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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 29 Dec 2010 22:09:38 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/29/t12936604600dff4kxg6eijc4r.htm/, Retrieved Fri, 03 May 2024 08:20:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117161, Retrieved Fri, 03 May 2024 08:20:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Exponential Smoot...] [2010-12-28 02:37:58] [17d39bb3ec485d4ce196f61215d11ba1]
-         [Exponential Smoothing] [Exponential Smoot...] [2010-12-29 22:09:38] [5d543145eb38bc0730d6bf6b0284f470] [Current]
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Dataseries X:
20503
22885
26217
26583
27751
28158
27373
28367
26851
26733
26849
26733
27951
29781
32914
33488
35652
36488
35387
35676
34844
32447
31068
29010
29812
30951
32974
32936
34012
32946
31948
30599
27691
25073
23406
22248
22896
25317
26558
26471
27543
26198
24725
25005
23462
20780
19815
19761
21454
23899
24939
23580
24562
24696
23785
23812
21917
19713
19282
18788
21453
24482
27474
27264
27349
30632
29429
30084
26290
24379
23335
21346
21106
24514
28353
30805
31348
34556
33855
34787
32529
29998
29257
28155
30466
35704
39327
39351
42234
43630
43722
43121
37985
37135
34646
33026
35087
38846
42013
43908
42868
44423
44167
43636
44382
42142
43452
36912
42413
45344
44873
47510
49554
47369
45998
48140
48441
44928
40454
38661
37246
36843
36424
37594
38144
38737
34560
36080
33508
35462
33374
32110
35533
35532
37903
36763
40399
44164
44496
43110
43880
43930
44327




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117161&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117161&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117161&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.957106985347542
beta0.0213231419809285
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.957106985347542 \tabularnewline
beta & 0.0213231419809285 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117161&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.957106985347542[/C][/ROW]
[ROW][C]beta[/C][C]0.0213231419809285[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117161&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117161&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.957106985347542
beta0.0213231419809285
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132795124203.10657051283747.89342948717
142978129654.6202551849126.379744815073
153291432946.412119304-32.4121193039537
163348833593.0200307428-105.020030742766
173565235915.2410986994-263.241098699371
183648836895.8636472486-407.86364724861
193538734286.11804762071100.88195237935
203567636417.4957808124-741.495780812395
213484434291.6797450762552.32025492382
223244734813.0811183624-2366.0811183624
233106832676.8052514774-1608.8052514774
242901030941.1150593774-1931.11505937738
252981230347.5787971139-535.578797113856
263095131417.2352441558-466.23524415584
273297433996.1472928091-1022.14729280914
283293633533.2865375479-597.286537547945
293401235208.4510334614-1196.45103346142
303294635101.5248152055-2155.52481520546
313194830659.96423633771288.03576366226
323059932671.4316738823-2072.43167388231
332769129080.0894447366-1389.08944473662
342507327331.3798624235-2258.37986242351
352340625046.0703511283-1640.07035112833
362224822981.3960861217-733.396086121684
372289623333.2722700384-437.272270038433
382531724241.20771945541075.79228054459
392655828044.8456366518-1486.84563665182
402647126918.6438964958-447.643896495847
412754328477.5879114903-934.58791149029
422619828351.7548651247-2153.75486512472
432472523831.2288487051893.771151294939
442500525084.7917687-79.791768699979
452346223234.1860439709227.813956029069
462078022832.9944567301-2052.99445673013
471981520612.2284668622-797.228466862165
481976119251.7817676982509.218232301817
492145420689.6820866713764.317913328661
502389922721.09812873991177.90187126014
512493926423.1608238929-1484.16082389287
522358025254.77226647-1674.77226646998
532456225503.9618002243-941.961800224315
542469625204.2520675708-508.252067570837
552378522308.42280145711476.57719854289
562381224008.9855756807-196.985575680679
572191721987.9663872987-70.9663872986566
581971321125.4410414518-1412.44104145183
591928219507.1512849844-225.151284984386
601878818697.490839573790.5091604262525
612145319684.24828891721768.75171108282
622448222653.91832686331828.08167313667
632747426836.521499678637.478500321988
642726427706.3251380426-442.325138042648
652734929207.4155870462-1858.41558704625
663063228071.34588779182560.65411220821
672942928282.73656923931146.26343076072
683008429673.4414532652410.558546734756
692629028329.7832894657-2039.7832894657
702437925575.6399447567-1196.63994475665
712333524269.5158481258-934.51584812579
722134622834.6746514598-1488.67465145977
732110622389.9577075278-1283.95770752776
742451422386.09035345852127.90964654151
752835326756.39873815831596.60126184173
763080528469.25004543842335.74995456163
773134832596.5922140575-1248.59221405754
783455632274.25857478922281.74142521078
793385532192.86292607481662.13707392518
803478734091.1161300118695.883869988247
813252932966.6240006515-437.624000651507
822999831865.9628984149-1867.96289841495
832925729998.7329284109-741.732928410947
842815528798.7492071101-643.749207110133
853046629262.85405756711203.14594243286
863570431927.87120402343776.12879597661
873932738028.6649060471298.33509395298
883935139657.4133971206-306.413397120552
894223441217.92216001091016.07783998913
904363043376.5081197733253.491880226655
914372241447.85179537362274.14820462636
924312144023.4776915287-902.477691528664
933798541421.0008466682-3436.00084666823
943713537428.4661847129-293.466184712888
953464637187.8839885004-2541.88398850036
963302634303.8060686305-1277.8060686305
973508734261.9695397592825.030460240792
983884636689.43589895012156.56410104987
994201341114.7831357914898.216864208553
1004390842264.50760864071643.49239135929
1014286845760.5696005895-2892.5696005895
1024442344078.2415818128344.758418187201
1034416742258.26115630711908.7388436929
1044363644275.0906888206-639.090688820557
1054438241748.60282867082633.3971713292
1064214243756.3615625213-1614.36156252131
1074345242184.57959562991267.4204043701
1083691243107.8557682616-6195.85576826164
1094241338455.96849597663957.03150402343
1104534444008.97993603311335.02006396691
1114487347648.0523369253-2775.05233692529
1124751045293.07130173962216.92869826043
1134955449134.1497955218419.850204478171
1144736950819.3642618563-3450.36426185632
1154599845415.0199694621582.980030537889
1164814046007.5063306292132.49366937105
1174844146284.48598636512156.51401363491
1184492847654.2827542829-2726.28275428293
1194045445119.8543019029-4665.85430190287
1203866139901.1127273158-1240.11272731575
1213724640385.9124353145-3139.91243531455
1223684338847.1078568753-2004.10785687529
1233642438859.0220934941-2435.02209349412
1243759436795.584901452798.415098547994
1253814438924.9396374968-780.939637496784
1263873738993.3858705737-256.385870573657
1273456036582.7285794763-2022.72857947634
1283608034458.26333806121621.73666193877
1293350833947.5273990168-439.527399016821
1303546232270.31873897113191.68126102889
1313337435084.7196646531-1710.71966465309
1323211032669.5071767581-559.507176758118
1333553333566.32993146411966.67006853594
1343553236910.1059105796-1378.10591057956
1353790337461.7802399509441.219760049113
1363676338307.698416921-1544.69841692103
1374039938096.67238648012302.32761351993
1384416441171.53271452952992.46728547053
1394449641893.8137997332602.18620026704
1404311044545.7986950497-1435.79869504966
1414388041151.45047534672728.54952465331
1424393042858.02963940161071.97036059837
1434432743585.9473051438741.052694856175

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 27951 & 24203.1065705128 & 3747.89342948717 \tabularnewline
14 & 29781 & 29654.6202551849 & 126.379744815073 \tabularnewline
15 & 32914 & 32946.412119304 & -32.4121193039537 \tabularnewline
16 & 33488 & 33593.0200307428 & -105.020030742766 \tabularnewline
17 & 35652 & 35915.2410986994 & -263.241098699371 \tabularnewline
18 & 36488 & 36895.8636472486 & -407.86364724861 \tabularnewline
19 & 35387 & 34286.1180476207 & 1100.88195237935 \tabularnewline
20 & 35676 & 36417.4957808124 & -741.495780812395 \tabularnewline
21 & 34844 & 34291.6797450762 & 552.32025492382 \tabularnewline
22 & 32447 & 34813.0811183624 & -2366.0811183624 \tabularnewline
23 & 31068 & 32676.8052514774 & -1608.8052514774 \tabularnewline
24 & 29010 & 30941.1150593774 & -1931.11505937738 \tabularnewline
25 & 29812 & 30347.5787971139 & -535.578797113856 \tabularnewline
26 & 30951 & 31417.2352441558 & -466.23524415584 \tabularnewline
27 & 32974 & 33996.1472928091 & -1022.14729280914 \tabularnewline
28 & 32936 & 33533.2865375479 & -597.286537547945 \tabularnewline
29 & 34012 & 35208.4510334614 & -1196.45103346142 \tabularnewline
30 & 32946 & 35101.5248152055 & -2155.52481520546 \tabularnewline
31 & 31948 & 30659.9642363377 & 1288.03576366226 \tabularnewline
32 & 30599 & 32671.4316738823 & -2072.43167388231 \tabularnewline
33 & 27691 & 29080.0894447366 & -1389.08944473662 \tabularnewline
34 & 25073 & 27331.3798624235 & -2258.37986242351 \tabularnewline
35 & 23406 & 25046.0703511283 & -1640.07035112833 \tabularnewline
36 & 22248 & 22981.3960861217 & -733.396086121684 \tabularnewline
37 & 22896 & 23333.2722700384 & -437.272270038433 \tabularnewline
38 & 25317 & 24241.2077194554 & 1075.79228054459 \tabularnewline
39 & 26558 & 28044.8456366518 & -1486.84563665182 \tabularnewline
40 & 26471 & 26918.6438964958 & -447.643896495847 \tabularnewline
41 & 27543 & 28477.5879114903 & -934.58791149029 \tabularnewline
42 & 26198 & 28351.7548651247 & -2153.75486512472 \tabularnewline
43 & 24725 & 23831.2288487051 & 893.771151294939 \tabularnewline
44 & 25005 & 25084.7917687 & -79.791768699979 \tabularnewline
45 & 23462 & 23234.1860439709 & 227.813956029069 \tabularnewline
46 & 20780 & 22832.9944567301 & -2052.99445673013 \tabularnewline
47 & 19815 & 20612.2284668622 & -797.228466862165 \tabularnewline
48 & 19761 & 19251.7817676982 & 509.218232301817 \tabularnewline
49 & 21454 & 20689.6820866713 & 764.317913328661 \tabularnewline
50 & 23899 & 22721.0981287399 & 1177.90187126014 \tabularnewline
51 & 24939 & 26423.1608238929 & -1484.16082389287 \tabularnewline
52 & 23580 & 25254.77226647 & -1674.77226646998 \tabularnewline
53 & 24562 & 25503.9618002243 & -941.961800224315 \tabularnewline
54 & 24696 & 25204.2520675708 & -508.252067570837 \tabularnewline
55 & 23785 & 22308.4228014571 & 1476.57719854289 \tabularnewline
56 & 23812 & 24008.9855756807 & -196.985575680679 \tabularnewline
57 & 21917 & 21987.9663872987 & -70.9663872986566 \tabularnewline
58 & 19713 & 21125.4410414518 & -1412.44104145183 \tabularnewline
59 & 19282 & 19507.1512849844 & -225.151284984386 \tabularnewline
60 & 18788 & 18697.4908395737 & 90.5091604262525 \tabularnewline
61 & 21453 & 19684.2482889172 & 1768.75171108282 \tabularnewline
62 & 24482 & 22653.9183268633 & 1828.08167313667 \tabularnewline
63 & 27474 & 26836.521499678 & 637.478500321988 \tabularnewline
64 & 27264 & 27706.3251380426 & -442.325138042648 \tabularnewline
65 & 27349 & 29207.4155870462 & -1858.41558704625 \tabularnewline
66 & 30632 & 28071.3458877918 & 2560.65411220821 \tabularnewline
67 & 29429 & 28282.7365692393 & 1146.26343076072 \tabularnewline
68 & 30084 & 29673.4414532652 & 410.558546734756 \tabularnewline
69 & 26290 & 28329.7832894657 & -2039.7832894657 \tabularnewline
70 & 24379 & 25575.6399447567 & -1196.63994475665 \tabularnewline
71 & 23335 & 24269.5158481258 & -934.51584812579 \tabularnewline
72 & 21346 & 22834.6746514598 & -1488.67465145977 \tabularnewline
73 & 21106 & 22389.9577075278 & -1283.95770752776 \tabularnewline
74 & 24514 & 22386.0903534585 & 2127.90964654151 \tabularnewline
75 & 28353 & 26756.3987381583 & 1596.60126184173 \tabularnewline
76 & 30805 & 28469.2500454384 & 2335.74995456163 \tabularnewline
77 & 31348 & 32596.5922140575 & -1248.59221405754 \tabularnewline
78 & 34556 & 32274.2585747892 & 2281.74142521078 \tabularnewline
79 & 33855 & 32192.8629260748 & 1662.13707392518 \tabularnewline
80 & 34787 & 34091.1161300118 & 695.883869988247 \tabularnewline
81 & 32529 & 32966.6240006515 & -437.624000651507 \tabularnewline
82 & 29998 & 31865.9628984149 & -1867.96289841495 \tabularnewline
83 & 29257 & 29998.7329284109 & -741.732928410947 \tabularnewline
84 & 28155 & 28798.7492071101 & -643.749207110133 \tabularnewline
85 & 30466 & 29262.8540575671 & 1203.14594243286 \tabularnewline
86 & 35704 & 31927.8712040234 & 3776.12879597661 \tabularnewline
87 & 39327 & 38028.664906047 & 1298.33509395298 \tabularnewline
88 & 39351 & 39657.4133971206 & -306.413397120552 \tabularnewline
89 & 42234 & 41217.9221600109 & 1016.07783998913 \tabularnewline
90 & 43630 & 43376.5081197733 & 253.491880226655 \tabularnewline
91 & 43722 & 41447.8517953736 & 2274.14820462636 \tabularnewline
92 & 43121 & 44023.4776915287 & -902.477691528664 \tabularnewline
93 & 37985 & 41421.0008466682 & -3436.00084666823 \tabularnewline
94 & 37135 & 37428.4661847129 & -293.466184712888 \tabularnewline
95 & 34646 & 37187.8839885004 & -2541.88398850036 \tabularnewline
96 & 33026 & 34303.8060686305 & -1277.8060686305 \tabularnewline
97 & 35087 & 34261.9695397592 & 825.030460240792 \tabularnewline
98 & 38846 & 36689.4358989501 & 2156.56410104987 \tabularnewline
99 & 42013 & 41114.7831357914 & 898.216864208553 \tabularnewline
100 & 43908 & 42264.5076086407 & 1643.49239135929 \tabularnewline
101 & 42868 & 45760.5696005895 & -2892.5696005895 \tabularnewline
102 & 44423 & 44078.2415818128 & 344.758418187201 \tabularnewline
103 & 44167 & 42258.2611563071 & 1908.7388436929 \tabularnewline
104 & 43636 & 44275.0906888206 & -639.090688820557 \tabularnewline
105 & 44382 & 41748.6028286708 & 2633.3971713292 \tabularnewline
106 & 42142 & 43756.3615625213 & -1614.36156252131 \tabularnewline
107 & 43452 & 42184.5795956299 & 1267.4204043701 \tabularnewline
108 & 36912 & 43107.8557682616 & -6195.85576826164 \tabularnewline
109 & 42413 & 38455.9684959766 & 3957.03150402343 \tabularnewline
110 & 45344 & 44008.9799360331 & 1335.02006396691 \tabularnewline
111 & 44873 & 47648.0523369253 & -2775.05233692529 \tabularnewline
112 & 47510 & 45293.0713017396 & 2216.92869826043 \tabularnewline
113 & 49554 & 49134.1497955218 & 419.850204478171 \tabularnewline
114 & 47369 & 50819.3642618563 & -3450.36426185632 \tabularnewline
115 & 45998 & 45415.0199694621 & 582.980030537889 \tabularnewline
116 & 48140 & 46007.506330629 & 2132.49366937105 \tabularnewline
117 & 48441 & 46284.4859863651 & 2156.51401363491 \tabularnewline
118 & 44928 & 47654.2827542829 & -2726.28275428293 \tabularnewline
119 & 40454 & 45119.8543019029 & -4665.85430190287 \tabularnewline
120 & 38661 & 39901.1127273158 & -1240.11272731575 \tabularnewline
121 & 37246 & 40385.9124353145 & -3139.91243531455 \tabularnewline
122 & 36843 & 38847.1078568753 & -2004.10785687529 \tabularnewline
123 & 36424 & 38859.0220934941 & -2435.02209349412 \tabularnewline
124 & 37594 & 36795.584901452 & 798.415098547994 \tabularnewline
125 & 38144 & 38924.9396374968 & -780.939637496784 \tabularnewline
126 & 38737 & 38993.3858705737 & -256.385870573657 \tabularnewline
127 & 34560 & 36582.7285794763 & -2022.72857947634 \tabularnewline
128 & 36080 & 34458.2633380612 & 1621.73666193877 \tabularnewline
129 & 33508 & 33947.5273990168 & -439.527399016821 \tabularnewline
130 & 35462 & 32270.3187389711 & 3191.68126102889 \tabularnewline
131 & 33374 & 35084.7196646531 & -1710.71966465309 \tabularnewline
132 & 32110 & 32669.5071767581 & -559.507176758118 \tabularnewline
133 & 35533 & 33566.3299314641 & 1966.67006853594 \tabularnewline
134 & 35532 & 36910.1059105796 & -1378.10591057956 \tabularnewline
135 & 37903 & 37461.7802399509 & 441.219760049113 \tabularnewline
136 & 36763 & 38307.698416921 & -1544.69841692103 \tabularnewline
137 & 40399 & 38096.6723864801 & 2302.32761351993 \tabularnewline
138 & 44164 & 41171.5327145295 & 2992.46728547053 \tabularnewline
139 & 44496 & 41893.813799733 & 2602.18620026704 \tabularnewline
140 & 43110 & 44545.7986950497 & -1435.79869504966 \tabularnewline
141 & 43880 & 41151.4504753467 & 2728.54952465331 \tabularnewline
142 & 43930 & 42858.0296394016 & 1071.97036059837 \tabularnewline
143 & 44327 & 43585.9473051438 & 741.052694856175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117161&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]27951[/C][C]24203.1065705128[/C][C]3747.89342948717[/C][/ROW]
[ROW][C]14[/C][C]29781[/C][C]29654.6202551849[/C][C]126.379744815073[/C][/ROW]
[ROW][C]15[/C][C]32914[/C][C]32946.412119304[/C][C]-32.4121193039537[/C][/ROW]
[ROW][C]16[/C][C]33488[/C][C]33593.0200307428[/C][C]-105.020030742766[/C][/ROW]
[ROW][C]17[/C][C]35652[/C][C]35915.2410986994[/C][C]-263.241098699371[/C][/ROW]
[ROW][C]18[/C][C]36488[/C][C]36895.8636472486[/C][C]-407.86364724861[/C][/ROW]
[ROW][C]19[/C][C]35387[/C][C]34286.1180476207[/C][C]1100.88195237935[/C][/ROW]
[ROW][C]20[/C][C]35676[/C][C]36417.4957808124[/C][C]-741.495780812395[/C][/ROW]
[ROW][C]21[/C][C]34844[/C][C]34291.6797450762[/C][C]552.32025492382[/C][/ROW]
[ROW][C]22[/C][C]32447[/C][C]34813.0811183624[/C][C]-2366.0811183624[/C][/ROW]
[ROW][C]23[/C][C]31068[/C][C]32676.8052514774[/C][C]-1608.8052514774[/C][/ROW]
[ROW][C]24[/C][C]29010[/C][C]30941.1150593774[/C][C]-1931.11505937738[/C][/ROW]
[ROW][C]25[/C][C]29812[/C][C]30347.5787971139[/C][C]-535.578797113856[/C][/ROW]
[ROW][C]26[/C][C]30951[/C][C]31417.2352441558[/C][C]-466.23524415584[/C][/ROW]
[ROW][C]27[/C][C]32974[/C][C]33996.1472928091[/C][C]-1022.14729280914[/C][/ROW]
[ROW][C]28[/C][C]32936[/C][C]33533.2865375479[/C][C]-597.286537547945[/C][/ROW]
[ROW][C]29[/C][C]34012[/C][C]35208.4510334614[/C][C]-1196.45103346142[/C][/ROW]
[ROW][C]30[/C][C]32946[/C][C]35101.5248152055[/C][C]-2155.52481520546[/C][/ROW]
[ROW][C]31[/C][C]31948[/C][C]30659.9642363377[/C][C]1288.03576366226[/C][/ROW]
[ROW][C]32[/C][C]30599[/C][C]32671.4316738823[/C][C]-2072.43167388231[/C][/ROW]
[ROW][C]33[/C][C]27691[/C][C]29080.0894447366[/C][C]-1389.08944473662[/C][/ROW]
[ROW][C]34[/C][C]25073[/C][C]27331.3798624235[/C][C]-2258.37986242351[/C][/ROW]
[ROW][C]35[/C][C]23406[/C][C]25046.0703511283[/C][C]-1640.07035112833[/C][/ROW]
[ROW][C]36[/C][C]22248[/C][C]22981.3960861217[/C][C]-733.396086121684[/C][/ROW]
[ROW][C]37[/C][C]22896[/C][C]23333.2722700384[/C][C]-437.272270038433[/C][/ROW]
[ROW][C]38[/C][C]25317[/C][C]24241.2077194554[/C][C]1075.79228054459[/C][/ROW]
[ROW][C]39[/C][C]26558[/C][C]28044.8456366518[/C][C]-1486.84563665182[/C][/ROW]
[ROW][C]40[/C][C]26471[/C][C]26918.6438964958[/C][C]-447.643896495847[/C][/ROW]
[ROW][C]41[/C][C]27543[/C][C]28477.5879114903[/C][C]-934.58791149029[/C][/ROW]
[ROW][C]42[/C][C]26198[/C][C]28351.7548651247[/C][C]-2153.75486512472[/C][/ROW]
[ROW][C]43[/C][C]24725[/C][C]23831.2288487051[/C][C]893.771151294939[/C][/ROW]
[ROW][C]44[/C][C]25005[/C][C]25084.7917687[/C][C]-79.791768699979[/C][/ROW]
[ROW][C]45[/C][C]23462[/C][C]23234.1860439709[/C][C]227.813956029069[/C][/ROW]
[ROW][C]46[/C][C]20780[/C][C]22832.9944567301[/C][C]-2052.99445673013[/C][/ROW]
[ROW][C]47[/C][C]19815[/C][C]20612.2284668622[/C][C]-797.228466862165[/C][/ROW]
[ROW][C]48[/C][C]19761[/C][C]19251.7817676982[/C][C]509.218232301817[/C][/ROW]
[ROW][C]49[/C][C]21454[/C][C]20689.6820866713[/C][C]764.317913328661[/C][/ROW]
[ROW][C]50[/C][C]23899[/C][C]22721.0981287399[/C][C]1177.90187126014[/C][/ROW]
[ROW][C]51[/C][C]24939[/C][C]26423.1608238929[/C][C]-1484.16082389287[/C][/ROW]
[ROW][C]52[/C][C]23580[/C][C]25254.77226647[/C][C]-1674.77226646998[/C][/ROW]
[ROW][C]53[/C][C]24562[/C][C]25503.9618002243[/C][C]-941.961800224315[/C][/ROW]
[ROW][C]54[/C][C]24696[/C][C]25204.2520675708[/C][C]-508.252067570837[/C][/ROW]
[ROW][C]55[/C][C]23785[/C][C]22308.4228014571[/C][C]1476.57719854289[/C][/ROW]
[ROW][C]56[/C][C]23812[/C][C]24008.9855756807[/C][C]-196.985575680679[/C][/ROW]
[ROW][C]57[/C][C]21917[/C][C]21987.9663872987[/C][C]-70.9663872986566[/C][/ROW]
[ROW][C]58[/C][C]19713[/C][C]21125.4410414518[/C][C]-1412.44104145183[/C][/ROW]
[ROW][C]59[/C][C]19282[/C][C]19507.1512849844[/C][C]-225.151284984386[/C][/ROW]
[ROW][C]60[/C][C]18788[/C][C]18697.4908395737[/C][C]90.5091604262525[/C][/ROW]
[ROW][C]61[/C][C]21453[/C][C]19684.2482889172[/C][C]1768.75171108282[/C][/ROW]
[ROW][C]62[/C][C]24482[/C][C]22653.9183268633[/C][C]1828.08167313667[/C][/ROW]
[ROW][C]63[/C][C]27474[/C][C]26836.521499678[/C][C]637.478500321988[/C][/ROW]
[ROW][C]64[/C][C]27264[/C][C]27706.3251380426[/C][C]-442.325138042648[/C][/ROW]
[ROW][C]65[/C][C]27349[/C][C]29207.4155870462[/C][C]-1858.41558704625[/C][/ROW]
[ROW][C]66[/C][C]30632[/C][C]28071.3458877918[/C][C]2560.65411220821[/C][/ROW]
[ROW][C]67[/C][C]29429[/C][C]28282.7365692393[/C][C]1146.26343076072[/C][/ROW]
[ROW][C]68[/C][C]30084[/C][C]29673.4414532652[/C][C]410.558546734756[/C][/ROW]
[ROW][C]69[/C][C]26290[/C][C]28329.7832894657[/C][C]-2039.7832894657[/C][/ROW]
[ROW][C]70[/C][C]24379[/C][C]25575.6399447567[/C][C]-1196.63994475665[/C][/ROW]
[ROW][C]71[/C][C]23335[/C][C]24269.5158481258[/C][C]-934.51584812579[/C][/ROW]
[ROW][C]72[/C][C]21346[/C][C]22834.6746514598[/C][C]-1488.67465145977[/C][/ROW]
[ROW][C]73[/C][C]21106[/C][C]22389.9577075278[/C][C]-1283.95770752776[/C][/ROW]
[ROW][C]74[/C][C]24514[/C][C]22386.0903534585[/C][C]2127.90964654151[/C][/ROW]
[ROW][C]75[/C][C]28353[/C][C]26756.3987381583[/C][C]1596.60126184173[/C][/ROW]
[ROW][C]76[/C][C]30805[/C][C]28469.2500454384[/C][C]2335.74995456163[/C][/ROW]
[ROW][C]77[/C][C]31348[/C][C]32596.5922140575[/C][C]-1248.59221405754[/C][/ROW]
[ROW][C]78[/C][C]34556[/C][C]32274.2585747892[/C][C]2281.74142521078[/C][/ROW]
[ROW][C]79[/C][C]33855[/C][C]32192.8629260748[/C][C]1662.13707392518[/C][/ROW]
[ROW][C]80[/C][C]34787[/C][C]34091.1161300118[/C][C]695.883869988247[/C][/ROW]
[ROW][C]81[/C][C]32529[/C][C]32966.6240006515[/C][C]-437.624000651507[/C][/ROW]
[ROW][C]82[/C][C]29998[/C][C]31865.9628984149[/C][C]-1867.96289841495[/C][/ROW]
[ROW][C]83[/C][C]29257[/C][C]29998.7329284109[/C][C]-741.732928410947[/C][/ROW]
[ROW][C]84[/C][C]28155[/C][C]28798.7492071101[/C][C]-643.749207110133[/C][/ROW]
[ROW][C]85[/C][C]30466[/C][C]29262.8540575671[/C][C]1203.14594243286[/C][/ROW]
[ROW][C]86[/C][C]35704[/C][C]31927.8712040234[/C][C]3776.12879597661[/C][/ROW]
[ROW][C]87[/C][C]39327[/C][C]38028.664906047[/C][C]1298.33509395298[/C][/ROW]
[ROW][C]88[/C][C]39351[/C][C]39657.4133971206[/C][C]-306.413397120552[/C][/ROW]
[ROW][C]89[/C][C]42234[/C][C]41217.9221600109[/C][C]1016.07783998913[/C][/ROW]
[ROW][C]90[/C][C]43630[/C][C]43376.5081197733[/C][C]253.491880226655[/C][/ROW]
[ROW][C]91[/C][C]43722[/C][C]41447.8517953736[/C][C]2274.14820462636[/C][/ROW]
[ROW][C]92[/C][C]43121[/C][C]44023.4776915287[/C][C]-902.477691528664[/C][/ROW]
[ROW][C]93[/C][C]37985[/C][C]41421.0008466682[/C][C]-3436.00084666823[/C][/ROW]
[ROW][C]94[/C][C]37135[/C][C]37428.4661847129[/C][C]-293.466184712888[/C][/ROW]
[ROW][C]95[/C][C]34646[/C][C]37187.8839885004[/C][C]-2541.88398850036[/C][/ROW]
[ROW][C]96[/C][C]33026[/C][C]34303.8060686305[/C][C]-1277.8060686305[/C][/ROW]
[ROW][C]97[/C][C]35087[/C][C]34261.9695397592[/C][C]825.030460240792[/C][/ROW]
[ROW][C]98[/C][C]38846[/C][C]36689.4358989501[/C][C]2156.56410104987[/C][/ROW]
[ROW][C]99[/C][C]42013[/C][C]41114.7831357914[/C][C]898.216864208553[/C][/ROW]
[ROW][C]100[/C][C]43908[/C][C]42264.5076086407[/C][C]1643.49239135929[/C][/ROW]
[ROW][C]101[/C][C]42868[/C][C]45760.5696005895[/C][C]-2892.5696005895[/C][/ROW]
[ROW][C]102[/C][C]44423[/C][C]44078.2415818128[/C][C]344.758418187201[/C][/ROW]
[ROW][C]103[/C][C]44167[/C][C]42258.2611563071[/C][C]1908.7388436929[/C][/ROW]
[ROW][C]104[/C][C]43636[/C][C]44275.0906888206[/C][C]-639.090688820557[/C][/ROW]
[ROW][C]105[/C][C]44382[/C][C]41748.6028286708[/C][C]2633.3971713292[/C][/ROW]
[ROW][C]106[/C][C]42142[/C][C]43756.3615625213[/C][C]-1614.36156252131[/C][/ROW]
[ROW][C]107[/C][C]43452[/C][C]42184.5795956299[/C][C]1267.4204043701[/C][/ROW]
[ROW][C]108[/C][C]36912[/C][C]43107.8557682616[/C][C]-6195.85576826164[/C][/ROW]
[ROW][C]109[/C][C]42413[/C][C]38455.9684959766[/C][C]3957.03150402343[/C][/ROW]
[ROW][C]110[/C][C]45344[/C][C]44008.9799360331[/C][C]1335.02006396691[/C][/ROW]
[ROW][C]111[/C][C]44873[/C][C]47648.0523369253[/C][C]-2775.05233692529[/C][/ROW]
[ROW][C]112[/C][C]47510[/C][C]45293.0713017396[/C][C]2216.92869826043[/C][/ROW]
[ROW][C]113[/C][C]49554[/C][C]49134.1497955218[/C][C]419.850204478171[/C][/ROW]
[ROW][C]114[/C][C]47369[/C][C]50819.3642618563[/C][C]-3450.36426185632[/C][/ROW]
[ROW][C]115[/C][C]45998[/C][C]45415.0199694621[/C][C]582.980030537889[/C][/ROW]
[ROW][C]116[/C][C]48140[/C][C]46007.506330629[/C][C]2132.49366937105[/C][/ROW]
[ROW][C]117[/C][C]48441[/C][C]46284.4859863651[/C][C]2156.51401363491[/C][/ROW]
[ROW][C]118[/C][C]44928[/C][C]47654.2827542829[/C][C]-2726.28275428293[/C][/ROW]
[ROW][C]119[/C][C]40454[/C][C]45119.8543019029[/C][C]-4665.85430190287[/C][/ROW]
[ROW][C]120[/C][C]38661[/C][C]39901.1127273158[/C][C]-1240.11272731575[/C][/ROW]
[ROW][C]121[/C][C]37246[/C][C]40385.9124353145[/C][C]-3139.91243531455[/C][/ROW]
[ROW][C]122[/C][C]36843[/C][C]38847.1078568753[/C][C]-2004.10785687529[/C][/ROW]
[ROW][C]123[/C][C]36424[/C][C]38859.0220934941[/C][C]-2435.02209349412[/C][/ROW]
[ROW][C]124[/C][C]37594[/C][C]36795.584901452[/C][C]798.415098547994[/C][/ROW]
[ROW][C]125[/C][C]38144[/C][C]38924.9396374968[/C][C]-780.939637496784[/C][/ROW]
[ROW][C]126[/C][C]38737[/C][C]38993.3858705737[/C][C]-256.385870573657[/C][/ROW]
[ROW][C]127[/C][C]34560[/C][C]36582.7285794763[/C][C]-2022.72857947634[/C][/ROW]
[ROW][C]128[/C][C]36080[/C][C]34458.2633380612[/C][C]1621.73666193877[/C][/ROW]
[ROW][C]129[/C][C]33508[/C][C]33947.5273990168[/C][C]-439.527399016821[/C][/ROW]
[ROW][C]130[/C][C]35462[/C][C]32270.3187389711[/C][C]3191.68126102889[/C][/ROW]
[ROW][C]131[/C][C]33374[/C][C]35084.7196646531[/C][C]-1710.71966465309[/C][/ROW]
[ROW][C]132[/C][C]32110[/C][C]32669.5071767581[/C][C]-559.507176758118[/C][/ROW]
[ROW][C]133[/C][C]35533[/C][C]33566.3299314641[/C][C]1966.67006853594[/C][/ROW]
[ROW][C]134[/C][C]35532[/C][C]36910.1059105796[/C][C]-1378.10591057956[/C][/ROW]
[ROW][C]135[/C][C]37903[/C][C]37461.7802399509[/C][C]441.219760049113[/C][/ROW]
[ROW][C]136[/C][C]36763[/C][C]38307.698416921[/C][C]-1544.69841692103[/C][/ROW]
[ROW][C]137[/C][C]40399[/C][C]38096.6723864801[/C][C]2302.32761351993[/C][/ROW]
[ROW][C]138[/C][C]44164[/C][C]41171.5327145295[/C][C]2992.46728547053[/C][/ROW]
[ROW][C]139[/C][C]44496[/C][C]41893.813799733[/C][C]2602.18620026704[/C][/ROW]
[ROW][C]140[/C][C]43110[/C][C]44545.7986950497[/C][C]-1435.79869504966[/C][/ROW]
[ROW][C]141[/C][C]43880[/C][C]41151.4504753467[/C][C]2728.54952465331[/C][/ROW]
[ROW][C]142[/C][C]43930[/C][C]42858.0296394016[/C][C]1071.97036059837[/C][/ROW]
[ROW][C]143[/C][C]44327[/C][C]43585.9473051438[/C][C]741.052694856175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117161&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117161&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132795124203.10657051283747.89342948717
142978129654.6202551849126.379744815073
153291432946.412119304-32.4121193039537
163348833593.0200307428-105.020030742766
173565235915.2410986994-263.241098699371
183648836895.8636472486-407.86364724861
193538734286.11804762071100.88195237935
203567636417.4957808124-741.495780812395
213484434291.6797450762552.32025492382
223244734813.0811183624-2366.0811183624
233106832676.8052514774-1608.8052514774
242901030941.1150593774-1931.11505937738
252981230347.5787971139-535.578797113856
263095131417.2352441558-466.23524415584
273297433996.1472928091-1022.14729280914
283293633533.2865375479-597.286537547945
293401235208.4510334614-1196.45103346142
303294635101.5248152055-2155.52481520546
313194830659.96423633771288.03576366226
323059932671.4316738823-2072.43167388231
332769129080.0894447366-1389.08944473662
342507327331.3798624235-2258.37986242351
352340625046.0703511283-1640.07035112833
362224822981.3960861217-733.396086121684
372289623333.2722700384-437.272270038433
382531724241.20771945541075.79228054459
392655828044.8456366518-1486.84563665182
402647126918.6438964958-447.643896495847
412754328477.5879114903-934.58791149029
422619828351.7548651247-2153.75486512472
432472523831.2288487051893.771151294939
442500525084.7917687-79.791768699979
452346223234.1860439709227.813956029069
462078022832.9944567301-2052.99445673013
471981520612.2284668622-797.228466862165
481976119251.7817676982509.218232301817
492145420689.6820866713764.317913328661
502389922721.09812873991177.90187126014
512493926423.1608238929-1484.16082389287
522358025254.77226647-1674.77226646998
532456225503.9618002243-941.961800224315
542469625204.2520675708-508.252067570837
552378522308.42280145711476.57719854289
562381224008.9855756807-196.985575680679
572191721987.9663872987-70.9663872986566
581971321125.4410414518-1412.44104145183
591928219507.1512849844-225.151284984386
601878818697.490839573790.5091604262525
612145319684.24828891721768.75171108282
622448222653.91832686331828.08167313667
632747426836.521499678637.478500321988
642726427706.3251380426-442.325138042648
652734929207.4155870462-1858.41558704625
663063228071.34588779182560.65411220821
672942928282.73656923931146.26343076072
683008429673.4414532652410.558546734756
692629028329.7832894657-2039.7832894657
702437925575.6399447567-1196.63994475665
712333524269.5158481258-934.51584812579
722134622834.6746514598-1488.67465145977
732110622389.9577075278-1283.95770752776
742451422386.09035345852127.90964654151
752835326756.39873815831596.60126184173
763080528469.25004543842335.74995456163
773134832596.5922140575-1248.59221405754
783455632274.25857478922281.74142521078
793385532192.86292607481662.13707392518
803478734091.1161300118695.883869988247
813252932966.6240006515-437.624000651507
822999831865.9628984149-1867.96289841495
832925729998.7329284109-741.732928410947
842815528798.7492071101-643.749207110133
853046629262.85405756711203.14594243286
863570431927.87120402343776.12879597661
873932738028.6649060471298.33509395298
883935139657.4133971206-306.413397120552
894223441217.92216001091016.07783998913
904363043376.5081197733253.491880226655
914372241447.85179537362274.14820462636
924312144023.4776915287-902.477691528664
933798541421.0008466682-3436.00084666823
943713537428.4661847129-293.466184712888
953464637187.8839885004-2541.88398850036
963302634303.8060686305-1277.8060686305
973508734261.9695397592825.030460240792
983884636689.43589895012156.56410104987
994201341114.7831357914898.216864208553
1004390842264.50760864071643.49239135929
1014286845760.5696005895-2892.5696005895
1024442344078.2415818128344.758418187201
1034416742258.26115630711908.7388436929
1044363644275.0906888206-639.090688820557
1054438241748.60282867082633.3971713292
1064214243756.3615625213-1614.36156252131
1074345242184.57959562991267.4204043701
1083691243107.8557682616-6195.85576826164
1094241338455.96849597663957.03150402343
1104534444008.97993603311335.02006396691
1114487347648.0523369253-2775.05233692529
1124751045293.07130173962216.92869826043
1134955449134.1497955218419.850204478171
1144736950819.3642618563-3450.36426185632
1154599845415.0199694621582.980030537889
1164814046007.5063306292132.49366937105
1174844146284.48598636512156.51401363491
1184492847654.2827542829-2726.28275428293
1194045445119.8543019029-4665.85430190287
1203866139901.1127273158-1240.11272731575
1213724640385.9124353145-3139.91243531455
1223684338847.1078568753-2004.10785687529
1233642438859.0220934941-2435.02209349412
1243759436795.584901452798.415098547994
1253814438924.9396374968-780.939637496784
1263873738993.3858705737-256.385870573657
1273456036582.7285794763-2022.72857947634
1283608034458.26333806121621.73666193877
1293350833947.5273990168-439.527399016821
1303546232270.31873897113191.68126102889
1313337435084.7196646531-1710.71966465309
1323211032669.5071767581-559.507176758118
1333553333566.32993146411966.67006853594
1343553236910.1059105796-1378.10591057956
1353790337461.7802399509441.219760049113
1363676338307.698416921-1544.69841692103
1374039938096.67238648012302.32761351993
1384416441171.53271452952992.46728547053
1394449641893.8137997332602.18620026704
1404311044545.7986950497-1435.79869504966
1414388041151.45047534672728.54952465331
1424393042858.02963940161071.97036059837
1434432743585.9473051438741.052694856175







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
14443769.344912836440271.368608504647267.3212171682
14545524.072640035640632.485042298350415.6602377729
14647015.971979834141006.586154146953025.3578055213
14749166.707124907142180.914599925556152.4996498887
14849698.173783598241823.939885864457572.407681332
14951355.149976849242652.868811896760057.4311418018
15052433.60155132442947.300699853161919.9024027949
15150391.52202589440154.609833346260628.4342184417
15250443.11926020739481.673538799761404.5649816143
15348694.292262093337029.093605815760359.490918371
15447755.303073923935403.166981383360107.4391664646
15547458.160157942334432.850026219760483.4702896649

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
144 & 43769.3449128364 & 40271.3686085046 & 47267.3212171682 \tabularnewline
145 & 45524.0726400356 & 40632.4850422983 & 50415.6602377729 \tabularnewline
146 & 47015.9719798341 & 41006.5861541469 & 53025.3578055213 \tabularnewline
147 & 49166.7071249071 & 42180.9145999255 & 56152.4996498887 \tabularnewline
148 & 49698.1737835982 & 41823.9398858644 & 57572.407681332 \tabularnewline
149 & 51355.1499768492 & 42652.8688118967 & 60057.4311418018 \tabularnewline
150 & 52433.601551324 & 42947.3006998531 & 61919.9024027949 \tabularnewline
151 & 50391.522025894 & 40154.6098333462 & 60628.4342184417 \tabularnewline
152 & 50443.119260207 & 39481.6735387997 & 61404.5649816143 \tabularnewline
153 & 48694.2922620933 & 37029.0936058157 & 60359.490918371 \tabularnewline
154 & 47755.3030739239 & 35403.1669813833 & 60107.4391664646 \tabularnewline
155 & 47458.1601579423 & 34432.8500262197 & 60483.4702896649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117161&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]144[/C][C]43769.3449128364[/C][C]40271.3686085046[/C][C]47267.3212171682[/C][/ROW]
[ROW][C]145[/C][C]45524.0726400356[/C][C]40632.4850422983[/C][C]50415.6602377729[/C][/ROW]
[ROW][C]146[/C][C]47015.9719798341[/C][C]41006.5861541469[/C][C]53025.3578055213[/C][/ROW]
[ROW][C]147[/C][C]49166.7071249071[/C][C]42180.9145999255[/C][C]56152.4996498887[/C][/ROW]
[ROW][C]148[/C][C]49698.1737835982[/C][C]41823.9398858644[/C][C]57572.407681332[/C][/ROW]
[ROW][C]149[/C][C]51355.1499768492[/C][C]42652.8688118967[/C][C]60057.4311418018[/C][/ROW]
[ROW][C]150[/C][C]52433.601551324[/C][C]42947.3006998531[/C][C]61919.9024027949[/C][/ROW]
[ROW][C]151[/C][C]50391.522025894[/C][C]40154.6098333462[/C][C]60628.4342184417[/C][/ROW]
[ROW][C]152[/C][C]50443.119260207[/C][C]39481.6735387997[/C][C]61404.5649816143[/C][/ROW]
[ROW][C]153[/C][C]48694.2922620933[/C][C]37029.0936058157[/C][C]60359.490918371[/C][/ROW]
[ROW][C]154[/C][C]47755.3030739239[/C][C]35403.1669813833[/C][C]60107.4391664646[/C][/ROW]
[ROW][C]155[/C][C]47458.1601579423[/C][C]34432.8500262197[/C][C]60483.4702896649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117161&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117161&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
14443769.344912836440271.368608504647267.3212171682
14545524.072640035640632.485042298350415.6602377729
14647015.971979834141006.586154146953025.3578055213
14749166.707124907142180.914599925556152.4996498887
14849698.173783598241823.939885864457572.407681332
14951355.149976849242652.868811896760057.4311418018
15052433.60155132442947.300699853161919.9024027949
15150391.52202589440154.609833346260628.4342184417
15250443.11926020739481.673538799761404.5649816143
15348694.292262093337029.093605815760359.490918371
15447755.303073923935403.166981383360107.4391664646
15547458.160157942334432.850026219760483.4702896649



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')