Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 17 Dec 2016 12:52:06 +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/17/t1481975542szt5j4zal3p1697.htm/, Retrieved Thu, 02 May 2024 02:24:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300731, Retrieved Thu, 02 May 2024 02:24:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-17 11:52:06] [349958aef20b862f8399a5ba04d6f6e3] [Current]
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Dataseries X:
990
1384
1350
716
2068
1392
734
758
558
1620
3132
1392
918
776
1348
502
1274
1638
912
1250
1614
2840
1150
1652
1526
1412
882
848
820
1226
1212
2110
1178
2548
1568
2088
2178
3016
5514
1358
3604
1962
2036
2246
3434
4316
3032
5296
3850
2098
3992
4860
7336
9614
2988
2756
3540
2710
3730
3508
2640
2788
3502
3700
3250
4866
2836
3498
3468
3924
5738
7028
5608
6030
11976
7774
7906
10940
7626
5930
6286
6788
6932
6660
4910
4182
3550
3184
3872
3226
2504
3648
4448
2954
3842
3982
4864
6796
5844
5656
6118
7068
7696
7016
5820
4904
3860
7222
7738
7142
13804
7964
9716
8462
6884
8072
7320
11700
10792
10930
7112
8196
16818
10524
14878
13696




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=300731&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=300731&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300731&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
alpha0.462005621612651
beta0.00478961576064138
gamma0.28415857245498

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.462005621612651 \tabularnewline
beta & 0.00478961576064138 \tabularnewline
gamma & 0.28415857245498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300731&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]0.462005621612651[/C][/ROW]
[ROW][C]beta[/C][C]0.00478961576064138[/C][/ROW]
[ROW][C]gamma[/C][C]0.28415857245498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300731&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300731&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
alpha0.462005621612651
beta0.00478961576064138
gamma0.28415857245498







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139181032.70405982906-114.70405982906
14776815.159116052371-39.1591160523712
1513481309.8463752080538.1536247919539
16502392.003649385663109.996350614337
1712741252.1794032578121.8205967421914
1816381703.66574840923-65.6657484092341
19912748.670936520591163.329063479409
201250882.334434399282367.665565600718
211614884.299459467439729.700540532561
2228402300.72471432207539.27528567793
2311504113.36575514734-2963.36575514734
2416521030.04285506744621.957144932559
251526812.500110072785713.499889927215
261412989.663933790591422.336066209409
278821710.92991171395-828.929911713951
28848403.100127430847444.899872569153
298201404.89174589387-584.891745893874
3012261561.72497573309-335.724975733092
311212515.397368364639696.602631635361
322110926.2827250091621183.71727499084
3311781362.02874969707-184.028749697072
3425482326.58677875531221.413221244689
3515683455.59387228484-1887.59387228484
3620881418.46179486756669.538205132441
3721781238.07108345007939.928916549926
3830161477.010215299631538.98978470037
3955142527.034974815272986.96502518473
4013583189.49833260485-1831.49833260485
4136042989.70436410023614.295635899773
4219623748.86736119174-1786.86736119174
4320362196.91741153046-160.91741153046
4422462291.18991811175-45.1899181117474
4534341952.45762967551481.5423703245
4643163754.56560452808561.434395471918
4730324725.06532858585-1693.06532858585
4852963175.977286926062120.02271307394
4938503717.51178169594132.488218304063
5020983683.66093783434-1585.66093783434
5139923513.1957362189478.804263781097
5248602276.454550294662583.54544970534
5373364496.313725002092839.68627499791
5496145927.440204092483686.55979590752
5529887175.82439683272-4187.82439683272
5627565441.43606950239-2685.43606950239
5735404124.55399964054-584.553999640535
5827104835.13824728581-2125.13824728581
5937304217.50969893027-487.509698930266
6035083808.73303098558-300.733030985576
6126402923.07162449983-283.071624499828
6227882428.69957128986359.300428710138
6335023470.8609695016631.1390304983361
6437002346.506056952381353.49394304762
6532504031.95665326572-781.95665326572
6648663906.04047755828959.959522441719
6728362671.59474757402164.405252425985
6834983167.94725720197330.052742798026
6934683562.39216384818-94.3921638481752
7039244261.98100766544-337.981007665442
7157384722.402449535451015.59755046455
7270285041.969181510111986.03081848989
7356085225.91153145024382.088468549758
7460305148.92815548913881.071844510874
75119766395.015452235625580.98454776438
7677748062.18966073293-288.189660732929
7779068684.3952424762-778.395242476203
78109408848.109594505132091.89040549487
7976268039.19459410073-413.194594100725
8059308316.93130194462-2386.93130194462
8162867408.12986140428-1122.12986140428
8267887610.28795836013-822.28795836013
8369328067.44313254427-1135.44313254427
8466607550.36974669222-890.369746692218
8549106162.62713967292-1252.62713967292
8641825405.49316336547-1223.49316336547
8735506391.91982516595-2841.91982516595
8831843245.92992852962-61.9299285296192
8938723873.74819051467-1.7481905146692
9032264812.8133439994-1586.8133439994
9125041890.94805596094613.051944039058
9236482312.949116761171335.05088323883
9344483297.186997659891150.81300234011
9429544580.43085961313-1626.43085961313
9538424601.54907992329-759.549079923286
9639824279.79382600968-297.793826009681
9748643095.942734714741768.05726528526
9867963731.018538281433064.98146171857
9958446452.99884162293-608.998841622925
10056564770.23739609024885.762603909765
10161185853.80580592505264.19419407495
10270686682.71889739542385.281102604582
10376965021.941245678672674.05875432133
10470166524.7387370381491.261262961898
10558207107.33200402712-1287.33200402712
10649046850.52725969081-1946.52725969081
10738606866.53722932003-3006.53722932003
10872225582.532695735621639.46730426438
10977385619.093139952682118.90686004732
11071426624.87555324459517.124446755414
111138047612.775166915916191.22483308409
11279649320.02168473996-1356.02168473996
11397169287.64342313109428.356576868908
114846210226.0679564735-1764.06795647347
11568847932.57758330639-1048.57758330639
11680727383.96198178738688.038018212618
11773207788.16148124592-468.161481245922
118117007813.453844305593886.54615569441
1191079210379.6450045191412.354995480926
1201093011410.3328495503-480.332849550297
121711210561.0213027565-3449.02130275652
12281968757.38803000878-561.388030008777
1231681810119.92646020656698.07353979349
1241052410914.1562880276-390.156288027589
1251487811609.54572904493268.45427095509
1261369613539.9719053958156.028094604215

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 918 & 1032.70405982906 & -114.70405982906 \tabularnewline
14 & 776 & 815.159116052371 & -39.1591160523712 \tabularnewline
15 & 1348 & 1309.84637520805 & 38.1536247919539 \tabularnewline
16 & 502 & 392.003649385663 & 109.996350614337 \tabularnewline
17 & 1274 & 1252.17940325781 & 21.8205967421914 \tabularnewline
18 & 1638 & 1703.66574840923 & -65.6657484092341 \tabularnewline
19 & 912 & 748.670936520591 & 163.329063479409 \tabularnewline
20 & 1250 & 882.334434399282 & 367.665565600718 \tabularnewline
21 & 1614 & 884.299459467439 & 729.700540532561 \tabularnewline
22 & 2840 & 2300.72471432207 & 539.27528567793 \tabularnewline
23 & 1150 & 4113.36575514734 & -2963.36575514734 \tabularnewline
24 & 1652 & 1030.04285506744 & 621.957144932559 \tabularnewline
25 & 1526 & 812.500110072785 & 713.499889927215 \tabularnewline
26 & 1412 & 989.663933790591 & 422.336066209409 \tabularnewline
27 & 882 & 1710.92991171395 & -828.929911713951 \tabularnewline
28 & 848 & 403.100127430847 & 444.899872569153 \tabularnewline
29 & 820 & 1404.89174589387 & -584.891745893874 \tabularnewline
30 & 1226 & 1561.72497573309 & -335.724975733092 \tabularnewline
31 & 1212 & 515.397368364639 & 696.602631635361 \tabularnewline
32 & 2110 & 926.282725009162 & 1183.71727499084 \tabularnewline
33 & 1178 & 1362.02874969707 & -184.028749697072 \tabularnewline
34 & 2548 & 2326.58677875531 & 221.413221244689 \tabularnewline
35 & 1568 & 3455.59387228484 & -1887.59387228484 \tabularnewline
36 & 2088 & 1418.46179486756 & 669.538205132441 \tabularnewline
37 & 2178 & 1238.07108345007 & 939.928916549926 \tabularnewline
38 & 3016 & 1477.01021529963 & 1538.98978470037 \tabularnewline
39 & 5514 & 2527.03497481527 & 2986.96502518473 \tabularnewline
40 & 1358 & 3189.49833260485 & -1831.49833260485 \tabularnewline
41 & 3604 & 2989.70436410023 & 614.295635899773 \tabularnewline
42 & 1962 & 3748.86736119174 & -1786.86736119174 \tabularnewline
43 & 2036 & 2196.91741153046 & -160.91741153046 \tabularnewline
44 & 2246 & 2291.18991811175 & -45.1899181117474 \tabularnewline
45 & 3434 & 1952.4576296755 & 1481.5423703245 \tabularnewline
46 & 4316 & 3754.56560452808 & 561.434395471918 \tabularnewline
47 & 3032 & 4725.06532858585 & -1693.06532858585 \tabularnewline
48 & 5296 & 3175.97728692606 & 2120.02271307394 \tabularnewline
49 & 3850 & 3717.51178169594 & 132.488218304063 \tabularnewline
50 & 2098 & 3683.66093783434 & -1585.66093783434 \tabularnewline
51 & 3992 & 3513.1957362189 & 478.804263781097 \tabularnewline
52 & 4860 & 2276.45455029466 & 2583.54544970534 \tabularnewline
53 & 7336 & 4496.31372500209 & 2839.68627499791 \tabularnewline
54 & 9614 & 5927.44020409248 & 3686.55979590752 \tabularnewline
55 & 2988 & 7175.82439683272 & -4187.82439683272 \tabularnewline
56 & 2756 & 5441.43606950239 & -2685.43606950239 \tabularnewline
57 & 3540 & 4124.55399964054 & -584.553999640535 \tabularnewline
58 & 2710 & 4835.13824728581 & -2125.13824728581 \tabularnewline
59 & 3730 & 4217.50969893027 & -487.509698930266 \tabularnewline
60 & 3508 & 3808.73303098558 & -300.733030985576 \tabularnewline
61 & 2640 & 2923.07162449983 & -283.071624499828 \tabularnewline
62 & 2788 & 2428.69957128986 & 359.300428710138 \tabularnewline
63 & 3502 & 3470.86096950166 & 31.1390304983361 \tabularnewline
64 & 3700 & 2346.50605695238 & 1353.49394304762 \tabularnewline
65 & 3250 & 4031.95665326572 & -781.95665326572 \tabularnewline
66 & 4866 & 3906.04047755828 & 959.959522441719 \tabularnewline
67 & 2836 & 2671.59474757402 & 164.405252425985 \tabularnewline
68 & 3498 & 3167.94725720197 & 330.052742798026 \tabularnewline
69 & 3468 & 3562.39216384818 & -94.3921638481752 \tabularnewline
70 & 3924 & 4261.98100766544 & -337.981007665442 \tabularnewline
71 & 5738 & 4722.40244953545 & 1015.59755046455 \tabularnewline
72 & 7028 & 5041.96918151011 & 1986.03081848989 \tabularnewline
73 & 5608 & 5225.91153145024 & 382.088468549758 \tabularnewline
74 & 6030 & 5148.92815548913 & 881.071844510874 \tabularnewline
75 & 11976 & 6395.01545223562 & 5580.98454776438 \tabularnewline
76 & 7774 & 8062.18966073293 & -288.189660732929 \tabularnewline
77 & 7906 & 8684.3952424762 & -778.395242476203 \tabularnewline
78 & 10940 & 8848.10959450513 & 2091.89040549487 \tabularnewline
79 & 7626 & 8039.19459410073 & -413.194594100725 \tabularnewline
80 & 5930 & 8316.93130194462 & -2386.93130194462 \tabularnewline
81 & 6286 & 7408.12986140428 & -1122.12986140428 \tabularnewline
82 & 6788 & 7610.28795836013 & -822.28795836013 \tabularnewline
83 & 6932 & 8067.44313254427 & -1135.44313254427 \tabularnewline
84 & 6660 & 7550.36974669222 & -890.369746692218 \tabularnewline
85 & 4910 & 6162.62713967292 & -1252.62713967292 \tabularnewline
86 & 4182 & 5405.49316336547 & -1223.49316336547 \tabularnewline
87 & 3550 & 6391.91982516595 & -2841.91982516595 \tabularnewline
88 & 3184 & 3245.92992852962 & -61.9299285296192 \tabularnewline
89 & 3872 & 3873.74819051467 & -1.7481905146692 \tabularnewline
90 & 3226 & 4812.8133439994 & -1586.8133439994 \tabularnewline
91 & 2504 & 1890.94805596094 & 613.051944039058 \tabularnewline
92 & 3648 & 2312.94911676117 & 1335.05088323883 \tabularnewline
93 & 4448 & 3297.18699765989 & 1150.81300234011 \tabularnewline
94 & 2954 & 4580.43085961313 & -1626.43085961313 \tabularnewline
95 & 3842 & 4601.54907992329 & -759.549079923286 \tabularnewline
96 & 3982 & 4279.79382600968 & -297.793826009681 \tabularnewline
97 & 4864 & 3095.94273471474 & 1768.05726528526 \tabularnewline
98 & 6796 & 3731.01853828143 & 3064.98146171857 \tabularnewline
99 & 5844 & 6452.99884162293 & -608.998841622925 \tabularnewline
100 & 5656 & 4770.23739609024 & 885.762603909765 \tabularnewline
101 & 6118 & 5853.80580592505 & 264.19419407495 \tabularnewline
102 & 7068 & 6682.71889739542 & 385.281102604582 \tabularnewline
103 & 7696 & 5021.94124567867 & 2674.05875432133 \tabularnewline
104 & 7016 & 6524.7387370381 & 491.261262961898 \tabularnewline
105 & 5820 & 7107.33200402712 & -1287.33200402712 \tabularnewline
106 & 4904 & 6850.52725969081 & -1946.52725969081 \tabularnewline
107 & 3860 & 6866.53722932003 & -3006.53722932003 \tabularnewline
108 & 7222 & 5582.53269573562 & 1639.46730426438 \tabularnewline
109 & 7738 & 5619.09313995268 & 2118.90686004732 \tabularnewline
110 & 7142 & 6624.87555324459 & 517.124446755414 \tabularnewline
111 & 13804 & 7612.77516691591 & 6191.22483308409 \tabularnewline
112 & 7964 & 9320.02168473996 & -1356.02168473996 \tabularnewline
113 & 9716 & 9287.64342313109 & 428.356576868908 \tabularnewline
114 & 8462 & 10226.0679564735 & -1764.06795647347 \tabularnewline
115 & 6884 & 7932.57758330639 & -1048.57758330639 \tabularnewline
116 & 8072 & 7383.96198178738 & 688.038018212618 \tabularnewline
117 & 7320 & 7788.16148124592 & -468.161481245922 \tabularnewline
118 & 11700 & 7813.45384430559 & 3886.54615569441 \tabularnewline
119 & 10792 & 10379.6450045191 & 412.354995480926 \tabularnewline
120 & 10930 & 11410.3328495503 & -480.332849550297 \tabularnewline
121 & 7112 & 10561.0213027565 & -3449.02130275652 \tabularnewline
122 & 8196 & 8757.38803000878 & -561.388030008777 \tabularnewline
123 & 16818 & 10119.9264602065 & 6698.07353979349 \tabularnewline
124 & 10524 & 10914.1562880276 & -390.156288027589 \tabularnewline
125 & 14878 & 11609.5457290449 & 3268.45427095509 \tabularnewline
126 & 13696 & 13539.9719053958 & 156.028094604215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300731&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]918[/C][C]1032.70405982906[/C][C]-114.70405982906[/C][/ROW]
[ROW][C]14[/C][C]776[/C][C]815.159116052371[/C][C]-39.1591160523712[/C][/ROW]
[ROW][C]15[/C][C]1348[/C][C]1309.84637520805[/C][C]38.1536247919539[/C][/ROW]
[ROW][C]16[/C][C]502[/C][C]392.003649385663[/C][C]109.996350614337[/C][/ROW]
[ROW][C]17[/C][C]1274[/C][C]1252.17940325781[/C][C]21.8205967421914[/C][/ROW]
[ROW][C]18[/C][C]1638[/C][C]1703.66574840923[/C][C]-65.6657484092341[/C][/ROW]
[ROW][C]19[/C][C]912[/C][C]748.670936520591[/C][C]163.329063479409[/C][/ROW]
[ROW][C]20[/C][C]1250[/C][C]882.334434399282[/C][C]367.665565600718[/C][/ROW]
[ROW][C]21[/C][C]1614[/C][C]884.299459467439[/C][C]729.700540532561[/C][/ROW]
[ROW][C]22[/C][C]2840[/C][C]2300.72471432207[/C][C]539.27528567793[/C][/ROW]
[ROW][C]23[/C][C]1150[/C][C]4113.36575514734[/C][C]-2963.36575514734[/C][/ROW]
[ROW][C]24[/C][C]1652[/C][C]1030.04285506744[/C][C]621.957144932559[/C][/ROW]
[ROW][C]25[/C][C]1526[/C][C]812.500110072785[/C][C]713.499889927215[/C][/ROW]
[ROW][C]26[/C][C]1412[/C][C]989.663933790591[/C][C]422.336066209409[/C][/ROW]
[ROW][C]27[/C][C]882[/C][C]1710.92991171395[/C][C]-828.929911713951[/C][/ROW]
[ROW][C]28[/C][C]848[/C][C]403.100127430847[/C][C]444.899872569153[/C][/ROW]
[ROW][C]29[/C][C]820[/C][C]1404.89174589387[/C][C]-584.891745893874[/C][/ROW]
[ROW][C]30[/C][C]1226[/C][C]1561.72497573309[/C][C]-335.724975733092[/C][/ROW]
[ROW][C]31[/C][C]1212[/C][C]515.397368364639[/C][C]696.602631635361[/C][/ROW]
[ROW][C]32[/C][C]2110[/C][C]926.282725009162[/C][C]1183.71727499084[/C][/ROW]
[ROW][C]33[/C][C]1178[/C][C]1362.02874969707[/C][C]-184.028749697072[/C][/ROW]
[ROW][C]34[/C][C]2548[/C][C]2326.58677875531[/C][C]221.413221244689[/C][/ROW]
[ROW][C]35[/C][C]1568[/C][C]3455.59387228484[/C][C]-1887.59387228484[/C][/ROW]
[ROW][C]36[/C][C]2088[/C][C]1418.46179486756[/C][C]669.538205132441[/C][/ROW]
[ROW][C]37[/C][C]2178[/C][C]1238.07108345007[/C][C]939.928916549926[/C][/ROW]
[ROW][C]38[/C][C]3016[/C][C]1477.01021529963[/C][C]1538.98978470037[/C][/ROW]
[ROW][C]39[/C][C]5514[/C][C]2527.03497481527[/C][C]2986.96502518473[/C][/ROW]
[ROW][C]40[/C][C]1358[/C][C]3189.49833260485[/C][C]-1831.49833260485[/C][/ROW]
[ROW][C]41[/C][C]3604[/C][C]2989.70436410023[/C][C]614.295635899773[/C][/ROW]
[ROW][C]42[/C][C]1962[/C][C]3748.86736119174[/C][C]-1786.86736119174[/C][/ROW]
[ROW][C]43[/C][C]2036[/C][C]2196.91741153046[/C][C]-160.91741153046[/C][/ROW]
[ROW][C]44[/C][C]2246[/C][C]2291.18991811175[/C][C]-45.1899181117474[/C][/ROW]
[ROW][C]45[/C][C]3434[/C][C]1952.4576296755[/C][C]1481.5423703245[/C][/ROW]
[ROW][C]46[/C][C]4316[/C][C]3754.56560452808[/C][C]561.434395471918[/C][/ROW]
[ROW][C]47[/C][C]3032[/C][C]4725.06532858585[/C][C]-1693.06532858585[/C][/ROW]
[ROW][C]48[/C][C]5296[/C][C]3175.97728692606[/C][C]2120.02271307394[/C][/ROW]
[ROW][C]49[/C][C]3850[/C][C]3717.51178169594[/C][C]132.488218304063[/C][/ROW]
[ROW][C]50[/C][C]2098[/C][C]3683.66093783434[/C][C]-1585.66093783434[/C][/ROW]
[ROW][C]51[/C][C]3992[/C][C]3513.1957362189[/C][C]478.804263781097[/C][/ROW]
[ROW][C]52[/C][C]4860[/C][C]2276.45455029466[/C][C]2583.54544970534[/C][/ROW]
[ROW][C]53[/C][C]7336[/C][C]4496.31372500209[/C][C]2839.68627499791[/C][/ROW]
[ROW][C]54[/C][C]9614[/C][C]5927.44020409248[/C][C]3686.55979590752[/C][/ROW]
[ROW][C]55[/C][C]2988[/C][C]7175.82439683272[/C][C]-4187.82439683272[/C][/ROW]
[ROW][C]56[/C][C]2756[/C][C]5441.43606950239[/C][C]-2685.43606950239[/C][/ROW]
[ROW][C]57[/C][C]3540[/C][C]4124.55399964054[/C][C]-584.553999640535[/C][/ROW]
[ROW][C]58[/C][C]2710[/C][C]4835.13824728581[/C][C]-2125.13824728581[/C][/ROW]
[ROW][C]59[/C][C]3730[/C][C]4217.50969893027[/C][C]-487.509698930266[/C][/ROW]
[ROW][C]60[/C][C]3508[/C][C]3808.73303098558[/C][C]-300.733030985576[/C][/ROW]
[ROW][C]61[/C][C]2640[/C][C]2923.07162449983[/C][C]-283.071624499828[/C][/ROW]
[ROW][C]62[/C][C]2788[/C][C]2428.69957128986[/C][C]359.300428710138[/C][/ROW]
[ROW][C]63[/C][C]3502[/C][C]3470.86096950166[/C][C]31.1390304983361[/C][/ROW]
[ROW][C]64[/C][C]3700[/C][C]2346.50605695238[/C][C]1353.49394304762[/C][/ROW]
[ROW][C]65[/C][C]3250[/C][C]4031.95665326572[/C][C]-781.95665326572[/C][/ROW]
[ROW][C]66[/C][C]4866[/C][C]3906.04047755828[/C][C]959.959522441719[/C][/ROW]
[ROW][C]67[/C][C]2836[/C][C]2671.59474757402[/C][C]164.405252425985[/C][/ROW]
[ROW][C]68[/C][C]3498[/C][C]3167.94725720197[/C][C]330.052742798026[/C][/ROW]
[ROW][C]69[/C][C]3468[/C][C]3562.39216384818[/C][C]-94.3921638481752[/C][/ROW]
[ROW][C]70[/C][C]3924[/C][C]4261.98100766544[/C][C]-337.981007665442[/C][/ROW]
[ROW][C]71[/C][C]5738[/C][C]4722.40244953545[/C][C]1015.59755046455[/C][/ROW]
[ROW][C]72[/C][C]7028[/C][C]5041.96918151011[/C][C]1986.03081848989[/C][/ROW]
[ROW][C]73[/C][C]5608[/C][C]5225.91153145024[/C][C]382.088468549758[/C][/ROW]
[ROW][C]74[/C][C]6030[/C][C]5148.92815548913[/C][C]881.071844510874[/C][/ROW]
[ROW][C]75[/C][C]11976[/C][C]6395.01545223562[/C][C]5580.98454776438[/C][/ROW]
[ROW][C]76[/C][C]7774[/C][C]8062.18966073293[/C][C]-288.189660732929[/C][/ROW]
[ROW][C]77[/C][C]7906[/C][C]8684.3952424762[/C][C]-778.395242476203[/C][/ROW]
[ROW][C]78[/C][C]10940[/C][C]8848.10959450513[/C][C]2091.89040549487[/C][/ROW]
[ROW][C]79[/C][C]7626[/C][C]8039.19459410073[/C][C]-413.194594100725[/C][/ROW]
[ROW][C]80[/C][C]5930[/C][C]8316.93130194462[/C][C]-2386.93130194462[/C][/ROW]
[ROW][C]81[/C][C]6286[/C][C]7408.12986140428[/C][C]-1122.12986140428[/C][/ROW]
[ROW][C]82[/C][C]6788[/C][C]7610.28795836013[/C][C]-822.28795836013[/C][/ROW]
[ROW][C]83[/C][C]6932[/C][C]8067.44313254427[/C][C]-1135.44313254427[/C][/ROW]
[ROW][C]84[/C][C]6660[/C][C]7550.36974669222[/C][C]-890.369746692218[/C][/ROW]
[ROW][C]85[/C][C]4910[/C][C]6162.62713967292[/C][C]-1252.62713967292[/C][/ROW]
[ROW][C]86[/C][C]4182[/C][C]5405.49316336547[/C][C]-1223.49316336547[/C][/ROW]
[ROW][C]87[/C][C]3550[/C][C]6391.91982516595[/C][C]-2841.91982516595[/C][/ROW]
[ROW][C]88[/C][C]3184[/C][C]3245.92992852962[/C][C]-61.9299285296192[/C][/ROW]
[ROW][C]89[/C][C]3872[/C][C]3873.74819051467[/C][C]-1.7481905146692[/C][/ROW]
[ROW][C]90[/C][C]3226[/C][C]4812.8133439994[/C][C]-1586.8133439994[/C][/ROW]
[ROW][C]91[/C][C]2504[/C][C]1890.94805596094[/C][C]613.051944039058[/C][/ROW]
[ROW][C]92[/C][C]3648[/C][C]2312.94911676117[/C][C]1335.05088323883[/C][/ROW]
[ROW][C]93[/C][C]4448[/C][C]3297.18699765989[/C][C]1150.81300234011[/C][/ROW]
[ROW][C]94[/C][C]2954[/C][C]4580.43085961313[/C][C]-1626.43085961313[/C][/ROW]
[ROW][C]95[/C][C]3842[/C][C]4601.54907992329[/C][C]-759.549079923286[/C][/ROW]
[ROW][C]96[/C][C]3982[/C][C]4279.79382600968[/C][C]-297.793826009681[/C][/ROW]
[ROW][C]97[/C][C]4864[/C][C]3095.94273471474[/C][C]1768.05726528526[/C][/ROW]
[ROW][C]98[/C][C]6796[/C][C]3731.01853828143[/C][C]3064.98146171857[/C][/ROW]
[ROW][C]99[/C][C]5844[/C][C]6452.99884162293[/C][C]-608.998841622925[/C][/ROW]
[ROW][C]100[/C][C]5656[/C][C]4770.23739609024[/C][C]885.762603909765[/C][/ROW]
[ROW][C]101[/C][C]6118[/C][C]5853.80580592505[/C][C]264.19419407495[/C][/ROW]
[ROW][C]102[/C][C]7068[/C][C]6682.71889739542[/C][C]385.281102604582[/C][/ROW]
[ROW][C]103[/C][C]7696[/C][C]5021.94124567867[/C][C]2674.05875432133[/C][/ROW]
[ROW][C]104[/C][C]7016[/C][C]6524.7387370381[/C][C]491.261262961898[/C][/ROW]
[ROW][C]105[/C][C]5820[/C][C]7107.33200402712[/C][C]-1287.33200402712[/C][/ROW]
[ROW][C]106[/C][C]4904[/C][C]6850.52725969081[/C][C]-1946.52725969081[/C][/ROW]
[ROW][C]107[/C][C]3860[/C][C]6866.53722932003[/C][C]-3006.53722932003[/C][/ROW]
[ROW][C]108[/C][C]7222[/C][C]5582.53269573562[/C][C]1639.46730426438[/C][/ROW]
[ROW][C]109[/C][C]7738[/C][C]5619.09313995268[/C][C]2118.90686004732[/C][/ROW]
[ROW][C]110[/C][C]7142[/C][C]6624.87555324459[/C][C]517.124446755414[/C][/ROW]
[ROW][C]111[/C][C]13804[/C][C]7612.77516691591[/C][C]6191.22483308409[/C][/ROW]
[ROW][C]112[/C][C]7964[/C][C]9320.02168473996[/C][C]-1356.02168473996[/C][/ROW]
[ROW][C]113[/C][C]9716[/C][C]9287.64342313109[/C][C]428.356576868908[/C][/ROW]
[ROW][C]114[/C][C]8462[/C][C]10226.0679564735[/C][C]-1764.06795647347[/C][/ROW]
[ROW][C]115[/C][C]6884[/C][C]7932.57758330639[/C][C]-1048.57758330639[/C][/ROW]
[ROW][C]116[/C][C]8072[/C][C]7383.96198178738[/C][C]688.038018212618[/C][/ROW]
[ROW][C]117[/C][C]7320[/C][C]7788.16148124592[/C][C]-468.161481245922[/C][/ROW]
[ROW][C]118[/C][C]11700[/C][C]7813.45384430559[/C][C]3886.54615569441[/C][/ROW]
[ROW][C]119[/C][C]10792[/C][C]10379.6450045191[/C][C]412.354995480926[/C][/ROW]
[ROW][C]120[/C][C]10930[/C][C]11410.3328495503[/C][C]-480.332849550297[/C][/ROW]
[ROW][C]121[/C][C]7112[/C][C]10561.0213027565[/C][C]-3449.02130275652[/C][/ROW]
[ROW][C]122[/C][C]8196[/C][C]8757.38803000878[/C][C]-561.388030008777[/C][/ROW]
[ROW][C]123[/C][C]16818[/C][C]10119.9264602065[/C][C]6698.07353979349[/C][/ROW]
[ROW][C]124[/C][C]10524[/C][C]10914.1562880276[/C][C]-390.156288027589[/C][/ROW]
[ROW][C]125[/C][C]14878[/C][C]11609.5457290449[/C][C]3268.45427095509[/C][/ROW]
[ROW][C]126[/C][C]13696[/C][C]13539.9719053958[/C][C]156.028094604215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300731&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300731&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
139181032.70405982906-114.70405982906
14776815.159116052371-39.1591160523712
1513481309.8463752080538.1536247919539
16502392.003649385663109.996350614337
1712741252.1794032578121.8205967421914
1816381703.66574840923-65.6657484092341
19912748.670936520591163.329063479409
201250882.334434399282367.665565600718
211614884.299459467439729.700540532561
2228402300.72471432207539.27528567793
2311504113.36575514734-2963.36575514734
2416521030.04285506744621.957144932559
251526812.500110072785713.499889927215
261412989.663933790591422.336066209409
278821710.92991171395-828.929911713951
28848403.100127430847444.899872569153
298201404.89174589387-584.891745893874
3012261561.72497573309-335.724975733092
311212515.397368364639696.602631635361
322110926.2827250091621183.71727499084
3311781362.02874969707-184.028749697072
3425482326.58677875531221.413221244689
3515683455.59387228484-1887.59387228484
3620881418.46179486756669.538205132441
3721781238.07108345007939.928916549926
3830161477.010215299631538.98978470037
3955142527.034974815272986.96502518473
4013583189.49833260485-1831.49833260485
4136042989.70436410023614.295635899773
4219623748.86736119174-1786.86736119174
4320362196.91741153046-160.91741153046
4422462291.18991811175-45.1899181117474
4534341952.45762967551481.5423703245
4643163754.56560452808561.434395471918
4730324725.06532858585-1693.06532858585
4852963175.977286926062120.02271307394
4938503717.51178169594132.488218304063
5020983683.66093783434-1585.66093783434
5139923513.1957362189478.804263781097
5248602276.454550294662583.54544970534
5373364496.313725002092839.68627499791
5496145927.440204092483686.55979590752
5529887175.82439683272-4187.82439683272
5627565441.43606950239-2685.43606950239
5735404124.55399964054-584.553999640535
5827104835.13824728581-2125.13824728581
5937304217.50969893027-487.509698930266
6035083808.73303098558-300.733030985576
6126402923.07162449983-283.071624499828
6227882428.69957128986359.300428710138
6335023470.8609695016631.1390304983361
6437002346.506056952381353.49394304762
6532504031.95665326572-781.95665326572
6648663906.04047755828959.959522441719
6728362671.59474757402164.405252425985
6834983167.94725720197330.052742798026
6934683562.39216384818-94.3921638481752
7039244261.98100766544-337.981007665442
7157384722.402449535451015.59755046455
7270285041.969181510111986.03081848989
7356085225.91153145024382.088468549758
7460305148.92815548913881.071844510874
75119766395.015452235625580.98454776438
7677748062.18966073293-288.189660732929
7779068684.3952424762-778.395242476203
78109408848.109594505132091.89040549487
7976268039.19459410073-413.194594100725
8059308316.93130194462-2386.93130194462
8162867408.12986140428-1122.12986140428
8267887610.28795836013-822.28795836013
8369328067.44313254427-1135.44313254427
8466607550.36974669222-890.369746692218
8549106162.62713967292-1252.62713967292
8641825405.49316336547-1223.49316336547
8735506391.91982516595-2841.91982516595
8831843245.92992852962-61.9299285296192
8938723873.74819051467-1.7481905146692
9032264812.8133439994-1586.8133439994
9125041890.94805596094613.051944039058
9236482312.949116761171335.05088323883
9344483297.186997659891150.81300234011
9429544580.43085961313-1626.43085961313
9538424601.54907992329-759.549079923286
9639824279.79382600968-297.793826009681
9748643095.942734714741768.05726528526
9867963731.018538281433064.98146171857
9958446452.99884162293-608.998841622925
10056564770.23739609024885.762603909765
10161185853.80580592505264.19419407495
10270686682.71889739542385.281102604582
10376965021.941245678672674.05875432133
10470166524.7387370381491.261262961898
10558207107.33200402712-1287.33200402712
10649046850.52725969081-1946.52725969081
10738606866.53722932003-3006.53722932003
10872225582.532695735621639.46730426438
10977385619.093139952682118.90686004732
11071426624.87555324459517.124446755414
111138047612.775166915916191.22483308409
11279649320.02168473996-1356.02168473996
11397169287.64342313109428.356576868908
114846210226.0679564735-1764.06795647347
11568847932.57758330639-1048.57758330639
11680727383.96198178738688.038018212618
11773207788.16148124592-468.161481245922
118117007813.453844305593886.54615569441
1191079210379.6450045191412.354995480926
1201093011410.3328495503-480.332849550297
121711210561.0213027565-3449.02130275652
12281968757.38803000878-561.388030008777
1231681810119.92646020656698.07353979349
1241052410914.1562880276-390.156288027589
1251487811609.54572904493268.45427095509
1261369613539.9719053958156.028094604215







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12712262.23565846728800.0177760949915724.4535408395
12812485.15332397958668.069853111116302.2367948479
12912414.79623360088270.1629154440116559.4295517575
13013343.22250307478892.3071577582817794.137848391
13113595.19939956728855.1329630991918335.2658360351
13214310.50552011819295.4432108534619325.5678293828
13313241.93186986467963.8048125492518520.0589271799
13413493.5087121167962.5347458818119024.4826783503
13516246.743082897210471.787610968722021.6985548258
13612869.52152750056858.3606007814918880.6824542196
13714312.05586564538071.5730831523320552.5386481382
13814256.9686826897793.3058581949220720.6315071832
13912883.29367247116048.7607927725319717.8265521697
14013106.21133798346063.6274539477720148.7952220191
14113035.85424760475789.3909657659720282.3175294433
14213964.28051707866517.7589083867121410.8021257704
14314216.2574135716573.1908120246821859.3240151174
14414931.5635341227095.1934237410122767.933644503

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 12262.2356584672 & 8800.01777609499 & 15724.4535408395 \tabularnewline
128 & 12485.1533239795 & 8668.0698531111 & 16302.2367948479 \tabularnewline
129 & 12414.7962336008 & 8270.16291544401 & 16559.4295517575 \tabularnewline
130 & 13343.2225030747 & 8892.30715775828 & 17794.137848391 \tabularnewline
131 & 13595.1993995672 & 8855.13296309919 & 18335.2658360351 \tabularnewline
132 & 14310.5055201181 & 9295.44321085346 & 19325.5678293828 \tabularnewline
133 & 13241.9318698646 & 7963.80481254925 & 18520.0589271799 \tabularnewline
134 & 13493.508712116 & 7962.53474588181 & 19024.4826783503 \tabularnewline
135 & 16246.7430828972 & 10471.7876109687 & 22021.6985548258 \tabularnewline
136 & 12869.5215275005 & 6858.36060078149 & 18880.6824542196 \tabularnewline
137 & 14312.0558656453 & 8071.57308315233 & 20552.5386481382 \tabularnewline
138 & 14256.968682689 & 7793.30585819492 & 20720.6315071832 \tabularnewline
139 & 12883.2936724711 & 6048.76079277253 & 19717.8265521697 \tabularnewline
140 & 13106.2113379834 & 6063.62745394777 & 20148.7952220191 \tabularnewline
141 & 13035.8542476047 & 5789.39096576597 & 20282.3175294433 \tabularnewline
142 & 13964.2805170786 & 6517.75890838671 & 21410.8021257704 \tabularnewline
143 & 14216.257413571 & 6573.19081202468 & 21859.3240151174 \tabularnewline
144 & 14931.563534122 & 7095.19342374101 & 22767.933644503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300731&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]12262.2356584672[/C][C]8800.01777609499[/C][C]15724.4535408395[/C][/ROW]
[ROW][C]128[/C][C]12485.1533239795[/C][C]8668.0698531111[/C][C]16302.2367948479[/C][/ROW]
[ROW][C]129[/C][C]12414.7962336008[/C][C]8270.16291544401[/C][C]16559.4295517575[/C][/ROW]
[ROW][C]130[/C][C]13343.2225030747[/C][C]8892.30715775828[/C][C]17794.137848391[/C][/ROW]
[ROW][C]131[/C][C]13595.1993995672[/C][C]8855.13296309919[/C][C]18335.2658360351[/C][/ROW]
[ROW][C]132[/C][C]14310.5055201181[/C][C]9295.44321085346[/C][C]19325.5678293828[/C][/ROW]
[ROW][C]133[/C][C]13241.9318698646[/C][C]7963.80481254925[/C][C]18520.0589271799[/C][/ROW]
[ROW][C]134[/C][C]13493.508712116[/C][C]7962.53474588181[/C][C]19024.4826783503[/C][/ROW]
[ROW][C]135[/C][C]16246.7430828972[/C][C]10471.7876109687[/C][C]22021.6985548258[/C][/ROW]
[ROW][C]136[/C][C]12869.5215275005[/C][C]6858.36060078149[/C][C]18880.6824542196[/C][/ROW]
[ROW][C]137[/C][C]14312.0558656453[/C][C]8071.57308315233[/C][C]20552.5386481382[/C][/ROW]
[ROW][C]138[/C][C]14256.968682689[/C][C]7793.30585819492[/C][C]20720.6315071832[/C][/ROW]
[ROW][C]139[/C][C]12883.2936724711[/C][C]6048.76079277253[/C][C]19717.8265521697[/C][/ROW]
[ROW][C]140[/C][C]13106.2113379834[/C][C]6063.62745394777[/C][C]20148.7952220191[/C][/ROW]
[ROW][C]141[/C][C]13035.8542476047[/C][C]5789.39096576597[/C][C]20282.3175294433[/C][/ROW]
[ROW][C]142[/C][C]13964.2805170786[/C][C]6517.75890838671[/C][C]21410.8021257704[/C][/ROW]
[ROW][C]143[/C][C]14216.257413571[/C][C]6573.19081202468[/C][C]21859.3240151174[/C][/ROW]
[ROW][C]144[/C][C]14931.563534122[/C][C]7095.19342374101[/C][C]22767.933644503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300731&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300731&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
12712262.23565846728800.0177760949915724.4535408395
12812485.15332397958668.069853111116302.2367948479
12912414.79623360088270.1629154440116559.4295517575
13013343.22250307478892.3071577582817794.137848391
13113595.19939956728855.1329630991918335.2658360351
13214310.50552011819295.4432108534619325.5678293828
13313241.93186986467963.8048125492518520.0589271799
13413493.5087121167962.5347458818119024.4826783503
13516246.743082897210471.787610968722021.6985548258
13612869.52152750056858.3606007814918880.6824542196
13714312.05586564538071.5730831523320552.5386481382
13814256.9686826897793.3058581949220720.6315071832
13912883.29367247116048.7607927725319717.8265521697
14013106.21133798346063.6274539477720148.7952220191
14113035.85424760475789.3909657659720282.3175294433
14213964.28051707866517.7589083867121410.8021257704
14314216.2574135716573.1908120246821859.3240151174
14414931.5635341227095.1934237410122767.933644503



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '18'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')