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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 28 Dec 2010 02:37:58 +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/28/t1293503965od9kzj67rhkq3l7.htm/, Retrieved Sun, 05 May 2024 05:02:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116210, Retrieved Sun, 05 May 2024 05:02:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
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] [63a115f47699ab31b1a302b9539c58a2] [Current]
-         [Exponential Smoothing] [Exponential Smoot...] [2010-12-29 22:09:38] [442b6d00ecbe55ac6a674160c9c5510a]
-         [Exponential Smoothing] [] [2010-12-29 22:36:06] [c420bdd199bcbe079f7d532ca3855317]
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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'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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116210&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116210&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116210&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.957106985347539
beta0.0213231419809721
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.957106985347539 \tabularnewline
beta & 0.0213231419809721 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116210&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]0.957106985347539[/C][/ROW]
[ROW][C]beta[/C][C]0.0213231419809721[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116210&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116210&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
alpha0.957106985347539
beta0.0213231419809721
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132795124203.10657051283747.89342948717
142978129654.6202551851126.379744814931
153291432946.4121193041-32.412119304121
163348833593.0200307429-105.020030742926
173565235915.2410986995-263.241098699524
183648836895.8636472487-407.863647248749
193538734286.11804762081100.88195237923
203567636417.4957808125-741.495780812547
213484434291.6797450763552.320254923688
223244734813.0811183625-2366.08111836253
233106832676.8052514775-1608.80525147745
242901030941.1150593774-1931.11505937737
252981230347.5787971138-535.578797113765
263095131417.2352441557-466.235244155694
273297433996.147292809-1022.14729280899
283293633533.2865375478-597.286537547756
293401235208.4510334612-1196.45103346121
303294635101.5248152052-2155.52481520519
313194830659.96423633741288.0357636626
323059932671.431673882-2072.43167388201
332769129080.0894447363-1389.08944473627
342507327331.3798624231-2258.37986242307
352340625046.0703511278-1640.07035112784
362224822981.3960861211-733.39608612112
372289623333.2722700379-437.272270037862
382531724241.20771945481075.7922805452
392655828044.8456366513-1486.84563665127
402647126918.6438964953-447.643896495269
412754328477.5879114897-934.587911489689
422619828351.7548651241-2153.75486512409
432472523831.2288487044893.771151295619
442500525084.7917686993-79.7917686992987
452346223234.1860439703227.813956029706
462078022832.9944567295-2052.99445672949
471981520612.2284668615-797.228466861485
481976119251.7817676975509.218232302523
492145420689.6820866707764.31791332933
502389922721.09812873921177.90187126078
512493926423.1608238923-1484.16082389229
522358025254.7722664694-1674.77226646938
532456225503.9618002236-941.961800223642
542469625204.2520675701-508.252067570131
552378522308.42280145641476.57719854357
562381224008.98557568-196.985575680013
572191721987.966387298-70.9663872980345
581971321125.4410414512-1412.44104145119
591928219507.1512849837-225.151284983735
601878818697.490839573190.5091604269
612145319684.24828891661768.75171108344
622448222653.91832686281828.08167313724
632747426836.5214996775637.47850032249
642726427706.3251380422-442.32513804223
652734929207.4155870458-1858.41558704582
663063228071.34588779132560.6541122087
672942928282.73656923891146.26343076108
683008429673.4414532649410.558546735116
692629028329.7832894654-2039.7832894654
702437925575.6399447563-1196.63994475625
712333524269.5158481254-934.515848125386
722134622834.6746514593-1488.67465145932
732110622389.9577075273-1283.95770752727
742451422386.09035345792127.90964654207
752835326756.39873815781596.60126184223
763080528469.2500454382335.74995456201
773134832596.5922140573-1248.59221405726
783455632274.25857478892281.74142521108
793385532192.86292607461662.13707392537
803478734091.1161300116695.883869988422
813252932966.6240006514-437.624000651398
822999831865.9628984148-1867.96289841482
832925729998.7329284108-741.732928410791
842815528798.7492071099-643.749207109926
853046629262.85405756691203.14594243308
863570431927.87120402323776.12879597679
873932738028.66490604691298.33509395306
883935139657.4133971206-306.413397120574
894223441217.92216001091016.07783998913
904363043376.5081197734253.49188022656
914372241447.85179537372274.14820462626
924312144023.4776915288-902.477691528788
933798541421.0008466684-3436.00084666835
943713537428.4661847129-293.466184712874
953464637187.8839885004-2541.88398850035
963302634303.8060686304-1277.80606863038
973508734261.9695397591825.030460240945
983884636689.435898952156.56410105001
994201341114.7831357913898.216864208669
1004390842264.50760864071643.49239135932
1014286845760.5696005895-2892.56960058953
1024442344078.2415818128344.758418187237
1034416742258.26115630711908.73884369292
1044363644275.0906888205-639.090688820528
1054438241748.60282867082633.39717132922
1064214243756.3615625214-1614.36156252142
1074345242184.579595631267.42040437003
1083691243107.8557682617-6195.85576826174
1094241338455.96849597653957.03150402353
1104534444008.97993603311335.02006396692
1114487347648.0523369253-2775.05233692529
1124751045293.07130173952216.92869826049
1134955449134.1497955218419.850204478178
1144736950819.3642618564-3450.36426185641
1154599845415.0199694621582.980030537932
1164814046007.50633062882132.49366937119
1174844146284.48598636512156.51401363491
1184492847654.282754283-2726.28275428301
1194045445119.8543019029-4665.85430190292
1203866139901.1127273156-1240.11272731556
1213724640385.9124353144-3139.91243531439
1223684338847.1078568749-2004.10785687491
1233642438859.0220934936-2435.02209349359
1243759436795.5849014515798.415098548547
1253814438924.9396374962-780.939637496209
1263873738993.3858705731-256.385870573133
1273456036582.7285794758-2022.72857947585
1283608034458.26333806061621.73666193943
1293350833947.5273990163-439.52739901626
1303546232270.31873897053191.68126102947
1313337435084.7196646527-1710.71966465272
1323211032669.5071767577-559.507176757666
1333553333566.32993146371966.67006853631
1343553236910.1059105792-1378.10591057919
1353790337461.7802399504441.219760049586
1363676338307.6984169206-1544.69841692065
1374039938096.67238647962302.32761352043
1384416441171.53271452912992.46728547088
1394449641893.81379973282602.18620026722
1404311044545.7986950495-1435.79869504952
1414388041151.45047534652728.54952465348
1424393042858.02963940161071.97036059845
1434432743585.9473051438741.05269485616

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 27951 & 24203.1065705128 & 3747.89342948717 \tabularnewline
14 & 29781 & 29654.6202551851 & 126.379744814931 \tabularnewline
15 & 32914 & 32946.4121193041 & -32.412119304121 \tabularnewline
16 & 33488 & 33593.0200307429 & -105.020030742926 \tabularnewline
17 & 35652 & 35915.2410986995 & -263.241098699524 \tabularnewline
18 & 36488 & 36895.8636472487 & -407.863647248749 \tabularnewline
19 & 35387 & 34286.1180476208 & 1100.88195237923 \tabularnewline
20 & 35676 & 36417.4957808125 & -741.495780812547 \tabularnewline
21 & 34844 & 34291.6797450763 & 552.320254923688 \tabularnewline
22 & 32447 & 34813.0811183625 & -2366.08111836253 \tabularnewline
23 & 31068 & 32676.8052514775 & -1608.80525147745 \tabularnewline
24 & 29010 & 30941.1150593774 & -1931.11505937737 \tabularnewline
25 & 29812 & 30347.5787971138 & -535.578797113765 \tabularnewline
26 & 30951 & 31417.2352441557 & -466.235244155694 \tabularnewline
27 & 32974 & 33996.147292809 & -1022.14729280899 \tabularnewline
28 & 32936 & 33533.2865375478 & -597.286537547756 \tabularnewline
29 & 34012 & 35208.4510334612 & -1196.45103346121 \tabularnewline
30 & 32946 & 35101.5248152052 & -2155.52481520519 \tabularnewline
31 & 31948 & 30659.9642363374 & 1288.0357636626 \tabularnewline
32 & 30599 & 32671.431673882 & -2072.43167388201 \tabularnewline
33 & 27691 & 29080.0894447363 & -1389.08944473627 \tabularnewline
34 & 25073 & 27331.3798624231 & -2258.37986242307 \tabularnewline
35 & 23406 & 25046.0703511278 & -1640.07035112784 \tabularnewline
36 & 22248 & 22981.3960861211 & -733.39608612112 \tabularnewline
37 & 22896 & 23333.2722700379 & -437.272270037862 \tabularnewline
38 & 25317 & 24241.2077194548 & 1075.7922805452 \tabularnewline
39 & 26558 & 28044.8456366513 & -1486.84563665127 \tabularnewline
40 & 26471 & 26918.6438964953 & -447.643896495269 \tabularnewline
41 & 27543 & 28477.5879114897 & -934.587911489689 \tabularnewline
42 & 26198 & 28351.7548651241 & -2153.75486512409 \tabularnewline
43 & 24725 & 23831.2288487044 & 893.771151295619 \tabularnewline
44 & 25005 & 25084.7917686993 & -79.7917686992987 \tabularnewline
45 & 23462 & 23234.1860439703 & 227.813956029706 \tabularnewline
46 & 20780 & 22832.9944567295 & -2052.99445672949 \tabularnewline
47 & 19815 & 20612.2284668615 & -797.228466861485 \tabularnewline
48 & 19761 & 19251.7817676975 & 509.218232302523 \tabularnewline
49 & 21454 & 20689.6820866707 & 764.31791332933 \tabularnewline
50 & 23899 & 22721.0981287392 & 1177.90187126078 \tabularnewline
51 & 24939 & 26423.1608238923 & -1484.16082389229 \tabularnewline
52 & 23580 & 25254.7722664694 & -1674.77226646938 \tabularnewline
53 & 24562 & 25503.9618002236 & -941.961800223642 \tabularnewline
54 & 24696 & 25204.2520675701 & -508.252067570131 \tabularnewline
55 & 23785 & 22308.4228014564 & 1476.57719854357 \tabularnewline
56 & 23812 & 24008.98557568 & -196.985575680013 \tabularnewline
57 & 21917 & 21987.966387298 & -70.9663872980345 \tabularnewline
58 & 19713 & 21125.4410414512 & -1412.44104145119 \tabularnewline
59 & 19282 & 19507.1512849837 & -225.151284983735 \tabularnewline
60 & 18788 & 18697.4908395731 & 90.5091604269 \tabularnewline
61 & 21453 & 19684.2482889166 & 1768.75171108344 \tabularnewline
62 & 24482 & 22653.9183268628 & 1828.08167313724 \tabularnewline
63 & 27474 & 26836.5214996775 & 637.47850032249 \tabularnewline
64 & 27264 & 27706.3251380422 & -442.32513804223 \tabularnewline
65 & 27349 & 29207.4155870458 & -1858.41558704582 \tabularnewline
66 & 30632 & 28071.3458877913 & 2560.6541122087 \tabularnewline
67 & 29429 & 28282.7365692389 & 1146.26343076108 \tabularnewline
68 & 30084 & 29673.4414532649 & 410.558546735116 \tabularnewline
69 & 26290 & 28329.7832894654 & -2039.7832894654 \tabularnewline
70 & 24379 & 25575.6399447563 & -1196.63994475625 \tabularnewline
71 & 23335 & 24269.5158481254 & -934.515848125386 \tabularnewline
72 & 21346 & 22834.6746514593 & -1488.67465145932 \tabularnewline
73 & 21106 & 22389.9577075273 & -1283.95770752727 \tabularnewline
74 & 24514 & 22386.0903534579 & 2127.90964654207 \tabularnewline
75 & 28353 & 26756.3987381578 & 1596.60126184223 \tabularnewline
76 & 30805 & 28469.250045438 & 2335.74995456201 \tabularnewline
77 & 31348 & 32596.5922140573 & -1248.59221405726 \tabularnewline
78 & 34556 & 32274.2585747889 & 2281.74142521108 \tabularnewline
79 & 33855 & 32192.8629260746 & 1662.13707392537 \tabularnewline
80 & 34787 & 34091.1161300116 & 695.883869988422 \tabularnewline
81 & 32529 & 32966.6240006514 & -437.624000651398 \tabularnewline
82 & 29998 & 31865.9628984148 & -1867.96289841482 \tabularnewline
83 & 29257 & 29998.7329284108 & -741.732928410791 \tabularnewline
84 & 28155 & 28798.7492071099 & -643.749207109926 \tabularnewline
85 & 30466 & 29262.8540575669 & 1203.14594243308 \tabularnewline
86 & 35704 & 31927.8712040232 & 3776.12879597679 \tabularnewline
87 & 39327 & 38028.6649060469 & 1298.33509395306 \tabularnewline
88 & 39351 & 39657.4133971206 & -306.413397120574 \tabularnewline
89 & 42234 & 41217.9221600109 & 1016.07783998913 \tabularnewline
90 & 43630 & 43376.5081197734 & 253.49188022656 \tabularnewline
91 & 43722 & 41447.8517953737 & 2274.14820462626 \tabularnewline
92 & 43121 & 44023.4776915288 & -902.477691528788 \tabularnewline
93 & 37985 & 41421.0008466684 & -3436.00084666835 \tabularnewline
94 & 37135 & 37428.4661847129 & -293.466184712874 \tabularnewline
95 & 34646 & 37187.8839885004 & -2541.88398850035 \tabularnewline
96 & 33026 & 34303.8060686304 & -1277.80606863038 \tabularnewline
97 & 35087 & 34261.9695397591 & 825.030460240945 \tabularnewline
98 & 38846 & 36689.43589895 & 2156.56410105001 \tabularnewline
99 & 42013 & 41114.7831357913 & 898.216864208669 \tabularnewline
100 & 43908 & 42264.5076086407 & 1643.49239135932 \tabularnewline
101 & 42868 & 45760.5696005895 & -2892.56960058953 \tabularnewline
102 & 44423 & 44078.2415818128 & 344.758418187237 \tabularnewline
103 & 44167 & 42258.2611563071 & 1908.73884369292 \tabularnewline
104 & 43636 & 44275.0906888205 & -639.090688820528 \tabularnewline
105 & 44382 & 41748.6028286708 & 2633.39717132922 \tabularnewline
106 & 42142 & 43756.3615625214 & -1614.36156252142 \tabularnewline
107 & 43452 & 42184.57959563 & 1267.42040437003 \tabularnewline
108 & 36912 & 43107.8557682617 & -6195.85576826174 \tabularnewline
109 & 42413 & 38455.9684959765 & 3957.03150402353 \tabularnewline
110 & 45344 & 44008.9799360331 & 1335.02006396692 \tabularnewline
111 & 44873 & 47648.0523369253 & -2775.05233692529 \tabularnewline
112 & 47510 & 45293.0713017395 & 2216.92869826049 \tabularnewline
113 & 49554 & 49134.1497955218 & 419.850204478178 \tabularnewline
114 & 47369 & 50819.3642618564 & -3450.36426185641 \tabularnewline
115 & 45998 & 45415.0199694621 & 582.980030537932 \tabularnewline
116 & 48140 & 46007.5063306288 & 2132.49366937119 \tabularnewline
117 & 48441 & 46284.4859863651 & 2156.51401363491 \tabularnewline
118 & 44928 & 47654.282754283 & -2726.28275428301 \tabularnewline
119 & 40454 & 45119.8543019029 & -4665.85430190292 \tabularnewline
120 & 38661 & 39901.1127273156 & -1240.11272731556 \tabularnewline
121 & 37246 & 40385.9124353144 & -3139.91243531439 \tabularnewline
122 & 36843 & 38847.1078568749 & -2004.10785687491 \tabularnewline
123 & 36424 & 38859.0220934936 & -2435.02209349359 \tabularnewline
124 & 37594 & 36795.5849014515 & 798.415098548547 \tabularnewline
125 & 38144 & 38924.9396374962 & -780.939637496209 \tabularnewline
126 & 38737 & 38993.3858705731 & -256.385870573133 \tabularnewline
127 & 34560 & 36582.7285794758 & -2022.72857947585 \tabularnewline
128 & 36080 & 34458.2633380606 & 1621.73666193943 \tabularnewline
129 & 33508 & 33947.5273990163 & -439.52739901626 \tabularnewline
130 & 35462 & 32270.3187389705 & 3191.68126102947 \tabularnewline
131 & 33374 & 35084.7196646527 & -1710.71966465272 \tabularnewline
132 & 32110 & 32669.5071767577 & -559.507176757666 \tabularnewline
133 & 35533 & 33566.3299314637 & 1966.67006853631 \tabularnewline
134 & 35532 & 36910.1059105792 & -1378.10591057919 \tabularnewline
135 & 37903 & 37461.7802399504 & 441.219760049586 \tabularnewline
136 & 36763 & 38307.6984169206 & -1544.69841692065 \tabularnewline
137 & 40399 & 38096.6723864796 & 2302.32761352043 \tabularnewline
138 & 44164 & 41171.5327145291 & 2992.46728547088 \tabularnewline
139 & 44496 & 41893.8137997328 & 2602.18620026722 \tabularnewline
140 & 43110 & 44545.7986950495 & -1435.79869504952 \tabularnewline
141 & 43880 & 41151.4504753465 & 2728.54952465348 \tabularnewline
142 & 43930 & 42858.0296394016 & 1071.97036059845 \tabularnewline
143 & 44327 & 43585.9473051438 & 741.05269485616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116210&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]29654.6202551851[/C][C]126.379744814931[/C][/ROW]
[ROW][C]15[/C][C]32914[/C][C]32946.4121193041[/C][C]-32.412119304121[/C][/ROW]
[ROW][C]16[/C][C]33488[/C][C]33593.0200307429[/C][C]-105.020030742926[/C][/ROW]
[ROW][C]17[/C][C]35652[/C][C]35915.2410986995[/C][C]-263.241098699524[/C][/ROW]
[ROW][C]18[/C][C]36488[/C][C]36895.8636472487[/C][C]-407.863647248749[/C][/ROW]
[ROW][C]19[/C][C]35387[/C][C]34286.1180476208[/C][C]1100.88195237923[/C][/ROW]
[ROW][C]20[/C][C]35676[/C][C]36417.4957808125[/C][C]-741.495780812547[/C][/ROW]
[ROW][C]21[/C][C]34844[/C][C]34291.6797450763[/C][C]552.320254923688[/C][/ROW]
[ROW][C]22[/C][C]32447[/C][C]34813.0811183625[/C][C]-2366.08111836253[/C][/ROW]
[ROW][C]23[/C][C]31068[/C][C]32676.8052514775[/C][C]-1608.80525147745[/C][/ROW]
[ROW][C]24[/C][C]29010[/C][C]30941.1150593774[/C][C]-1931.11505937737[/C][/ROW]
[ROW][C]25[/C][C]29812[/C][C]30347.5787971138[/C][C]-535.578797113765[/C][/ROW]
[ROW][C]26[/C][C]30951[/C][C]31417.2352441557[/C][C]-466.235244155694[/C][/ROW]
[ROW][C]27[/C][C]32974[/C][C]33996.147292809[/C][C]-1022.14729280899[/C][/ROW]
[ROW][C]28[/C][C]32936[/C][C]33533.2865375478[/C][C]-597.286537547756[/C][/ROW]
[ROW][C]29[/C][C]34012[/C][C]35208.4510334612[/C][C]-1196.45103346121[/C][/ROW]
[ROW][C]30[/C][C]32946[/C][C]35101.5248152052[/C][C]-2155.52481520519[/C][/ROW]
[ROW][C]31[/C][C]31948[/C][C]30659.9642363374[/C][C]1288.0357636626[/C][/ROW]
[ROW][C]32[/C][C]30599[/C][C]32671.431673882[/C][C]-2072.43167388201[/C][/ROW]
[ROW][C]33[/C][C]27691[/C][C]29080.0894447363[/C][C]-1389.08944473627[/C][/ROW]
[ROW][C]34[/C][C]25073[/C][C]27331.3798624231[/C][C]-2258.37986242307[/C][/ROW]
[ROW][C]35[/C][C]23406[/C][C]25046.0703511278[/C][C]-1640.07035112784[/C][/ROW]
[ROW][C]36[/C][C]22248[/C][C]22981.3960861211[/C][C]-733.39608612112[/C][/ROW]
[ROW][C]37[/C][C]22896[/C][C]23333.2722700379[/C][C]-437.272270037862[/C][/ROW]
[ROW][C]38[/C][C]25317[/C][C]24241.2077194548[/C][C]1075.7922805452[/C][/ROW]
[ROW][C]39[/C][C]26558[/C][C]28044.8456366513[/C][C]-1486.84563665127[/C][/ROW]
[ROW][C]40[/C][C]26471[/C][C]26918.6438964953[/C][C]-447.643896495269[/C][/ROW]
[ROW][C]41[/C][C]27543[/C][C]28477.5879114897[/C][C]-934.587911489689[/C][/ROW]
[ROW][C]42[/C][C]26198[/C][C]28351.7548651241[/C][C]-2153.75486512409[/C][/ROW]
[ROW][C]43[/C][C]24725[/C][C]23831.2288487044[/C][C]893.771151295619[/C][/ROW]
[ROW][C]44[/C][C]25005[/C][C]25084.7917686993[/C][C]-79.7917686992987[/C][/ROW]
[ROW][C]45[/C][C]23462[/C][C]23234.1860439703[/C][C]227.813956029706[/C][/ROW]
[ROW][C]46[/C][C]20780[/C][C]22832.9944567295[/C][C]-2052.99445672949[/C][/ROW]
[ROW][C]47[/C][C]19815[/C][C]20612.2284668615[/C][C]-797.228466861485[/C][/ROW]
[ROW][C]48[/C][C]19761[/C][C]19251.7817676975[/C][C]509.218232302523[/C][/ROW]
[ROW][C]49[/C][C]21454[/C][C]20689.6820866707[/C][C]764.31791332933[/C][/ROW]
[ROW][C]50[/C][C]23899[/C][C]22721.0981287392[/C][C]1177.90187126078[/C][/ROW]
[ROW][C]51[/C][C]24939[/C][C]26423.1608238923[/C][C]-1484.16082389229[/C][/ROW]
[ROW][C]52[/C][C]23580[/C][C]25254.7722664694[/C][C]-1674.77226646938[/C][/ROW]
[ROW][C]53[/C][C]24562[/C][C]25503.9618002236[/C][C]-941.961800223642[/C][/ROW]
[ROW][C]54[/C][C]24696[/C][C]25204.2520675701[/C][C]-508.252067570131[/C][/ROW]
[ROW][C]55[/C][C]23785[/C][C]22308.4228014564[/C][C]1476.57719854357[/C][/ROW]
[ROW][C]56[/C][C]23812[/C][C]24008.98557568[/C][C]-196.985575680013[/C][/ROW]
[ROW][C]57[/C][C]21917[/C][C]21987.966387298[/C][C]-70.9663872980345[/C][/ROW]
[ROW][C]58[/C][C]19713[/C][C]21125.4410414512[/C][C]-1412.44104145119[/C][/ROW]
[ROW][C]59[/C][C]19282[/C][C]19507.1512849837[/C][C]-225.151284983735[/C][/ROW]
[ROW][C]60[/C][C]18788[/C][C]18697.4908395731[/C][C]90.5091604269[/C][/ROW]
[ROW][C]61[/C][C]21453[/C][C]19684.2482889166[/C][C]1768.75171108344[/C][/ROW]
[ROW][C]62[/C][C]24482[/C][C]22653.9183268628[/C][C]1828.08167313724[/C][/ROW]
[ROW][C]63[/C][C]27474[/C][C]26836.5214996775[/C][C]637.47850032249[/C][/ROW]
[ROW][C]64[/C][C]27264[/C][C]27706.3251380422[/C][C]-442.32513804223[/C][/ROW]
[ROW][C]65[/C][C]27349[/C][C]29207.4155870458[/C][C]-1858.41558704582[/C][/ROW]
[ROW][C]66[/C][C]30632[/C][C]28071.3458877913[/C][C]2560.6541122087[/C][/ROW]
[ROW][C]67[/C][C]29429[/C][C]28282.7365692389[/C][C]1146.26343076108[/C][/ROW]
[ROW][C]68[/C][C]30084[/C][C]29673.4414532649[/C][C]410.558546735116[/C][/ROW]
[ROW][C]69[/C][C]26290[/C][C]28329.7832894654[/C][C]-2039.7832894654[/C][/ROW]
[ROW][C]70[/C][C]24379[/C][C]25575.6399447563[/C][C]-1196.63994475625[/C][/ROW]
[ROW][C]71[/C][C]23335[/C][C]24269.5158481254[/C][C]-934.515848125386[/C][/ROW]
[ROW][C]72[/C][C]21346[/C][C]22834.6746514593[/C][C]-1488.67465145932[/C][/ROW]
[ROW][C]73[/C][C]21106[/C][C]22389.9577075273[/C][C]-1283.95770752727[/C][/ROW]
[ROW][C]74[/C][C]24514[/C][C]22386.0903534579[/C][C]2127.90964654207[/C][/ROW]
[ROW][C]75[/C][C]28353[/C][C]26756.3987381578[/C][C]1596.60126184223[/C][/ROW]
[ROW][C]76[/C][C]30805[/C][C]28469.250045438[/C][C]2335.74995456201[/C][/ROW]
[ROW][C]77[/C][C]31348[/C][C]32596.5922140573[/C][C]-1248.59221405726[/C][/ROW]
[ROW][C]78[/C][C]34556[/C][C]32274.2585747889[/C][C]2281.74142521108[/C][/ROW]
[ROW][C]79[/C][C]33855[/C][C]32192.8629260746[/C][C]1662.13707392537[/C][/ROW]
[ROW][C]80[/C][C]34787[/C][C]34091.1161300116[/C][C]695.883869988422[/C][/ROW]
[ROW][C]81[/C][C]32529[/C][C]32966.6240006514[/C][C]-437.624000651398[/C][/ROW]
[ROW][C]82[/C][C]29998[/C][C]31865.9628984148[/C][C]-1867.96289841482[/C][/ROW]
[ROW][C]83[/C][C]29257[/C][C]29998.7329284108[/C][C]-741.732928410791[/C][/ROW]
[ROW][C]84[/C][C]28155[/C][C]28798.7492071099[/C][C]-643.749207109926[/C][/ROW]
[ROW][C]85[/C][C]30466[/C][C]29262.8540575669[/C][C]1203.14594243308[/C][/ROW]
[ROW][C]86[/C][C]35704[/C][C]31927.8712040232[/C][C]3776.12879597679[/C][/ROW]
[ROW][C]87[/C][C]39327[/C][C]38028.6649060469[/C][C]1298.33509395306[/C][/ROW]
[ROW][C]88[/C][C]39351[/C][C]39657.4133971206[/C][C]-306.413397120574[/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]43376.5081197734[/C][C]253.49188022656[/C][/ROW]
[ROW][C]91[/C][C]43722[/C][C]41447.8517953737[/C][C]2274.14820462626[/C][/ROW]
[ROW][C]92[/C][C]43121[/C][C]44023.4776915288[/C][C]-902.477691528788[/C][/ROW]
[ROW][C]93[/C][C]37985[/C][C]41421.0008466684[/C][C]-3436.00084666835[/C][/ROW]
[ROW][C]94[/C][C]37135[/C][C]37428.4661847129[/C][C]-293.466184712874[/C][/ROW]
[ROW][C]95[/C][C]34646[/C][C]37187.8839885004[/C][C]-2541.88398850035[/C][/ROW]
[ROW][C]96[/C][C]33026[/C][C]34303.8060686304[/C][C]-1277.80606863038[/C][/ROW]
[ROW][C]97[/C][C]35087[/C][C]34261.9695397591[/C][C]825.030460240945[/C][/ROW]
[ROW][C]98[/C][C]38846[/C][C]36689.43589895[/C][C]2156.56410105001[/C][/ROW]
[ROW][C]99[/C][C]42013[/C][C]41114.7831357913[/C][C]898.216864208669[/C][/ROW]
[ROW][C]100[/C][C]43908[/C][C]42264.5076086407[/C][C]1643.49239135932[/C][/ROW]
[ROW][C]101[/C][C]42868[/C][C]45760.5696005895[/C][C]-2892.56960058953[/C][/ROW]
[ROW][C]102[/C][C]44423[/C][C]44078.2415818128[/C][C]344.758418187237[/C][/ROW]
[ROW][C]103[/C][C]44167[/C][C]42258.2611563071[/C][C]1908.73884369292[/C][/ROW]
[ROW][C]104[/C][C]43636[/C][C]44275.0906888205[/C][C]-639.090688820528[/C][/ROW]
[ROW][C]105[/C][C]44382[/C][C]41748.6028286708[/C][C]2633.39717132922[/C][/ROW]
[ROW][C]106[/C][C]42142[/C][C]43756.3615625214[/C][C]-1614.36156252142[/C][/ROW]
[ROW][C]107[/C][C]43452[/C][C]42184.57959563[/C][C]1267.42040437003[/C][/ROW]
[ROW][C]108[/C][C]36912[/C][C]43107.8557682617[/C][C]-6195.85576826174[/C][/ROW]
[ROW][C]109[/C][C]42413[/C][C]38455.9684959765[/C][C]3957.03150402353[/C][/ROW]
[ROW][C]110[/C][C]45344[/C][C]44008.9799360331[/C][C]1335.02006396692[/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]45293.0713017395[/C][C]2216.92869826049[/C][/ROW]
[ROW][C]113[/C][C]49554[/C][C]49134.1497955218[/C][C]419.850204478178[/C][/ROW]
[ROW][C]114[/C][C]47369[/C][C]50819.3642618564[/C][C]-3450.36426185641[/C][/ROW]
[ROW][C]115[/C][C]45998[/C][C]45415.0199694621[/C][C]582.980030537932[/C][/ROW]
[ROW][C]116[/C][C]48140[/C][C]46007.5063306288[/C][C]2132.49366937119[/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]47654.282754283[/C][C]-2726.28275428301[/C][/ROW]
[ROW][C]119[/C][C]40454[/C][C]45119.8543019029[/C][C]-4665.85430190292[/C][/ROW]
[ROW][C]120[/C][C]38661[/C][C]39901.1127273156[/C][C]-1240.11272731556[/C][/ROW]
[ROW][C]121[/C][C]37246[/C][C]40385.9124353144[/C][C]-3139.91243531439[/C][/ROW]
[ROW][C]122[/C][C]36843[/C][C]38847.1078568749[/C][C]-2004.10785687491[/C][/ROW]
[ROW][C]123[/C][C]36424[/C][C]38859.0220934936[/C][C]-2435.02209349359[/C][/ROW]
[ROW][C]124[/C][C]37594[/C][C]36795.5849014515[/C][C]798.415098548547[/C][/ROW]
[ROW][C]125[/C][C]38144[/C][C]38924.9396374962[/C][C]-780.939637496209[/C][/ROW]
[ROW][C]126[/C][C]38737[/C][C]38993.3858705731[/C][C]-256.385870573133[/C][/ROW]
[ROW][C]127[/C][C]34560[/C][C]36582.7285794758[/C][C]-2022.72857947585[/C][/ROW]
[ROW][C]128[/C][C]36080[/C][C]34458.2633380606[/C][C]1621.73666193943[/C][/ROW]
[ROW][C]129[/C][C]33508[/C][C]33947.5273990163[/C][C]-439.52739901626[/C][/ROW]
[ROW][C]130[/C][C]35462[/C][C]32270.3187389705[/C][C]3191.68126102947[/C][/ROW]
[ROW][C]131[/C][C]33374[/C][C]35084.7196646527[/C][C]-1710.71966465272[/C][/ROW]
[ROW][C]132[/C][C]32110[/C][C]32669.5071767577[/C][C]-559.507176757666[/C][/ROW]
[ROW][C]133[/C][C]35533[/C][C]33566.3299314637[/C][C]1966.67006853631[/C][/ROW]
[ROW][C]134[/C][C]35532[/C][C]36910.1059105792[/C][C]-1378.10591057919[/C][/ROW]
[ROW][C]135[/C][C]37903[/C][C]37461.7802399504[/C][C]441.219760049586[/C][/ROW]
[ROW][C]136[/C][C]36763[/C][C]38307.6984169206[/C][C]-1544.69841692065[/C][/ROW]
[ROW][C]137[/C][C]40399[/C][C]38096.6723864796[/C][C]2302.32761352043[/C][/ROW]
[ROW][C]138[/C][C]44164[/C][C]41171.5327145291[/C][C]2992.46728547088[/C][/ROW]
[ROW][C]139[/C][C]44496[/C][C]41893.8137997328[/C][C]2602.18620026722[/C][/ROW]
[ROW][C]140[/C][C]43110[/C][C]44545.7986950495[/C][C]-1435.79869504952[/C][/ROW]
[ROW][C]141[/C][C]43880[/C][C]41151.4504753465[/C][C]2728.54952465348[/C][/ROW]
[ROW][C]142[/C][C]43930[/C][C]42858.0296394016[/C][C]1071.97036059845[/C][/ROW]
[ROW][C]143[/C][C]44327[/C][C]43585.9473051438[/C][C]741.05269485616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116210&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116210&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
142978129654.6202551851126.379744814931
153291432946.4121193041-32.412119304121
163348833593.0200307429-105.020030742926
173565235915.2410986995-263.241098699524
183648836895.8636472487-407.863647248749
193538734286.11804762081100.88195237923
203567636417.4957808125-741.495780812547
213484434291.6797450763552.320254923688
223244734813.0811183625-2366.08111836253
233106832676.8052514775-1608.80525147745
242901030941.1150593774-1931.11505937737
252981230347.5787971138-535.578797113765
263095131417.2352441557-466.235244155694
273297433996.147292809-1022.14729280899
283293633533.2865375478-597.286537547756
293401235208.4510334612-1196.45103346121
303294635101.5248152052-2155.52481520519
313194830659.96423633741288.0357636626
323059932671.431673882-2072.43167388201
332769129080.0894447363-1389.08944473627
342507327331.3798624231-2258.37986242307
352340625046.0703511278-1640.07035112784
362224822981.3960861211-733.39608612112
372289623333.2722700379-437.272270037862
382531724241.20771945481075.7922805452
392655828044.8456366513-1486.84563665127
402647126918.6438964953-447.643896495269
412754328477.5879114897-934.587911489689
422619828351.7548651241-2153.75486512409
432472523831.2288487044893.771151295619
442500525084.7917686993-79.7917686992987
452346223234.1860439703227.813956029706
462078022832.9944567295-2052.99445672949
471981520612.2284668615-797.228466861485
481976119251.7817676975509.218232302523
492145420689.6820866707764.31791332933
502389922721.09812873921177.90187126078
512493926423.1608238923-1484.16082389229
522358025254.7722664694-1674.77226646938
532456225503.9618002236-941.961800223642
542469625204.2520675701-508.252067570131
552378522308.42280145641476.57719854357
562381224008.98557568-196.985575680013
572191721987.966387298-70.9663872980345
581971321125.4410414512-1412.44104145119
591928219507.1512849837-225.151284983735
601878818697.490839573190.5091604269
612145319684.24828891661768.75171108344
622448222653.91832686281828.08167313724
632747426836.5214996775637.47850032249
642726427706.3251380422-442.32513804223
652734929207.4155870458-1858.41558704582
663063228071.34588779132560.6541122087
672942928282.73656923891146.26343076108
683008429673.4414532649410.558546735116
692629028329.7832894654-2039.7832894654
702437925575.6399447563-1196.63994475625
712333524269.5158481254-934.515848125386
722134622834.6746514593-1488.67465145932
732110622389.9577075273-1283.95770752727
742451422386.09035345792127.90964654207
752835326756.39873815781596.60126184223
763080528469.2500454382335.74995456201
773134832596.5922140573-1248.59221405726
783455632274.25857478892281.74142521108
793385532192.86292607461662.13707392537
803478734091.1161300116695.883869988422
813252932966.6240006514-437.624000651398
822999831865.9628984148-1867.96289841482
832925729998.7329284108-741.732928410791
842815528798.7492071099-643.749207109926
853046629262.85405756691203.14594243308
863570431927.87120402323776.12879597679
873932738028.66490604691298.33509395306
883935139657.4133971206-306.413397120574
894223441217.92216001091016.07783998913
904363043376.5081197734253.49188022656
914372241447.85179537372274.14820462626
924312144023.4776915288-902.477691528788
933798541421.0008466684-3436.00084666835
943713537428.4661847129-293.466184712874
953464637187.8839885004-2541.88398850035
963302634303.8060686304-1277.80606863038
973508734261.9695397591825.030460240945
983884636689.435898952156.56410105001
994201341114.7831357913898.216864208669
1004390842264.50760864071643.49239135932
1014286845760.5696005895-2892.56960058953
1024442344078.2415818128344.758418187237
1034416742258.26115630711908.73884369292
1044363644275.0906888205-639.090688820528
1054438241748.60282867082633.39717132922
1064214243756.3615625214-1614.36156252142
1074345242184.579595631267.42040437003
1083691243107.8557682617-6195.85576826174
1094241338455.96849597653957.03150402353
1104534444008.97993603311335.02006396692
1114487347648.0523369253-2775.05233692529
1124751045293.07130173952216.92869826049
1134955449134.1497955218419.850204478178
1144736950819.3642618564-3450.36426185641
1154599845415.0199694621582.980030537932
1164814046007.50633062882132.49366937119
1174844146284.48598636512156.51401363491
1184492847654.282754283-2726.28275428301
1194045445119.8543019029-4665.85430190292
1203866139901.1127273156-1240.11272731556
1213724640385.9124353144-3139.91243531439
1223684338847.1078568749-2004.10785687491
1233642438859.0220934936-2435.02209349359
1243759436795.5849014515798.415098548547
1253814438924.9396374962-780.939637496209
1263873738993.3858705731-256.385870573133
1273456036582.7285794758-2022.72857947585
1283608034458.26333806061621.73666193943
1293350833947.5273990163-439.52739901626
1303546232270.31873897053191.68126102947
1313337435084.7196646527-1710.71966465272
1323211032669.5071767577-559.507176757666
1333553333566.32993146371966.67006853631
1343553236910.1059105792-1378.10591057919
1353790337461.7802399504441.219760049586
1363676338307.6984169206-1544.69841692065
1374039938096.67238647962302.32761352043
1384416441171.53271452912992.46728547088
1394449641893.81379973282602.18620026722
1404311044545.7986950495-1435.79869504952
1414388041151.45047534652728.54952465348
1424393042858.02963940161071.97036059845
1434432743585.9473051438741.05269485616







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
14443769.344912836440271.368608504647267.3212171683
14545524.072640035840632.485042298350415.6602377733
14647015.971979834441006.586154146953025.3578055218
14749166.707124907342180.914599925256152.4996498895
14849698.173783598541823.93988586457572.407681333
14951355.149976849542652.86881189660057.431141803
15052433.601551324442947.300699852261919.9024027965
15150391.522025894440154.609833345160628.4342184437
15250443.119260207539481.673538798361404.5649816167
15348694.292262093837029.09360581460359.4909183737
15447755.303073924435403.166981381260107.4391664677
15547458.160157942934432.850026217260483.4702896685

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
144 & 43769.3449128364 & 40271.3686085046 & 47267.3212171683 \tabularnewline
145 & 45524.0726400358 & 40632.4850422983 & 50415.6602377733 \tabularnewline
146 & 47015.9719798344 & 41006.5861541469 & 53025.3578055218 \tabularnewline
147 & 49166.7071249073 & 42180.9145999252 & 56152.4996498895 \tabularnewline
148 & 49698.1737835985 & 41823.939885864 & 57572.407681333 \tabularnewline
149 & 51355.1499768495 & 42652.868811896 & 60057.431141803 \tabularnewline
150 & 52433.6015513244 & 42947.3006998522 & 61919.9024027965 \tabularnewline
151 & 50391.5220258944 & 40154.6098333451 & 60628.4342184437 \tabularnewline
152 & 50443.1192602075 & 39481.6735387983 & 61404.5649816167 \tabularnewline
153 & 48694.2922620938 & 37029.093605814 & 60359.4909183737 \tabularnewline
154 & 47755.3030739244 & 35403.1669813812 & 60107.4391664677 \tabularnewline
155 & 47458.1601579429 & 34432.8500262172 & 60483.4702896685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116210&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]47267.3212171683[/C][/ROW]
[ROW][C]145[/C][C]45524.0726400358[/C][C]40632.4850422983[/C][C]50415.6602377733[/C][/ROW]
[ROW][C]146[/C][C]47015.9719798344[/C][C]41006.5861541469[/C][C]53025.3578055218[/C][/ROW]
[ROW][C]147[/C][C]49166.7071249073[/C][C]42180.9145999252[/C][C]56152.4996498895[/C][/ROW]
[ROW][C]148[/C][C]49698.1737835985[/C][C]41823.939885864[/C][C]57572.407681333[/C][/ROW]
[ROW][C]149[/C][C]51355.1499768495[/C][C]42652.868811896[/C][C]60057.431141803[/C][/ROW]
[ROW][C]150[/C][C]52433.6015513244[/C][C]42947.3006998522[/C][C]61919.9024027965[/C][/ROW]
[ROW][C]151[/C][C]50391.5220258944[/C][C]40154.6098333451[/C][C]60628.4342184437[/C][/ROW]
[ROW][C]152[/C][C]50443.1192602075[/C][C]39481.6735387983[/C][C]61404.5649816167[/C][/ROW]
[ROW][C]153[/C][C]48694.2922620938[/C][C]37029.093605814[/C][C]60359.4909183737[/C][/ROW]
[ROW][C]154[/C][C]47755.3030739244[/C][C]35403.1669813812[/C][C]60107.4391664677[/C][/ROW]
[ROW][C]155[/C][C]47458.1601579429[/C][C]34432.8500262172[/C][C]60483.4702896685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116210&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116210&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
14443769.344912836440271.368608504647267.3212171683
14545524.072640035840632.485042298350415.6602377733
14647015.971979834441006.586154146953025.3578055218
14749166.707124907342180.914599925256152.4996498895
14849698.173783598541823.93988586457572.407681333
14951355.149976849542652.86881189660057.431141803
15052433.601551324442947.300699852261919.9024027965
15150391.522025894440154.609833345160628.4342184437
15250443.119260207539481.673538798361404.5649816167
15348694.292262093837029.09360581460359.4909183737
15447755.303073924435403.166981381260107.4391664677
15547458.160157942934432.850026217260483.4702896685



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')