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R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Fri, 17 Dec 2010 16:42:30 +0000

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/2010/Dec/17/t12926040327vcnf0lrbl0ks1a.htm/, Retrieved Fri, 09 May 2025 19:55:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111574, Retrieved Fri, 09 May 2025 19:55:14 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

430

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] [74be16979710d4c4e7c6647856088456]
- R  D    [Structural Time Series Models] [HPC Retail Sales] [2008-03-08 11:33:35] [74be16979710d4c4e7c6647856088456]
-  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] [7a87ed98a7b21a29d6a45388a9b7b229] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111574&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111574&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111574&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 Output	view raw output of R engine
Computing time	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	989236	989236	0	0	0
2	1008380	1007464.82396763	18304.4583479359	915.176032371456	0.205158156588241
3	1207763	1190887.15417499	164849.202032658	16875.8458250149	1.68381616733103
4	1368839	1371096.55868827	178472.562432723	-2257.55868826592	0.14847010537782
5	1469798	1475942.25957356	113401.039471187	-6144.2595735563	-0.712754757498346
6	1498721	1503786.81736731	37693.4894229754	-5065.81736731116	-0.828882468346857
7	1761769	1741127.72496455	214372.611004934	20641.2750354532	1.93433688951141
8	1653214	1681601.15695943	-27997.9408651255	-28387.1569594327	-2.65354152616664
9	1599104	1596784.5114017	-78275.3155976183	2319.48859830071	-0.550450693824062
10	1421179	1427148.81367717	-159118.311904447	-5969.81367716915	-0.885091652012392
11	1163995	1169751.58806709	-246083.610723971	-5756.5880670883	-0.952120316062697
12	1037735	1025502.96921664	-155971.649565475	12232.0307833575	0.98657085251419
13	1015407	1006998.77809958	-34428.92199906	8408.22190042487	1.33218656308679
14	1039210	1050488.39296539	34586.3292676019	-11278.392965389	0.763051783989928
15	1258049	1233257.84531859	160152.958912378	24791.1546814107	1.38987413167301
16	1469445	1459806.03739443	216956.595676824	9638.96260557271	0.622455115941462
17	1552346	1555364.24688723	113678.637191466	-3018.24688723112	-1.12989323953066
18	1549144	1596435.21063852	51863.3106968983	-47291.2106385222	-0.676935426438004
19	1785895	1725616.81096116	117714.651268571	60278.1890388438	0.72094603575268
20	1662335	1706520.01100887	1195.99598397061	-44185.0110088708	-1.27568394604374
21	1629440	1628079.48332224	-66624.2140614589	1360.51667775942	-0.742514535171335
22	1467430	1465088.59365848	-148692.705242063	2341.40634152317	-0.898509045970153
23	1202209	1221073.46751818	-229874.489388055	-18864.4675181832	-0.888806448412663
24	1076982	1064615.55352724	-167362.50994988	12366.4464727641	0.684409797630143
25	1039367	1020007.1367768	-62890.7906012321	19359.8632231954	1.14547865516439
26	1063449	1083917.53658343	45164.8794267508	-20468.5365834302	1.185080709421
27	1335135	1309673.38194462	196678.198229775	25461.6180553813	1.66334635408133
28	1491602	1472031.75864276	167735.584703412	19570.2413572367	-0.317588360261953
29	1591972	1588490.14551138	124610.668068207	3481.85448862488	-0.471632508292719
30	1641248	1707721.93334476	120088.897975009	-66473.9333447636	-0.0495148007978715
31	1898849	1823942.98877171	116835.558845995	74906.0112282916	-0.0356191897324393
32	1798580	1848904.65893691	39552.8558076856	-50324.6589369119	-0.846106047608183
33	1762444	1764562.08133564	-64662.476808368	-2118.08133564485	-1.14098031432421
34	1622044	1609137.65111193	-141007.301035442	12906.3488880725	-0.83584892020799
35	1368955	1396424.86450519	-201320.55315407	-27469.8645051933	-0.660328170259007
36	1262973	1250238.41963702	-154962.61477317	12734.5803629803	0.507591915967803
37	1195650	1178211.66189516	-85223.3191993464	17438.3381048432	0.764564637363084
38	1269530	1299013.74935171	88010.0568999051	-29483.7493517064	1.89658182688081
39	1479279	1446327.56839184	137524.818977763	32951.4316081645	0.542615428927656
40	1607819	1581536.34651634	135585.953079742	26282.6534836635	-0.0212684448479848
41	1712466	1711511.77715323	130893.192539172	954.222846766093	-0.0513357024751949
42	1721766	1799806.99356781	95297.5878839816	-78040.9935678123	-0.389706535103795
43	1949843	1871248.31946547	75353.375776242	78594.6805345342	-0.21837085052715
44	1821326	1867719.92146283	9396.032132246	-46393.9214628335	-0.722108632902278
45	1757802	1761259.23649648	-87478.384271377	-3457.23649648099	-1.06061136852694
46	1590367	1572182.40923038	-172429.180155389	18184.5907696164	-0.930079379400444
47	1260647	1297721.38495309	-257731.673197424	-37074.3849530888	-0.933906473497344
48	1149235	1126798.59856733	-185181.564775639	22436.4014326662	0.794472369105847
49	1016367	1019680.90166342	-119917.971686716	-3313.90166341636	0.715242109788243
50	1027885	1050169.30788461	5746.21322480324	-22284.3078846106	1.37533144544749
51	1262159	1213280.5680722	136714.030597653	48878.4319278	1.434508435879
52	1520854	1481908.87526815	246666.669429353	38945.1247318533	1.20554623439595
53	1544144	1559351.85250321	105621.747152111	-15207.8525032085	-1.54342577943302
54	1564709	1647632.06503192	91182.5317806887	-82923.0650319214	-0.158059884367885
55	1821776	1739555.73745449	91799.8088902114	82220.2625455126	0.00675873584822836
56	1741365	1781923.57523916	50619.5636596885	-40558.575239164	-0.450848752998997
57	1623386	1634953.41940773	-113991.416630682	-11567.4194077305	-1.80221286015641
58	1498658	1463629.86899661	-161752.955039778	35028.1310033859	-0.522916605514228
59	1241822	1286066.64976003	-174921.488185682	-44244.6497600334	-0.144171435539331
60	1136029	1113060.38478289	-173326.690795354	22968.6152171129	0.0174653046580764

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 989236 & 989236 & 0 & 0 & 0 \tabularnewline
2 & 1008380 & 1007464.82396763 & 18304.4583479359 & 915.176032371456 & 0.205158156588241 \tabularnewline
3 & 1207763 & 1190887.15417499 & 164849.202032658 & 16875.8458250149 & 1.68381616733103 \tabularnewline
4 & 1368839 & 1371096.55868827 & 178472.562432723 & -2257.55868826592 & 0.14847010537782 \tabularnewline
5 & 1469798 & 1475942.25957356 & 113401.039471187 & -6144.2595735563 & -0.712754757498346 \tabularnewline
6 & 1498721 & 1503786.81736731 & 37693.4894229754 & -5065.81736731116 & -0.828882468346857 \tabularnewline
7 & 1761769 & 1741127.72496455 & 214372.611004934 & 20641.2750354532 & 1.93433688951141 \tabularnewline
8 & 1653214 & 1681601.15695943 & -27997.9408651255 & -28387.1569594327 & -2.65354152616664 \tabularnewline
9 & 1599104 & 1596784.5114017 & -78275.3155976183 & 2319.48859830071 & -0.550450693824062 \tabularnewline
10 & 1421179 & 1427148.81367717 & -159118.311904447 & -5969.81367716915 & -0.885091652012392 \tabularnewline
11 & 1163995 & 1169751.58806709 & -246083.610723971 & -5756.5880670883 & -0.952120316062697 \tabularnewline
12 & 1037735 & 1025502.96921664 & -155971.649565475 & 12232.0307833575 & 0.98657085251419 \tabularnewline
13 & 1015407 & 1006998.77809958 & -34428.92199906 & 8408.22190042487 & 1.33218656308679 \tabularnewline
14 & 1039210 & 1050488.39296539 & 34586.3292676019 & -11278.392965389 & 0.763051783989928 \tabularnewline
15 & 1258049 & 1233257.84531859 & 160152.958912378 & 24791.1546814107 & 1.38987413167301 \tabularnewline
16 & 1469445 & 1459806.03739443 & 216956.595676824 & 9638.96260557271 & 0.622455115941462 \tabularnewline
17 & 1552346 & 1555364.24688723 & 113678.637191466 & -3018.24688723112 & -1.12989323953066 \tabularnewline
18 & 1549144 & 1596435.21063852 & 51863.3106968983 & -47291.2106385222 & -0.676935426438004 \tabularnewline
19 & 1785895 & 1725616.81096116 & 117714.651268571 & 60278.1890388438 & 0.72094603575268 \tabularnewline
20 & 1662335 & 1706520.01100887 & 1195.99598397061 & -44185.0110088708 & -1.27568394604374 \tabularnewline
21 & 1629440 & 1628079.48332224 & -66624.2140614589 & 1360.51667775942 & -0.742514535171335 \tabularnewline
22 & 1467430 & 1465088.59365848 & -148692.705242063 & 2341.40634152317 & -0.898509045970153 \tabularnewline
23 & 1202209 & 1221073.46751818 & -229874.489388055 & -18864.4675181832 & -0.888806448412663 \tabularnewline
24 & 1076982 & 1064615.55352724 & -167362.50994988 & 12366.4464727641 & 0.684409797630143 \tabularnewline
25 & 1039367 & 1020007.1367768 & -62890.7906012321 & 19359.8632231954 & 1.14547865516439 \tabularnewline
26 & 1063449 & 1083917.53658343 & 45164.8794267508 & -20468.5365834302 & 1.185080709421 \tabularnewline
27 & 1335135 & 1309673.38194462 & 196678.198229775 & 25461.6180553813 & 1.66334635408133 \tabularnewline
28 & 1491602 & 1472031.75864276 & 167735.584703412 & 19570.2413572367 & -0.317588360261953 \tabularnewline
29 & 1591972 & 1588490.14551138 & 124610.668068207 & 3481.85448862488 & -0.471632508292719 \tabularnewline
30 & 1641248 & 1707721.93334476 & 120088.897975009 & -66473.9333447636 & -0.0495148007978715 \tabularnewline
31 & 1898849 & 1823942.98877171 & 116835.558845995 & 74906.0112282916 & -0.0356191897324393 \tabularnewline
32 & 1798580 & 1848904.65893691 & 39552.8558076856 & -50324.6589369119 & -0.846106047608183 \tabularnewline
33 & 1762444 & 1764562.08133564 & -64662.476808368 & -2118.08133564485 & -1.14098031432421 \tabularnewline
34 & 1622044 & 1609137.65111193 & -141007.301035442 & 12906.3488880725 & -0.83584892020799 \tabularnewline
35 & 1368955 & 1396424.86450519 & -201320.55315407 & -27469.8645051933 & -0.660328170259007 \tabularnewline
36 & 1262973 & 1250238.41963702 & -154962.61477317 & 12734.5803629803 & 0.507591915967803 \tabularnewline
37 & 1195650 & 1178211.66189516 & -85223.3191993464 & 17438.3381048432 & 0.764564637363084 \tabularnewline
38 & 1269530 & 1299013.74935171 & 88010.0568999051 & -29483.7493517064 & 1.89658182688081 \tabularnewline
39 & 1479279 & 1446327.56839184 & 137524.818977763 & 32951.4316081645 & 0.542615428927656 \tabularnewline
40 & 1607819 & 1581536.34651634 & 135585.953079742 & 26282.6534836635 & -0.0212684448479848 \tabularnewline
41 & 1712466 & 1711511.77715323 & 130893.192539172 & 954.222846766093 & -0.0513357024751949 \tabularnewline
42 & 1721766 & 1799806.99356781 & 95297.5878839816 & -78040.9935678123 & -0.389706535103795 \tabularnewline
43 & 1949843 & 1871248.31946547 & 75353.375776242 & 78594.6805345342 & -0.21837085052715 \tabularnewline
44 & 1821326 & 1867719.92146283 & 9396.032132246 & -46393.9214628335 & -0.722108632902278 \tabularnewline
45 & 1757802 & 1761259.23649648 & -87478.384271377 & -3457.23649648099 & -1.06061136852694 \tabularnewline
46 & 1590367 & 1572182.40923038 & -172429.180155389 & 18184.5907696164 & -0.930079379400444 \tabularnewline
47 & 1260647 & 1297721.38495309 & -257731.673197424 & -37074.3849530888 & -0.933906473497344 \tabularnewline
48 & 1149235 & 1126798.59856733 & -185181.564775639 & 22436.4014326662 & 0.794472369105847 \tabularnewline
49 & 1016367 & 1019680.90166342 & -119917.971686716 & -3313.90166341636 & 0.715242109788243 \tabularnewline
50 & 1027885 & 1050169.30788461 & 5746.21322480324 & -22284.3078846106 & 1.37533144544749 \tabularnewline
51 & 1262159 & 1213280.5680722 & 136714.030597653 & 48878.4319278 & 1.434508435879 \tabularnewline
52 & 1520854 & 1481908.87526815 & 246666.669429353 & 38945.1247318533 & 1.20554623439595 \tabularnewline
53 & 1544144 & 1559351.85250321 & 105621.747152111 & -15207.8525032085 & -1.54342577943302 \tabularnewline
54 & 1564709 & 1647632.06503192 & 91182.5317806887 & -82923.0650319214 & -0.158059884367885 \tabularnewline
55 & 1821776 & 1739555.73745449 & 91799.8088902114 & 82220.2625455126 & 0.00675873584822836 \tabularnewline
56 & 1741365 & 1781923.57523916 & 50619.5636596885 & -40558.575239164 & -0.450848752998997 \tabularnewline
57 & 1623386 & 1634953.41940773 & -113991.416630682 & -11567.4194077305 & -1.80221286015641 \tabularnewline
58 & 1498658 & 1463629.86899661 & -161752.955039778 & 35028.1310033859 & -0.522916605514228 \tabularnewline
59 & 1241822 & 1286066.64976003 & -174921.488185682 & -44244.6497600334 & -0.144171435539331 \tabularnewline
60 & 1136029 & 1113060.38478289 & -173326.690795354 & 22968.6152171129 & 0.0174653046580764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111574&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]989236[/C][C]989236[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]1008380[/C][C]1007464.82396763[/C][C]18304.4583479359[/C][C]915.176032371456[/C][C]0.205158156588241[/C][/ROW]
[ROW][C]3[/C][C]1207763[/C][C]1190887.15417499[/C][C]164849.202032658[/C][C]16875.8458250149[/C][C]1.68381616733103[/C][/ROW]
[ROW][C]4[/C][C]1368839[/C][C]1371096.55868827[/C][C]178472.562432723[/C][C]-2257.55868826592[/C][C]0.14847010537782[/C][/ROW]
[ROW][C]5[/C][C]1469798[/C][C]1475942.25957356[/C][C]113401.039471187[/C][C]-6144.2595735563[/C][C]-0.712754757498346[/C][/ROW]
[ROW][C]6[/C][C]1498721[/C][C]1503786.81736731[/C][C]37693.4894229754[/C][C]-5065.81736731116[/C][C]-0.828882468346857[/C][/ROW]
[ROW][C]7[/C][C]1761769[/C][C]1741127.72496455[/C][C]214372.611004934[/C][C]20641.2750354532[/C][C]1.93433688951141[/C][/ROW]
[ROW][C]8[/C][C]1653214[/C][C]1681601.15695943[/C][C]-27997.9408651255[/C][C]-28387.1569594327[/C][C]-2.65354152616664[/C][/ROW]
[ROW][C]9[/C][C]1599104[/C][C]1596784.5114017[/C][C]-78275.3155976183[/C][C]2319.48859830071[/C][C]-0.550450693824062[/C][/ROW]
[ROW][C]10[/C][C]1421179[/C][C]1427148.81367717[/C][C]-159118.311904447[/C][C]-5969.81367716915[/C][C]-0.885091652012392[/C][/ROW]
[ROW][C]11[/C][C]1163995[/C][C]1169751.58806709[/C][C]-246083.610723971[/C][C]-5756.5880670883[/C][C]-0.952120316062697[/C][/ROW]
[ROW][C]12[/C][C]1037735[/C][C]1025502.96921664[/C][C]-155971.649565475[/C][C]12232.0307833575[/C][C]0.98657085251419[/C][/ROW]
[ROW][C]13[/C][C]1015407[/C][C]1006998.77809958[/C][C]-34428.92199906[/C][C]8408.22190042487[/C][C]1.33218656308679[/C][/ROW]
[ROW][C]14[/C][C]1039210[/C][C]1050488.39296539[/C][C]34586.3292676019[/C][C]-11278.392965389[/C][C]0.763051783989928[/C][/ROW]
[ROW][C]15[/C][C]1258049[/C][C]1233257.84531859[/C][C]160152.958912378[/C][C]24791.1546814107[/C][C]1.38987413167301[/C][/ROW]
[ROW][C]16[/C][C]1469445[/C][C]1459806.03739443[/C][C]216956.595676824[/C][C]9638.96260557271[/C][C]0.622455115941462[/C][/ROW]
[ROW][C]17[/C][C]1552346[/C][C]1555364.24688723[/C][C]113678.637191466[/C][C]-3018.24688723112[/C][C]-1.12989323953066[/C][/ROW]
[ROW][C]18[/C][C]1549144[/C][C]1596435.21063852[/C][C]51863.3106968983[/C][C]-47291.2106385222[/C][C]-0.676935426438004[/C][/ROW]
[ROW][C]19[/C][C]1785895[/C][C]1725616.81096116[/C][C]117714.651268571[/C][C]60278.1890388438[/C][C]0.72094603575268[/C][/ROW]
[ROW][C]20[/C][C]1662335[/C][C]1706520.01100887[/C][C]1195.99598397061[/C][C]-44185.0110088708[/C][C]-1.27568394604374[/C][/ROW]
[ROW][C]21[/C][C]1629440[/C][C]1628079.48332224[/C][C]-66624.2140614589[/C][C]1360.51667775942[/C][C]-0.742514535171335[/C][/ROW]
[ROW][C]22[/C][C]1467430[/C][C]1465088.59365848[/C][C]-148692.705242063[/C][C]2341.40634152317[/C][C]-0.898509045970153[/C][/ROW]
[ROW][C]23[/C][C]1202209[/C][C]1221073.46751818[/C][C]-229874.489388055[/C][C]-18864.4675181832[/C][C]-0.888806448412663[/C][/ROW]
[ROW][C]24[/C][C]1076982[/C][C]1064615.55352724[/C][C]-167362.50994988[/C][C]12366.4464727641[/C][C]0.684409797630143[/C][/ROW]
[ROW][C]25[/C][C]1039367[/C][C]1020007.1367768[/C][C]-62890.7906012321[/C][C]19359.8632231954[/C][C]1.14547865516439[/C][/ROW]
[ROW][C]26[/C][C]1063449[/C][C]1083917.53658343[/C][C]45164.8794267508[/C][C]-20468.5365834302[/C][C]1.185080709421[/C][/ROW]
[ROW][C]27[/C][C]1335135[/C][C]1309673.38194462[/C][C]196678.198229775[/C][C]25461.6180553813[/C][C]1.66334635408133[/C][/ROW]
[ROW][C]28[/C][C]1491602[/C][C]1472031.75864276[/C][C]167735.584703412[/C][C]19570.2413572367[/C][C]-0.317588360261953[/C][/ROW]
[ROW][C]29[/C][C]1591972[/C][C]1588490.14551138[/C][C]124610.668068207[/C][C]3481.85448862488[/C][C]-0.471632508292719[/C][/ROW]
[ROW][C]30[/C][C]1641248[/C][C]1707721.93334476[/C][C]120088.897975009[/C][C]-66473.9333447636[/C][C]-0.0495148007978715[/C][/ROW]
[ROW][C]31[/C][C]1898849[/C][C]1823942.98877171[/C][C]116835.558845995[/C][C]74906.0112282916[/C][C]-0.0356191897324393[/C][/ROW]
[ROW][C]32[/C][C]1798580[/C][C]1848904.65893691[/C][C]39552.8558076856[/C][C]-50324.6589369119[/C][C]-0.846106047608183[/C][/ROW]
[ROW][C]33[/C][C]1762444[/C][C]1764562.08133564[/C][C]-64662.476808368[/C][C]-2118.08133564485[/C][C]-1.14098031432421[/C][/ROW]
[ROW][C]34[/C][C]1622044[/C][C]1609137.65111193[/C][C]-141007.301035442[/C][C]12906.3488880725[/C][C]-0.83584892020799[/C][/ROW]
[ROW][C]35[/C][C]1368955[/C][C]1396424.86450519[/C][C]-201320.55315407[/C][C]-27469.8645051933[/C][C]-0.660328170259007[/C][/ROW]
[ROW][C]36[/C][C]1262973[/C][C]1250238.41963702[/C][C]-154962.61477317[/C][C]12734.5803629803[/C][C]0.507591915967803[/C][/ROW]
[ROW][C]37[/C][C]1195650[/C][C]1178211.66189516[/C][C]-85223.3191993464[/C][C]17438.3381048432[/C][C]0.764564637363084[/C][/ROW]
[ROW][C]38[/C][C]1269530[/C][C]1299013.74935171[/C][C]88010.0568999051[/C][C]-29483.7493517064[/C][C]1.89658182688081[/C][/ROW]
[ROW][C]39[/C][C]1479279[/C][C]1446327.56839184[/C][C]137524.818977763[/C][C]32951.4316081645[/C][C]0.542615428927656[/C][/ROW]
[ROW][C]40[/C][C]1607819[/C][C]1581536.34651634[/C][C]135585.953079742[/C][C]26282.6534836635[/C][C]-0.0212684448479848[/C][/ROW]
[ROW][C]41[/C][C]1712466[/C][C]1711511.77715323[/C][C]130893.192539172[/C][C]954.222846766093[/C][C]-0.0513357024751949[/C][/ROW]
[ROW][C]42[/C][C]1721766[/C][C]1799806.99356781[/C][C]95297.5878839816[/C][C]-78040.9935678123[/C][C]-0.389706535103795[/C][/ROW]
[ROW][C]43[/C][C]1949843[/C][C]1871248.31946547[/C][C]75353.375776242[/C][C]78594.6805345342[/C][C]-0.21837085052715[/C][/ROW]
[ROW][C]44[/C][C]1821326[/C][C]1867719.92146283[/C][C]9396.032132246[/C][C]-46393.9214628335[/C][C]-0.722108632902278[/C][/ROW]
[ROW][C]45[/C][C]1757802[/C][C]1761259.23649648[/C][C]-87478.384271377[/C][C]-3457.23649648099[/C][C]-1.06061136852694[/C][/ROW]
[ROW][C]46[/C][C]1590367[/C][C]1572182.40923038[/C][C]-172429.180155389[/C][C]18184.5907696164[/C][C]-0.930079379400444[/C][/ROW]
[ROW][C]47[/C][C]1260647[/C][C]1297721.38495309[/C][C]-257731.673197424[/C][C]-37074.3849530888[/C][C]-0.933906473497344[/C][/ROW]
[ROW][C]48[/C][C]1149235[/C][C]1126798.59856733[/C][C]-185181.564775639[/C][C]22436.4014326662[/C][C]0.794472369105847[/C][/ROW]
[ROW][C]49[/C][C]1016367[/C][C]1019680.90166342[/C][C]-119917.971686716[/C][C]-3313.90166341636[/C][C]0.715242109788243[/C][/ROW]
[ROW][C]50[/C][C]1027885[/C][C]1050169.30788461[/C][C]5746.21322480324[/C][C]-22284.3078846106[/C][C]1.37533144544749[/C][/ROW]
[ROW][C]51[/C][C]1262159[/C][C]1213280.5680722[/C][C]136714.030597653[/C][C]48878.4319278[/C][C]1.434508435879[/C][/ROW]
[ROW][C]52[/C][C]1520854[/C][C]1481908.87526815[/C][C]246666.669429353[/C][C]38945.1247318533[/C][C]1.20554623439595[/C][/ROW]
[ROW][C]53[/C][C]1544144[/C][C]1559351.85250321[/C][C]105621.747152111[/C][C]-15207.8525032085[/C][C]-1.54342577943302[/C][/ROW]
[ROW][C]54[/C][C]1564709[/C][C]1647632.06503192[/C][C]91182.5317806887[/C][C]-82923.0650319214[/C][C]-0.158059884367885[/C][/ROW]
[ROW][C]55[/C][C]1821776[/C][C]1739555.73745449[/C][C]91799.8088902114[/C][C]82220.2625455126[/C][C]0.00675873584822836[/C][/ROW]
[ROW][C]56[/C][C]1741365[/C][C]1781923.57523916[/C][C]50619.5636596885[/C][C]-40558.575239164[/C][C]-0.450848752998997[/C][/ROW]
[ROW][C]57[/C][C]1623386[/C][C]1634953.41940773[/C][C]-113991.416630682[/C][C]-11567.4194077305[/C][C]-1.80221286015641[/C][/ROW]
[ROW][C]58[/C][C]1498658[/C][C]1463629.86899661[/C][C]-161752.955039778[/C][C]35028.1310033859[/C][C]-0.522916605514228[/C][/ROW]
[ROW][C]59[/C][C]1241822[/C][C]1286066.64976003[/C][C]-174921.488185682[/C][C]-44244.6497600334[/C][C]-0.144171435539331[/C][/ROW]
[ROW][C]60[/C][C]1136029[/C][C]1113060.38478289[/C][C]-173326.690795354[/C][C]22968.6152171129[/C][C]0.0174653046580764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111574&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111574&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	Level	Slope	Seasonal	Stand. Residuals
1	989236	989236	0	0	0
2	1008380	1007464.82396763	18304.4583479359	915.176032371456	0.205158156588241
3	1207763	1190887.15417499	164849.202032658	16875.8458250149	1.68381616733103
4	1368839	1371096.55868827	178472.562432723	-2257.55868826592	0.14847010537782
5	1469798	1475942.25957356	113401.039471187	-6144.2595735563	-0.712754757498346
6	1498721	1503786.81736731	37693.4894229754	-5065.81736731116	-0.828882468346857
7	1761769	1741127.72496455	214372.611004934	20641.2750354532	1.93433688951141
8	1653214	1681601.15695943	-27997.9408651255	-28387.1569594327	-2.65354152616664
9	1599104	1596784.5114017	-78275.3155976183	2319.48859830071	-0.550450693824062
10	1421179	1427148.81367717	-159118.311904447	-5969.81367716915	-0.885091652012392
11	1163995	1169751.58806709	-246083.610723971	-5756.5880670883	-0.952120316062697
12	1037735	1025502.96921664	-155971.649565475	12232.0307833575	0.98657085251419
13	1015407	1006998.77809958	-34428.92199906	8408.22190042487	1.33218656308679
14	1039210	1050488.39296539	34586.3292676019	-11278.392965389	0.763051783989928
15	1258049	1233257.84531859	160152.958912378	24791.1546814107	1.38987413167301
16	1469445	1459806.03739443	216956.595676824	9638.96260557271	0.622455115941462
17	1552346	1555364.24688723	113678.637191466	-3018.24688723112	-1.12989323953066
18	1549144	1596435.21063852	51863.3106968983	-47291.2106385222	-0.676935426438004
19	1785895	1725616.81096116	117714.651268571	60278.1890388438	0.72094603575268
20	1662335	1706520.01100887	1195.99598397061	-44185.0110088708	-1.27568394604374
21	1629440	1628079.48332224	-66624.2140614589	1360.51667775942	-0.742514535171335
22	1467430	1465088.59365848	-148692.705242063	2341.40634152317	-0.898509045970153
23	1202209	1221073.46751818	-229874.489388055	-18864.4675181832	-0.888806448412663
24	1076982	1064615.55352724	-167362.50994988	12366.4464727641	0.684409797630143
25	1039367	1020007.1367768	-62890.7906012321	19359.8632231954	1.14547865516439
26	1063449	1083917.53658343	45164.8794267508	-20468.5365834302	1.185080709421
27	1335135	1309673.38194462	196678.198229775	25461.6180553813	1.66334635408133
28	1491602	1472031.75864276	167735.584703412	19570.2413572367	-0.317588360261953
29	1591972	1588490.14551138	124610.668068207	3481.85448862488	-0.471632508292719
30	1641248	1707721.93334476	120088.897975009	-66473.9333447636	-0.0495148007978715
31	1898849	1823942.98877171	116835.558845995	74906.0112282916	-0.0356191897324393
32	1798580	1848904.65893691	39552.8558076856	-50324.6589369119	-0.846106047608183
33	1762444	1764562.08133564	-64662.476808368	-2118.08133564485	-1.14098031432421
34	1622044	1609137.65111193	-141007.301035442	12906.3488880725	-0.83584892020799
35	1368955	1396424.86450519	-201320.55315407	-27469.8645051933	-0.660328170259007
36	1262973	1250238.41963702	-154962.61477317	12734.5803629803	0.507591915967803
37	1195650	1178211.66189516	-85223.3191993464	17438.3381048432	0.764564637363084
38	1269530	1299013.74935171	88010.0568999051	-29483.7493517064	1.89658182688081
39	1479279	1446327.56839184	137524.818977763	32951.4316081645	0.542615428927656
40	1607819	1581536.34651634	135585.953079742	26282.6534836635	-0.0212684448479848
41	1712466	1711511.77715323	130893.192539172	954.222846766093	-0.0513357024751949
42	1721766	1799806.99356781	95297.5878839816	-78040.9935678123	-0.389706535103795
43	1949843	1871248.31946547	75353.375776242	78594.6805345342	-0.21837085052715
44	1821326	1867719.92146283	9396.032132246	-46393.9214628335	-0.722108632902278
45	1757802	1761259.23649648	-87478.384271377	-3457.23649648099	-1.06061136852694
46	1590367	1572182.40923038	-172429.180155389	18184.5907696164	-0.930079379400444
47	1260647	1297721.38495309	-257731.673197424	-37074.3849530888	-0.933906473497344
48	1149235	1126798.59856733	-185181.564775639	22436.4014326662	0.794472369105847
49	1016367	1019680.90166342	-119917.971686716	-3313.90166341636	0.715242109788243
50	1027885	1050169.30788461	5746.21322480324	-22284.3078846106	1.37533144544749
51	1262159	1213280.5680722	136714.030597653	48878.4319278	1.434508435879
52	1520854	1481908.87526815	246666.669429353	38945.1247318533	1.20554623439595
53	1544144	1559351.85250321	105621.747152111	-15207.8525032085	-1.54342577943302
54	1564709	1647632.06503192	91182.5317806887	-82923.0650319214	-0.158059884367885
55	1821776	1739555.73745449	91799.8088902114	82220.2625455126	0.00675873584822836
56	1741365	1781923.57523916	50619.5636596885	-40558.575239164	-0.450848752998997
57	1623386	1634953.41940773	-113991.416630682	-11567.4194077305	-1.80221286015641
58	1498658	1463629.86899661	-161752.955039778	35028.1310033859	-0.522916605514228
59	1241822	1286066.64976003	-174921.488185682	-44244.6497600334	-0.144171435539331
60	1136029	1113060.38478289	-173326.690795354	22968.6152171129	0.0174653046580764

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$resid)
myfit <- mylevel+myseas
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time')
grid()
dev.off()
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='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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code