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Author

*Unverified author*

R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Thu, 06 Mar 2008 09:52:55 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Mar/06/t1204824677qpuklllbvmmq7ks.htm/, Retrieved Fri, 26 Apr 2024 08:31:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10033, Retrieved Fri, 26 Apr 2024 08:31:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

474

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD    [Structural Time Series Models] [HPC Retail Sales] [2008-03-06 16:52:55] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- R  D      [Structural Time Series Models] [HPC Retail Sales] [2008-03-08 11:12:03] [74be16979710d4c4e7c6647856088456] 
- R  D      [Structural Time Series Models] [HPC Retail Sales] [2008-03-08 11:33:35] [74be16979710d4c4e7c6647856088456] 
- RM D        [Structural Time Series Models] [] [2010-11-26 10:41:09] [d39e5c40c631ed6c22677d2e41dbfc7d] 
- R             [Structural Time Series Models] [WS8] [2011-12-01 14:36:00] [bab4e1d4a779bb46523d87231e2a2e96] 
- RMP           [Exponential Smoothing] [Exponential smoot...] [2011-12-01 14:49:47] [bab4e1d4a779bb46523d87231e2a2e96] 
- RMP           [Exponential Smoothing] [Exponential smoot...] [2011-12-01 14:53:25] [bab4e1d4a779bb46523d87231e2a2e96] 
-  M D        [Structural Time Series Models] [WS8 residu's] [2010-11-28 15:36:37] [65eb19f81eab2b6e672eafaed2a27190] 
-  M D        [Structural Time Series Models] [WS8 Structural Ti...] [2010-11-29 10:27:42] [f4dc4aa51d65be851b8508203d9f6001] 
-    D          [Structural Time Series Models] [Structural Time S...] [2010-12-17 16:42:30] [f4dc4aa51d65be851b8508203d9f6001] 
- RM D        [Multiple Regression] [Basic Structural ...] [2010-11-29 14:58:28] [2843717cd92615903379c14ebee3c5df] 
-  M D        [Structural Time Series Models] [Basis Structual T...] [2010-11-29 15:22:20] [2843717cd92615903379c14ebee3c5df] 
-  M D        [Structural Time Series Models] [] [2010-11-29 19:38:40] [de55ccbf69577500a5f46ed42a101114] 
-  M D        [Structural Time Series Models] [model 2 ws 8] [2010-11-29 22:32:28] [f74ab32c8351972dfcced0581a68b6bb] 
-               [Structural Time Series Models] [] [2010-11-30 16:45:24] [fc9068db680cd880760a7c0fccd81a61] 
-  M D        [Structural Time Series Models] [] [2010-11-29 23:28:06] [2db311435ed525bc1ed0ddec922afb8f] 
-  M D        [Structural Time Series Models] [Structural decomp...] [2010-11-30 15:46:51] [cbb1f7583f1ea41fcafd5f9709bd0e0a] 
-  M D        [Structural Time Series Models] [ws8 structural ti...] [2010-11-30 17:53:54] [74be16979710d4c4e7c6647856088456] 
- RMPD        [Multiple Regression] [ws8 multiple regr...] [2010-11-30 18:01:16] [74be16979710d4c4e7c6647856088456] 
-    D          [Multiple Regression] [PaperTimDamen] [2011-02-03 09:33:21] [74be16979710d4c4e7c6647856088456] 
- RMPD        [Multiple Regression] [ws8 multiple regr...] [2010-11-30 18:39:59] [74be16979710d4c4e7c6647856088456] 
- R PD          [Multiple Regression] [PaperTimDamen] [2011-02-03 09:54:47] [74be16979710d4c4e7c6647856088456] 
-   PD            [Multiple Regression] [PaperTimDamen] [2011-02-03 11:54:00] [74be16979710d4c4e7c6647856088456] 
- R PD          [Multiple Regression] [PaperTimDamen] [2011-02-03 10:03:20] [74be16979710d4c4e7c6647856088456] 
- RMPD        [Multiple Regression] [ws8 multiple regr...] [2010-11-30 20:45:11] [74be16979710d4c4e7c6647856088456] 
-  M D        [Structural Time Series Models] [] [2010-12-07 12:42:20] [b2f924a86c4fbfa8afa1027f3839f526] 
-  M D        [Structural Time Series Models] [] [2010-12-07 12:42:20] [b2f924a86c4fbfa8afa1027f3839f526] 
- RMP           [Exponential Smoothing] [] [2010-12-07 12:46:53] [b2f924a86c4fbfa8afa1027f3839f526] 
- RMPD            [Multiple Regression] [] [2010-12-07 12:51:30] [b2f924a86c4fbfa8afa1027f3839f526] 
-    D              [Multiple Regression] [] [2010-12-09 16:17:21] [b2f924a86c4fbfa8afa1027f3839f526] 
-    D            [Exponential Smoothing] [] [2010-12-09 16:12:25] [b2f924a86c4fbfa8afa1027f3839f526] 
-    D          [Structural Time Series Models] [] [2010-12-09 16:08:50] [b2f924a86c4fbfa8afa1027f3839f526] 
- R               [Structural Time Series Models] [] [2010-12-10 12:32:01] [b2f924a86c4fbfa8afa1027f3839f526] 
- RM D        [Structural Time Series Models] [] [2010-12-07 13:10:14] [253127ae8da904b75450fbd69fe4eb21] 
-  M D        [Structural Time Series Models] [Workshop 8 - STSM] [2010-12-07 13:12:32] [ed447cc2ebcc70947ad11d93fa385845] 
-  M D        [Structural Time Series Models] [] [2010-12-07 13:18:37] [253127ae8da904b75450fbd69fe4eb21] 
-  M D        [Structural Time Series Models] [WS5] [2010-12-07 13:51:52] [fa854ea294f510d944d2dbf77761bfce] 
-  M D        [Structural Time Series Models] [WS5] [2010-12-07 13:51:52] [fa854ea294f510d944d2dbf77761bfce] 
-               [Structural Time Series Models] [ws5q5] [2010-12-08 19:32:28] [df61ce38492c371f14c407a12b3bb2eb] 
- R               [Structural Time Series Models] [ws5q5] [2010-12-09 18:54:41] [a2638725f7f7c6bd63902ba17eba666b] 
-                 [Structural Time Series Models] [ws5q5] [2010-12-09 19:20:09] [c4f608d390ad7371b1365a9b84541edb] 
-                 [Structural Time Series Models] [Workshop 5 assign...] [2010-12-10 00:01:25] [17d39bb3ec485d4ce196f61215d11ba1] 
-                 [Structural Time Series Models] [WSvraag5] [2010-12-10 13:55:58] [9c3137400ced3280b419f1e434c29e1d] 
-                 [Structural Time Series Models] [] [2010-12-10 19:01:52] [c420bdd199bcbe079f7d532ca3855317] 
-  M D        [Structural Time Series Models] [] [2010-12-07 19:00:52] [1ec36cc0fd92fd0f07d0b885ce2c369b] 
-  M D        [Structural Time Series Models] [WS5 - monthly bir...] [2010-12-08 15:29:30] [8ed0bd3560b9ca2814a2ed0a29182575] 
-    D          [Structural Time Series Models] [STSM Dollar] [2010-12-26 13:32:25] [8ed0bd3560b9ca2814a2ed0a29182575] 
-    D          [Structural Time Series Models] [STSM Yuan] [2010-12-26 13:34:39] [8ed0bd3560b9ca2814a2ed0a29182575] 
- RM D        [Structural Time Series Models] [] [2010-12-08 18:48:54] [bcc4ad4a6c0f95d5b548de29638ac6c2] 

[Truncated]

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Dataseries X:

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Histogram

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10033&T=0

[TABLE]
[ROW][C]Summary of compuational 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]4 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=10033&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10033&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Fitted	Level	Slope	Seasonal	Residuals
1	13328	13328	13328	0	0	0
2	12873	12876.8257891851	13200.6819478145	3.82578918514634	-327.68194781448	-1.30937963159356
3	14000	14022.0031954161	13460.2391750261	22.0031954161445	539.760824973865	1.31765525270691
4	13477	13503.285105943	13535.9804208991	26.285105942988	-58.9804208991019	0.311977226123143
5	14237	14279.1871681780	13789.3673061054	42.1871681780315	447.632693894581	1.58162610681454
6	13674	13716.3300535845	13834.0894067324	42.3300535845046	-160.089406732357	0.0192376923718027
7	13529	13565.7762045799	13756.2214150021	36.7762045798851	-227.221415002069	-0.937057013630214
8	14058	14096.0529624696	13824.1263117638	38.052962469584	233.873688236230	0.243826417267901
9	12975	13001.9841057964	13582.4987752674	26.9841057964398	-607.498775267415	-2.18590323595731
10	14326	14357.8225898324	13729.7204596292	31.8225898323746	596.279540370772	0.935766933751675
11	14008	14044.3499767304	13869.9742390004	36.3499767303937	138.025760999587	0.840035252978843
12	16193	16261.9600450982	14657.8365021228	68.9600450982356	1535.16349787723	5.79802749363536
13	14483	14556.6530809516	14941.1548111521	73.6530809516055	-458.154811152081	1.70324729921804
14	14011	14083.5661000211	14973.5337540679	72.56610002109	-962.533754067875	-0.330836466619584
15	15057	15123.9424354256	14910.4226513923	66.9424354256193	146.577348607663	-1.01555961592100
16	14884	14950.3965410181	14966.9570940873	66.3965410181129	-82.9570940873432	-0.0738137548231807
17	15414	15477.5594131343	14983.5563712051	63.5594131342866	430.443628794902	-0.353622835038707
18	14440	14491.8576431762	14842.0470949073	51.8576431761596	-402.04709490728	-1.49507756240521
19	14900	14950.9658922650	14877.7132990105	50.965892265038	22.2867009895442	-0.120639961851066
20	15074	15121.104965195	14855.4215561017	47.1049651949951	218.578443898257	-0.551266726939755
21	14442	14493.8605348171	14996.3157694375	51.8605348170913	-554.315769437457	0.706960235998102
22	15307	15360.7716010294	15087.0676218772	53.7716010293883	219.932378122800	0.292538866816767
23	14938	14995.9402455145	15228.0596750919	57.9402455145203	-290.059675091854	0.654261787956202
24	17193	17259.2993886137	15465.3750700089	66.2993886136976	1727.62492999106	1.34474028856297
25	15528	15602.0185876088	15699.5442321763	74.0185876088331	-171.544232176331	1.26208555258566
26	14765	14838.8065274304	15769.0633384170	73.806527430363	-1004.06333841696	-0.0337794511447212
27	15838	15908.2059502489	15770.3671276436	70.2059502489409	67.6328723564073	-0.537689018234094
28	15723	15789.4079039139	15767.9178383391	66.4079039138715	-44.9178383390633	-0.531044660759293
29	16150	16210.5361068853	15725.6628456300	60.5361068853177	424.337154370023	-0.790177339025636
30	15486	15546.2124988847	15780.2862005268	60.2124988847452	-294.286200526844	-0.0432200309184316
31	15986	16048.2262083617	15877.3981740204	62.22620836171	108.601825979555	0.271983421683458
32	15983	16044.6397511119	15928.7468785298	61.6397511119189	54.2531214702492	-0.0806101036648515
33	15692	15759.4797360290	16100.4317237832	67.4797360289696	-408.431723783209	0.81632027217282
34	16490	16563.4467240256	16282.1067353452	73.4467240256002	207.893264654839	0.845799882141688
35	15686	15757.8873726201	16325.3374782275	71.8873726200522	-639.337478227512	-0.223472602865751
36	18897	18982.4097568336	16661.1131040203	85.4097568335573	2235.88689597968	1.95194819402148
37	16316	16400.2053883081	16723.0230360093	84.2053883081234	-407.023036009263	-0.174005251309701
38	15636	15715.3759710443	16713.7172262334	79.3759710442796	-1077.71722623338	-0.692066109425585
39	17163	17244.4053879884	16831.8964758517	81.4053879883748	331.103524148294	0.286209760715423
40	16534	16609.1967487352	16796.1361257456	75.1967487352262	-262.136125745639	-0.86037097664727
41	16518	16578.4514073538	16595.8167794313	60.4514073538403	-77.8167794313284	-2.01850104025196
42	16375	16432.4101151607	16599.7307850088	57.4101151607113	-224.730785008773	-0.414637749542108
43	16290	16339.6847772582	16513.5878467130	49.6847772582255	-223.587846712959	-1.05576587816445
44	16352	16397.4561734050	16484.4540742751	45.4561734049545	-132.454074275099	-0.580951664466268
45	15943	15986.3849047873	16491.1092344588	43.3849047873067	-548.109234458764	-0.286122147509981
46	16362	16399.8153997367	16429.5983468821	37.815399736733	-67.598346882089	-0.772925383912537
47	16393	16441.4259559579	16668.1332559756	48.4259559578775	-275.133255975595	1.47794698241834
48	19051	19103.1624974509	16787.415970105	52.1624974509109	2263.58402989500	0.521772960478365
49	16747	16803.8111048941	16927.7340247171	56.8111048941409	-180.734024717103	0.649499979507535
50	16320	16383.6042499082	17113.0928791237	63.6042499082173	-793.092879123735	0.947131566555392
51	17910	17978.5861444166	17270.6418196161	68.5861444166098	639.358180383852	0.69150670359207
52	16961	17024.7246326603	17247.8924516135	63.7246326602895	-286.892451613550	-0.6713115311164
53	17480	17544.4454361622	17325.1191475745	64.44543616219	154.880852425541	0.0991472221876955
54	17049	17109.3022709007	17312.0858576788	60.3022709007103	-263.085857678771	-0.569037817998455
55	16879	16932.3470467336	17242.3671612108	53.3470467335768	-363.367161210762	-0.955814972472107
56	17473	17529.3300330641	17351.5209957029	56.3300330641291	121.479004297149	0.410589954146277
57	16998	17058.1143242072	17478.7527685271	60.1143242071860	-480.752768527121	0.521754101189441
58	17307	17368.6918986107	17568.4741109014	61.691898610739	-261.474110901357	0.217805644509610
59	17418	17483.0524784500	17693.3269836827	65.0524784499592	-275.326983682686	0.464495230746059
60	20169	20239.4679492649	17860.2494361084	70.4679492648824	2308.75056389164	0.749166786818708
61	17871	17946.7261447210	18029.6405522991	75.7261447209669	-158.640552299091	0.727666511577185
62	17226	17302.0004589059	18110.5245115710	76.0004589058506	-884.52451157104	0.037944235448267
63	19062	19140.5575403847	18234.5572700254	78.5575403847418	827.442729974551	0.353264630573422
64	17804	17878.777052663	18242.1787611418	74.7770526629889	-438.178761141842	-0.521457348362567
65	19100	19182.7777917259	18466.9457325059	82.7777917258623	633.05426749405	1.10218502294869
66	18522	18610.1403602174	18650.2015252305	88.1403602173717	-128.201525230506	0.73835603786959
67	18060	18145.5454667379	18689.7287819752	85.5454667378949	-629.728781975174	-0.357337570795217
68	18869	18954.6273208045	18776.8080028470	85.6273208044576	92.1919971530416	0.0112775352566685
69	18127	18209.5480841698	18804.7135859381	82.5480841697832	-677.713585938127	-0.42445991711634
70	18871	18958.5518061361	18981.1065816888	87.5518061361308	-110.106581688841	0.690013654175918
71	18890	18982.4956725489	19161.4235663533	92.4956725488576	-271.423566353257	0.681978362131513
72	21263	21353.0762168967	19208.5077582331	90.07621689668	2054.49224176685	-0.333844069038362
73	19547	19643.5548995782	19420.1933481326	96.5548995781493	126.806651867427	0.894098448192825
74	18450	18545.9495720152	19505.3874021292	95.9495720151657	-1055.38740212923	-0.0835331354626137
75	20254	20347.1562649718	19548.9265106949	93.156264971797	705.073489305116	-0.385335983346102
76	19240	19335.1799098198	19680.0400912674	95.179909819775	-440.040091267412	0.279026604563751
77	20216	20309.3334981260	19740.5963761845	93.3334981259738	475.403623815547	-0.254484208719289
78	19420	19507.3984851367	19722.6563448177	87.3984851366954	-302.656344817737	-0.817847173612272
79	19415	19504.7818362795	19854.7369503513	89.781836279546	-439.736950351284	0.328439734536982
80	20018	20108.4601293099	19957.2357168735	90.4601293098559	60.7642831264537	0.0934873708840648
81	18652	18732.2626073329	19856.4860911417	80.262607332886	-1204.48609114171	-1.40571677346299
82	19978	20059.1259262908	19952.9388984069	81.125926290822	25.0611015931302	0.119020635507625
83	19509	19586.4195110991	19964.5467537368	77.4195110990556	-455.54675373678	-0.51102528352137
84	21971	22046.5318898164	20006.5581952663	75.5318898164371	1964.44180473367	-0.260279917278426

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Fitted & Level & Slope & Seasonal & Residuals \tabularnewline
1 & 13328 & 13328 & 13328 & 0 & 0 & 0 \tabularnewline
2 & 12873 & 12876.8257891851 & 13200.6819478145 & 3.82578918514634 & -327.68194781448 & -1.30937963159356 \tabularnewline
3 & 14000 & 14022.0031954161 & 13460.2391750261 & 22.0031954161445 & 539.760824973865 & 1.31765525270691 \tabularnewline
4 & 13477 & 13503.285105943 & 13535.9804208991 & 26.285105942988 & -58.9804208991019 & 0.311977226123143 \tabularnewline
5 & 14237 & 14279.1871681780 & 13789.3673061054 & 42.1871681780315 & 447.632693894581 & 1.58162610681454 \tabularnewline
6 & 13674 & 13716.3300535845 & 13834.0894067324 & 42.3300535845046 & -160.089406732357 & 0.0192376923718027 \tabularnewline
7 & 13529 & 13565.7762045799 & 13756.2214150021 & 36.7762045798851 & -227.221415002069 & -0.937057013630214 \tabularnewline
8 & 14058 & 14096.0529624696 & 13824.1263117638 & 38.052962469584 & 233.873688236230 & 0.243826417267901 \tabularnewline
9 & 12975 & 13001.9841057964 & 13582.4987752674 & 26.9841057964398 & -607.498775267415 & -2.18590323595731 \tabularnewline
10 & 14326 & 14357.8225898324 & 13729.7204596292 & 31.8225898323746 & 596.279540370772 & 0.935766933751675 \tabularnewline
11 & 14008 & 14044.3499767304 & 13869.9742390004 & 36.3499767303937 & 138.025760999587 & 0.840035252978843 \tabularnewline
12 & 16193 & 16261.9600450982 & 14657.8365021228 & 68.9600450982356 & 1535.16349787723 & 5.79802749363536 \tabularnewline
13 & 14483 & 14556.6530809516 & 14941.1548111521 & 73.6530809516055 & -458.154811152081 & 1.70324729921804 \tabularnewline
14 & 14011 & 14083.5661000211 & 14973.5337540679 & 72.56610002109 & -962.533754067875 & -0.330836466619584 \tabularnewline
15 & 15057 & 15123.9424354256 & 14910.4226513923 & 66.9424354256193 & 146.577348607663 & -1.01555961592100 \tabularnewline
16 & 14884 & 14950.3965410181 & 14966.9570940873 & 66.3965410181129 & -82.9570940873432 & -0.0738137548231807 \tabularnewline
17 & 15414 & 15477.5594131343 & 14983.5563712051 & 63.5594131342866 & 430.443628794902 & -0.353622835038707 \tabularnewline
18 & 14440 & 14491.8576431762 & 14842.0470949073 & 51.8576431761596 & -402.04709490728 & -1.49507756240521 \tabularnewline
19 & 14900 & 14950.9658922650 & 14877.7132990105 & 50.965892265038 & 22.2867009895442 & -0.120639961851066 \tabularnewline
20 & 15074 & 15121.104965195 & 14855.4215561017 & 47.1049651949951 & 218.578443898257 & -0.551266726939755 \tabularnewline
21 & 14442 & 14493.8605348171 & 14996.3157694375 & 51.8605348170913 & -554.315769437457 & 0.706960235998102 \tabularnewline
22 & 15307 & 15360.7716010294 & 15087.0676218772 & 53.7716010293883 & 219.932378122800 & 0.292538866816767 \tabularnewline
23 & 14938 & 14995.9402455145 & 15228.0596750919 & 57.9402455145203 & -290.059675091854 & 0.654261787956202 \tabularnewline
24 & 17193 & 17259.2993886137 & 15465.3750700089 & 66.2993886136976 & 1727.62492999106 & 1.34474028856297 \tabularnewline
25 & 15528 & 15602.0185876088 & 15699.5442321763 & 74.0185876088331 & -171.544232176331 & 1.26208555258566 \tabularnewline
26 & 14765 & 14838.8065274304 & 15769.0633384170 & 73.806527430363 & -1004.06333841696 & -0.0337794511447212 \tabularnewline
27 & 15838 & 15908.2059502489 & 15770.3671276436 & 70.2059502489409 & 67.6328723564073 & -0.537689018234094 \tabularnewline
28 & 15723 & 15789.4079039139 & 15767.9178383391 & 66.4079039138715 & -44.9178383390633 & -0.531044660759293 \tabularnewline
29 & 16150 & 16210.5361068853 & 15725.6628456300 & 60.5361068853177 & 424.337154370023 & -0.790177339025636 \tabularnewline
30 & 15486 & 15546.2124988847 & 15780.2862005268 & 60.2124988847452 & -294.286200526844 & -0.0432200309184316 \tabularnewline
31 & 15986 & 16048.2262083617 & 15877.3981740204 & 62.22620836171 & 108.601825979555 & 0.271983421683458 \tabularnewline
32 & 15983 & 16044.6397511119 & 15928.7468785298 & 61.6397511119189 & 54.2531214702492 & -0.0806101036648515 \tabularnewline
33 & 15692 & 15759.4797360290 & 16100.4317237832 & 67.4797360289696 & -408.431723783209 & 0.81632027217282 \tabularnewline
34 & 16490 & 16563.4467240256 & 16282.1067353452 & 73.4467240256002 & 207.893264654839 & 0.845799882141688 \tabularnewline
35 & 15686 & 15757.8873726201 & 16325.3374782275 & 71.8873726200522 & -639.337478227512 & -0.223472602865751 \tabularnewline
36 & 18897 & 18982.4097568336 & 16661.1131040203 & 85.4097568335573 & 2235.88689597968 & 1.95194819402148 \tabularnewline
37 & 16316 & 16400.2053883081 & 16723.0230360093 & 84.2053883081234 & -407.023036009263 & -0.174005251309701 \tabularnewline
38 & 15636 & 15715.3759710443 & 16713.7172262334 & 79.3759710442796 & -1077.71722623338 & -0.692066109425585 \tabularnewline
39 & 17163 & 17244.4053879884 & 16831.8964758517 & 81.4053879883748 & 331.103524148294 & 0.286209760715423 \tabularnewline
40 & 16534 & 16609.1967487352 & 16796.1361257456 & 75.1967487352262 & -262.136125745639 & -0.86037097664727 \tabularnewline
41 & 16518 & 16578.4514073538 & 16595.8167794313 & 60.4514073538403 & -77.8167794313284 & -2.01850104025196 \tabularnewline
42 & 16375 & 16432.4101151607 & 16599.7307850088 & 57.4101151607113 & -224.730785008773 & -0.414637749542108 \tabularnewline
43 & 16290 & 16339.6847772582 & 16513.5878467130 & 49.6847772582255 & -223.587846712959 & -1.05576587816445 \tabularnewline
44 & 16352 & 16397.4561734050 & 16484.4540742751 & 45.4561734049545 & -132.454074275099 & -0.580951664466268 \tabularnewline
45 & 15943 & 15986.3849047873 & 16491.1092344588 & 43.3849047873067 & -548.109234458764 & -0.286122147509981 \tabularnewline
46 & 16362 & 16399.8153997367 & 16429.5983468821 & 37.815399736733 & -67.598346882089 & -0.772925383912537 \tabularnewline
47 & 16393 & 16441.4259559579 & 16668.1332559756 & 48.4259559578775 & -275.133255975595 & 1.47794698241834 \tabularnewline
48 & 19051 & 19103.1624974509 & 16787.415970105 & 52.1624974509109 & 2263.58402989500 & 0.521772960478365 \tabularnewline
49 & 16747 & 16803.8111048941 & 16927.7340247171 & 56.8111048941409 & -180.734024717103 & 0.649499979507535 \tabularnewline
50 & 16320 & 16383.6042499082 & 17113.0928791237 & 63.6042499082173 & -793.092879123735 & 0.947131566555392 \tabularnewline
51 & 17910 & 17978.5861444166 & 17270.6418196161 & 68.5861444166098 & 639.358180383852 & 0.69150670359207 \tabularnewline
52 & 16961 & 17024.7246326603 & 17247.8924516135 & 63.7246326602895 & -286.892451613550 & -0.6713115311164 \tabularnewline
53 & 17480 & 17544.4454361622 & 17325.1191475745 & 64.44543616219 & 154.880852425541 & 0.0991472221876955 \tabularnewline
54 & 17049 & 17109.3022709007 & 17312.0858576788 & 60.3022709007103 & -263.085857678771 & -0.569037817998455 \tabularnewline
55 & 16879 & 16932.3470467336 & 17242.3671612108 & 53.3470467335768 & -363.367161210762 & -0.955814972472107 \tabularnewline
56 & 17473 & 17529.3300330641 & 17351.5209957029 & 56.3300330641291 & 121.479004297149 & 0.410589954146277 \tabularnewline
57 & 16998 & 17058.1143242072 & 17478.7527685271 & 60.1143242071860 & -480.752768527121 & 0.521754101189441 \tabularnewline
58 & 17307 & 17368.6918986107 & 17568.4741109014 & 61.691898610739 & -261.474110901357 & 0.217805644509610 \tabularnewline
59 & 17418 & 17483.0524784500 & 17693.3269836827 & 65.0524784499592 & -275.326983682686 & 0.464495230746059 \tabularnewline
60 & 20169 & 20239.4679492649 & 17860.2494361084 & 70.4679492648824 & 2308.75056389164 & 0.749166786818708 \tabularnewline
61 & 17871 & 17946.7261447210 & 18029.6405522991 & 75.7261447209669 & -158.640552299091 & 0.727666511577185 \tabularnewline
62 & 17226 & 17302.0004589059 & 18110.5245115710 & 76.0004589058506 & -884.52451157104 & 0.037944235448267 \tabularnewline
63 & 19062 & 19140.5575403847 & 18234.5572700254 & 78.5575403847418 & 827.442729974551 & 0.353264630573422 \tabularnewline
64 & 17804 & 17878.777052663 & 18242.1787611418 & 74.7770526629889 & -438.178761141842 & -0.521457348362567 \tabularnewline
65 & 19100 & 19182.7777917259 & 18466.9457325059 & 82.7777917258623 & 633.05426749405 & 1.10218502294869 \tabularnewline
66 & 18522 & 18610.1403602174 & 18650.2015252305 & 88.1403602173717 & -128.201525230506 & 0.73835603786959 \tabularnewline
67 & 18060 & 18145.5454667379 & 18689.7287819752 & 85.5454667378949 & -629.728781975174 & -0.357337570795217 \tabularnewline
68 & 18869 & 18954.6273208045 & 18776.8080028470 & 85.6273208044576 & 92.1919971530416 & 0.0112775352566685 \tabularnewline
69 & 18127 & 18209.5480841698 & 18804.7135859381 & 82.5480841697832 & -677.713585938127 & -0.42445991711634 \tabularnewline
70 & 18871 & 18958.5518061361 & 18981.1065816888 & 87.5518061361308 & -110.106581688841 & 0.690013654175918 \tabularnewline
71 & 18890 & 18982.4956725489 & 19161.4235663533 & 92.4956725488576 & -271.423566353257 & 0.681978362131513 \tabularnewline
72 & 21263 & 21353.0762168967 & 19208.5077582331 & 90.07621689668 & 2054.49224176685 & -0.333844069038362 \tabularnewline
73 & 19547 & 19643.5548995782 & 19420.1933481326 & 96.5548995781493 & 126.806651867427 & 0.894098448192825 \tabularnewline
74 & 18450 & 18545.9495720152 & 19505.3874021292 & 95.9495720151657 & -1055.38740212923 & -0.0835331354626137 \tabularnewline
75 & 20254 & 20347.1562649718 & 19548.9265106949 & 93.156264971797 & 705.073489305116 & -0.385335983346102 \tabularnewline
76 & 19240 & 19335.1799098198 & 19680.0400912674 & 95.179909819775 & -440.040091267412 & 0.279026604563751 \tabularnewline
77 & 20216 & 20309.3334981260 & 19740.5963761845 & 93.3334981259738 & 475.403623815547 & -0.254484208719289 \tabularnewline
78 & 19420 & 19507.3984851367 & 19722.6563448177 & 87.3984851366954 & -302.656344817737 & -0.817847173612272 \tabularnewline
79 & 19415 & 19504.7818362795 & 19854.7369503513 & 89.781836279546 & -439.736950351284 & 0.328439734536982 \tabularnewline
80 & 20018 & 20108.4601293099 & 19957.2357168735 & 90.4601293098559 & 60.7642831264537 & 0.0934873708840648 \tabularnewline
81 & 18652 & 18732.2626073329 & 19856.4860911417 & 80.262607332886 & -1204.48609114171 & -1.40571677346299 \tabularnewline
82 & 19978 & 20059.1259262908 & 19952.9388984069 & 81.125926290822 & 25.0611015931302 & 0.119020635507625 \tabularnewline
83 & 19509 & 19586.4195110991 & 19964.5467537368 & 77.4195110990556 & -455.54675373678 & -0.51102528352137 \tabularnewline
84 & 21971 & 22046.5318898164 & 20006.5581952663 & 75.5318898164371 & 1964.44180473367 & -0.260279917278426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10033&T=1

[TABLE]
[ROW][C]Structural Time Series Model[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Level[/C][C]Slope[/C][C]Seasonal[/C][C]Residuals[/C][/ROW]
[ROW][C]1[/C][C]13328[/C][C]13328[/C][C]13328[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]12873[/C][C]12876.8257891851[/C][C]13200.6819478145[/C][C]3.82578918514634[/C][C]-327.68194781448[/C][C]-1.30937963159356[/C][/ROW]
[ROW][C]3[/C][C]14000[/C][C]14022.0031954161[/C][C]13460.2391750261[/C][C]22.0031954161445[/C][C]539.760824973865[/C][C]1.31765525270691[/C][/ROW]
[ROW][C]4[/C][C]13477[/C][C]13503.285105943[/C][C]13535.9804208991[/C][C]26.285105942988[/C][C]-58.9804208991019[/C][C]0.311977226123143[/C][/ROW]
[ROW][C]5[/C][C]14237[/C][C]14279.1871681780[/C][C]13789.3673061054[/C][C]42.1871681780315[/C][C]447.632693894581[/C][C]1.58162610681454[/C][/ROW]
[ROW][C]6[/C][C]13674[/C][C]13716.3300535845[/C][C]13834.0894067324[/C][C]42.3300535845046[/C][C]-160.089406732357[/C][C]0.0192376923718027[/C][/ROW]
[ROW][C]7[/C][C]13529[/C][C]13565.7762045799[/C][C]13756.2214150021[/C][C]36.7762045798851[/C][C]-227.221415002069[/C][C]-0.937057013630214[/C][/ROW]
[ROW][C]8[/C][C]14058[/C][C]14096.0529624696[/C][C]13824.1263117638[/C][C]38.052962469584[/C][C]233.873688236230[/C][C]0.243826417267901[/C][/ROW]
[ROW][C]9[/C][C]12975[/C][C]13001.9841057964[/C][C]13582.4987752674[/C][C]26.9841057964398[/C][C]-607.498775267415[/C][C]-2.18590323595731[/C][/ROW]
[ROW][C]10[/C][C]14326[/C][C]14357.8225898324[/C][C]13729.7204596292[/C][C]31.8225898323746[/C][C]596.279540370772[/C][C]0.935766933751675[/C][/ROW]
[ROW][C]11[/C][C]14008[/C][C]14044.3499767304[/C][C]13869.9742390004[/C][C]36.3499767303937[/C][C]138.025760999587[/C][C]0.840035252978843[/C][/ROW]
[ROW][C]12[/C][C]16193[/C][C]16261.9600450982[/C][C]14657.8365021228[/C][C]68.9600450982356[/C][C]1535.16349787723[/C][C]5.79802749363536[/C][/ROW]
[ROW][C]13[/C][C]14483[/C][C]14556.6530809516[/C][C]14941.1548111521[/C][C]73.6530809516055[/C][C]-458.154811152081[/C][C]1.70324729921804[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]14083.5661000211[/C][C]14973.5337540679[/C][C]72.56610002109[/C][C]-962.533754067875[/C][C]-0.330836466619584[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]15123.9424354256[/C][C]14910.4226513923[/C][C]66.9424354256193[/C][C]146.577348607663[/C][C]-1.01555961592100[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]14950.3965410181[/C][C]14966.9570940873[/C][C]66.3965410181129[/C][C]-82.9570940873432[/C][C]-0.0738137548231807[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]15477.5594131343[/C][C]14983.5563712051[/C][C]63.5594131342866[/C][C]430.443628794902[/C][C]-0.353622835038707[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]14491.8576431762[/C][C]14842.0470949073[/C][C]51.8576431761596[/C][C]-402.04709490728[/C][C]-1.49507756240521[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]14950.9658922650[/C][C]14877.7132990105[/C][C]50.965892265038[/C][C]22.2867009895442[/C][C]-0.120639961851066[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]15121.104965195[/C][C]14855.4215561017[/C][C]47.1049651949951[/C][C]218.578443898257[/C][C]-0.551266726939755[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]14493.8605348171[/C][C]14996.3157694375[/C][C]51.8605348170913[/C][C]-554.315769437457[/C][C]0.706960235998102[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]15360.7716010294[/C][C]15087.0676218772[/C][C]53.7716010293883[/C][C]219.932378122800[/C][C]0.292538866816767[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]14995.9402455145[/C][C]15228.0596750919[/C][C]57.9402455145203[/C][C]-290.059675091854[/C][C]0.654261787956202[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]17259.2993886137[/C][C]15465.3750700089[/C][C]66.2993886136976[/C][C]1727.62492999106[/C][C]1.34474028856297[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15602.0185876088[/C][C]15699.5442321763[/C][C]74.0185876088331[/C][C]-171.544232176331[/C][C]1.26208555258566[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]14838.8065274304[/C][C]15769.0633384170[/C][C]73.806527430363[/C][C]-1004.06333841696[/C][C]-0.0337794511447212[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15908.2059502489[/C][C]15770.3671276436[/C][C]70.2059502489409[/C][C]67.6328723564073[/C][C]-0.537689018234094[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15789.4079039139[/C][C]15767.9178383391[/C][C]66.4079039138715[/C][C]-44.9178383390633[/C][C]-0.531044660759293[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]16210.5361068853[/C][C]15725.6628456300[/C][C]60.5361068853177[/C][C]424.337154370023[/C][C]-0.790177339025636[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15546.2124988847[/C][C]15780.2862005268[/C][C]60.2124988847452[/C][C]-294.286200526844[/C][C]-0.0432200309184316[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]16048.2262083617[/C][C]15877.3981740204[/C][C]62.22620836171[/C][C]108.601825979555[/C][C]0.271983421683458[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]16044.6397511119[/C][C]15928.7468785298[/C][C]61.6397511119189[/C][C]54.2531214702492[/C][C]-0.0806101036648515[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]15759.4797360290[/C][C]16100.4317237832[/C][C]67.4797360289696[/C][C]-408.431723783209[/C][C]0.81632027217282[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]16563.4467240256[/C][C]16282.1067353452[/C][C]73.4467240256002[/C][C]207.893264654839[/C][C]0.845799882141688[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]15757.8873726201[/C][C]16325.3374782275[/C][C]71.8873726200522[/C][C]-639.337478227512[/C][C]-0.223472602865751[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]18982.4097568336[/C][C]16661.1131040203[/C][C]85.4097568335573[/C][C]2235.88689597968[/C][C]1.95194819402148[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]16400.2053883081[/C][C]16723.0230360093[/C][C]84.2053883081234[/C][C]-407.023036009263[/C][C]-0.174005251309701[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]15715.3759710443[/C][C]16713.7172262334[/C][C]79.3759710442796[/C][C]-1077.71722623338[/C][C]-0.692066109425585[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]17244.4053879884[/C][C]16831.8964758517[/C][C]81.4053879883748[/C][C]331.103524148294[/C][C]0.286209760715423[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16609.1967487352[/C][C]16796.1361257456[/C][C]75.1967487352262[/C][C]-262.136125745639[/C][C]-0.86037097664727[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]16578.4514073538[/C][C]16595.8167794313[/C][C]60.4514073538403[/C][C]-77.8167794313284[/C][C]-2.01850104025196[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16432.4101151607[/C][C]16599.7307850088[/C][C]57.4101151607113[/C][C]-224.730785008773[/C][C]-0.414637749542108[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16339.6847772582[/C][C]16513.5878467130[/C][C]49.6847772582255[/C][C]-223.587846712959[/C][C]-1.05576587816445[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16397.4561734050[/C][C]16484.4540742751[/C][C]45.4561734049545[/C][C]-132.454074275099[/C][C]-0.580951664466268[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]15986.3849047873[/C][C]16491.1092344588[/C][C]43.3849047873067[/C][C]-548.109234458764[/C][C]-0.286122147509981[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16399.8153997367[/C][C]16429.5983468821[/C][C]37.815399736733[/C][C]-67.598346882089[/C][C]-0.772925383912537[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]16441.4259559579[/C][C]16668.1332559756[/C][C]48.4259559578775[/C][C]-275.133255975595[/C][C]1.47794698241834[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]19103.1624974509[/C][C]16787.415970105[/C][C]52.1624974509109[/C][C]2263.58402989500[/C][C]0.521772960478365[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]16803.8111048941[/C][C]16927.7340247171[/C][C]56.8111048941409[/C][C]-180.734024717103[/C][C]0.649499979507535[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]16383.6042499082[/C][C]17113.0928791237[/C][C]63.6042499082173[/C][C]-793.092879123735[/C][C]0.947131566555392[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]17978.5861444166[/C][C]17270.6418196161[/C][C]68.5861444166098[/C][C]639.358180383852[/C][C]0.69150670359207[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17024.7246326603[/C][C]17247.8924516135[/C][C]63.7246326602895[/C][C]-286.892451613550[/C][C]-0.6713115311164[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17544.4454361622[/C][C]17325.1191475745[/C][C]64.44543616219[/C][C]154.880852425541[/C][C]0.0991472221876955[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17109.3022709007[/C][C]17312.0858576788[/C][C]60.3022709007103[/C][C]-263.085857678771[/C][C]-0.569037817998455[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]16932.3470467336[/C][C]17242.3671612108[/C][C]53.3470467335768[/C][C]-363.367161210762[/C][C]-0.955814972472107[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17529.3300330641[/C][C]17351.5209957029[/C][C]56.3300330641291[/C][C]121.479004297149[/C][C]0.410589954146277[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]17058.1143242072[/C][C]17478.7527685271[/C][C]60.1143242071860[/C][C]-480.752768527121[/C][C]0.521754101189441[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17368.6918986107[/C][C]17568.4741109014[/C][C]61.691898610739[/C][C]-261.474110901357[/C][C]0.217805644509610[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17483.0524784500[/C][C]17693.3269836827[/C][C]65.0524784499592[/C][C]-275.326983682686[/C][C]0.464495230746059[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]20239.4679492649[/C][C]17860.2494361084[/C][C]70.4679492648824[/C][C]2308.75056389164[/C][C]0.749166786818708[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]17946.7261447210[/C][C]18029.6405522991[/C][C]75.7261447209669[/C][C]-158.640552299091[/C][C]0.727666511577185[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]17302.0004589059[/C][C]18110.5245115710[/C][C]76.0004589058506[/C][C]-884.52451157104[/C][C]0.037944235448267[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]19140.5575403847[/C][C]18234.5572700254[/C][C]78.5575403847418[/C][C]827.442729974551[/C][C]0.353264630573422[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]17878.777052663[/C][C]18242.1787611418[/C][C]74.7770526629889[/C][C]-438.178761141842[/C][C]-0.521457348362567[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]19182.7777917259[/C][C]18466.9457325059[/C][C]82.7777917258623[/C][C]633.05426749405[/C][C]1.10218502294869[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18610.1403602174[/C][C]18650.2015252305[/C][C]88.1403602173717[/C][C]-128.201525230506[/C][C]0.73835603786959[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18145.5454667379[/C][C]18689.7287819752[/C][C]85.5454667378949[/C][C]-629.728781975174[/C][C]-0.357337570795217[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18954.6273208045[/C][C]18776.8080028470[/C][C]85.6273208044576[/C][C]92.1919971530416[/C][C]0.0112775352566685[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18209.5480841698[/C][C]18804.7135859381[/C][C]82.5480841697832[/C][C]-677.713585938127[/C][C]-0.42445991711634[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18958.5518061361[/C][C]18981.1065816888[/C][C]87.5518061361308[/C][C]-110.106581688841[/C][C]0.690013654175918[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18982.4956725489[/C][C]19161.4235663533[/C][C]92.4956725488576[/C][C]-271.423566353257[/C][C]0.681978362131513[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]21353.0762168967[/C][C]19208.5077582331[/C][C]90.07621689668[/C][C]2054.49224176685[/C][C]-0.333844069038362[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19643.5548995782[/C][C]19420.1933481326[/C][C]96.5548995781493[/C][C]126.806651867427[/C][C]0.894098448192825[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]18545.9495720152[/C][C]19505.3874021292[/C][C]95.9495720151657[/C][C]-1055.38740212923[/C][C]-0.0835331354626137[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]20347.1562649718[/C][C]19548.9265106949[/C][C]93.156264971797[/C][C]705.073489305116[/C][C]-0.385335983346102[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19335.1799098198[/C][C]19680.0400912674[/C][C]95.179909819775[/C][C]-440.040091267412[/C][C]0.279026604563751[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]20309.3334981260[/C][C]19740.5963761845[/C][C]93.3334981259738[/C][C]475.403623815547[/C][C]-0.254484208719289[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]19507.3984851367[/C][C]19722.6563448177[/C][C]87.3984851366954[/C][C]-302.656344817737[/C][C]-0.817847173612272[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19504.7818362795[/C][C]19854.7369503513[/C][C]89.781836279546[/C][C]-439.736950351284[/C][C]0.328439734536982[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]20108.4601293099[/C][C]19957.2357168735[/C][C]90.4601293098559[/C][C]60.7642831264537[/C][C]0.0934873708840648[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]18732.2626073329[/C][C]19856.4860911417[/C][C]80.262607332886[/C][C]-1204.48609114171[/C][C]-1.40571677346299[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]20059.1259262908[/C][C]19952.9388984069[/C][C]81.125926290822[/C][C]25.0611015931302[/C][C]0.119020635507625[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19586.4195110991[/C][C]19964.5467537368[/C][C]77.4195110990556[/C][C]-455.54675373678[/C][C]-0.51102528352137[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]22046.5318898164[/C][C]20006.5581952663[/C][C]75.5318898164371[/C][C]1964.44180473367[/C][C]-0.260279917278426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10033&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10033&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
t	Observed	Fitted	Level	Slope	Seasonal	Residuals
1	13328	13328	13328	0	0	0
2	12873	12876.8257891851	13200.6819478145	3.82578918514634	-327.68194781448	-1.30937963159356
3	14000	14022.0031954161	13460.2391750261	22.0031954161445	539.760824973865	1.31765525270691
4	13477	13503.285105943	13535.9804208991	26.285105942988	-58.9804208991019	0.311977226123143
5	14237	14279.1871681780	13789.3673061054	42.1871681780315	447.632693894581	1.58162610681454
6	13674	13716.3300535845	13834.0894067324	42.3300535845046	-160.089406732357	0.0192376923718027
7	13529	13565.7762045799	13756.2214150021	36.7762045798851	-227.221415002069	-0.937057013630214
8	14058	14096.0529624696	13824.1263117638	38.052962469584	233.873688236230	0.243826417267901
9	12975	13001.9841057964	13582.4987752674	26.9841057964398	-607.498775267415	-2.18590323595731
10	14326	14357.8225898324	13729.7204596292	31.8225898323746	596.279540370772	0.935766933751675
11	14008	14044.3499767304	13869.9742390004	36.3499767303937	138.025760999587	0.840035252978843
12	16193	16261.9600450982	14657.8365021228	68.9600450982356	1535.16349787723	5.79802749363536
13	14483	14556.6530809516	14941.1548111521	73.6530809516055	-458.154811152081	1.70324729921804
14	14011	14083.5661000211	14973.5337540679	72.56610002109	-962.533754067875	-0.330836466619584
15	15057	15123.9424354256	14910.4226513923	66.9424354256193	146.577348607663	-1.01555961592100
16	14884	14950.3965410181	14966.9570940873	66.3965410181129	-82.9570940873432	-0.0738137548231807
17	15414	15477.5594131343	14983.5563712051	63.5594131342866	430.443628794902	-0.353622835038707
18	14440	14491.8576431762	14842.0470949073	51.8576431761596	-402.04709490728	-1.49507756240521
19	14900	14950.9658922650	14877.7132990105	50.965892265038	22.2867009895442	-0.120639961851066
20	15074	15121.104965195	14855.4215561017	47.1049651949951	218.578443898257	-0.551266726939755
21	14442	14493.8605348171	14996.3157694375	51.8605348170913	-554.315769437457	0.706960235998102
22	15307	15360.7716010294	15087.0676218772	53.7716010293883	219.932378122800	0.292538866816767
23	14938	14995.9402455145	15228.0596750919	57.9402455145203	-290.059675091854	0.654261787956202
24	17193	17259.2993886137	15465.3750700089	66.2993886136976	1727.62492999106	1.34474028856297
25	15528	15602.0185876088	15699.5442321763	74.0185876088331	-171.544232176331	1.26208555258566
26	14765	14838.8065274304	15769.0633384170	73.806527430363	-1004.06333841696	-0.0337794511447212
27	15838	15908.2059502489	15770.3671276436	70.2059502489409	67.6328723564073	-0.537689018234094
28	15723	15789.4079039139	15767.9178383391	66.4079039138715	-44.9178383390633	-0.531044660759293
29	16150	16210.5361068853	15725.6628456300	60.5361068853177	424.337154370023	-0.790177339025636
30	15486	15546.2124988847	15780.2862005268	60.2124988847452	-294.286200526844	-0.0432200309184316
31	15986	16048.2262083617	15877.3981740204	62.22620836171	108.601825979555	0.271983421683458
32	15983	16044.6397511119	15928.7468785298	61.6397511119189	54.2531214702492	-0.0806101036648515
33	15692	15759.4797360290	16100.4317237832	67.4797360289696	-408.431723783209	0.81632027217282
34	16490	16563.4467240256	16282.1067353452	73.4467240256002	207.893264654839	0.845799882141688
35	15686	15757.8873726201	16325.3374782275	71.8873726200522	-639.337478227512	-0.223472602865751
36	18897	18982.4097568336	16661.1131040203	85.4097568335573	2235.88689597968	1.95194819402148
37	16316	16400.2053883081	16723.0230360093	84.2053883081234	-407.023036009263	-0.174005251309701
38	15636	15715.3759710443	16713.7172262334	79.3759710442796	-1077.71722623338	-0.692066109425585
39	17163	17244.4053879884	16831.8964758517	81.4053879883748	331.103524148294	0.286209760715423
40	16534	16609.1967487352	16796.1361257456	75.1967487352262	-262.136125745639	-0.86037097664727
41	16518	16578.4514073538	16595.8167794313	60.4514073538403	-77.8167794313284	-2.01850104025196
42	16375	16432.4101151607	16599.7307850088	57.4101151607113	-224.730785008773	-0.414637749542108
43	16290	16339.6847772582	16513.5878467130	49.6847772582255	-223.587846712959	-1.05576587816445
44	16352	16397.4561734050	16484.4540742751	45.4561734049545	-132.454074275099	-0.580951664466268
45	15943	15986.3849047873	16491.1092344588	43.3849047873067	-548.109234458764	-0.286122147509981
46	16362	16399.8153997367	16429.5983468821	37.815399736733	-67.598346882089	-0.772925383912537
47	16393	16441.4259559579	16668.1332559756	48.4259559578775	-275.133255975595	1.47794698241834
48	19051	19103.1624974509	16787.415970105	52.1624974509109	2263.58402989500	0.521772960478365
49	16747	16803.8111048941	16927.7340247171	56.8111048941409	-180.734024717103	0.649499979507535
50	16320	16383.6042499082	17113.0928791237	63.6042499082173	-793.092879123735	0.947131566555392
51	17910	17978.5861444166	17270.6418196161	68.5861444166098	639.358180383852	0.69150670359207
52	16961	17024.7246326603	17247.8924516135	63.7246326602895	-286.892451613550	-0.6713115311164
53	17480	17544.4454361622	17325.1191475745	64.44543616219	154.880852425541	0.0991472221876955
54	17049	17109.3022709007	17312.0858576788	60.3022709007103	-263.085857678771	-0.569037817998455
55	16879	16932.3470467336	17242.3671612108	53.3470467335768	-363.367161210762	-0.955814972472107
56	17473	17529.3300330641	17351.5209957029	56.3300330641291	121.479004297149	0.410589954146277
57	16998	17058.1143242072	17478.7527685271	60.1143242071860	-480.752768527121	0.521754101189441
58	17307	17368.6918986107	17568.4741109014	61.691898610739	-261.474110901357	0.217805644509610
59	17418	17483.0524784500	17693.3269836827	65.0524784499592	-275.326983682686	0.464495230746059
60	20169	20239.4679492649	17860.2494361084	70.4679492648824	2308.75056389164	0.749166786818708
61	17871	17946.7261447210	18029.6405522991	75.7261447209669	-158.640552299091	0.727666511577185
62	17226	17302.0004589059	18110.5245115710	76.0004589058506	-884.52451157104	0.037944235448267
63	19062	19140.5575403847	18234.5572700254	78.5575403847418	827.442729974551	0.353264630573422
64	17804	17878.777052663	18242.1787611418	74.7770526629889	-438.178761141842	-0.521457348362567
65	19100	19182.7777917259	18466.9457325059	82.7777917258623	633.05426749405	1.10218502294869
66	18522	18610.1403602174	18650.2015252305	88.1403602173717	-128.201525230506	0.73835603786959
67	18060	18145.5454667379	18689.7287819752	85.5454667378949	-629.728781975174	-0.357337570795217
68	18869	18954.6273208045	18776.8080028470	85.6273208044576	92.1919971530416	0.0112775352566685
69	18127	18209.5480841698	18804.7135859381	82.5480841697832	-677.713585938127	-0.42445991711634
70	18871	18958.5518061361	18981.1065816888	87.5518061361308	-110.106581688841	0.690013654175918
71	18890	18982.4956725489	19161.4235663533	92.4956725488576	-271.423566353257	0.681978362131513
72	21263	21353.0762168967	19208.5077582331	90.07621689668	2054.49224176685	-0.333844069038362
73	19547	19643.5548995782	19420.1933481326	96.5548995781493	126.806651867427	0.894098448192825
74	18450	18545.9495720152	19505.3874021292	95.9495720151657	-1055.38740212923	-0.0835331354626137
75	20254	20347.1562649718	19548.9265106949	93.156264971797	705.073489305116	-0.385335983346102
76	19240	19335.1799098198	19680.0400912674	95.179909819775	-440.040091267412	0.279026604563751
77	20216	20309.3334981260	19740.5963761845	93.3334981259738	475.403623815547	-0.254484208719289
78	19420	19507.3984851367	19722.6563448177	87.3984851366954	-302.656344817737	-0.817847173612272
79	19415	19504.7818362795	19854.7369503513	89.781836279546	-439.736950351284	0.328439734536982
80	20018	20108.4601293099	19957.2357168735	90.4601293098559	60.7642831264537	0.0934873708840648
81	18652	18732.2626073329	19856.4860911417	80.262607332886	-1204.48609114171	-1.40571677346299
82	19978	20059.1259262908	19952.9388984069	81.125926290822	25.0611015931302	0.119020635507625
83	19509	19586.4195110991	19964.5467537368	77.4195110990556	-455.54675373678	-0.51102528352137
84	21971	22046.5318898164	20006.5581952663	75.5318898164371	1964.44180473367	-0.260279917278426

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

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$resid)
myfit <- mylevel+myslope+myseas
bitmap(file='test1.png')
op <- par(mfrow = c(2,1))
plot(as.numeric(x),main='Interpolation Fit',ylab='Observed (black) / Fitted (red)',xlab='time',type='b')
lines(myfit, col = 'red')
grid()
plot(as.numeric(m$resid),main='Residuals',ylab='Residuals',xlab='time')
grid()
par(op)
dev.off()
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(3,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myslope,na.action=na.pass,lag.max = mylagmax,main='Slope')
acf(mylevel + myslope,na.action=na.pass,lag.max = mylagmax,main='Level+Slope')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(3,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myslope,main='Slope')
spectrum(mylevel + myslope,main='Level+Slope')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel + myslope,main='Level+Slope')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Residals')
par(op)
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',7,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,'Fitted',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,'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,myfit[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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code