.089067729197[/C][/ROW]
[ROW][C]11[/C][C]9337.64918811916[/C][C]9339.28204852356[/C][C]-1.63286040440295[/C][/ROW]
[ROW][C]12[/C][C]9103.52719467711[/C][C]9446.45098141332[/C][C]-342.923786736213[/C][/ROW]
[ROW][C]13[/C][C]10017.2656291729[/C][C]9553.61991430308[/C][C]463.645714869813[/C][/ROW]
[ROW][C]14[/C][C]9541.69977946364[/C][C]9660.78884719284[/C][C]-119.089067729197[/C][/ROW]
[ROW][C]15[/C][C]9766.3249196782[/C][C]9767.9577800826[/C][C]-1.63286040440295[/C][/ROW]
[ROW][C]16[/C][C]9532.20292623615[/C][C]9875.12671297236[/C][C]-342.923786736213[/C][/ROW]
[ROW][C]17[/C][C]10445.9413607319[/C][C]9982.29564586212[/C][C]463.645714869813[/C][/ROW]
[ROW][C]18[/C][C]9970.37551102268[/C][C]10089.4645787519[/C][C]-119.089067729197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299487&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299487&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
18731.238434495798267.59271962597463.645714869813
28255.672584786538374.76165251573-119.089067729197
38480.297725001098481.93058540549-1.63286040440295
48246.175731559048589.09951829525-342.923786736213
59159.914166054828696.26845118501463.645714869813
68684.348316345578803.43738407477-119.089067729197
78908.973456560128910.60631696453-1.63286040440295
88674.851463118079017.77524985429-342.923786736213
99588.589897613869124.94418274405463.645714869813
109113.024047904619232.11311563381-119.089067729197
119337.649188119169339.28204852356-1.63286040440295
129103.527194677119446.45098141332-342.923786736213
1310017.26562917299553.61991430308463.645714869813
149541.699779463649660.78884719284-119.089067729197
159766.32491967829767.9577800826-1.63286040440295
169532.202926236159875.12671297236-342.923786736213
1710445.94136073199982.29564586212463.645714869813
189970.3755110226810089.4645787519-119.089067729197



Parameters (Session):
par1 = 4 ; par2 = 18 ; par3 = BFGS ;
Parameters (R input):
par1 = 4 ; 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')