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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 computationThu, 22 Dec 2016 22:03:00 +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/22/t1482440608nsbabnzcwkudg6q.htm/, Retrieved Sun, 28 Apr 2024 22:36:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302689, Retrieved Sun, 28 Apr 2024 22:36:05 +0000
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User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-22 21:03:00] [2802fcbee976b89d2ab84425d3d65dcf] [Current]
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Dataseries X:
1550.61
1488.54
1200.03
1451.49
2576.19
2434.2
2586.21
1898.55
2958.18
3290.73
3408.39
3214.71
4205.43
4378.53
4279.68
4799.25
4902.84
5379.84
5527.05
6004.83
5827.71
6496.02
6858.99
6696.84
6831
7366.47
7881.03
7494.66
5813.55
6911.25
7252.59
7425.63
7603.5
6045.72
6064.35
5486.85
5808.27
6467.88




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302689&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302689&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302689&T=0

As an alternative you can also use a QR Code:  

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

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







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
11550.611550.61000
21488.541541.87411880368-3.71619979417485-2.50984105026682-0.121640395402886
31200.031462.30874410868-32.2487496598456-14.8384847658667-0.624107205833838
41451.491441.17250165357-28.5211227058129-13.82712951734060.0640879440901445
52576.191841.0150575844102.5476636716477.093091362374822.00515128267896
62434.22135.7444603151157.71440210421311.51712779469820.806703184425096
72586.212410.12220261593189.94371490271712.34233417721490.464750536915753
81898.552297.91043088693108.07030852642313.0652827273127-1.17511454529535
92958.182636.35492960002170.03214214436911.35807390096080.886048336140352
103290.733009.40006435145224.5747119850159.449278547629830.776629915119879
113408.393304.91734803624243.6651337911348.778829851876710.27068196185692
123214.713401.15662424201203.89843729954910.0144439616679-0.561908746813709
134205.433829.84933232461259.637216635794123.295199518350.916937717891285
144378.534226.80753397417296.711966796471-7.373752592750680.473341195979596
154279.684419.9834122645268.973369389551-9.3252994441453-0.381140262601036
164799.254740.33005829439282.810045693587-8.741202055503550.194836454709073
174902.844975.49210548531269.89448105286-9.01256952423005-0.182480709224659
185379.845306.69832541348286.573493867325-8.90427197034970.234965649985142
195527.055568.72321934001279.889313949227-8.88751416020357-0.0938830967199804
206004.835919.44910937359299.167300479343-9.029011829470380.270389737827841
215827.716054.64491679961254.579390500104-8.61673777587303-0.625328568513534
226496.026393.13158043257277.383043537236-8.827937614031790.319989567022142
236858.996755.19543296181300.393357620626-9.016453953006190.32310546006778
246696.846905.58090956137259.624634577554-8.74628780351389-0.572767537632557
2568317013.86518126834220.7591201391225.23226815669004-0.616220793426771
267366.477294.49821605503236.950304005310.7589998146689320.210230296249312
277881.037683.78570155825277.8732660879362.885623346502630.563904474586278
287494.667759.75743356581223.409100079761.17511436566617-0.766055334744596
295813.557055.12394569468-28.2598098675264-2.8174044591463-3.55143110414567
306911.256978.63982972476-41.3781155222816-2.88502314532386-0.184733491553034
317252.597073.51410843909-4.27928760066462-2.942061508889750.521215863777162
327425.637223.2963561245337.6571516225478-3.158969730690140.588505552637397
337603.57409.2632677984578.0036704799364-3.427150725184460.566132548615157
346045.726870.28614095638-89.7661111807368-2.30021482926472-2.3550765089233
356064.356474.3553296375-173.006086157341-1.80281670340875-1.16909200081094
365486.855952.96036108792-267.73559162843-1.34289629533784-1.3310163091408
375808.275725.4143138365-257.23187101760631.83877183015080.160960484536215
386467.885915.76058304586-136.0003940480434.164474524158771.60522487827609

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 1550.61 & 1550.61 & 0 & 0 & 0 \tabularnewline
2 & 1488.54 & 1541.87411880368 & -3.71619979417485 & -2.50984105026682 & -0.121640395402886 \tabularnewline
3 & 1200.03 & 1462.30874410868 & -32.2487496598456 & -14.8384847658667 & -0.624107205833838 \tabularnewline
4 & 1451.49 & 1441.17250165357 & -28.5211227058129 & -13.8271295173406 & 0.0640879440901445 \tabularnewline
5 & 2576.19 & 1841.0150575844 & 102.547663671647 & 7.09309136237482 & 2.00515128267896 \tabularnewline
6 & 2434.2 & 2135.7444603151 & 157.714402104213 & 11.5171277946982 & 0.806703184425096 \tabularnewline
7 & 2586.21 & 2410.12220261593 & 189.943714902717 & 12.3423341772149 & 0.464750536915753 \tabularnewline
8 & 1898.55 & 2297.91043088693 & 108.070308526423 & 13.0652827273127 & -1.17511454529535 \tabularnewline
9 & 2958.18 & 2636.35492960002 & 170.032142144369 & 11.3580739009608 & 0.886048336140352 \tabularnewline
10 & 3290.73 & 3009.40006435145 & 224.574711985015 & 9.44927854762983 & 0.776629915119879 \tabularnewline
11 & 3408.39 & 3304.91734803624 & 243.665133791134 & 8.77882985187671 & 0.27068196185692 \tabularnewline
12 & 3214.71 & 3401.15662424201 & 203.898437299549 & 10.0144439616679 & -0.561908746813709 \tabularnewline
13 & 4205.43 & 3829.84933232461 & 259.637216635794 & 123.29519951835 & 0.916937717891285 \tabularnewline
14 & 4378.53 & 4226.80753397417 & 296.711966796471 & -7.37375259275068 & 0.473341195979596 \tabularnewline
15 & 4279.68 & 4419.9834122645 & 268.973369389551 & -9.3252994441453 & -0.381140262601036 \tabularnewline
16 & 4799.25 & 4740.33005829439 & 282.810045693587 & -8.74120205550355 & 0.194836454709073 \tabularnewline
17 & 4902.84 & 4975.49210548531 & 269.89448105286 & -9.01256952423005 & -0.182480709224659 \tabularnewline
18 & 5379.84 & 5306.69832541348 & 286.573493867325 & -8.9042719703497 & 0.234965649985142 \tabularnewline
19 & 5527.05 & 5568.72321934001 & 279.889313949227 & -8.88751416020357 & -0.0938830967199804 \tabularnewline
20 & 6004.83 & 5919.44910937359 & 299.167300479343 & -9.02901182947038 & 0.270389737827841 \tabularnewline
21 & 5827.71 & 6054.64491679961 & 254.579390500104 & -8.61673777587303 & -0.625328568513534 \tabularnewline
22 & 6496.02 & 6393.13158043257 & 277.383043537236 & -8.82793761403179 & 0.319989567022142 \tabularnewline
23 & 6858.99 & 6755.19543296181 & 300.393357620626 & -9.01645395300619 & 0.32310546006778 \tabularnewline
24 & 6696.84 & 6905.58090956137 & 259.624634577554 & -8.74628780351389 & -0.572767537632557 \tabularnewline
25 & 6831 & 7013.86518126834 & 220.759120139122 & 5.23226815669004 & -0.616220793426771 \tabularnewline
26 & 7366.47 & 7294.49821605503 & 236.95030400531 & 0.758999814668932 & 0.210230296249312 \tabularnewline
27 & 7881.03 & 7683.78570155825 & 277.873266087936 & 2.88562334650263 & 0.563904474586278 \tabularnewline
28 & 7494.66 & 7759.75743356581 & 223.40910007976 & 1.17511436566617 & -0.766055334744596 \tabularnewline
29 & 5813.55 & 7055.12394569468 & -28.2598098675264 & -2.8174044591463 & -3.55143110414567 \tabularnewline
30 & 6911.25 & 6978.63982972476 & -41.3781155222816 & -2.88502314532386 & -0.184733491553034 \tabularnewline
31 & 7252.59 & 7073.51410843909 & -4.27928760066462 & -2.94206150888975 & 0.521215863777162 \tabularnewline
32 & 7425.63 & 7223.29635612453 & 37.6571516225478 & -3.15896973069014 & 0.588505552637397 \tabularnewline
33 & 7603.5 & 7409.26326779845 & 78.0036704799364 & -3.42715072518446 & 0.566132548615157 \tabularnewline
34 & 6045.72 & 6870.28614095638 & -89.7661111807368 & -2.30021482926472 & -2.3550765089233 \tabularnewline
35 & 6064.35 & 6474.3553296375 & -173.006086157341 & -1.80281670340875 & -1.16909200081094 \tabularnewline
36 & 5486.85 & 5952.96036108792 & -267.73559162843 & -1.34289629533784 & -1.3310163091408 \tabularnewline
37 & 5808.27 & 5725.4143138365 & -257.231871017606 & 31.8387718301508 & 0.160960484536215 \tabularnewline
38 & 6467.88 & 5915.76058304586 & -136.000394048043 & 4.16447452415877 & 1.60522487827609 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302689&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]1550.61[/C][C]1550.61[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]1488.54[/C][C]1541.87411880368[/C][C]-3.71619979417485[/C][C]-2.50984105026682[/C][C]-0.121640395402886[/C][/ROW]
[ROW][C]3[/C][C]1200.03[/C][C]1462.30874410868[/C][C]-32.2487496598456[/C][C]-14.8384847658667[/C][C]-0.624107205833838[/C][/ROW]
[ROW][C]4[/C][C]1451.49[/C][C]1441.17250165357[/C][C]-28.5211227058129[/C][C]-13.8271295173406[/C][C]0.0640879440901445[/C][/ROW]
[ROW][C]5[/C][C]2576.19[/C][C]1841.0150575844[/C][C]102.547663671647[/C][C]7.09309136237482[/C][C]2.00515128267896[/C][/ROW]
[ROW][C]6[/C][C]2434.2[/C][C]2135.7444603151[/C][C]157.714402104213[/C][C]11.5171277946982[/C][C]0.806703184425096[/C][/ROW]
[ROW][C]7[/C][C]2586.21[/C][C]2410.12220261593[/C][C]189.943714902717[/C][C]12.3423341772149[/C][C]0.464750536915753[/C][/ROW]
[ROW][C]8[/C][C]1898.55[/C][C]2297.91043088693[/C][C]108.070308526423[/C][C]13.0652827273127[/C][C]-1.17511454529535[/C][/ROW]
[ROW][C]9[/C][C]2958.18[/C][C]2636.35492960002[/C][C]170.032142144369[/C][C]11.3580739009608[/C][C]0.886048336140352[/C][/ROW]
[ROW][C]10[/C][C]3290.73[/C][C]3009.40006435145[/C][C]224.574711985015[/C][C]9.44927854762983[/C][C]0.776629915119879[/C][/ROW]
[ROW][C]11[/C][C]3408.39[/C][C]3304.91734803624[/C][C]243.665133791134[/C][C]8.77882985187671[/C][C]0.27068196185692[/C][/ROW]
[ROW][C]12[/C][C]3214.71[/C][C]3401.15662424201[/C][C]203.898437299549[/C][C]10.0144439616679[/C][C]-0.561908746813709[/C][/ROW]
[ROW][C]13[/C][C]4205.43[/C][C]3829.84933232461[/C][C]259.637216635794[/C][C]123.29519951835[/C][C]0.916937717891285[/C][/ROW]
[ROW][C]14[/C][C]4378.53[/C][C]4226.80753397417[/C][C]296.711966796471[/C][C]-7.37375259275068[/C][C]0.473341195979596[/C][/ROW]
[ROW][C]15[/C][C]4279.68[/C][C]4419.9834122645[/C][C]268.973369389551[/C][C]-9.3252994441453[/C][C]-0.381140262601036[/C][/ROW]
[ROW][C]16[/C][C]4799.25[/C][C]4740.33005829439[/C][C]282.810045693587[/C][C]-8.74120205550355[/C][C]0.194836454709073[/C][/ROW]
[ROW][C]17[/C][C]4902.84[/C][C]4975.49210548531[/C][C]269.89448105286[/C][C]-9.01256952423005[/C][C]-0.182480709224659[/C][/ROW]
[ROW][C]18[/C][C]5379.84[/C][C]5306.69832541348[/C][C]286.573493867325[/C][C]-8.9042719703497[/C][C]0.234965649985142[/C][/ROW]
[ROW][C]19[/C][C]5527.05[/C][C]5568.72321934001[/C][C]279.889313949227[/C][C]-8.88751416020357[/C][C]-0.0938830967199804[/C][/ROW]
[ROW][C]20[/C][C]6004.83[/C][C]5919.44910937359[/C][C]299.167300479343[/C][C]-9.02901182947038[/C][C]0.270389737827841[/C][/ROW]
[ROW][C]21[/C][C]5827.71[/C][C]6054.64491679961[/C][C]254.579390500104[/C][C]-8.61673777587303[/C][C]-0.625328568513534[/C][/ROW]
[ROW][C]22[/C][C]6496.02[/C][C]6393.13158043257[/C][C]277.383043537236[/C][C]-8.82793761403179[/C][C]0.319989567022142[/C][/ROW]
[ROW][C]23[/C][C]6858.99[/C][C]6755.19543296181[/C][C]300.393357620626[/C][C]-9.01645395300619[/C][C]0.32310546006778[/C][/ROW]
[ROW][C]24[/C][C]6696.84[/C][C]6905.58090956137[/C][C]259.624634577554[/C][C]-8.74628780351389[/C][C]-0.572767537632557[/C][/ROW]
[ROW][C]25[/C][C]6831[/C][C]7013.86518126834[/C][C]220.759120139122[/C][C]5.23226815669004[/C][C]-0.616220793426771[/C][/ROW]
[ROW][C]26[/C][C]7366.47[/C][C]7294.49821605503[/C][C]236.95030400531[/C][C]0.758999814668932[/C][C]0.210230296249312[/C][/ROW]
[ROW][C]27[/C][C]7881.03[/C][C]7683.78570155825[/C][C]277.873266087936[/C][C]2.88562334650263[/C][C]0.563904474586278[/C][/ROW]
[ROW][C]28[/C][C]7494.66[/C][C]7759.75743356581[/C][C]223.40910007976[/C][C]1.17511436566617[/C][C]-0.766055334744596[/C][/ROW]
[ROW][C]29[/C][C]5813.55[/C][C]7055.12394569468[/C][C]-28.2598098675264[/C][C]-2.8174044591463[/C][C]-3.55143110414567[/C][/ROW]
[ROW][C]30[/C][C]6911.25[/C][C]6978.63982972476[/C][C]-41.3781155222816[/C][C]-2.88502314532386[/C][C]-0.184733491553034[/C][/ROW]
[ROW][C]31[/C][C]7252.59[/C][C]7073.51410843909[/C][C]-4.27928760066462[/C][C]-2.94206150888975[/C][C]0.521215863777162[/C][/ROW]
[ROW][C]32[/C][C]7425.63[/C][C]7223.29635612453[/C][C]37.6571516225478[/C][C]-3.15896973069014[/C][C]0.588505552637397[/C][/ROW]
[ROW][C]33[/C][C]7603.5[/C][C]7409.26326779845[/C][C]78.0036704799364[/C][C]-3.42715072518446[/C][C]0.566132548615157[/C][/ROW]
[ROW][C]34[/C][C]6045.72[/C][C]6870.28614095638[/C][C]-89.7661111807368[/C][C]-2.30021482926472[/C][C]-2.3550765089233[/C][/ROW]
[ROW][C]35[/C][C]6064.35[/C][C]6474.3553296375[/C][C]-173.006086157341[/C][C]-1.80281670340875[/C][C]-1.16909200081094[/C][/ROW]
[ROW][C]36[/C][C]5486.85[/C][C]5952.96036108792[/C][C]-267.73559162843[/C][C]-1.34289629533784[/C][C]-1.3310163091408[/C][/ROW]
[ROW][C]37[/C][C]5808.27[/C][C]5725.4143138365[/C][C]-257.231871017606[/C][C]31.8387718301508[/C][C]0.160960484536215[/C][/ROW]
[ROW][C]38[/C][C]6467.88[/C][C]5915.76058304586[/C][C]-136.000394048043[/C][C]4.16447452415877[/C][C]1.60522487827609[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302689&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302689&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
11550.611550.61000
21488.541541.87411880368-3.71619979417485-2.50984105026682-0.121640395402886
31200.031462.30874410868-32.2487496598456-14.8384847658667-0.624107205833838
41451.491441.17250165357-28.5211227058129-13.82712951734060.0640879440901445
52576.191841.0150575844102.5476636716477.093091362374822.00515128267896
62434.22135.7444603151157.71440210421311.51712779469820.806703184425096
72586.212410.12220261593189.94371490271712.34233417721490.464750536915753
81898.552297.91043088693108.07030852642313.0652827273127-1.17511454529535
92958.182636.35492960002170.03214214436911.35807390096080.886048336140352
103290.733009.40006435145224.5747119850159.449278547629830.776629915119879
113408.393304.91734803624243.6651337911348.778829851876710.27068196185692
123214.713401.15662424201203.89843729954910.0144439616679-0.561908746813709
134205.433829.84933232461259.637216635794123.295199518350.916937717891285
144378.534226.80753397417296.711966796471-7.373752592750680.473341195979596
154279.684419.9834122645268.973369389551-9.3252994441453-0.381140262601036
164799.254740.33005829439282.810045693587-8.741202055503550.194836454709073
174902.844975.49210548531269.89448105286-9.01256952423005-0.182480709224659
185379.845306.69832541348286.573493867325-8.90427197034970.234965649985142
195527.055568.72321934001279.889313949227-8.88751416020357-0.0938830967199804
206004.835919.44910937359299.167300479343-9.029011829470380.270389737827841
215827.716054.64491679961254.579390500104-8.61673777587303-0.625328568513534
226496.026393.13158043257277.383043537236-8.827937614031790.319989567022142
236858.996755.19543296181300.393357620626-9.016453953006190.32310546006778
246696.846905.58090956137259.624634577554-8.74628780351389-0.572767537632557
2568317013.86518126834220.7591201391225.23226815669004-0.616220793426771
267366.477294.49821605503236.950304005310.7589998146689320.210230296249312
277881.037683.78570155825277.8732660879362.885623346502630.563904474586278
287494.667759.75743356581223.409100079761.17511436566617-0.766055334744596
295813.557055.12394569468-28.2598098675264-2.8174044591463-3.55143110414567
306911.256978.63982972476-41.3781155222816-2.88502314532386-0.184733491553034
317252.597073.51410843909-4.27928760066462-2.942061508889750.521215863777162
327425.637223.2963561245337.6571516225478-3.158969730690140.588505552637397
337603.57409.2632677984578.0036704799364-3.427150725184460.566132548615157
346045.726870.28614095638-89.7661111807368-2.30021482926472-2.3550765089233
356064.356474.3553296375-173.006086157341-1.80281670340875-1.16909200081094
365486.855952.96036108792-267.73559162843-1.34289629533784-1.3310163091408
375808.275725.4143138365-257.23187101760631.83877183015080.160960484536215
386467.885915.76058304586-136.0003940480434.164474524158771.60522487827609







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15788.73086795755712.3403393863276.3905285711834
25574.355860729655543.1315348361431.2243258935147
35091.270279014465373.92273028596-282.652451271491
45247.142354714235204.7139257357742.4284289784549
55149.41382432555035.50512118559113.908703139909
64836.334616958064866.29631663541-29.9616996773517
74899.443585537334697.08751208523202.356073452103
84433.902490617354527.87870753504-93.9762169176959
94330.869601112844358.66990298486-27.8003018720243
103760.756531011924189.46109843468-428.704567422764
114107.087800651854020.252293884586.8355067673501
124160.995159693133851.04348933431309.951670358811

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 5788.7308679575 & 5712.34033938632 & 76.3905285711834 \tabularnewline
2 & 5574.35586072965 & 5543.13153483614 & 31.2243258935147 \tabularnewline
3 & 5091.27027901446 & 5373.92273028596 & -282.652451271491 \tabularnewline
4 & 5247.14235471423 & 5204.71392573577 & 42.4284289784549 \tabularnewline
5 & 5149.4138243255 & 5035.50512118559 & 113.908703139909 \tabularnewline
6 & 4836.33461695806 & 4866.29631663541 & -29.9616996773517 \tabularnewline
7 & 4899.44358553733 & 4697.08751208523 & 202.356073452103 \tabularnewline
8 & 4433.90249061735 & 4527.87870753504 & -93.9762169176959 \tabularnewline
9 & 4330.86960111284 & 4358.66990298486 & -27.8003018720243 \tabularnewline
10 & 3760.75653101192 & 4189.46109843468 & -428.704567422764 \tabularnewline
11 & 4107.08780065185 & 4020.2522938845 & 86.8355067673501 \tabularnewline
12 & 4160.99515969313 & 3851.04348933431 & 309.951670358811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302689&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]5788.7308679575[/C][C]5712.34033938632[/C][C]76.3905285711834[/C][/ROW]
[ROW][C]2[/C][C]5574.35586072965[/C][C]5543.13153483614[/C][C]31.2243258935147[/C][/ROW]
[ROW][C]3[/C][C]5091.27027901446[/C][C]5373.92273028596[/C][C]-282.652451271491[/C][/ROW]
[ROW][C]4[/C][C]5247.14235471423[/C][C]5204.71392573577[/C][C]42.4284289784549[/C][/ROW]
[ROW][C]5[/C][C]5149.4138243255[/C][C]5035.50512118559[/C][C]113.908703139909[/C][/ROW]
[ROW][C]6[/C][C]4836.33461695806[/C][C]4866.29631663541[/C][C]-29.9616996773517[/C][/ROW]
[ROW][C]7[/C][C]4899.44358553733[/C][C]4697.08751208523[/C][C]202.356073452103[/C][/ROW]
[ROW][C]8[/C][C]4433.90249061735[/C][C]4527.87870753504[/C][C]-93.9762169176959[/C][/ROW]
[ROW][C]9[/C][C]4330.86960111284[/C][C]4358.66990298486[/C][C]-27.8003018720243[/C][/ROW]
[ROW][C]10[/C][C]3760.75653101192[/C][C]4189.46109843468[/C][C]-428.704567422764[/C][/ROW]
[ROW][C]11[/C][C]4107.08780065185[/C][C]4020.2522938845[/C][C]86.8355067673501[/C][/ROW]
[ROW][C]12[/C][C]4160.99515969313[/C][C]3851.04348933431[/C][C]309.951670358811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302689&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302689&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
15788.73086795755712.3403393863276.3905285711834
25574.355860729655543.1315348361431.2243258935147
35091.270279014465373.92273028596-282.652451271491
45247.142354714235204.7139257357742.4284289784549
55149.41382432555035.50512118559113.908703139909
64836.334616958064866.29631663541-29.9616996773517
74899.443585537334697.08751208523202.356073452103
84433.902490617354527.87870753504-93.9762169176959
94330.869601112844358.66990298486-27.8003018720243
103760.756531011924189.46109843468-428.704567422764
114107.087800651854020.252293884586.8355067673501
124160.995159693133851.04348933431309.951670358811



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')