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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 computationThu, 15 Dec 2016 10:34:17 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/15/t1481794572j1wt38uxnvzxxx8.htm/, Retrieved Fri, 03 May 2024 14:05:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299791, Retrieved Fri, 03 May 2024 14:05:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsN1910
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ML Fitting and QQ Plot- Normal Distribution] [Normal distribution] [2016-12-15 09:27:42] [061bcad4f8cbfaa4a6cadfe6faec1e5a]
- RMP     [Exponential Smoothing] [Exponential smoot...] [2016-12-15 09:34:17] [9a9519454d094169f95f881e5b6f16f7] [Current]
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Dataseries X:
4738.4
4687.2
5930.8
5532
5429.8
6107.4
5960.8
5541.8
5362.2
5237
4827
4781.6
4983.2
4718.4
5523.8
5286.6
5389
5810.4
5057.4
5604.4
5285
5215.2
4625.4
4270.4
4685.4
4233.8
5278.4
4978.8
5333.4
5451
5224
5790.2
5079.4
4705.8
4139.6
3720.8
4594
4638.8
4969.4
4764.4
5010.8
5267.8
5312.2
5723.2
4579.6
5015.2
4282.4
3834.2
4523.4
3884.2
3897.8
4845.6
4929
4955.4
5198.4
5122.2
4643.2
4789.8
3950.8
3824.4
4511.8
4262.4
4616.6
5139.6
4972.8
5222
5242
4979.8
4691.8
4821.6
4123.6
4027.4
4365.2
4333.6
4930
5053
5031.4
5342
5191.4
4852.2
4675.6
4689.2
3809.4
4054.2
4409.6
4210.2
4566.4
4907
5021.8
5215.2
4933.6
5197.8
4734.6
4681.8
4172
4037.8
4462.6
4282.6
4962.4
4969.2
5214.6
5416.8
4764.2
5326.2
4545.4
4797.2
4259
4117
4469.2
4203.2
5033.8
4883
5361.6
5044.6
5005.6
5382
4565.4
4825
4290.2
3933.6
4177.6
3949.4
4492.6
4894.2
5224.4
5071




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299791&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299791&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299791&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.758563067988586
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.758563067988586 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299791&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]0.758563067988586[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299791&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299791&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
alpha0.758563067988586
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24687.24738.4-51.1999999999998
35930.84699.561570918981231.23842908102
455325633.53357110813-101.533571108126
55429.85556.51395390451-126.713953904509
66107.45460.39342827374647.00657172626
75960.85951.188718331199.6112816688119
85541.85958.47948164118-416.679481641185
95362.25642.40181567955-280.201815679555
1052375429.8510667217-192.8510667217
1148275283.56136988442-456.561369884415
124781.64937.23077641982-155.630776419822
134983.24819.17501718536164.024982814643
144718.44943.59831137601-225.198311376008
155523.84772.77118939277751.028810607226
165286.65342.47390811481-55.8739081148096
1753895300.0900249547388.9099750452724
185810.45367.53384839986442.866151600141
195057.45703.47575506596-646.07575506596
205604.45213.38654815008391.013451849916
2152855509.99491181016-224.994911810163
225215.25339.32208122562-124.122081225624
234625.45245.16765448599-619.767654485986
244270.44775.03480105901-504.634801059006
254685.44392.23747815388293.162521846123
264233.84614.61974014474-380.819740144742
275278.44325.74394970993952.656050290068
284978.85048.39364595585-69.5936459558534
295333.44995.60247636707337.797523632929
3054515251.84320225301199.156797746988
3152245402.91619376275-178.91619376275
325790.25267.19697690924523.003023090762
335079.45663.92775467227-584.527754672272
344705.85220.52658776359-514.726587763594
354139.64830.07400817435-690.474008174346
363720.84306.30592616724-585.505926167239
3745943862.16275448832731.83724551168
384638.84417.30746071198221.492539288024
394969.44585.32352085088384.076479149117
404764.44876.66975321649-112.269753216491
415010.84791.50606477427219.293935225733
425267.84957.85434507039309.945654929611
435312.25192.96767198353119.232328016474
445723.25283.41291252712439.787087472876
454579.65617.01915486231-1037.41915486231
465015.24830.07129795983185.128702040168
474282.44970.50309415217-688.103094152167
483834.24448.53349995966-614.33349995966
494523.43982.52279546209540.877204537906
503884.24392.81226714146-508.612267141458
513897.84006.997785362-109.197785362003
524845.63924.16437828024921.435621719757
5349294623.13141044595305.868589554048
544955.44855.15202613941100.247973860588
555198.44931.19643675074267.203563249261
565122.25133.88719146658-11.6871914665808
574643.25125.02171965152-481.821719651521
584789.84759.5295577691330.2704422308734
593950.84782.49159729715-831.691597297149
603824.44151.6010676311-327.201067631096
614511.83903.39842191971608.401578080289
624262.44364.90938955739-102.509389557393
634616.64287.1495525171329.450447482901
645139.64537.05849470994602.541505290059
654972.84994.12422755323-21.3242275532293
6652224977.94845607797244.051543922034
6752425163.0769439828278.9230560171845
684979.85222.94505949025-243.145059490245
694691.85038.50419719706-346.704197197058
704821.64775.5071976867446.0928023132619
714123.64810.47149522168-686.871495221678
724027.44289.43614649241-262.036146492415
734365.24090.66520328522274.534796714777
744333.64298.9171609508134.6828390491937
7549304325.22628174652604.773718253482
7650534783.98528890374269.014711096256
775031.44988.0499134869843.3500865130172
7853425020.93368810987321.066311890132
795191.45264.48273468503-73.0827346850265
804852.25209.04487124536-356.844871245356
814675.64938.35553091749-262.755530917487
824689.24739.03888925375-49.8388892537487
833809.44701.23294851628-891.832948516282
844054.24024.7214109564629.4785890435351
854409.64047.0827799013362.517220098697
864210.24322.07495457806-111.874954578064
874566.44237.21074580224329.189254197756
8849074486.92155641537420.078443584633
895021.84805.5775493768216.222450623204
905215.24969.59591488954245.604085110455
914933.65155.90210320146-222.30210320146
925197.84987.27193777665210.528062223354
934734.65146.97075055449-412.370750554485
944681.84834.16152886512-152.361528865119
9541724718.58570008576-546.585700085763
964037.84303.96597451002-266.165974510018
974462.64102.06229629153360.537703708473
984282.64375.55288294219-92.9528829421861
994962.44305.04225887918657.357741120822
1004969.24803.68956374983165.510436250165
1015214.64929.23966805589285.360331944112
1025416.85145.70347693766271.096523062345
1034764.25351.34728719287-587.147287192866
1045326.24905.95903965867420.24096034133
1054545.45224.73831182966-679.338311829659
1064797.24709.4173578059787.7826421940335
10742594776.00602818482-517.006028184816
10841174383.82434927635-266.824349276349
1094469.24181.42125227522287.778747724776
1104203.24399.71958205124-196.519582051244
1115033.84250.64708497062783.152915029383
11248834844.7179628995138.28203710049
1135361.64873.75730241131487.84269758869
1145044.65243.81675579002-199.216755790015
1155005.65092.69828232321-87.098282323208
11653825026.62874206758355.37125793242
1174565.45296.20025375976-730.800253759759
11848254741.8421711809283.1578288190804
1194290.24804.92262893719-514.722628937191
1203933.64414.47305236745-480.873052367445
1214177.64049.70051445056127.89948554944
1223949.44146.7203406031-197.320340603105
1234492.63997.04041765866495.559582341339
1244894.24372.95361481065521.246385189351
1255224.44768.35187193784456.048128062157
12650715114.29313911112-43.2931391111242

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 4687.2 & 4738.4 & -51.1999999999998 \tabularnewline
3 & 5930.8 & 4699.56157091898 & 1231.23842908102 \tabularnewline
4 & 5532 & 5633.53357110813 & -101.533571108126 \tabularnewline
5 & 5429.8 & 5556.51395390451 & -126.713953904509 \tabularnewline
6 & 6107.4 & 5460.39342827374 & 647.00657172626 \tabularnewline
7 & 5960.8 & 5951.18871833119 & 9.6112816688119 \tabularnewline
8 & 5541.8 & 5958.47948164118 & -416.679481641185 \tabularnewline
9 & 5362.2 & 5642.40181567955 & -280.201815679555 \tabularnewline
10 & 5237 & 5429.8510667217 & -192.8510667217 \tabularnewline
11 & 4827 & 5283.56136988442 & -456.561369884415 \tabularnewline
12 & 4781.6 & 4937.23077641982 & -155.630776419822 \tabularnewline
13 & 4983.2 & 4819.17501718536 & 164.024982814643 \tabularnewline
14 & 4718.4 & 4943.59831137601 & -225.198311376008 \tabularnewline
15 & 5523.8 & 4772.77118939277 & 751.028810607226 \tabularnewline
16 & 5286.6 & 5342.47390811481 & -55.8739081148096 \tabularnewline
17 & 5389 & 5300.09002495473 & 88.9099750452724 \tabularnewline
18 & 5810.4 & 5367.53384839986 & 442.866151600141 \tabularnewline
19 & 5057.4 & 5703.47575506596 & -646.07575506596 \tabularnewline
20 & 5604.4 & 5213.38654815008 & 391.013451849916 \tabularnewline
21 & 5285 & 5509.99491181016 & -224.994911810163 \tabularnewline
22 & 5215.2 & 5339.32208122562 & -124.122081225624 \tabularnewline
23 & 4625.4 & 5245.16765448599 & -619.767654485986 \tabularnewline
24 & 4270.4 & 4775.03480105901 & -504.634801059006 \tabularnewline
25 & 4685.4 & 4392.23747815388 & 293.162521846123 \tabularnewline
26 & 4233.8 & 4614.61974014474 & -380.819740144742 \tabularnewline
27 & 5278.4 & 4325.74394970993 & 952.656050290068 \tabularnewline
28 & 4978.8 & 5048.39364595585 & -69.5936459558534 \tabularnewline
29 & 5333.4 & 4995.60247636707 & 337.797523632929 \tabularnewline
30 & 5451 & 5251.84320225301 & 199.156797746988 \tabularnewline
31 & 5224 & 5402.91619376275 & -178.91619376275 \tabularnewline
32 & 5790.2 & 5267.19697690924 & 523.003023090762 \tabularnewline
33 & 5079.4 & 5663.92775467227 & -584.527754672272 \tabularnewline
34 & 4705.8 & 5220.52658776359 & -514.726587763594 \tabularnewline
35 & 4139.6 & 4830.07400817435 & -690.474008174346 \tabularnewline
36 & 3720.8 & 4306.30592616724 & -585.505926167239 \tabularnewline
37 & 4594 & 3862.16275448832 & 731.83724551168 \tabularnewline
38 & 4638.8 & 4417.30746071198 & 221.492539288024 \tabularnewline
39 & 4969.4 & 4585.32352085088 & 384.076479149117 \tabularnewline
40 & 4764.4 & 4876.66975321649 & -112.269753216491 \tabularnewline
41 & 5010.8 & 4791.50606477427 & 219.293935225733 \tabularnewline
42 & 5267.8 & 4957.85434507039 & 309.945654929611 \tabularnewline
43 & 5312.2 & 5192.96767198353 & 119.232328016474 \tabularnewline
44 & 5723.2 & 5283.41291252712 & 439.787087472876 \tabularnewline
45 & 4579.6 & 5617.01915486231 & -1037.41915486231 \tabularnewline
46 & 5015.2 & 4830.07129795983 & 185.128702040168 \tabularnewline
47 & 4282.4 & 4970.50309415217 & -688.103094152167 \tabularnewline
48 & 3834.2 & 4448.53349995966 & -614.33349995966 \tabularnewline
49 & 4523.4 & 3982.52279546209 & 540.877204537906 \tabularnewline
50 & 3884.2 & 4392.81226714146 & -508.612267141458 \tabularnewline
51 & 3897.8 & 4006.997785362 & -109.197785362003 \tabularnewline
52 & 4845.6 & 3924.16437828024 & 921.435621719757 \tabularnewline
53 & 4929 & 4623.13141044595 & 305.868589554048 \tabularnewline
54 & 4955.4 & 4855.15202613941 & 100.247973860588 \tabularnewline
55 & 5198.4 & 4931.19643675074 & 267.203563249261 \tabularnewline
56 & 5122.2 & 5133.88719146658 & -11.6871914665808 \tabularnewline
57 & 4643.2 & 5125.02171965152 & -481.821719651521 \tabularnewline
58 & 4789.8 & 4759.52955776913 & 30.2704422308734 \tabularnewline
59 & 3950.8 & 4782.49159729715 & -831.691597297149 \tabularnewline
60 & 3824.4 & 4151.6010676311 & -327.201067631096 \tabularnewline
61 & 4511.8 & 3903.39842191971 & 608.401578080289 \tabularnewline
62 & 4262.4 & 4364.90938955739 & -102.509389557393 \tabularnewline
63 & 4616.6 & 4287.1495525171 & 329.450447482901 \tabularnewline
64 & 5139.6 & 4537.05849470994 & 602.541505290059 \tabularnewline
65 & 4972.8 & 4994.12422755323 & -21.3242275532293 \tabularnewline
66 & 5222 & 4977.94845607797 & 244.051543922034 \tabularnewline
67 & 5242 & 5163.07694398282 & 78.9230560171845 \tabularnewline
68 & 4979.8 & 5222.94505949025 & -243.145059490245 \tabularnewline
69 & 4691.8 & 5038.50419719706 & -346.704197197058 \tabularnewline
70 & 4821.6 & 4775.50719768674 & 46.0928023132619 \tabularnewline
71 & 4123.6 & 4810.47149522168 & -686.871495221678 \tabularnewline
72 & 4027.4 & 4289.43614649241 & -262.036146492415 \tabularnewline
73 & 4365.2 & 4090.66520328522 & 274.534796714777 \tabularnewline
74 & 4333.6 & 4298.91716095081 & 34.6828390491937 \tabularnewline
75 & 4930 & 4325.22628174652 & 604.773718253482 \tabularnewline
76 & 5053 & 4783.98528890374 & 269.014711096256 \tabularnewline
77 & 5031.4 & 4988.04991348698 & 43.3500865130172 \tabularnewline
78 & 5342 & 5020.93368810987 & 321.066311890132 \tabularnewline
79 & 5191.4 & 5264.48273468503 & -73.0827346850265 \tabularnewline
80 & 4852.2 & 5209.04487124536 & -356.844871245356 \tabularnewline
81 & 4675.6 & 4938.35553091749 & -262.755530917487 \tabularnewline
82 & 4689.2 & 4739.03888925375 & -49.8388892537487 \tabularnewline
83 & 3809.4 & 4701.23294851628 & -891.832948516282 \tabularnewline
84 & 4054.2 & 4024.72141095646 & 29.4785890435351 \tabularnewline
85 & 4409.6 & 4047.0827799013 & 362.517220098697 \tabularnewline
86 & 4210.2 & 4322.07495457806 & -111.874954578064 \tabularnewline
87 & 4566.4 & 4237.21074580224 & 329.189254197756 \tabularnewline
88 & 4907 & 4486.92155641537 & 420.078443584633 \tabularnewline
89 & 5021.8 & 4805.5775493768 & 216.222450623204 \tabularnewline
90 & 5215.2 & 4969.59591488954 & 245.604085110455 \tabularnewline
91 & 4933.6 & 5155.90210320146 & -222.30210320146 \tabularnewline
92 & 5197.8 & 4987.27193777665 & 210.528062223354 \tabularnewline
93 & 4734.6 & 5146.97075055449 & -412.370750554485 \tabularnewline
94 & 4681.8 & 4834.16152886512 & -152.361528865119 \tabularnewline
95 & 4172 & 4718.58570008576 & -546.585700085763 \tabularnewline
96 & 4037.8 & 4303.96597451002 & -266.165974510018 \tabularnewline
97 & 4462.6 & 4102.06229629153 & 360.537703708473 \tabularnewline
98 & 4282.6 & 4375.55288294219 & -92.9528829421861 \tabularnewline
99 & 4962.4 & 4305.04225887918 & 657.357741120822 \tabularnewline
100 & 4969.2 & 4803.68956374983 & 165.510436250165 \tabularnewline
101 & 5214.6 & 4929.23966805589 & 285.360331944112 \tabularnewline
102 & 5416.8 & 5145.70347693766 & 271.096523062345 \tabularnewline
103 & 4764.2 & 5351.34728719287 & -587.147287192866 \tabularnewline
104 & 5326.2 & 4905.95903965867 & 420.24096034133 \tabularnewline
105 & 4545.4 & 5224.73831182966 & -679.338311829659 \tabularnewline
106 & 4797.2 & 4709.41735780597 & 87.7826421940335 \tabularnewline
107 & 4259 & 4776.00602818482 & -517.006028184816 \tabularnewline
108 & 4117 & 4383.82434927635 & -266.824349276349 \tabularnewline
109 & 4469.2 & 4181.42125227522 & 287.778747724776 \tabularnewline
110 & 4203.2 & 4399.71958205124 & -196.519582051244 \tabularnewline
111 & 5033.8 & 4250.64708497062 & 783.152915029383 \tabularnewline
112 & 4883 & 4844.71796289951 & 38.28203710049 \tabularnewline
113 & 5361.6 & 4873.75730241131 & 487.84269758869 \tabularnewline
114 & 5044.6 & 5243.81675579002 & -199.216755790015 \tabularnewline
115 & 5005.6 & 5092.69828232321 & -87.098282323208 \tabularnewline
116 & 5382 & 5026.62874206758 & 355.37125793242 \tabularnewline
117 & 4565.4 & 5296.20025375976 & -730.800253759759 \tabularnewline
118 & 4825 & 4741.84217118092 & 83.1578288190804 \tabularnewline
119 & 4290.2 & 4804.92262893719 & -514.722628937191 \tabularnewline
120 & 3933.6 & 4414.47305236745 & -480.873052367445 \tabularnewline
121 & 4177.6 & 4049.70051445056 & 127.89948554944 \tabularnewline
122 & 3949.4 & 4146.7203406031 & -197.320340603105 \tabularnewline
123 & 4492.6 & 3997.04041765866 & 495.559582341339 \tabularnewline
124 & 4894.2 & 4372.95361481065 & 521.246385189351 \tabularnewline
125 & 5224.4 & 4768.35187193784 & 456.048128062157 \tabularnewline
126 & 5071 & 5114.29313911112 & -43.2931391111242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299791&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]2[/C][C]4687.2[/C][C]4738.4[/C][C]-51.1999999999998[/C][/ROW]
[ROW][C]3[/C][C]5930.8[/C][C]4699.56157091898[/C][C]1231.23842908102[/C][/ROW]
[ROW][C]4[/C][C]5532[/C][C]5633.53357110813[/C][C]-101.533571108126[/C][/ROW]
[ROW][C]5[/C][C]5429.8[/C][C]5556.51395390451[/C][C]-126.713953904509[/C][/ROW]
[ROW][C]6[/C][C]6107.4[/C][C]5460.39342827374[/C][C]647.00657172626[/C][/ROW]
[ROW][C]7[/C][C]5960.8[/C][C]5951.18871833119[/C][C]9.6112816688119[/C][/ROW]
[ROW][C]8[/C][C]5541.8[/C][C]5958.47948164118[/C][C]-416.679481641185[/C][/ROW]
[ROW][C]9[/C][C]5362.2[/C][C]5642.40181567955[/C][C]-280.201815679555[/C][/ROW]
[ROW][C]10[/C][C]5237[/C][C]5429.8510667217[/C][C]-192.8510667217[/C][/ROW]
[ROW][C]11[/C][C]4827[/C][C]5283.56136988442[/C][C]-456.561369884415[/C][/ROW]
[ROW][C]12[/C][C]4781.6[/C][C]4937.23077641982[/C][C]-155.630776419822[/C][/ROW]
[ROW][C]13[/C][C]4983.2[/C][C]4819.17501718536[/C][C]164.024982814643[/C][/ROW]
[ROW][C]14[/C][C]4718.4[/C][C]4943.59831137601[/C][C]-225.198311376008[/C][/ROW]
[ROW][C]15[/C][C]5523.8[/C][C]4772.77118939277[/C][C]751.028810607226[/C][/ROW]
[ROW][C]16[/C][C]5286.6[/C][C]5342.47390811481[/C][C]-55.8739081148096[/C][/ROW]
[ROW][C]17[/C][C]5389[/C][C]5300.09002495473[/C][C]88.9099750452724[/C][/ROW]
[ROW][C]18[/C][C]5810.4[/C][C]5367.53384839986[/C][C]442.866151600141[/C][/ROW]
[ROW][C]19[/C][C]5057.4[/C][C]5703.47575506596[/C][C]-646.07575506596[/C][/ROW]
[ROW][C]20[/C][C]5604.4[/C][C]5213.38654815008[/C][C]391.013451849916[/C][/ROW]
[ROW][C]21[/C][C]5285[/C][C]5509.99491181016[/C][C]-224.994911810163[/C][/ROW]
[ROW][C]22[/C][C]5215.2[/C][C]5339.32208122562[/C][C]-124.122081225624[/C][/ROW]
[ROW][C]23[/C][C]4625.4[/C][C]5245.16765448599[/C][C]-619.767654485986[/C][/ROW]
[ROW][C]24[/C][C]4270.4[/C][C]4775.03480105901[/C][C]-504.634801059006[/C][/ROW]
[ROW][C]25[/C][C]4685.4[/C][C]4392.23747815388[/C][C]293.162521846123[/C][/ROW]
[ROW][C]26[/C][C]4233.8[/C][C]4614.61974014474[/C][C]-380.819740144742[/C][/ROW]
[ROW][C]27[/C][C]5278.4[/C][C]4325.74394970993[/C][C]952.656050290068[/C][/ROW]
[ROW][C]28[/C][C]4978.8[/C][C]5048.39364595585[/C][C]-69.5936459558534[/C][/ROW]
[ROW][C]29[/C][C]5333.4[/C][C]4995.60247636707[/C][C]337.797523632929[/C][/ROW]
[ROW][C]30[/C][C]5451[/C][C]5251.84320225301[/C][C]199.156797746988[/C][/ROW]
[ROW][C]31[/C][C]5224[/C][C]5402.91619376275[/C][C]-178.91619376275[/C][/ROW]
[ROW][C]32[/C][C]5790.2[/C][C]5267.19697690924[/C][C]523.003023090762[/C][/ROW]
[ROW][C]33[/C][C]5079.4[/C][C]5663.92775467227[/C][C]-584.527754672272[/C][/ROW]
[ROW][C]34[/C][C]4705.8[/C][C]5220.52658776359[/C][C]-514.726587763594[/C][/ROW]
[ROW][C]35[/C][C]4139.6[/C][C]4830.07400817435[/C][C]-690.474008174346[/C][/ROW]
[ROW][C]36[/C][C]3720.8[/C][C]4306.30592616724[/C][C]-585.505926167239[/C][/ROW]
[ROW][C]37[/C][C]4594[/C][C]3862.16275448832[/C][C]731.83724551168[/C][/ROW]
[ROW][C]38[/C][C]4638.8[/C][C]4417.30746071198[/C][C]221.492539288024[/C][/ROW]
[ROW][C]39[/C][C]4969.4[/C][C]4585.32352085088[/C][C]384.076479149117[/C][/ROW]
[ROW][C]40[/C][C]4764.4[/C][C]4876.66975321649[/C][C]-112.269753216491[/C][/ROW]
[ROW][C]41[/C][C]5010.8[/C][C]4791.50606477427[/C][C]219.293935225733[/C][/ROW]
[ROW][C]42[/C][C]5267.8[/C][C]4957.85434507039[/C][C]309.945654929611[/C][/ROW]
[ROW][C]43[/C][C]5312.2[/C][C]5192.96767198353[/C][C]119.232328016474[/C][/ROW]
[ROW][C]44[/C][C]5723.2[/C][C]5283.41291252712[/C][C]439.787087472876[/C][/ROW]
[ROW][C]45[/C][C]4579.6[/C][C]5617.01915486231[/C][C]-1037.41915486231[/C][/ROW]
[ROW][C]46[/C][C]5015.2[/C][C]4830.07129795983[/C][C]185.128702040168[/C][/ROW]
[ROW][C]47[/C][C]4282.4[/C][C]4970.50309415217[/C][C]-688.103094152167[/C][/ROW]
[ROW][C]48[/C][C]3834.2[/C][C]4448.53349995966[/C][C]-614.33349995966[/C][/ROW]
[ROW][C]49[/C][C]4523.4[/C][C]3982.52279546209[/C][C]540.877204537906[/C][/ROW]
[ROW][C]50[/C][C]3884.2[/C][C]4392.81226714146[/C][C]-508.612267141458[/C][/ROW]
[ROW][C]51[/C][C]3897.8[/C][C]4006.997785362[/C][C]-109.197785362003[/C][/ROW]
[ROW][C]52[/C][C]4845.6[/C][C]3924.16437828024[/C][C]921.435621719757[/C][/ROW]
[ROW][C]53[/C][C]4929[/C][C]4623.13141044595[/C][C]305.868589554048[/C][/ROW]
[ROW][C]54[/C][C]4955.4[/C][C]4855.15202613941[/C][C]100.247973860588[/C][/ROW]
[ROW][C]55[/C][C]5198.4[/C][C]4931.19643675074[/C][C]267.203563249261[/C][/ROW]
[ROW][C]56[/C][C]5122.2[/C][C]5133.88719146658[/C][C]-11.6871914665808[/C][/ROW]
[ROW][C]57[/C][C]4643.2[/C][C]5125.02171965152[/C][C]-481.821719651521[/C][/ROW]
[ROW][C]58[/C][C]4789.8[/C][C]4759.52955776913[/C][C]30.2704422308734[/C][/ROW]
[ROW][C]59[/C][C]3950.8[/C][C]4782.49159729715[/C][C]-831.691597297149[/C][/ROW]
[ROW][C]60[/C][C]3824.4[/C][C]4151.6010676311[/C][C]-327.201067631096[/C][/ROW]
[ROW][C]61[/C][C]4511.8[/C][C]3903.39842191971[/C][C]608.401578080289[/C][/ROW]
[ROW][C]62[/C][C]4262.4[/C][C]4364.90938955739[/C][C]-102.509389557393[/C][/ROW]
[ROW][C]63[/C][C]4616.6[/C][C]4287.1495525171[/C][C]329.450447482901[/C][/ROW]
[ROW][C]64[/C][C]5139.6[/C][C]4537.05849470994[/C][C]602.541505290059[/C][/ROW]
[ROW][C]65[/C][C]4972.8[/C][C]4994.12422755323[/C][C]-21.3242275532293[/C][/ROW]
[ROW][C]66[/C][C]5222[/C][C]4977.94845607797[/C][C]244.051543922034[/C][/ROW]
[ROW][C]67[/C][C]5242[/C][C]5163.07694398282[/C][C]78.9230560171845[/C][/ROW]
[ROW][C]68[/C][C]4979.8[/C][C]5222.94505949025[/C][C]-243.145059490245[/C][/ROW]
[ROW][C]69[/C][C]4691.8[/C][C]5038.50419719706[/C][C]-346.704197197058[/C][/ROW]
[ROW][C]70[/C][C]4821.6[/C][C]4775.50719768674[/C][C]46.0928023132619[/C][/ROW]
[ROW][C]71[/C][C]4123.6[/C][C]4810.47149522168[/C][C]-686.871495221678[/C][/ROW]
[ROW][C]72[/C][C]4027.4[/C][C]4289.43614649241[/C][C]-262.036146492415[/C][/ROW]
[ROW][C]73[/C][C]4365.2[/C][C]4090.66520328522[/C][C]274.534796714777[/C][/ROW]
[ROW][C]74[/C][C]4333.6[/C][C]4298.91716095081[/C][C]34.6828390491937[/C][/ROW]
[ROW][C]75[/C][C]4930[/C][C]4325.22628174652[/C][C]604.773718253482[/C][/ROW]
[ROW][C]76[/C][C]5053[/C][C]4783.98528890374[/C][C]269.014711096256[/C][/ROW]
[ROW][C]77[/C][C]5031.4[/C][C]4988.04991348698[/C][C]43.3500865130172[/C][/ROW]
[ROW][C]78[/C][C]5342[/C][C]5020.93368810987[/C][C]321.066311890132[/C][/ROW]
[ROW][C]79[/C][C]5191.4[/C][C]5264.48273468503[/C][C]-73.0827346850265[/C][/ROW]
[ROW][C]80[/C][C]4852.2[/C][C]5209.04487124536[/C][C]-356.844871245356[/C][/ROW]
[ROW][C]81[/C][C]4675.6[/C][C]4938.35553091749[/C][C]-262.755530917487[/C][/ROW]
[ROW][C]82[/C][C]4689.2[/C][C]4739.03888925375[/C][C]-49.8388892537487[/C][/ROW]
[ROW][C]83[/C][C]3809.4[/C][C]4701.23294851628[/C][C]-891.832948516282[/C][/ROW]
[ROW][C]84[/C][C]4054.2[/C][C]4024.72141095646[/C][C]29.4785890435351[/C][/ROW]
[ROW][C]85[/C][C]4409.6[/C][C]4047.0827799013[/C][C]362.517220098697[/C][/ROW]
[ROW][C]86[/C][C]4210.2[/C][C]4322.07495457806[/C][C]-111.874954578064[/C][/ROW]
[ROW][C]87[/C][C]4566.4[/C][C]4237.21074580224[/C][C]329.189254197756[/C][/ROW]
[ROW][C]88[/C][C]4907[/C][C]4486.92155641537[/C][C]420.078443584633[/C][/ROW]
[ROW][C]89[/C][C]5021.8[/C][C]4805.5775493768[/C][C]216.222450623204[/C][/ROW]
[ROW][C]90[/C][C]5215.2[/C][C]4969.59591488954[/C][C]245.604085110455[/C][/ROW]
[ROW][C]91[/C][C]4933.6[/C][C]5155.90210320146[/C][C]-222.30210320146[/C][/ROW]
[ROW][C]92[/C][C]5197.8[/C][C]4987.27193777665[/C][C]210.528062223354[/C][/ROW]
[ROW][C]93[/C][C]4734.6[/C][C]5146.97075055449[/C][C]-412.370750554485[/C][/ROW]
[ROW][C]94[/C][C]4681.8[/C][C]4834.16152886512[/C][C]-152.361528865119[/C][/ROW]
[ROW][C]95[/C][C]4172[/C][C]4718.58570008576[/C][C]-546.585700085763[/C][/ROW]
[ROW][C]96[/C][C]4037.8[/C][C]4303.96597451002[/C][C]-266.165974510018[/C][/ROW]
[ROW][C]97[/C][C]4462.6[/C][C]4102.06229629153[/C][C]360.537703708473[/C][/ROW]
[ROW][C]98[/C][C]4282.6[/C][C]4375.55288294219[/C][C]-92.9528829421861[/C][/ROW]
[ROW][C]99[/C][C]4962.4[/C][C]4305.04225887918[/C][C]657.357741120822[/C][/ROW]
[ROW][C]100[/C][C]4969.2[/C][C]4803.68956374983[/C][C]165.510436250165[/C][/ROW]
[ROW][C]101[/C][C]5214.6[/C][C]4929.23966805589[/C][C]285.360331944112[/C][/ROW]
[ROW][C]102[/C][C]5416.8[/C][C]5145.70347693766[/C][C]271.096523062345[/C][/ROW]
[ROW][C]103[/C][C]4764.2[/C][C]5351.34728719287[/C][C]-587.147287192866[/C][/ROW]
[ROW][C]104[/C][C]5326.2[/C][C]4905.95903965867[/C][C]420.24096034133[/C][/ROW]
[ROW][C]105[/C][C]4545.4[/C][C]5224.73831182966[/C][C]-679.338311829659[/C][/ROW]
[ROW][C]106[/C][C]4797.2[/C][C]4709.41735780597[/C][C]87.7826421940335[/C][/ROW]
[ROW][C]107[/C][C]4259[/C][C]4776.00602818482[/C][C]-517.006028184816[/C][/ROW]
[ROW][C]108[/C][C]4117[/C][C]4383.82434927635[/C][C]-266.824349276349[/C][/ROW]
[ROW][C]109[/C][C]4469.2[/C][C]4181.42125227522[/C][C]287.778747724776[/C][/ROW]
[ROW][C]110[/C][C]4203.2[/C][C]4399.71958205124[/C][C]-196.519582051244[/C][/ROW]
[ROW][C]111[/C][C]5033.8[/C][C]4250.64708497062[/C][C]783.152915029383[/C][/ROW]
[ROW][C]112[/C][C]4883[/C][C]4844.71796289951[/C][C]38.28203710049[/C][/ROW]
[ROW][C]113[/C][C]5361.6[/C][C]4873.75730241131[/C][C]487.84269758869[/C][/ROW]
[ROW][C]114[/C][C]5044.6[/C][C]5243.81675579002[/C][C]-199.216755790015[/C][/ROW]
[ROW][C]115[/C][C]5005.6[/C][C]5092.69828232321[/C][C]-87.098282323208[/C][/ROW]
[ROW][C]116[/C][C]5382[/C][C]5026.62874206758[/C][C]355.37125793242[/C][/ROW]
[ROW][C]117[/C][C]4565.4[/C][C]5296.20025375976[/C][C]-730.800253759759[/C][/ROW]
[ROW][C]118[/C][C]4825[/C][C]4741.84217118092[/C][C]83.1578288190804[/C][/ROW]
[ROW][C]119[/C][C]4290.2[/C][C]4804.92262893719[/C][C]-514.722628937191[/C][/ROW]
[ROW][C]120[/C][C]3933.6[/C][C]4414.47305236745[/C][C]-480.873052367445[/C][/ROW]
[ROW][C]121[/C][C]4177.6[/C][C]4049.70051445056[/C][C]127.89948554944[/C][/ROW]
[ROW][C]122[/C][C]3949.4[/C][C]4146.7203406031[/C][C]-197.320340603105[/C][/ROW]
[ROW][C]123[/C][C]4492.6[/C][C]3997.04041765866[/C][C]495.559582341339[/C][/ROW]
[ROW][C]124[/C][C]4894.2[/C][C]4372.95361481065[/C][C]521.246385189351[/C][/ROW]
[ROW][C]125[/C][C]5224.4[/C][C]4768.35187193784[/C][C]456.048128062157[/C][/ROW]
[ROW][C]126[/C][C]5071[/C][C]5114.29313911112[/C][C]-43.2931391111242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299791&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299791&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
24687.24738.4-51.1999999999998
35930.84699.561570918981231.23842908102
455325633.53357110813-101.533571108126
55429.85556.51395390451-126.713953904509
66107.45460.39342827374647.00657172626
75960.85951.188718331199.6112816688119
85541.85958.47948164118-416.679481641185
95362.25642.40181567955-280.201815679555
1052375429.8510667217-192.8510667217
1148275283.56136988442-456.561369884415
124781.64937.23077641982-155.630776419822
134983.24819.17501718536164.024982814643
144718.44943.59831137601-225.198311376008
155523.84772.77118939277751.028810607226
165286.65342.47390811481-55.8739081148096
1753895300.0900249547388.9099750452724
185810.45367.53384839986442.866151600141
195057.45703.47575506596-646.07575506596
205604.45213.38654815008391.013451849916
2152855509.99491181016-224.994911810163
225215.25339.32208122562-124.122081225624
234625.45245.16765448599-619.767654485986
244270.44775.03480105901-504.634801059006
254685.44392.23747815388293.162521846123
264233.84614.61974014474-380.819740144742
275278.44325.74394970993952.656050290068
284978.85048.39364595585-69.5936459558534
295333.44995.60247636707337.797523632929
3054515251.84320225301199.156797746988
3152245402.91619376275-178.91619376275
325790.25267.19697690924523.003023090762
335079.45663.92775467227-584.527754672272
344705.85220.52658776359-514.726587763594
354139.64830.07400817435-690.474008174346
363720.84306.30592616724-585.505926167239
3745943862.16275448832731.83724551168
384638.84417.30746071198221.492539288024
394969.44585.32352085088384.076479149117
404764.44876.66975321649-112.269753216491
415010.84791.50606477427219.293935225733
425267.84957.85434507039309.945654929611
435312.25192.96767198353119.232328016474
445723.25283.41291252712439.787087472876
454579.65617.01915486231-1037.41915486231
465015.24830.07129795983185.128702040168
474282.44970.50309415217-688.103094152167
483834.24448.53349995966-614.33349995966
494523.43982.52279546209540.877204537906
503884.24392.81226714146-508.612267141458
513897.84006.997785362-109.197785362003
524845.63924.16437828024921.435621719757
5349294623.13141044595305.868589554048
544955.44855.15202613941100.247973860588
555198.44931.19643675074267.203563249261
565122.25133.88719146658-11.6871914665808
574643.25125.02171965152-481.821719651521
584789.84759.5295577691330.2704422308734
593950.84782.49159729715-831.691597297149
603824.44151.6010676311-327.201067631096
614511.83903.39842191971608.401578080289
624262.44364.90938955739-102.509389557393
634616.64287.1495525171329.450447482901
645139.64537.05849470994602.541505290059
654972.84994.12422755323-21.3242275532293
6652224977.94845607797244.051543922034
6752425163.0769439828278.9230560171845
684979.85222.94505949025-243.145059490245
694691.85038.50419719706-346.704197197058
704821.64775.5071976867446.0928023132619
714123.64810.47149522168-686.871495221678
724027.44289.43614649241-262.036146492415
734365.24090.66520328522274.534796714777
744333.64298.9171609508134.6828390491937
7549304325.22628174652604.773718253482
7650534783.98528890374269.014711096256
775031.44988.0499134869843.3500865130172
7853425020.93368810987321.066311890132
795191.45264.48273468503-73.0827346850265
804852.25209.04487124536-356.844871245356
814675.64938.35553091749-262.755530917487
824689.24739.03888925375-49.8388892537487
833809.44701.23294851628-891.832948516282
844054.24024.7214109564629.4785890435351
854409.64047.0827799013362.517220098697
864210.24322.07495457806-111.874954578064
874566.44237.21074580224329.189254197756
8849074486.92155641537420.078443584633
895021.84805.5775493768216.222450623204
905215.24969.59591488954245.604085110455
914933.65155.90210320146-222.30210320146
925197.84987.27193777665210.528062223354
934734.65146.97075055449-412.370750554485
944681.84834.16152886512-152.361528865119
9541724718.58570008576-546.585700085763
964037.84303.96597451002-266.165974510018
974462.64102.06229629153360.537703708473
984282.64375.55288294219-92.9528829421861
994962.44305.04225887918657.357741120822
1004969.24803.68956374983165.510436250165
1015214.64929.23966805589285.360331944112
1025416.85145.70347693766271.096523062345
1034764.25351.34728719287-587.147287192866
1045326.24905.95903965867420.24096034133
1054545.45224.73831182966-679.338311829659
1064797.24709.4173578059787.7826421940335
10742594776.00602818482-517.006028184816
10841174383.82434927635-266.824349276349
1094469.24181.42125227522287.778747724776
1104203.24399.71958205124-196.519582051244
1115033.84250.64708497062783.152915029383
11248834844.7179628995138.28203710049
1135361.64873.75730241131487.84269758869
1145044.65243.81675579002-199.216755790015
1155005.65092.69828232321-87.098282323208
11653825026.62874206758355.37125793242
1174565.45296.20025375976-730.800253759759
11848254741.8421711809283.1578288190804
1194290.24804.92262893719-514.722628937191
1203933.64414.47305236745-480.873052367445
1214177.64049.70051445056127.89948554944
1223949.44146.7203406031-197.320340603105
1234492.63997.04041765866495.559582341339
1244894.24372.95361481065521.246385189351
1255224.44768.35187193784456.048128062157
12650715114.29313911112-43.2931391111242







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1275081.452562684134240.715348287865922.1897770804
1285081.452562684134026.195753561416136.70937180686
1295081.452562684133848.450209592726314.45491577555
1305081.452562684133693.28014102396469.62498434437
1315081.452562684133553.790773613296609.11435175498
1325081.452562684133426.013523843926736.89160152435
1335081.452562684133307.415843547446855.48928182083
1345081.452562684133196.264468521016966.64065684725
1355081.452562684133091.311356662957071.59376870532
1365081.452562684132991.622452499927171.28267286834
1375081.452562684132896.477103105327266.42802226294
1385081.452562684132805.305461003157357.59966436511

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 5081.45256268413 & 4240.71534828786 & 5922.1897770804 \tabularnewline
128 & 5081.45256268413 & 4026.19575356141 & 6136.70937180686 \tabularnewline
129 & 5081.45256268413 & 3848.45020959272 & 6314.45491577555 \tabularnewline
130 & 5081.45256268413 & 3693.2801410239 & 6469.62498434437 \tabularnewline
131 & 5081.45256268413 & 3553.79077361329 & 6609.11435175498 \tabularnewline
132 & 5081.45256268413 & 3426.01352384392 & 6736.89160152435 \tabularnewline
133 & 5081.45256268413 & 3307.41584354744 & 6855.48928182083 \tabularnewline
134 & 5081.45256268413 & 3196.26446852101 & 6966.64065684725 \tabularnewline
135 & 5081.45256268413 & 3091.31135666295 & 7071.59376870532 \tabularnewline
136 & 5081.45256268413 & 2991.62245249992 & 7171.28267286834 \tabularnewline
137 & 5081.45256268413 & 2896.47710310532 & 7266.42802226294 \tabularnewline
138 & 5081.45256268413 & 2805.30546100315 & 7357.59966436511 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299791&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]127[/C][C]5081.45256268413[/C][C]4240.71534828786[/C][C]5922.1897770804[/C][/ROW]
[ROW][C]128[/C][C]5081.45256268413[/C][C]4026.19575356141[/C][C]6136.70937180686[/C][/ROW]
[ROW][C]129[/C][C]5081.45256268413[/C][C]3848.45020959272[/C][C]6314.45491577555[/C][/ROW]
[ROW][C]130[/C][C]5081.45256268413[/C][C]3693.2801410239[/C][C]6469.62498434437[/C][/ROW]
[ROW][C]131[/C][C]5081.45256268413[/C][C]3553.79077361329[/C][C]6609.11435175498[/C][/ROW]
[ROW][C]132[/C][C]5081.45256268413[/C][C]3426.01352384392[/C][C]6736.89160152435[/C][/ROW]
[ROW][C]133[/C][C]5081.45256268413[/C][C]3307.41584354744[/C][C]6855.48928182083[/C][/ROW]
[ROW][C]134[/C][C]5081.45256268413[/C][C]3196.26446852101[/C][C]6966.64065684725[/C][/ROW]
[ROW][C]135[/C][C]5081.45256268413[/C][C]3091.31135666295[/C][C]7071.59376870532[/C][/ROW]
[ROW][C]136[/C][C]5081.45256268413[/C][C]2991.62245249992[/C][C]7171.28267286834[/C][/ROW]
[ROW][C]137[/C][C]5081.45256268413[/C][C]2896.47710310532[/C][C]7266.42802226294[/C][/ROW]
[ROW][C]138[/C][C]5081.45256268413[/C][C]2805.30546100315[/C][C]7357.59966436511[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299791&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299791&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
1275081.452562684134240.715348287865922.1897770804
1285081.452562684134026.195753561416136.70937180686
1295081.452562684133848.450209592726314.45491577555
1305081.452562684133693.28014102396469.62498434437
1315081.452562684133553.790773613296609.11435175498
1325081.452562684133426.013523843926736.89160152435
1335081.452562684133307.415843547446855.48928182083
1345081.452562684133196.264468521016966.64065684725
1355081.452562684133091.311356662957071.59376870532
1365081.452562684132991.622452499927171.28267286834
1375081.452562684132896.477103105327266.42802226294
1385081.452562684132805.305461003157357.59966436511



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')