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Description of Statistical Computation

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, 09 Dec 2009 09:15:18 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/09/t1260375367leizxlmqs2ai6ii.htm/, Retrieved Sat, 27 Apr 2024 16:47:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65020, Retrieved Sat, 27 Apr 2024 16:47:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Structural Time Series Models] [] [2009-11-27 15:02:30] [b98453cac15ba1066b407e146608df68]
-   PD    [Structural Time Series Models] [workshop 9 bereke...] [2009-12-03 17:57:55] [eaf42bcf5162b5692bb3c7f9d4636222]
-   PD        [Structural Time Series Models] [] [2009-12-09 16:15:18] [17416e80e7873ecccac25c455c5f767e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
153.4
145
137.7
148.3
152.2
169.4
168.6
161.1
174.1
179
190.6
190
181.6
174.8
180.5
196.8
193.8
197
216.3
221.4
217.9
229.7
227.4
204.2
196.6
198.8
207.5
190.7
201.6
210.5
223.5
223.8
231.2
244
234.7
250.2
265.7
287.6
283.3
295.4
312.3
333.8
347.7
383.2
407.1
413.6
362.7
321.9
239.4
191
159.7
163.4
157.6
166.2
176.7
198.3
226.2
216.2
235.9
226.9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65020&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65020&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65020&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
1153.4153.4000
2145145.876191167459-7.44134377868622-0.041232530240796-0.557950534988849
3137.7137.791193719566-7.99195450904879-0.0398729065246219-0.0397493044432643
4148.3147.0034852156496.86854273510676-0.05655744513024741.05522810977596
5152.2152.3736359823635.57296841526736-0.0563948021853457-0.0916881440644917
6169.4168.62076096854914.8031708653358-0.05595673533716080.653207893605105
7168.6169.7278336700482.96004521014379-0.0562167320232124-0.838115427451734
8161.1161.993016572943-6.28773277779368-0.0562398245501543-0.654446774325278
9174.1172.8173891503238.50894960012367-0.05625339692364091.04713164279455
10179179.2209777440916.68846225306813-0.0562526151651217-0.128832251264188
11190.6190.31180790537010.4951527359973-0.05625280416581980.269391877582786
12190190.8363609517281.87365858787821-0.0562529569762432-0.610125910298412
13181.6182.938653778518-6.48111459570032-0.582679721214916-0.627341256815093
14174.8174.860704709527-7.707929457364860.0323240020032319-0.0840417131388031
15180.5179.5602418125163.07890274373382-0.009631642283819080.749056934503394
16196.8195.81078294120414.4475557326564-0.03378712155713410.80214830106102
17193.8195.0216539271821.27646422051838-0.0299470804210284-0.93208399799127
18197196.9767992090481.86335423195363-0.02990286930926470.0415327406762524
19216.3215.06020688496715.8892024854284-0.02932022427382610.992580120109795
20221.4222.1201743997388.25459899185731-0.0293643167277498-0.540285629075005
21217.9218.832431119834-1.72595515304180-0.0293498305701368-0.706303868245136
22229.7228.8133993084018.39691627123799-0.02935804894539550.716375379228054
23227.4228.1390967597350.5531101339685-0.0293571517537865-0.555090484024443
24204.2206.004465437042-19.0647902955236-0.0293577002260322-1.38831960586255
25196.6195.003051588083-12.14337365850190.9706702683227440.509471571765212
26198.8197.797267133778-0.2898752338866510.05430444443483640.821434943482309
27207.5206.7569900328067.740327776154580.03112566028906030.560382308394789
28190.7192.361294330894-11.37464313852450.0612299935782609-1.34975235316270
29201.6200.0511058275345.106575047340810.05766866367807321.16633561543262
30210.5210.0586242948859.344594827595830.05790528405270040.299914624446646
31223.5223.14892084105912.58355797276660.05800500700961130.22921475523822
32223.8224.6121064933272.967829734917250.0579638471243436-0.680485867963241
33231.2230.8835611176115.824443843794850.0579607741115960.202156870978219
34244243.41711654005211.62575339716970.05795728333142850.410547082700231
35234.7236.122394870615-4.734621674088070.0579586702973887-1.15779104661693
36250.2248.78116741531910.30530085111420.05795898194367831.06434525893544
37265.7265.46122727223215.7876099604038-0.2572890474533760.399569953009538
38287.6287.13998149483520.54945423544460.0679385793545250.331845793567933
39283.3284.9433822354150.8183259956027240.113214930425090-1.38090746670211
40295.4294.6072518026698.458780868521660.1036556398603370.539754905519306
41312.3311.53511214844115.78063270811830.1023988247866560.518150260593486
42333.8333.23428669052820.89855256140380.1026258183503770.362183457773561
43347.7348.07173743876415.65745773502080.102497631958868-0.370901557770521
44383.2381.69201921454231.18980668961420.1025504472700451.09919329085371
45407.1407.42443591913526.4708507761410.102554479910365-0.333951078366074
46413.6414.97757456363910.11287035328230.102562299012752-1.15762158183954
47362.7367.132139880492-40.00318750707620.102565674062501-3.54661325487644
48321.9322.184307513508-44.27878055109050.102565603683433-0.302575174699811
49239.4244.69135337561-72.874940188163-2.70385583171962-2.07189404251916
50191189.435820702217-58.46229896346550.3561394552522891.00769419349876
51159.7157.346170983006-35.59769226639540.3125991882870561.60325199710515
52163.4160.129604881931-2.439417477221930.2781877414660312.34314407498757
53157.6157.348499499636-2.734828968041130.278229801234249-0.0209055951065479
54166.2165.1008849094036.333680666872410.2785634175315380.641758095721906
55176.7176.05949144334710.33288548623130.2786445481387840.28301557516907
56198.3197.17749085622219.65870579971220.2786708508726360.659969664214074
57226.2225.26208614201626.94449738352650.2786656865720930.515600908638063
58216.2218.554304103791-2.154336711160120.278677223600816-2.05926633270578
59235.9234.22655659216413.26016487042510.2786763625596691.09085347013727
60226.9228.135388232967-3.472771041512210.278676134099501-1.18415643272776

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 153.4 & 153.4 & 0 & 0 & 0 \tabularnewline
2 & 145 & 145.876191167459 & -7.44134377868622 & -0.041232530240796 & -0.557950534988849 \tabularnewline
3 & 137.7 & 137.791193719566 & -7.99195450904879 & -0.0398729065246219 & -0.0397493044432643 \tabularnewline
4 & 148.3 & 147.003485215649 & 6.86854273510676 & -0.0565574451302474 & 1.05522810977596 \tabularnewline
5 & 152.2 & 152.373635982363 & 5.57296841526736 & -0.0563948021853457 & -0.0916881440644917 \tabularnewline
6 & 169.4 & 168.620760968549 & 14.8031708653358 & -0.0559567353371608 & 0.653207893605105 \tabularnewline
7 & 168.6 & 169.727833670048 & 2.96004521014379 & -0.0562167320232124 & -0.838115427451734 \tabularnewline
8 & 161.1 & 161.993016572943 & -6.28773277779368 & -0.0562398245501543 & -0.654446774325278 \tabularnewline
9 & 174.1 & 172.817389150323 & 8.50894960012367 & -0.0562533969236409 & 1.04713164279455 \tabularnewline
10 & 179 & 179.220977744091 & 6.68846225306813 & -0.0562526151651217 & -0.128832251264188 \tabularnewline
11 & 190.6 & 190.311807905370 & 10.4951527359973 & -0.0562528041658198 & 0.269391877582786 \tabularnewline
12 & 190 & 190.836360951728 & 1.87365858787821 & -0.0562529569762432 & -0.610125910298412 \tabularnewline
13 & 181.6 & 182.938653778518 & -6.48111459570032 & -0.582679721214916 & -0.627341256815093 \tabularnewline
14 & 174.8 & 174.860704709527 & -7.70792945736486 & 0.0323240020032319 & -0.0840417131388031 \tabularnewline
15 & 180.5 & 179.560241812516 & 3.07890274373382 & -0.00963164228381908 & 0.749056934503394 \tabularnewline
16 & 196.8 & 195.810782941204 & 14.4475557326564 & -0.0337871215571341 & 0.80214830106102 \tabularnewline
17 & 193.8 & 195.021653927182 & 1.27646422051838 & -0.0299470804210284 & -0.93208399799127 \tabularnewline
18 & 197 & 196.976799209048 & 1.86335423195363 & -0.0299028693092647 & 0.0415327406762524 \tabularnewline
19 & 216.3 & 215.060206884967 & 15.8892024854284 & -0.0293202242738261 & 0.992580120109795 \tabularnewline
20 & 221.4 & 222.120174399738 & 8.25459899185731 & -0.0293643167277498 & -0.540285629075005 \tabularnewline
21 & 217.9 & 218.832431119834 & -1.72595515304180 & -0.0293498305701368 & -0.706303868245136 \tabularnewline
22 & 229.7 & 228.813399308401 & 8.39691627123799 & -0.0293580489453955 & 0.716375379228054 \tabularnewline
23 & 227.4 & 228.139096759735 & 0.5531101339685 & -0.0293571517537865 & -0.555090484024443 \tabularnewline
24 & 204.2 & 206.004465437042 & -19.0647902955236 & -0.0293577002260322 & -1.38831960586255 \tabularnewline
25 & 196.6 & 195.003051588083 & -12.1433736585019 & 0.970670268322744 & 0.509471571765212 \tabularnewline
26 & 198.8 & 197.797267133778 & -0.289875233886651 & 0.0543044444348364 & 0.821434943482309 \tabularnewline
27 & 207.5 & 206.756990032806 & 7.74032777615458 & 0.0311256602890603 & 0.560382308394789 \tabularnewline
28 & 190.7 & 192.361294330894 & -11.3746431385245 & 0.0612299935782609 & -1.34975235316270 \tabularnewline
29 & 201.6 & 200.051105827534 & 5.10657504734081 & 0.0576686636780732 & 1.16633561543262 \tabularnewline
30 & 210.5 & 210.058624294885 & 9.34459482759583 & 0.0579052840527004 & 0.299914624446646 \tabularnewline
31 & 223.5 & 223.148920841059 & 12.5835579727666 & 0.0580050070096113 & 0.22921475523822 \tabularnewline
32 & 223.8 & 224.612106493327 & 2.96782973491725 & 0.0579638471243436 & -0.680485867963241 \tabularnewline
33 & 231.2 & 230.883561117611 & 5.82444384379485 & 0.057960774111596 & 0.202156870978219 \tabularnewline
34 & 244 & 243.417116540052 & 11.6257533971697 & 0.0579572833314285 & 0.410547082700231 \tabularnewline
35 & 234.7 & 236.122394870615 & -4.73462167408807 & 0.0579586702973887 & -1.15779104661693 \tabularnewline
36 & 250.2 & 248.781167415319 & 10.3053008511142 & 0.0579589819436783 & 1.06434525893544 \tabularnewline
37 & 265.7 & 265.461227272232 & 15.7876099604038 & -0.257289047453376 & 0.399569953009538 \tabularnewline
38 & 287.6 & 287.139981494835 & 20.5494542354446 & 0.067938579354525 & 0.331845793567933 \tabularnewline
39 & 283.3 & 284.943382235415 & 0.818325995602724 & 0.113214930425090 & -1.38090746670211 \tabularnewline
40 & 295.4 & 294.607251802669 & 8.45878086852166 & 0.103655639860337 & 0.539754905519306 \tabularnewline
41 & 312.3 & 311.535112148441 & 15.7806327081183 & 0.102398824786656 & 0.518150260593486 \tabularnewline
42 & 333.8 & 333.234286690528 & 20.8985525614038 & 0.102625818350377 & 0.362183457773561 \tabularnewline
43 & 347.7 & 348.071737438764 & 15.6574577350208 & 0.102497631958868 & -0.370901557770521 \tabularnewline
44 & 383.2 & 381.692019214542 & 31.1898066896142 & 0.102550447270045 & 1.09919329085371 \tabularnewline
45 & 407.1 & 407.424435919135 & 26.470850776141 & 0.102554479910365 & -0.333951078366074 \tabularnewline
46 & 413.6 & 414.977574563639 & 10.1128703532823 & 0.102562299012752 & -1.15762158183954 \tabularnewline
47 & 362.7 & 367.132139880492 & -40.0031875070762 & 0.102565674062501 & -3.54661325487644 \tabularnewline
48 & 321.9 & 322.184307513508 & -44.2787805510905 & 0.102565603683433 & -0.302575174699811 \tabularnewline
49 & 239.4 & 244.69135337561 & -72.874940188163 & -2.70385583171962 & -2.07189404251916 \tabularnewline
50 & 191 & 189.435820702217 & -58.4622989634655 & 0.356139455252289 & 1.00769419349876 \tabularnewline
51 & 159.7 & 157.346170983006 & -35.5976922663954 & 0.312599188287056 & 1.60325199710515 \tabularnewline
52 & 163.4 & 160.129604881931 & -2.43941747722193 & 0.278187741466031 & 2.34314407498757 \tabularnewline
53 & 157.6 & 157.348499499636 & -2.73482896804113 & 0.278229801234249 & -0.0209055951065479 \tabularnewline
54 & 166.2 & 165.100884909403 & 6.33368066687241 & 0.278563417531538 & 0.641758095721906 \tabularnewline
55 & 176.7 & 176.059491443347 & 10.3328854862313 & 0.278644548138784 & 0.28301557516907 \tabularnewline
56 & 198.3 & 197.177490856222 & 19.6587057997122 & 0.278670850872636 & 0.659969664214074 \tabularnewline
57 & 226.2 & 225.262086142016 & 26.9444973835265 & 0.278665686572093 & 0.515600908638063 \tabularnewline
58 & 216.2 & 218.554304103791 & -2.15433671116012 & 0.278677223600816 & -2.05926633270578 \tabularnewline
59 & 235.9 & 234.226556592164 & 13.2601648704251 & 0.278676362559669 & 1.09085347013727 \tabularnewline
60 & 226.9 & 228.135388232967 & -3.47277104151221 & 0.278676134099501 & -1.18415643272776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65020&T=1

[TABLE]
[ROW][C]Structural Time Series Model[/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]153.4[/C][C]153.4[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]145[/C][C]145.876191167459[/C][C]-7.44134377868622[/C][C]-0.041232530240796[/C][C]-0.557950534988849[/C][/ROW]
[ROW][C]3[/C][C]137.7[/C][C]137.791193719566[/C][C]-7.99195450904879[/C][C]-0.0398729065246219[/C][C]-0.0397493044432643[/C][/ROW]
[ROW][C]4[/C][C]148.3[/C][C]147.003485215649[/C][C]6.86854273510676[/C][C]-0.0565574451302474[/C][C]1.05522810977596[/C][/ROW]
[ROW][C]5[/C][C]152.2[/C][C]152.373635982363[/C][C]5.57296841526736[/C][C]-0.0563948021853457[/C][C]-0.0916881440644917[/C][/ROW]
[ROW][C]6[/C][C]169.4[/C][C]168.620760968549[/C][C]14.8031708653358[/C][C]-0.0559567353371608[/C][C]0.653207893605105[/C][/ROW]
[ROW][C]7[/C][C]168.6[/C][C]169.727833670048[/C][C]2.96004521014379[/C][C]-0.0562167320232124[/C][C]-0.838115427451734[/C][/ROW]
[ROW][C]8[/C][C]161.1[/C][C]161.993016572943[/C][C]-6.28773277779368[/C][C]-0.0562398245501543[/C][C]-0.654446774325278[/C][/ROW]
[ROW][C]9[/C][C]174.1[/C][C]172.817389150323[/C][C]8.50894960012367[/C][C]-0.0562533969236409[/C][C]1.04713164279455[/C][/ROW]
[ROW][C]10[/C][C]179[/C][C]179.220977744091[/C][C]6.68846225306813[/C][C]-0.0562526151651217[/C][C]-0.128832251264188[/C][/ROW]
[ROW][C]11[/C][C]190.6[/C][C]190.311807905370[/C][C]10.4951527359973[/C][C]-0.0562528041658198[/C][C]0.269391877582786[/C][/ROW]
[ROW][C]12[/C][C]190[/C][C]190.836360951728[/C][C]1.87365858787821[/C][C]-0.0562529569762432[/C][C]-0.610125910298412[/C][/ROW]
[ROW][C]13[/C][C]181.6[/C][C]182.938653778518[/C][C]-6.48111459570032[/C][C]-0.582679721214916[/C][C]-0.627341256815093[/C][/ROW]
[ROW][C]14[/C][C]174.8[/C][C]174.860704709527[/C][C]-7.70792945736486[/C][C]0.0323240020032319[/C][C]-0.0840417131388031[/C][/ROW]
[ROW][C]15[/C][C]180.5[/C][C]179.560241812516[/C][C]3.07890274373382[/C][C]-0.00963164228381908[/C][C]0.749056934503394[/C][/ROW]
[ROW][C]16[/C][C]196.8[/C][C]195.810782941204[/C][C]14.4475557326564[/C][C]-0.0337871215571341[/C][C]0.80214830106102[/C][/ROW]
[ROW][C]17[/C][C]193.8[/C][C]195.021653927182[/C][C]1.27646422051838[/C][C]-0.0299470804210284[/C][C]-0.93208399799127[/C][/ROW]
[ROW][C]18[/C][C]197[/C][C]196.976799209048[/C][C]1.86335423195363[/C][C]-0.0299028693092647[/C][C]0.0415327406762524[/C][/ROW]
[ROW][C]19[/C][C]216.3[/C][C]215.060206884967[/C][C]15.8892024854284[/C][C]-0.0293202242738261[/C][C]0.992580120109795[/C][/ROW]
[ROW][C]20[/C][C]221.4[/C][C]222.120174399738[/C][C]8.25459899185731[/C][C]-0.0293643167277498[/C][C]-0.540285629075005[/C][/ROW]
[ROW][C]21[/C][C]217.9[/C][C]218.832431119834[/C][C]-1.72595515304180[/C][C]-0.0293498305701368[/C][C]-0.706303868245136[/C][/ROW]
[ROW][C]22[/C][C]229.7[/C][C]228.813399308401[/C][C]8.39691627123799[/C][C]-0.0293580489453955[/C][C]0.716375379228054[/C][/ROW]
[ROW][C]23[/C][C]227.4[/C][C]228.139096759735[/C][C]0.5531101339685[/C][C]-0.0293571517537865[/C][C]-0.555090484024443[/C][/ROW]
[ROW][C]24[/C][C]204.2[/C][C]206.004465437042[/C][C]-19.0647902955236[/C][C]-0.0293577002260322[/C][C]-1.38831960586255[/C][/ROW]
[ROW][C]25[/C][C]196.6[/C][C]195.003051588083[/C][C]-12.1433736585019[/C][C]0.970670268322744[/C][C]0.509471571765212[/C][/ROW]
[ROW][C]26[/C][C]198.8[/C][C]197.797267133778[/C][C]-0.289875233886651[/C][C]0.0543044444348364[/C][C]0.821434943482309[/C][/ROW]
[ROW][C]27[/C][C]207.5[/C][C]206.756990032806[/C][C]7.74032777615458[/C][C]0.0311256602890603[/C][C]0.560382308394789[/C][/ROW]
[ROW][C]28[/C][C]190.7[/C][C]192.361294330894[/C][C]-11.3746431385245[/C][C]0.0612299935782609[/C][C]-1.34975235316270[/C][/ROW]
[ROW][C]29[/C][C]201.6[/C][C]200.051105827534[/C][C]5.10657504734081[/C][C]0.0576686636780732[/C][C]1.16633561543262[/C][/ROW]
[ROW][C]30[/C][C]210.5[/C][C]210.058624294885[/C][C]9.34459482759583[/C][C]0.0579052840527004[/C][C]0.299914624446646[/C][/ROW]
[ROW][C]31[/C][C]223.5[/C][C]223.148920841059[/C][C]12.5835579727666[/C][C]0.0580050070096113[/C][C]0.22921475523822[/C][/ROW]
[ROW][C]32[/C][C]223.8[/C][C]224.612106493327[/C][C]2.96782973491725[/C][C]0.0579638471243436[/C][C]-0.680485867963241[/C][/ROW]
[ROW][C]33[/C][C]231.2[/C][C]230.883561117611[/C][C]5.82444384379485[/C][C]0.057960774111596[/C][C]0.202156870978219[/C][/ROW]
[ROW][C]34[/C][C]244[/C][C]243.417116540052[/C][C]11.6257533971697[/C][C]0.0579572833314285[/C][C]0.410547082700231[/C][/ROW]
[ROW][C]35[/C][C]234.7[/C][C]236.122394870615[/C][C]-4.73462167408807[/C][C]0.0579586702973887[/C][C]-1.15779104661693[/C][/ROW]
[ROW][C]36[/C][C]250.2[/C][C]248.781167415319[/C][C]10.3053008511142[/C][C]0.0579589819436783[/C][C]1.06434525893544[/C][/ROW]
[ROW][C]37[/C][C]265.7[/C][C]265.461227272232[/C][C]15.7876099604038[/C][C]-0.257289047453376[/C][C]0.399569953009538[/C][/ROW]
[ROW][C]38[/C][C]287.6[/C][C]287.139981494835[/C][C]20.5494542354446[/C][C]0.067938579354525[/C][C]0.331845793567933[/C][/ROW]
[ROW][C]39[/C][C]283.3[/C][C]284.943382235415[/C][C]0.818325995602724[/C][C]0.113214930425090[/C][C]-1.38090746670211[/C][/ROW]
[ROW][C]40[/C][C]295.4[/C][C]294.607251802669[/C][C]8.45878086852166[/C][C]0.103655639860337[/C][C]0.539754905519306[/C][/ROW]
[ROW][C]41[/C][C]312.3[/C][C]311.535112148441[/C][C]15.7806327081183[/C][C]0.102398824786656[/C][C]0.518150260593486[/C][/ROW]
[ROW][C]42[/C][C]333.8[/C][C]333.234286690528[/C][C]20.8985525614038[/C][C]0.102625818350377[/C][C]0.362183457773561[/C][/ROW]
[ROW][C]43[/C][C]347.7[/C][C]348.071737438764[/C][C]15.6574577350208[/C][C]0.102497631958868[/C][C]-0.370901557770521[/C][/ROW]
[ROW][C]44[/C][C]383.2[/C][C]381.692019214542[/C][C]31.1898066896142[/C][C]0.102550447270045[/C][C]1.09919329085371[/C][/ROW]
[ROW][C]45[/C][C]407.1[/C][C]407.424435919135[/C][C]26.470850776141[/C][C]0.102554479910365[/C][C]-0.333951078366074[/C][/ROW]
[ROW][C]46[/C][C]413.6[/C][C]414.977574563639[/C][C]10.1128703532823[/C][C]0.102562299012752[/C][C]-1.15762158183954[/C][/ROW]
[ROW][C]47[/C][C]362.7[/C][C]367.132139880492[/C][C]-40.0031875070762[/C][C]0.102565674062501[/C][C]-3.54661325487644[/C][/ROW]
[ROW][C]48[/C][C]321.9[/C][C]322.184307513508[/C][C]-44.2787805510905[/C][C]0.102565603683433[/C][C]-0.302575174699811[/C][/ROW]
[ROW][C]49[/C][C]239.4[/C][C]244.69135337561[/C][C]-72.874940188163[/C][C]-2.70385583171962[/C][C]-2.07189404251916[/C][/ROW]
[ROW][C]50[/C][C]191[/C][C]189.435820702217[/C][C]-58.4622989634655[/C][C]0.356139455252289[/C][C]1.00769419349876[/C][/ROW]
[ROW][C]51[/C][C]159.7[/C][C]157.346170983006[/C][C]-35.5976922663954[/C][C]0.312599188287056[/C][C]1.60325199710515[/C][/ROW]
[ROW][C]52[/C][C]163.4[/C][C]160.129604881931[/C][C]-2.43941747722193[/C][C]0.278187741466031[/C][C]2.34314407498757[/C][/ROW]
[ROW][C]53[/C][C]157.6[/C][C]157.348499499636[/C][C]-2.73482896804113[/C][C]0.278229801234249[/C][C]-0.0209055951065479[/C][/ROW]
[ROW][C]54[/C][C]166.2[/C][C]165.100884909403[/C][C]6.33368066687241[/C][C]0.278563417531538[/C][C]0.641758095721906[/C][/ROW]
[ROW][C]55[/C][C]176.7[/C][C]176.059491443347[/C][C]10.3328854862313[/C][C]0.278644548138784[/C][C]0.28301557516907[/C][/ROW]
[ROW][C]56[/C][C]198.3[/C][C]197.177490856222[/C][C]19.6587057997122[/C][C]0.278670850872636[/C][C]0.659969664214074[/C][/ROW]
[ROW][C]57[/C][C]226.2[/C][C]225.262086142016[/C][C]26.9444973835265[/C][C]0.278665686572093[/C][C]0.515600908638063[/C][/ROW]
[ROW][C]58[/C][C]216.2[/C][C]218.554304103791[/C][C]-2.15433671116012[/C][C]0.278677223600816[/C][C]-2.05926633270578[/C][/ROW]
[ROW][C]59[/C][C]235.9[/C][C]234.226556592164[/C][C]13.2601648704251[/C][C]0.278676362559669[/C][C]1.09085347013727[/C][/ROW]
[ROW][C]60[/C][C]226.9[/C][C]228.135388232967[/C][C]-3.47277104151221[/C][C]0.278676134099501[/C][C]-1.18415643272776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65020&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65020&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
1153.4153.4000
2145145.876191167459-7.44134377868622-0.041232530240796-0.557950534988849
3137.7137.791193719566-7.99195450904879-0.0398729065246219-0.0397493044432643
4148.3147.0034852156496.86854273510676-0.05655744513024741.05522810977596
5152.2152.3736359823635.57296841526736-0.0563948021853457-0.0916881440644917
6169.4168.62076096854914.8031708653358-0.05595673533716080.653207893605105
7168.6169.7278336700482.96004521014379-0.0562167320232124-0.838115427451734
8161.1161.993016572943-6.28773277779368-0.0562398245501543-0.654446774325278
9174.1172.8173891503238.50894960012367-0.05625339692364091.04713164279455
10179179.2209777440916.68846225306813-0.0562526151651217-0.128832251264188
11190.6190.31180790537010.4951527359973-0.05625280416581980.269391877582786
12190190.8363609517281.87365858787821-0.0562529569762432-0.610125910298412
13181.6182.938653778518-6.48111459570032-0.582679721214916-0.627341256815093
14174.8174.860704709527-7.707929457364860.0323240020032319-0.0840417131388031
15180.5179.5602418125163.07890274373382-0.009631642283819080.749056934503394
16196.8195.81078294120414.4475557326564-0.03378712155713410.80214830106102
17193.8195.0216539271821.27646422051838-0.0299470804210284-0.93208399799127
18197196.9767992090481.86335423195363-0.02990286930926470.0415327406762524
19216.3215.06020688496715.8892024854284-0.02932022427382610.992580120109795
20221.4222.1201743997388.25459899185731-0.0293643167277498-0.540285629075005
21217.9218.832431119834-1.72595515304180-0.0293498305701368-0.706303868245136
22229.7228.8133993084018.39691627123799-0.02935804894539550.716375379228054
23227.4228.1390967597350.5531101339685-0.0293571517537865-0.555090484024443
24204.2206.004465437042-19.0647902955236-0.0293577002260322-1.38831960586255
25196.6195.003051588083-12.14337365850190.9706702683227440.509471571765212
26198.8197.797267133778-0.2898752338866510.05430444443483640.821434943482309
27207.5206.7569900328067.740327776154580.03112566028906030.560382308394789
28190.7192.361294330894-11.37464313852450.0612299935782609-1.34975235316270
29201.6200.0511058275345.106575047340810.05766866367807321.16633561543262
30210.5210.0586242948859.344594827595830.05790528405270040.299914624446646
31223.5223.14892084105912.58355797276660.05800500700961130.22921475523822
32223.8224.6121064933272.967829734917250.0579638471243436-0.680485867963241
33231.2230.8835611176115.824443843794850.0579607741115960.202156870978219
34244243.41711654005211.62575339716970.05795728333142850.410547082700231
35234.7236.122394870615-4.734621674088070.0579586702973887-1.15779104661693
36250.2248.78116741531910.30530085111420.05795898194367831.06434525893544
37265.7265.46122727223215.7876099604038-0.2572890474533760.399569953009538
38287.6287.13998149483520.54945423544460.0679385793545250.331845793567933
39283.3284.9433822354150.8183259956027240.113214930425090-1.38090746670211
40295.4294.6072518026698.458780868521660.1036556398603370.539754905519306
41312.3311.53511214844115.78063270811830.1023988247866560.518150260593486
42333.8333.23428669052820.89855256140380.1026258183503770.362183457773561
43347.7348.07173743876415.65745773502080.102497631958868-0.370901557770521
44383.2381.69201921454231.18980668961420.1025504472700451.09919329085371
45407.1407.42443591913526.4708507761410.102554479910365-0.333951078366074
46413.6414.97757456363910.11287035328230.102562299012752-1.15762158183954
47362.7367.132139880492-40.00318750707620.102565674062501-3.54661325487644
48321.9322.184307513508-44.27878055109050.102565603683433-0.302575174699811
49239.4244.69135337561-72.874940188163-2.70385583171962-2.07189404251916
50191189.435820702217-58.46229896346550.3561394552522891.00769419349876
51159.7157.346170983006-35.59769226639540.3125991882870561.60325199710515
52163.4160.129604881931-2.439417477221930.2781877414660312.34314407498757
53157.6157.348499499636-2.734828968041130.278229801234249-0.0209055951065479
54166.2165.1008849094036.333680666872410.2785634175315380.641758095721906
55176.7176.05949144334710.33288548623130.2786445481387840.28301557516907
56198.3197.17749085622219.65870579971220.2786708508726360.659969664214074
57226.2225.26208614201626.94449738352650.2786656865720930.515600908638063
58216.2218.554304103791-2.154336711160120.278677223600816-2.05926633270578
59235.9234.22655659216413.26016487042510.2786763625596691.09085347013727
60226.9228.135388232967-3.472771041512210.278676134099501-1.18415643272776


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
m$coef
m$fitted
m$resid
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$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()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model',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')