Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 13 Jan 2014 05:07:16 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jan/13/t138960764108q4zmkc7pkb2ng.htm/, Retrieved Sun, 19 May 2024 09:39:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233130, Retrieved Sun, 19 May 2024 09:39:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-01-13 10:07:16] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
58608
46865
51378
46235
47206
45382
41227
33795
31295
42625
33625
21538
56421
53152
53536
52408
41454
38271
35306
26414
31917
38030
27534
18387
50556
43901
48572
43899
37532
40357
35489
29027
34485
42598
30306
26451
47460
50104
61465
53726
39477
43895
31481
29896
33842
39120
33702
25094
51442
45594
52518
48564
41745
49585
32747
33379
35645
37034
35681
20972
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577
23872
57276
56389
57657
62300
48929
51168
39636
33213
38127
43291
30600
21956
48033
46148
50736
48114
38390
44112
36287
30333
35908
40005
35263
26591
49771
47882
64830
57846
48188
54400
39778
37772
37214
43829
40701
29450
53597
53588
64172
53955
55509
48908
35331
38073
41776
42717
40736
49020
45099
44114
60487
48760
41281
48346
37025
31514
33977
42060
36036
22012




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233130&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233130&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233130&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 time6 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.268880922332634
beta0.00863507202718583
gamma0.437582399208988

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.268880922332634 \tabularnewline
beta & 0.00863507202718583 \tabularnewline
gamma & 0.437582399208988 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233130&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]0.268880922332634[/C][/ROW]
[ROW][C]beta[/C][C]0.00863507202718583[/C][/ROW]
[ROW][C]gamma[/C][C]0.437582399208988[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233130&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233130&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
alpha0.268880922332634
beta0.00863507202718583
gamma0.437582399208988







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135642157147.0916132479-726.09161324786
145315254006.4814246158-854.481424615762
155353654209.7407248744-673.740724874369
165240852831.9501225034-423.950122503404
174145441974.0474510276-520.047451027604
183827138799.9319251976-528.93192519759
193530639352.7827897048-4046.7827897048
202641430414.8548240424-4000.85482404236
213191726230.94513622145686.05486377857
223803038499.6125768591-469.612576859086
232753429111.6314624583-1577.63146245828
241838716888.56225373351498.43774626653
255055652240.8153763468-1684.81537634677
264390148783.7103020648-4882.71030206481
274857247934.6891132581637.310886741943
284389946965.3834710428-3066.38347104285
293753235336.15571826962195.84428173037
304035732865.67383372117491.32616627892
313548934444.41723145081044.58276854923
322902726896.82100947412130.17899052586
333448527481.41463291267003.5853670874
344259838158.95127042524439.04872957485
353030629771.6910322954534.308967704623
362645119140.85504195817310.14495804194
374746055091.1190489808-7631.1190489808
385010449052.02960686951051.9703931305
396146551618.45118235829846.54881764176
405372652015.54061780381710.45938219618
413947743440.4335667784-3963.43356677839
424389541079.89633667032815.10366332969
433148139399.8628499418-7918.86284994178
442989629829.708403474266.2915965258362
453384231453.92599318982388.07400681023
463912040094.7045393581-974.704539358092
473370229014.72023342894687.27976657106
482509421690.09364924833403.90635075168
495144251822.690130904-380.690130903968
504559450540.5998081105-4946.59980811047
515251854323.3579775283-1805.35797752834
524856448973.1149725292-409.114972529249
534174537996.53439615653748.46560384348
544958539879.76657892529705.23342107484
553274736635.8569728282-3888.85697282816
563337930730.86233243922648.13766756075
573564533824.99833675011820.0016632499
583703441268.791119968-4234.791119968
593568131147.66630360364533.33369639638
602097223394.7312427397-2422.73124273974
615855250760.00900650117791.99099349892
625495550243.76357668634711.23642331371
636554057679.82935129797860.17064870206
645157055449.1353030553-3879.13530305528
655114544935.56893114266209.4310688574
664664149457.8628244882-2816.86282448819
673570438540.4764097525-2836.47640975253
683325335054.8003897583-1801.80038975828
693519336722.1663714616-1529.16637146163
704166841355.2517378317312.748262168308
713486535299.471526128-434.471526127978
722121024011.2932622498-2801.29326224979
735612654567.77016231291558.22983768713
744923151400.3456481953-2169.34564819529
755972357988.3713483471734.62865165303
764810350335.3129180588-2232.31291805881
774747243476.3248333213995.67516667901
785049744494.70263707426002.29736292581
794005935941.87792464154117.12207535846
803414934672.5879967577-523.587996757735
813686036789.508619349470.4913806506447
824635642464.34509637483891.65490362517
833657737162.4793736358-585.479373635841
842387225106.8112455565-1234.81124555648
855727657513.1604039743-237.160403974318
865638952700.23256450233688.76743549771
875765762155.7597203864-4498.7597203864
886230051586.454461574310713.5455384257
894892950259.8221384122-1330.82213841222
905116850534.5809323439633.419067656054
913963639969.1935880563-333.193588056289
923321336042.4282004254-2829.42820042537
933812737747.8673665494379.13263345063
944329144747.3475569988-1456.3475569988
953060036581.9133468575-5981.91334685747
962195622861.7340206268-905.734020626816
974803355670.727447483-7637.72744748305
984614850101.7358646704-3953.73586467039
995073654843.0076697513-4107.00766975134
1004811449206.8022653751-1092.80226537512
1013839040785.9346754119-2395.93467541192
1024411241333.80042032452778.19957967549
1033628730971.92584204465315.07415795545
1043033327714.44422204352618.55577795651
1053590831873.069605254034.93039475003
1064000539238.6253651656766.374634834407
1073526330198.4755683315064.52443166896
1082659121073.59389879095517.40610120909
1094977153471.9539502443-3700.9539502443
1104788250165.2652044319-2283.26520443187
1116483055335.71688259229494.2831174078
1125784654381.59547134433464.40452865565
1134818846840.38756946781347.61243053221
1145440050130.06572790214269.93427209794
1153977841064.2728027913-1286.27280279133
1163777235237.17812326852534.82187673146
1173721439894.2744783208-2680.27447832079
1184382944460.8081731945-631.808173194549
1194070136468.81286424014232.18713575992
1202945027312.1014291232137.89857087701
1215359755891.8292104411-2294.82921044112
1225358853459.2743731751128.725626824948
1236417263094.29475585021077.70524414977
1245395557976.5666389985-4021.56663899848
1255550947756.48701695897752.5129830411
1264890853729.2925141907-4821.29251419066
1273533140446.4138423546-5115.41384235459
1283807334808.249126413264.75087359002
1294177637990.91518306453785.08481693554
1304271744963.971801709-2246.97180170898
1314073638102.80852942012633.19147057991
1324902027851.435974123921168.5640258761
1334509960179.4856679659-15080.4856679659
1344411455104.2600671204-10990.2600671204
1356048762047.1762877222-1560.17628772221
1364876054576.6405745278-5816.64057452777
1374128147624.4047088-6343.40470880001
1384834645735.37050568052610.62949431946
1393702534324.90900446682700.09099553317
1403151433455.5652269058-1941.56522690583
1413397735379.0898376983-1402.08983769828
1424206038989.83566327933070.16433672074
1433603635094.2059356068941.794064393223
1442201230288.6195109612-8276.61951096123

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 56421 & 57147.0916132479 & -726.09161324786 \tabularnewline
14 & 53152 & 54006.4814246158 & -854.481424615762 \tabularnewline
15 & 53536 & 54209.7407248744 & -673.740724874369 \tabularnewline
16 & 52408 & 52831.9501225034 & -423.950122503404 \tabularnewline
17 & 41454 & 41974.0474510276 & -520.047451027604 \tabularnewline
18 & 38271 & 38799.9319251976 & -528.93192519759 \tabularnewline
19 & 35306 & 39352.7827897048 & -4046.7827897048 \tabularnewline
20 & 26414 & 30414.8548240424 & -4000.85482404236 \tabularnewline
21 & 31917 & 26230.9451362214 & 5686.05486377857 \tabularnewline
22 & 38030 & 38499.6125768591 & -469.612576859086 \tabularnewline
23 & 27534 & 29111.6314624583 & -1577.63146245828 \tabularnewline
24 & 18387 & 16888.5622537335 & 1498.43774626653 \tabularnewline
25 & 50556 & 52240.8153763468 & -1684.81537634677 \tabularnewline
26 & 43901 & 48783.7103020648 & -4882.71030206481 \tabularnewline
27 & 48572 & 47934.6891132581 & 637.310886741943 \tabularnewline
28 & 43899 & 46965.3834710428 & -3066.38347104285 \tabularnewline
29 & 37532 & 35336.1557182696 & 2195.84428173037 \tabularnewline
30 & 40357 & 32865.6738337211 & 7491.32616627892 \tabularnewline
31 & 35489 & 34444.4172314508 & 1044.58276854923 \tabularnewline
32 & 29027 & 26896.8210094741 & 2130.17899052586 \tabularnewline
33 & 34485 & 27481.4146329126 & 7003.5853670874 \tabularnewline
34 & 42598 & 38158.9512704252 & 4439.04872957485 \tabularnewline
35 & 30306 & 29771.6910322954 & 534.308967704623 \tabularnewline
36 & 26451 & 19140.8550419581 & 7310.14495804194 \tabularnewline
37 & 47460 & 55091.1190489808 & -7631.1190489808 \tabularnewline
38 & 50104 & 49052.0296068695 & 1051.9703931305 \tabularnewline
39 & 61465 & 51618.4511823582 & 9846.54881764176 \tabularnewline
40 & 53726 & 52015.5406178038 & 1710.45938219618 \tabularnewline
41 & 39477 & 43440.4335667784 & -3963.43356677839 \tabularnewline
42 & 43895 & 41079.8963366703 & 2815.10366332969 \tabularnewline
43 & 31481 & 39399.8628499418 & -7918.86284994178 \tabularnewline
44 & 29896 & 29829.7084034742 & 66.2915965258362 \tabularnewline
45 & 33842 & 31453.9259931898 & 2388.07400681023 \tabularnewline
46 & 39120 & 40094.7045393581 & -974.704539358092 \tabularnewline
47 & 33702 & 29014.7202334289 & 4687.27976657106 \tabularnewline
48 & 25094 & 21690.0936492483 & 3403.90635075168 \tabularnewline
49 & 51442 & 51822.690130904 & -380.690130903968 \tabularnewline
50 & 45594 & 50540.5998081105 & -4946.59980811047 \tabularnewline
51 & 52518 & 54323.3579775283 & -1805.35797752834 \tabularnewline
52 & 48564 & 48973.1149725292 & -409.114972529249 \tabularnewline
53 & 41745 & 37996.5343961565 & 3748.46560384348 \tabularnewline
54 & 49585 & 39879.7665789252 & 9705.23342107484 \tabularnewline
55 & 32747 & 36635.8569728282 & -3888.85697282816 \tabularnewline
56 & 33379 & 30730.8623324392 & 2648.13766756075 \tabularnewline
57 & 35645 & 33824.9983367501 & 1820.0016632499 \tabularnewline
58 & 37034 & 41268.791119968 & -4234.791119968 \tabularnewline
59 & 35681 & 31147.6663036036 & 4533.33369639638 \tabularnewline
60 & 20972 & 23394.7312427397 & -2422.73124273974 \tabularnewline
61 & 58552 & 50760.0090065011 & 7791.99099349892 \tabularnewline
62 & 54955 & 50243.7635766863 & 4711.23642331371 \tabularnewline
63 & 65540 & 57679.8293512979 & 7860.17064870206 \tabularnewline
64 & 51570 & 55449.1353030553 & -3879.13530305528 \tabularnewline
65 & 51145 & 44935.5689311426 & 6209.4310688574 \tabularnewline
66 & 46641 & 49457.8628244882 & -2816.86282448819 \tabularnewline
67 & 35704 & 38540.4764097525 & -2836.47640975253 \tabularnewline
68 & 33253 & 35054.8003897583 & -1801.80038975828 \tabularnewline
69 & 35193 & 36722.1663714616 & -1529.16637146163 \tabularnewline
70 & 41668 & 41355.2517378317 & 312.748262168308 \tabularnewline
71 & 34865 & 35299.471526128 & -434.471526127978 \tabularnewline
72 & 21210 & 24011.2932622498 & -2801.29326224979 \tabularnewline
73 & 56126 & 54567.7701623129 & 1558.22983768713 \tabularnewline
74 & 49231 & 51400.3456481953 & -2169.34564819529 \tabularnewline
75 & 59723 & 57988.371348347 & 1734.62865165303 \tabularnewline
76 & 48103 & 50335.3129180588 & -2232.31291805881 \tabularnewline
77 & 47472 & 43476.324833321 & 3995.67516667901 \tabularnewline
78 & 50497 & 44494.7026370742 & 6002.29736292581 \tabularnewline
79 & 40059 & 35941.8779246415 & 4117.12207535846 \tabularnewline
80 & 34149 & 34672.5879967577 & -523.587996757735 \tabularnewline
81 & 36860 & 36789.5086193494 & 70.4913806506447 \tabularnewline
82 & 46356 & 42464.3450963748 & 3891.65490362517 \tabularnewline
83 & 36577 & 37162.4793736358 & -585.479373635841 \tabularnewline
84 & 23872 & 25106.8112455565 & -1234.81124555648 \tabularnewline
85 & 57276 & 57513.1604039743 & -237.160403974318 \tabularnewline
86 & 56389 & 52700.2325645023 & 3688.76743549771 \tabularnewline
87 & 57657 & 62155.7597203864 & -4498.7597203864 \tabularnewline
88 & 62300 & 51586.4544615743 & 10713.5455384257 \tabularnewline
89 & 48929 & 50259.8221384122 & -1330.82213841222 \tabularnewline
90 & 51168 & 50534.5809323439 & 633.419067656054 \tabularnewline
91 & 39636 & 39969.1935880563 & -333.193588056289 \tabularnewline
92 & 33213 & 36042.4282004254 & -2829.42820042537 \tabularnewline
93 & 38127 & 37747.8673665494 & 379.13263345063 \tabularnewline
94 & 43291 & 44747.3475569988 & -1456.3475569988 \tabularnewline
95 & 30600 & 36581.9133468575 & -5981.91334685747 \tabularnewline
96 & 21956 & 22861.7340206268 & -905.734020626816 \tabularnewline
97 & 48033 & 55670.727447483 & -7637.72744748305 \tabularnewline
98 & 46148 & 50101.7358646704 & -3953.73586467039 \tabularnewline
99 & 50736 & 54843.0076697513 & -4107.00766975134 \tabularnewline
100 & 48114 & 49206.8022653751 & -1092.80226537512 \tabularnewline
101 & 38390 & 40785.9346754119 & -2395.93467541192 \tabularnewline
102 & 44112 & 41333.8004203245 & 2778.19957967549 \tabularnewline
103 & 36287 & 30971.9258420446 & 5315.07415795545 \tabularnewline
104 & 30333 & 27714.4442220435 & 2618.55577795651 \tabularnewline
105 & 35908 & 31873.06960525 & 4034.93039475003 \tabularnewline
106 & 40005 & 39238.6253651656 & 766.374634834407 \tabularnewline
107 & 35263 & 30198.475568331 & 5064.52443166896 \tabularnewline
108 & 26591 & 21073.5938987909 & 5517.40610120909 \tabularnewline
109 & 49771 & 53471.9539502443 & -3700.9539502443 \tabularnewline
110 & 47882 & 50165.2652044319 & -2283.26520443187 \tabularnewline
111 & 64830 & 55335.7168825922 & 9494.2831174078 \tabularnewline
112 & 57846 & 54381.5954713443 & 3464.40452865565 \tabularnewline
113 & 48188 & 46840.3875694678 & 1347.61243053221 \tabularnewline
114 & 54400 & 50130.0657279021 & 4269.93427209794 \tabularnewline
115 & 39778 & 41064.2728027913 & -1286.27280279133 \tabularnewline
116 & 37772 & 35237.1781232685 & 2534.82187673146 \tabularnewline
117 & 37214 & 39894.2744783208 & -2680.27447832079 \tabularnewline
118 & 43829 & 44460.8081731945 & -631.808173194549 \tabularnewline
119 & 40701 & 36468.8128642401 & 4232.18713575992 \tabularnewline
120 & 29450 & 27312.101429123 & 2137.89857087701 \tabularnewline
121 & 53597 & 55891.8292104411 & -2294.82921044112 \tabularnewline
122 & 53588 & 53459.2743731751 & 128.725626824948 \tabularnewline
123 & 64172 & 63094.2947558502 & 1077.70524414977 \tabularnewline
124 & 53955 & 57976.5666389985 & -4021.56663899848 \tabularnewline
125 & 55509 & 47756.4870169589 & 7752.5129830411 \tabularnewline
126 & 48908 & 53729.2925141907 & -4821.29251419066 \tabularnewline
127 & 35331 & 40446.4138423546 & -5115.41384235459 \tabularnewline
128 & 38073 & 34808.24912641 & 3264.75087359002 \tabularnewline
129 & 41776 & 37990.9151830645 & 3785.08481693554 \tabularnewline
130 & 42717 & 44963.971801709 & -2246.97180170898 \tabularnewline
131 & 40736 & 38102.8085294201 & 2633.19147057991 \tabularnewline
132 & 49020 & 27851.4359741239 & 21168.5640258761 \tabularnewline
133 & 45099 & 60179.4856679659 & -15080.4856679659 \tabularnewline
134 & 44114 & 55104.2600671204 & -10990.2600671204 \tabularnewline
135 & 60487 & 62047.1762877222 & -1560.17628772221 \tabularnewline
136 & 48760 & 54576.6405745278 & -5816.64057452777 \tabularnewline
137 & 41281 & 47624.4047088 & -6343.40470880001 \tabularnewline
138 & 48346 & 45735.3705056805 & 2610.62949431946 \tabularnewline
139 & 37025 & 34324.9090044668 & 2700.09099553317 \tabularnewline
140 & 31514 & 33455.5652269058 & -1941.56522690583 \tabularnewline
141 & 33977 & 35379.0898376983 & -1402.08983769828 \tabularnewline
142 & 42060 & 38989.8356632793 & 3070.16433672074 \tabularnewline
143 & 36036 & 35094.2059356068 & 941.794064393223 \tabularnewline
144 & 22012 & 30288.6195109612 & -8276.61951096123 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233130&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]56421[/C][C]57147.0916132479[/C][C]-726.09161324786[/C][/ROW]
[ROW][C]14[/C][C]53152[/C][C]54006.4814246158[/C][C]-854.481424615762[/C][/ROW]
[ROW][C]15[/C][C]53536[/C][C]54209.7407248744[/C][C]-673.740724874369[/C][/ROW]
[ROW][C]16[/C][C]52408[/C][C]52831.9501225034[/C][C]-423.950122503404[/C][/ROW]
[ROW][C]17[/C][C]41454[/C][C]41974.0474510276[/C][C]-520.047451027604[/C][/ROW]
[ROW][C]18[/C][C]38271[/C][C]38799.9319251976[/C][C]-528.93192519759[/C][/ROW]
[ROW][C]19[/C][C]35306[/C][C]39352.7827897048[/C][C]-4046.7827897048[/C][/ROW]
[ROW][C]20[/C][C]26414[/C][C]30414.8548240424[/C][C]-4000.85482404236[/C][/ROW]
[ROW][C]21[/C][C]31917[/C][C]26230.9451362214[/C][C]5686.05486377857[/C][/ROW]
[ROW][C]22[/C][C]38030[/C][C]38499.6125768591[/C][C]-469.612576859086[/C][/ROW]
[ROW][C]23[/C][C]27534[/C][C]29111.6314624583[/C][C]-1577.63146245828[/C][/ROW]
[ROW][C]24[/C][C]18387[/C][C]16888.5622537335[/C][C]1498.43774626653[/C][/ROW]
[ROW][C]25[/C][C]50556[/C][C]52240.8153763468[/C][C]-1684.81537634677[/C][/ROW]
[ROW][C]26[/C][C]43901[/C][C]48783.7103020648[/C][C]-4882.71030206481[/C][/ROW]
[ROW][C]27[/C][C]48572[/C][C]47934.6891132581[/C][C]637.310886741943[/C][/ROW]
[ROW][C]28[/C][C]43899[/C][C]46965.3834710428[/C][C]-3066.38347104285[/C][/ROW]
[ROW][C]29[/C][C]37532[/C][C]35336.1557182696[/C][C]2195.84428173037[/C][/ROW]
[ROW][C]30[/C][C]40357[/C][C]32865.6738337211[/C][C]7491.32616627892[/C][/ROW]
[ROW][C]31[/C][C]35489[/C][C]34444.4172314508[/C][C]1044.58276854923[/C][/ROW]
[ROW][C]32[/C][C]29027[/C][C]26896.8210094741[/C][C]2130.17899052586[/C][/ROW]
[ROW][C]33[/C][C]34485[/C][C]27481.4146329126[/C][C]7003.5853670874[/C][/ROW]
[ROW][C]34[/C][C]42598[/C][C]38158.9512704252[/C][C]4439.04872957485[/C][/ROW]
[ROW][C]35[/C][C]30306[/C][C]29771.6910322954[/C][C]534.308967704623[/C][/ROW]
[ROW][C]36[/C][C]26451[/C][C]19140.8550419581[/C][C]7310.14495804194[/C][/ROW]
[ROW][C]37[/C][C]47460[/C][C]55091.1190489808[/C][C]-7631.1190489808[/C][/ROW]
[ROW][C]38[/C][C]50104[/C][C]49052.0296068695[/C][C]1051.9703931305[/C][/ROW]
[ROW][C]39[/C][C]61465[/C][C]51618.4511823582[/C][C]9846.54881764176[/C][/ROW]
[ROW][C]40[/C][C]53726[/C][C]52015.5406178038[/C][C]1710.45938219618[/C][/ROW]
[ROW][C]41[/C][C]39477[/C][C]43440.4335667784[/C][C]-3963.43356677839[/C][/ROW]
[ROW][C]42[/C][C]43895[/C][C]41079.8963366703[/C][C]2815.10366332969[/C][/ROW]
[ROW][C]43[/C][C]31481[/C][C]39399.8628499418[/C][C]-7918.86284994178[/C][/ROW]
[ROW][C]44[/C][C]29896[/C][C]29829.7084034742[/C][C]66.2915965258362[/C][/ROW]
[ROW][C]45[/C][C]33842[/C][C]31453.9259931898[/C][C]2388.07400681023[/C][/ROW]
[ROW][C]46[/C][C]39120[/C][C]40094.7045393581[/C][C]-974.704539358092[/C][/ROW]
[ROW][C]47[/C][C]33702[/C][C]29014.7202334289[/C][C]4687.27976657106[/C][/ROW]
[ROW][C]48[/C][C]25094[/C][C]21690.0936492483[/C][C]3403.90635075168[/C][/ROW]
[ROW][C]49[/C][C]51442[/C][C]51822.690130904[/C][C]-380.690130903968[/C][/ROW]
[ROW][C]50[/C][C]45594[/C][C]50540.5998081105[/C][C]-4946.59980811047[/C][/ROW]
[ROW][C]51[/C][C]52518[/C][C]54323.3579775283[/C][C]-1805.35797752834[/C][/ROW]
[ROW][C]52[/C][C]48564[/C][C]48973.1149725292[/C][C]-409.114972529249[/C][/ROW]
[ROW][C]53[/C][C]41745[/C][C]37996.5343961565[/C][C]3748.46560384348[/C][/ROW]
[ROW][C]54[/C][C]49585[/C][C]39879.7665789252[/C][C]9705.23342107484[/C][/ROW]
[ROW][C]55[/C][C]32747[/C][C]36635.8569728282[/C][C]-3888.85697282816[/C][/ROW]
[ROW][C]56[/C][C]33379[/C][C]30730.8623324392[/C][C]2648.13766756075[/C][/ROW]
[ROW][C]57[/C][C]35645[/C][C]33824.9983367501[/C][C]1820.0016632499[/C][/ROW]
[ROW][C]58[/C][C]37034[/C][C]41268.791119968[/C][C]-4234.791119968[/C][/ROW]
[ROW][C]59[/C][C]35681[/C][C]31147.6663036036[/C][C]4533.33369639638[/C][/ROW]
[ROW][C]60[/C][C]20972[/C][C]23394.7312427397[/C][C]-2422.73124273974[/C][/ROW]
[ROW][C]61[/C][C]58552[/C][C]50760.0090065011[/C][C]7791.99099349892[/C][/ROW]
[ROW][C]62[/C][C]54955[/C][C]50243.7635766863[/C][C]4711.23642331371[/C][/ROW]
[ROW][C]63[/C][C]65540[/C][C]57679.8293512979[/C][C]7860.17064870206[/C][/ROW]
[ROW][C]64[/C][C]51570[/C][C]55449.1353030553[/C][C]-3879.13530305528[/C][/ROW]
[ROW][C]65[/C][C]51145[/C][C]44935.5689311426[/C][C]6209.4310688574[/C][/ROW]
[ROW][C]66[/C][C]46641[/C][C]49457.8628244882[/C][C]-2816.86282448819[/C][/ROW]
[ROW][C]67[/C][C]35704[/C][C]38540.4764097525[/C][C]-2836.47640975253[/C][/ROW]
[ROW][C]68[/C][C]33253[/C][C]35054.8003897583[/C][C]-1801.80038975828[/C][/ROW]
[ROW][C]69[/C][C]35193[/C][C]36722.1663714616[/C][C]-1529.16637146163[/C][/ROW]
[ROW][C]70[/C][C]41668[/C][C]41355.2517378317[/C][C]312.748262168308[/C][/ROW]
[ROW][C]71[/C][C]34865[/C][C]35299.471526128[/C][C]-434.471526127978[/C][/ROW]
[ROW][C]72[/C][C]21210[/C][C]24011.2932622498[/C][C]-2801.29326224979[/C][/ROW]
[ROW][C]73[/C][C]56126[/C][C]54567.7701623129[/C][C]1558.22983768713[/C][/ROW]
[ROW][C]74[/C][C]49231[/C][C]51400.3456481953[/C][C]-2169.34564819529[/C][/ROW]
[ROW][C]75[/C][C]59723[/C][C]57988.371348347[/C][C]1734.62865165303[/C][/ROW]
[ROW][C]76[/C][C]48103[/C][C]50335.3129180588[/C][C]-2232.31291805881[/C][/ROW]
[ROW][C]77[/C][C]47472[/C][C]43476.324833321[/C][C]3995.67516667901[/C][/ROW]
[ROW][C]78[/C][C]50497[/C][C]44494.7026370742[/C][C]6002.29736292581[/C][/ROW]
[ROW][C]79[/C][C]40059[/C][C]35941.8779246415[/C][C]4117.12207535846[/C][/ROW]
[ROW][C]80[/C][C]34149[/C][C]34672.5879967577[/C][C]-523.587996757735[/C][/ROW]
[ROW][C]81[/C][C]36860[/C][C]36789.5086193494[/C][C]70.4913806506447[/C][/ROW]
[ROW][C]82[/C][C]46356[/C][C]42464.3450963748[/C][C]3891.65490362517[/C][/ROW]
[ROW][C]83[/C][C]36577[/C][C]37162.4793736358[/C][C]-585.479373635841[/C][/ROW]
[ROW][C]84[/C][C]23872[/C][C]25106.8112455565[/C][C]-1234.81124555648[/C][/ROW]
[ROW][C]85[/C][C]57276[/C][C]57513.1604039743[/C][C]-237.160403974318[/C][/ROW]
[ROW][C]86[/C][C]56389[/C][C]52700.2325645023[/C][C]3688.76743549771[/C][/ROW]
[ROW][C]87[/C][C]57657[/C][C]62155.7597203864[/C][C]-4498.7597203864[/C][/ROW]
[ROW][C]88[/C][C]62300[/C][C]51586.4544615743[/C][C]10713.5455384257[/C][/ROW]
[ROW][C]89[/C][C]48929[/C][C]50259.8221384122[/C][C]-1330.82213841222[/C][/ROW]
[ROW][C]90[/C][C]51168[/C][C]50534.5809323439[/C][C]633.419067656054[/C][/ROW]
[ROW][C]91[/C][C]39636[/C][C]39969.1935880563[/C][C]-333.193588056289[/C][/ROW]
[ROW][C]92[/C][C]33213[/C][C]36042.4282004254[/C][C]-2829.42820042537[/C][/ROW]
[ROW][C]93[/C][C]38127[/C][C]37747.8673665494[/C][C]379.13263345063[/C][/ROW]
[ROW][C]94[/C][C]43291[/C][C]44747.3475569988[/C][C]-1456.3475569988[/C][/ROW]
[ROW][C]95[/C][C]30600[/C][C]36581.9133468575[/C][C]-5981.91334685747[/C][/ROW]
[ROW][C]96[/C][C]21956[/C][C]22861.7340206268[/C][C]-905.734020626816[/C][/ROW]
[ROW][C]97[/C][C]48033[/C][C]55670.727447483[/C][C]-7637.72744748305[/C][/ROW]
[ROW][C]98[/C][C]46148[/C][C]50101.7358646704[/C][C]-3953.73586467039[/C][/ROW]
[ROW][C]99[/C][C]50736[/C][C]54843.0076697513[/C][C]-4107.00766975134[/C][/ROW]
[ROW][C]100[/C][C]48114[/C][C]49206.8022653751[/C][C]-1092.80226537512[/C][/ROW]
[ROW][C]101[/C][C]38390[/C][C]40785.9346754119[/C][C]-2395.93467541192[/C][/ROW]
[ROW][C]102[/C][C]44112[/C][C]41333.8004203245[/C][C]2778.19957967549[/C][/ROW]
[ROW][C]103[/C][C]36287[/C][C]30971.9258420446[/C][C]5315.07415795545[/C][/ROW]
[ROW][C]104[/C][C]30333[/C][C]27714.4442220435[/C][C]2618.55577795651[/C][/ROW]
[ROW][C]105[/C][C]35908[/C][C]31873.06960525[/C][C]4034.93039475003[/C][/ROW]
[ROW][C]106[/C][C]40005[/C][C]39238.6253651656[/C][C]766.374634834407[/C][/ROW]
[ROW][C]107[/C][C]35263[/C][C]30198.475568331[/C][C]5064.52443166896[/C][/ROW]
[ROW][C]108[/C][C]26591[/C][C]21073.5938987909[/C][C]5517.40610120909[/C][/ROW]
[ROW][C]109[/C][C]49771[/C][C]53471.9539502443[/C][C]-3700.9539502443[/C][/ROW]
[ROW][C]110[/C][C]47882[/C][C]50165.2652044319[/C][C]-2283.26520443187[/C][/ROW]
[ROW][C]111[/C][C]64830[/C][C]55335.7168825922[/C][C]9494.2831174078[/C][/ROW]
[ROW][C]112[/C][C]57846[/C][C]54381.5954713443[/C][C]3464.40452865565[/C][/ROW]
[ROW][C]113[/C][C]48188[/C][C]46840.3875694678[/C][C]1347.61243053221[/C][/ROW]
[ROW][C]114[/C][C]54400[/C][C]50130.0657279021[/C][C]4269.93427209794[/C][/ROW]
[ROW][C]115[/C][C]39778[/C][C]41064.2728027913[/C][C]-1286.27280279133[/C][/ROW]
[ROW][C]116[/C][C]37772[/C][C]35237.1781232685[/C][C]2534.82187673146[/C][/ROW]
[ROW][C]117[/C][C]37214[/C][C]39894.2744783208[/C][C]-2680.27447832079[/C][/ROW]
[ROW][C]118[/C][C]43829[/C][C]44460.8081731945[/C][C]-631.808173194549[/C][/ROW]
[ROW][C]119[/C][C]40701[/C][C]36468.8128642401[/C][C]4232.18713575992[/C][/ROW]
[ROW][C]120[/C][C]29450[/C][C]27312.101429123[/C][C]2137.89857087701[/C][/ROW]
[ROW][C]121[/C][C]53597[/C][C]55891.8292104411[/C][C]-2294.82921044112[/C][/ROW]
[ROW][C]122[/C][C]53588[/C][C]53459.2743731751[/C][C]128.725626824948[/C][/ROW]
[ROW][C]123[/C][C]64172[/C][C]63094.2947558502[/C][C]1077.70524414977[/C][/ROW]
[ROW][C]124[/C][C]53955[/C][C]57976.5666389985[/C][C]-4021.56663899848[/C][/ROW]
[ROW][C]125[/C][C]55509[/C][C]47756.4870169589[/C][C]7752.5129830411[/C][/ROW]
[ROW][C]126[/C][C]48908[/C][C]53729.2925141907[/C][C]-4821.29251419066[/C][/ROW]
[ROW][C]127[/C][C]35331[/C][C]40446.4138423546[/C][C]-5115.41384235459[/C][/ROW]
[ROW][C]128[/C][C]38073[/C][C]34808.24912641[/C][C]3264.75087359002[/C][/ROW]
[ROW][C]129[/C][C]41776[/C][C]37990.9151830645[/C][C]3785.08481693554[/C][/ROW]
[ROW][C]130[/C][C]42717[/C][C]44963.971801709[/C][C]-2246.97180170898[/C][/ROW]
[ROW][C]131[/C][C]40736[/C][C]38102.8085294201[/C][C]2633.19147057991[/C][/ROW]
[ROW][C]132[/C][C]49020[/C][C]27851.4359741239[/C][C]21168.5640258761[/C][/ROW]
[ROW][C]133[/C][C]45099[/C][C]60179.4856679659[/C][C]-15080.4856679659[/C][/ROW]
[ROW][C]134[/C][C]44114[/C][C]55104.2600671204[/C][C]-10990.2600671204[/C][/ROW]
[ROW][C]135[/C][C]60487[/C][C]62047.1762877222[/C][C]-1560.17628772221[/C][/ROW]
[ROW][C]136[/C][C]48760[/C][C]54576.6405745278[/C][C]-5816.64057452777[/C][/ROW]
[ROW][C]137[/C][C]41281[/C][C]47624.4047088[/C][C]-6343.40470880001[/C][/ROW]
[ROW][C]138[/C][C]48346[/C][C]45735.3705056805[/C][C]2610.62949431946[/C][/ROW]
[ROW][C]139[/C][C]37025[/C][C]34324.9090044668[/C][C]2700.09099553317[/C][/ROW]
[ROW][C]140[/C][C]31514[/C][C]33455.5652269058[/C][C]-1941.56522690583[/C][/ROW]
[ROW][C]141[/C][C]33977[/C][C]35379.0898376983[/C][C]-1402.08983769828[/C][/ROW]
[ROW][C]142[/C][C]42060[/C][C]38989.8356632793[/C][C]3070.16433672074[/C][/ROW]
[ROW][C]143[/C][C]36036[/C][C]35094.2059356068[/C][C]941.794064393223[/C][/ROW]
[ROW][C]144[/C][C]22012[/C][C]30288.6195109612[/C][C]-8276.61951096123[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233130&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233130&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
135642157147.0916132479-726.09161324786
145315254006.4814246158-854.481424615762
155353654209.7407248744-673.740724874369
165240852831.9501225034-423.950122503404
174145441974.0474510276-520.047451027604
183827138799.9319251976-528.93192519759
193530639352.7827897048-4046.7827897048
202641430414.8548240424-4000.85482404236
213191726230.94513622145686.05486377857
223803038499.6125768591-469.612576859086
232753429111.6314624583-1577.63146245828
241838716888.56225373351498.43774626653
255055652240.8153763468-1684.81537634677
264390148783.7103020648-4882.71030206481
274857247934.6891132581637.310886741943
284389946965.3834710428-3066.38347104285
293753235336.15571826962195.84428173037
304035732865.67383372117491.32616627892
313548934444.41723145081044.58276854923
322902726896.82100947412130.17899052586
333448527481.41463291267003.5853670874
344259838158.95127042524439.04872957485
353030629771.6910322954534.308967704623
362645119140.85504195817310.14495804194
374746055091.1190489808-7631.1190489808
385010449052.02960686951051.9703931305
396146551618.45118235829846.54881764176
405372652015.54061780381710.45938219618
413947743440.4335667784-3963.43356677839
424389541079.89633667032815.10366332969
433148139399.8628499418-7918.86284994178
442989629829.708403474266.2915965258362
453384231453.92599318982388.07400681023
463912040094.7045393581-974.704539358092
473370229014.72023342894687.27976657106
482509421690.09364924833403.90635075168
495144251822.690130904-380.690130903968
504559450540.5998081105-4946.59980811047
515251854323.3579775283-1805.35797752834
524856448973.1149725292-409.114972529249
534174537996.53439615653748.46560384348
544958539879.76657892529705.23342107484
553274736635.8569728282-3888.85697282816
563337930730.86233243922648.13766756075
573564533824.99833675011820.0016632499
583703441268.791119968-4234.791119968
593568131147.66630360364533.33369639638
602097223394.7312427397-2422.73124273974
615855250760.00900650117791.99099349892
625495550243.76357668634711.23642331371
636554057679.82935129797860.17064870206
645157055449.1353030553-3879.13530305528
655114544935.56893114266209.4310688574
664664149457.8628244882-2816.86282448819
673570438540.4764097525-2836.47640975253
683325335054.8003897583-1801.80038975828
693519336722.1663714616-1529.16637146163
704166841355.2517378317312.748262168308
713486535299.471526128-434.471526127978
722121024011.2932622498-2801.29326224979
735612654567.77016231291558.22983768713
744923151400.3456481953-2169.34564819529
755972357988.3713483471734.62865165303
764810350335.3129180588-2232.31291805881
774747243476.3248333213995.67516667901
785049744494.70263707426002.29736292581
794005935941.87792464154117.12207535846
803414934672.5879967577-523.587996757735
813686036789.508619349470.4913806506447
824635642464.34509637483891.65490362517
833657737162.4793736358-585.479373635841
842387225106.8112455565-1234.81124555648
855727657513.1604039743-237.160403974318
865638952700.23256450233688.76743549771
875765762155.7597203864-4498.7597203864
886230051586.454461574310713.5455384257
894892950259.8221384122-1330.82213841222
905116850534.5809323439633.419067656054
913963639969.1935880563-333.193588056289
923321336042.4282004254-2829.42820042537
933812737747.8673665494379.13263345063
944329144747.3475569988-1456.3475569988
953060036581.9133468575-5981.91334685747
962195622861.7340206268-905.734020626816
974803355670.727447483-7637.72744748305
984614850101.7358646704-3953.73586467039
995073654843.0076697513-4107.00766975134
1004811449206.8022653751-1092.80226537512
1013839040785.9346754119-2395.93467541192
1024411241333.80042032452778.19957967549
1033628730971.92584204465315.07415795545
1043033327714.44422204352618.55577795651
1053590831873.069605254034.93039475003
1064000539238.6253651656766.374634834407
1073526330198.4755683315064.52443166896
1082659121073.59389879095517.40610120909
1094977153471.9539502443-3700.9539502443
1104788250165.2652044319-2283.26520443187
1116483055335.71688259229494.2831174078
1125784654381.59547134433464.40452865565
1134818846840.38756946781347.61243053221
1145440050130.06572790214269.93427209794
1153977841064.2728027913-1286.27280279133
1163777235237.17812326852534.82187673146
1173721439894.2744783208-2680.27447832079
1184382944460.8081731945-631.808173194549
1194070136468.81286424014232.18713575992
1202945027312.1014291232137.89857087701
1215359755891.8292104411-2294.82921044112
1225358853459.2743731751128.725626824948
1236417263094.29475585021077.70524414977
1245395557976.5666389985-4021.56663899848
1255550947756.48701695897752.5129830411
1264890853729.2925141907-4821.29251419066
1273533140446.4138423546-5115.41384235459
1283807334808.249126413264.75087359002
1294177637990.91518306453785.08481693554
1304271744963.971801709-2246.97180170898
1314073638102.80852942012633.19147057991
1324902027851.435974123921168.5640258761
1334509960179.4856679659-15080.4856679659
1344411455104.2600671204-10990.2600671204
1356048762047.1762877222-1560.17628772221
1364876054576.6405745278-5816.64057452777
1374128147624.4047088-6343.40470880001
1384834645735.37050568052610.62949431946
1393702534324.90900446682700.09099553317
1403151433455.5652269058-1941.56522690583
1413397735379.0898376983-1402.08983769828
1424206038989.83566327933070.16433672074
1433603635094.2059356068941.794064393223
1442201230288.6195109612-8276.61951096123







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
14543004.728186008633896.45738817452112.9989838431
14643230.214732650433792.925654304552667.5038109963
14756107.929995841946347.336884970265868.5231067136
14847661.579426047937582.802240538657740.3566115572
14942084.739583750231692.384959750252477.0942077502
15044760.609278515434058.837109908955462.381447122
15132665.424320159321658.003062036543672.845578282
15229567.431425372218257.784450719340877.0784000252
15332172.44036568820563.68514359243781.1955877841
15437581.064885407125676.046340909149486.083429905
15532161.977977396219963.297091684144360.6588631082
15624134.744900951911644.783384934236624.7064169696

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
145 & 43004.7281860086 & 33896.457388174 & 52112.9989838431 \tabularnewline
146 & 43230.2147326504 & 33792.9256543045 & 52667.5038109963 \tabularnewline
147 & 56107.9299958419 & 46347.3368849702 & 65868.5231067136 \tabularnewline
148 & 47661.5794260479 & 37582.8022405386 & 57740.3566115572 \tabularnewline
149 & 42084.7395837502 & 31692.3849597502 & 52477.0942077502 \tabularnewline
150 & 44760.6092785154 & 34058.8371099089 & 55462.381447122 \tabularnewline
151 & 32665.4243201593 & 21658.0030620365 & 43672.845578282 \tabularnewline
152 & 29567.4314253722 & 18257.7844507193 & 40877.0784000252 \tabularnewline
153 & 32172.440365688 & 20563.685143592 & 43781.1955877841 \tabularnewline
154 & 37581.0648854071 & 25676.0463409091 & 49486.083429905 \tabularnewline
155 & 32161.9779773962 & 19963.2970916841 & 44360.6588631082 \tabularnewline
156 & 24134.7449009519 & 11644.7833849342 & 36624.7064169696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233130&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]145[/C][C]43004.7281860086[/C][C]33896.457388174[/C][C]52112.9989838431[/C][/ROW]
[ROW][C]146[/C][C]43230.2147326504[/C][C]33792.9256543045[/C][C]52667.5038109963[/C][/ROW]
[ROW][C]147[/C][C]56107.9299958419[/C][C]46347.3368849702[/C][C]65868.5231067136[/C][/ROW]
[ROW][C]148[/C][C]47661.5794260479[/C][C]37582.8022405386[/C][C]57740.3566115572[/C][/ROW]
[ROW][C]149[/C][C]42084.7395837502[/C][C]31692.3849597502[/C][C]52477.0942077502[/C][/ROW]
[ROW][C]150[/C][C]44760.6092785154[/C][C]34058.8371099089[/C][C]55462.381447122[/C][/ROW]
[ROW][C]151[/C][C]32665.4243201593[/C][C]21658.0030620365[/C][C]43672.845578282[/C][/ROW]
[ROW][C]152[/C][C]29567.4314253722[/C][C]18257.7844507193[/C][C]40877.0784000252[/C][/ROW]
[ROW][C]153[/C][C]32172.440365688[/C][C]20563.685143592[/C][C]43781.1955877841[/C][/ROW]
[ROW][C]154[/C][C]37581.0648854071[/C][C]25676.0463409091[/C][C]49486.083429905[/C][/ROW]
[ROW][C]155[/C][C]32161.9779773962[/C][C]19963.2970916841[/C][C]44360.6588631082[/C][/ROW]
[ROW][C]156[/C][C]24134.7449009519[/C][C]11644.7833849342[/C][C]36624.7064169696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233130&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233130&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
14543004.728186008633896.45738817452112.9989838431
14643230.214732650433792.925654304552667.5038109963
14756107.929995841946347.336884970265868.5231067136
14847661.579426047937582.802240538657740.3566115572
14942084.739583750231692.384959750252477.0942077502
15044760.609278515434058.837109908955462.381447122
15132665.424320159321658.003062036543672.845578282
15229567.431425372218257.784450719340877.0784000252
15332172.44036568820563.68514359243781.1955877841
15437581.064885407125676.046340909149486.083429905
15532161.977977396219963.297091684144360.6588631082
15624134.744900951911644.783384934236624.7064169696



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')