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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 21 Dec 2010 20:38:51 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t12929639171ayg83hp2n6dw8l.htm/, Retrieved Sun, 19 May 2024 17:44:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113960, Retrieved Sun, 19 May 2024 17:44:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Double exponentia...] [2010-12-21 20:32:31] [b11c112f8986de933f8b95cd30e75cc2]
-   P     [Exponential Smoothing] [Triple exponentia...] [2010-12-21 20:38:51] [be034431ba35f7eb1ce695fc7ca4deb9] [Current]
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Dataseries X:
27951
29781
32914
33488
35652
36488
35387
35676
34844
32447
31068
29010
29812
30951
32974
32936
34012
32946
31948
30599
27691
25073
23406
22248
22896
25317
26558
26471
27543
26198
24725
25005
23462
20780
19815
19761
21454
23899
24939
23580
24562
24696
23785
23812
21917
19713
19282
18788
21453
24482
27474
27264
27349
30632
29429
30084
26290
24379
23335
21346
21106
24514
28353
30805
31348
34556
33855
34787
32529
29998
29257
28155
30466
35704
39327
39351
42234
43630
43722
43121
37985
37135
34646
33026
35087
38846
42013
43908
42868
44423
44167
43636
44382
42142
43452
36912
42413
45344
44873
47510
49554
47369
45998
48140
48441
44928
40454
38661
37246
36843
36424
37594
38144
38737
34560
36080
33508
35462
33374
32110
35533
35532
37903
36763
40399
44164
44496
43110
43880
43930
44327




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time13 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 13 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113960&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]13 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113960&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113960&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 time13 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.916247210448925
beta0.041682819544113
gamma0.53947629784894

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.916247210448925 \tabularnewline
beta & 0.041682819544113 \tabularnewline
gamma & 0.53947629784894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113960&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]0.916247210448925[/C][/ROW]
[ROW][C]beta[/C][C]0.041682819544113[/C][/ROW]
[ROW][C]gamma[/C][C]0.53947629784894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113960&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113960&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
alpha0.916247210448925
beta0.041682819544113
gamma0.53947629784894







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132981230527.3862179487-715.386217948708
143095131047.1674454637-96.1674454637323
153297433169.383341243-195.383341243003
163293633227.9392475456-291.939247545641
173401234322.0847316208-310.084731620802
183294633220.2617826689-274.261782668931
193194831908.49530196139.5046980390071
203059931745.7252381622-1146.72523816215
212769129406.3215077756-1715.32150777561
222507324987.181871904485.8181280955978
232340623310.442282326495.5577176736297
242224821091.85941596441156.14058403558
252289622791.8229862359104.177013764132
262531723993.16589062211323.83410937788
272655827368.8649921360-810.864992136041
282647126792.5121484789-321.512148478851
292754327790.9994892360-247.999489236041
302619826682.3094967578-484.309496757764
312472525118.8710407817-393.871040781738
322500524415.4801313731589.519868626885
332346223617.5811942989-155.581194298909
342078020744.864501859535.1354981404584
351981519056.1264748894758.873525110637
361976117552.55732907172208.44267092833
372145420268.68105423791185.31894576205
382389922656.53709181021242.46290818983
392493925998.9335164244-1059.93351642441
402358025344.6750313823-1764.67503138226
412456225097.2654055416-535.265405541566
422469623776.7960171806919.203982819385
432378523619.1160900398165.883909960183
442381223610.1162954216201.883704578398
452191722545.6616580007-628.661658000696
461971319352.3161063817360.683893618301
471928218111.20726680021170.79273319976
481878817182.93121662051605.06878337952
492145319409.32185196042043.67814803963
502448222728.34527171101753.65472828905
512747426596.7309766793877.26902332074
522726427921.2115785828-657.211578582781
532734929021.9809662332-1672.98096623325
543063226959.26901085663672.7309891434
552942929630.0949590114-201.094959011432
563008429612.0942239926471.905776007392
572629029093.4487988619-2803.44879886193
582437924205.0313594758173.968640524181
592333523075.1865792973259.813420702729
602134621542.7966352568-196.796635256756
612110622280.1808332974-1174.18083329741
622451422656.98038671721857.01961328281
632835326603.65861689241749.34138310758
643080528714.32933991932090.67066008069
653134832448.3776406776-1100.37764067759
663455631335.14864738143220.85135261857
673385533582.9567129103272.043287089655
683478734212.9907907347574.009209265343
693252933827.9229410715-1298.92294107154
702999830698.0259899003-700.02598990026
712925728983.3606357208273.639364279239
722815527655.6317350005499.368264999532
733046629225.92595665081240.07404334917
743570432283.15379820693420.84620179306
753932738048.96023027581278.03976972422
763935140116.3661225652-765.366122565225
774223441353.4633928287880.536607171263
784363042590.20543039531039.79456960472
794372242962.8122646198759.187735380183
804312144327.8605201136-1206.86052011357
813798542433.4629753998-4448.4629753998
823713536531.5932570855603.406742914478
833464636191.6924389163-1545.69243891629
843302633274.2265354958-248.226535495778
853508734231.4758443396855.524155660401
863884637058.6770297551787.32297024497
874201341192.3506086852820.649391314837
884390842692.27472610731215.72527389266
894286845838.4964479147-2970.49644791472
904442343426.4468771271996.553122872894
914416743617.6148199731549.385180026882
924363644564.4476014687-928.447601468695
934438242652.16081787541729.83918212465
944214242748.8402027503-606.84020275026
954345241266.17069285822185.82930714175
963691242032.0562119294-5120.05621192943
974241338595.04385175503817.95614824496
984534444311.47504055021032.52495944980
994487347813.8719279095-2940.87192790951
1004751045845.48580582151664.51419417854
1014955449191.2271995566362.772800443418
1024736950117.2841589157-2748.28415891575
1034599846818.7952928201-820.795292820098
1044814046352.84616543871787.15383456134
1054844147061.95818847641379.04181152360
1064492846731.3736734092-1803.37367340922
1074045444232.5967428259-3778.59674282591
1083866138929.7351696376-268.735169637628
1093724640253.0966116523-3007.09661165235
1103684339241.0996663667-2398.09966636668
1113642438940.5066795011-2516.50667950107
1123759437105.0737663897488.926233610327
1133814438806.0182783147-662.018278314725
1143873738104.5573333210632.442666678951
1153456037571.8648115244-3011.86481152441
1163608034713.63334827691366.36665172310
1173350834500.1350615145-992.13506151447
1183546231243.99132075044218.00867924961
1193337433793.8255223271-419.825522327112
1203211031476.0730985790633.926901421037
1213553333286.30355153042246.69644846962
1223553237099.7813944856-1567.78139448558
1233790337570.5120480186332.487951981377
1243676338605.9608480421-1842.96084804205
1254039938153.96364235542245.03635764461
1264416440321.24215416323842.75784583678
1274449642834.61170603231661.38829396766
1284311044903.8144325821-1793.81443258212
1294388042015.31178841131864.68821158871
1304393042048.30569663351881.69430336646
1314432742594.89399847111732.10600152887

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 29812 & 30527.3862179487 & -715.386217948708 \tabularnewline
14 & 30951 & 31047.1674454637 & -96.1674454637323 \tabularnewline
15 & 32974 & 33169.383341243 & -195.383341243003 \tabularnewline
16 & 32936 & 33227.9392475456 & -291.939247545641 \tabularnewline
17 & 34012 & 34322.0847316208 & -310.084731620802 \tabularnewline
18 & 32946 & 33220.2617826689 & -274.261782668931 \tabularnewline
19 & 31948 & 31908.495301961 & 39.5046980390071 \tabularnewline
20 & 30599 & 31745.7252381622 & -1146.72523816215 \tabularnewline
21 & 27691 & 29406.3215077756 & -1715.32150777561 \tabularnewline
22 & 25073 & 24987.1818719044 & 85.8181280955978 \tabularnewline
23 & 23406 & 23310.4422823264 & 95.5577176736297 \tabularnewline
24 & 22248 & 21091.8594159644 & 1156.14058403558 \tabularnewline
25 & 22896 & 22791.8229862359 & 104.177013764132 \tabularnewline
26 & 25317 & 23993.1658906221 & 1323.83410937788 \tabularnewline
27 & 26558 & 27368.8649921360 & -810.864992136041 \tabularnewline
28 & 26471 & 26792.5121484789 & -321.512148478851 \tabularnewline
29 & 27543 & 27790.9994892360 & -247.999489236041 \tabularnewline
30 & 26198 & 26682.3094967578 & -484.309496757764 \tabularnewline
31 & 24725 & 25118.8710407817 & -393.871040781738 \tabularnewline
32 & 25005 & 24415.4801313731 & 589.519868626885 \tabularnewline
33 & 23462 & 23617.5811942989 & -155.581194298909 \tabularnewline
34 & 20780 & 20744.8645018595 & 35.1354981404584 \tabularnewline
35 & 19815 & 19056.1264748894 & 758.873525110637 \tabularnewline
36 & 19761 & 17552.5573290717 & 2208.44267092833 \tabularnewline
37 & 21454 & 20268.6810542379 & 1185.31894576205 \tabularnewline
38 & 23899 & 22656.5370918102 & 1242.46290818983 \tabularnewline
39 & 24939 & 25998.9335164244 & -1059.93351642441 \tabularnewline
40 & 23580 & 25344.6750313823 & -1764.67503138226 \tabularnewline
41 & 24562 & 25097.2654055416 & -535.265405541566 \tabularnewline
42 & 24696 & 23776.7960171806 & 919.203982819385 \tabularnewline
43 & 23785 & 23619.1160900398 & 165.883909960183 \tabularnewline
44 & 23812 & 23610.1162954216 & 201.883704578398 \tabularnewline
45 & 21917 & 22545.6616580007 & -628.661658000696 \tabularnewline
46 & 19713 & 19352.3161063817 & 360.683893618301 \tabularnewline
47 & 19282 & 18111.2072668002 & 1170.79273319976 \tabularnewline
48 & 18788 & 17182.9312166205 & 1605.06878337952 \tabularnewline
49 & 21453 & 19409.3218519604 & 2043.67814803963 \tabularnewline
50 & 24482 & 22728.3452717110 & 1753.65472828905 \tabularnewline
51 & 27474 & 26596.7309766793 & 877.26902332074 \tabularnewline
52 & 27264 & 27921.2115785828 & -657.211578582781 \tabularnewline
53 & 27349 & 29021.9809662332 & -1672.98096623325 \tabularnewline
54 & 30632 & 26959.2690108566 & 3672.7309891434 \tabularnewline
55 & 29429 & 29630.0949590114 & -201.094959011432 \tabularnewline
56 & 30084 & 29612.0942239926 & 471.905776007392 \tabularnewline
57 & 26290 & 29093.4487988619 & -2803.44879886193 \tabularnewline
58 & 24379 & 24205.0313594758 & 173.968640524181 \tabularnewline
59 & 23335 & 23075.1865792973 & 259.813420702729 \tabularnewline
60 & 21346 & 21542.7966352568 & -196.796635256756 \tabularnewline
61 & 21106 & 22280.1808332974 & -1174.18083329741 \tabularnewline
62 & 24514 & 22656.9803867172 & 1857.01961328281 \tabularnewline
63 & 28353 & 26603.6586168924 & 1749.34138310758 \tabularnewline
64 & 30805 & 28714.3293399193 & 2090.67066008069 \tabularnewline
65 & 31348 & 32448.3776406776 & -1100.37764067759 \tabularnewline
66 & 34556 & 31335.1486473814 & 3220.85135261857 \tabularnewline
67 & 33855 & 33582.9567129103 & 272.043287089655 \tabularnewline
68 & 34787 & 34212.9907907347 & 574.009209265343 \tabularnewline
69 & 32529 & 33827.9229410715 & -1298.92294107154 \tabularnewline
70 & 29998 & 30698.0259899003 & -700.02598990026 \tabularnewline
71 & 29257 & 28983.3606357208 & 273.639364279239 \tabularnewline
72 & 28155 & 27655.6317350005 & 499.368264999532 \tabularnewline
73 & 30466 & 29225.9259566508 & 1240.07404334917 \tabularnewline
74 & 35704 & 32283.1537982069 & 3420.84620179306 \tabularnewline
75 & 39327 & 38048.9602302758 & 1278.03976972422 \tabularnewline
76 & 39351 & 40116.3661225652 & -765.366122565225 \tabularnewline
77 & 42234 & 41353.4633928287 & 880.536607171263 \tabularnewline
78 & 43630 & 42590.2054303953 & 1039.79456960472 \tabularnewline
79 & 43722 & 42962.8122646198 & 759.187735380183 \tabularnewline
80 & 43121 & 44327.8605201136 & -1206.86052011357 \tabularnewline
81 & 37985 & 42433.4629753998 & -4448.4629753998 \tabularnewline
82 & 37135 & 36531.5932570855 & 603.406742914478 \tabularnewline
83 & 34646 & 36191.6924389163 & -1545.69243891629 \tabularnewline
84 & 33026 & 33274.2265354958 & -248.226535495778 \tabularnewline
85 & 35087 & 34231.4758443396 & 855.524155660401 \tabularnewline
86 & 38846 & 37058.677029755 & 1787.32297024497 \tabularnewline
87 & 42013 & 41192.3506086852 & 820.649391314837 \tabularnewline
88 & 43908 & 42692.2747261073 & 1215.72527389266 \tabularnewline
89 & 42868 & 45838.4964479147 & -2970.49644791472 \tabularnewline
90 & 44423 & 43426.4468771271 & 996.553122872894 \tabularnewline
91 & 44167 & 43617.6148199731 & 549.385180026882 \tabularnewline
92 & 43636 & 44564.4476014687 & -928.447601468695 \tabularnewline
93 & 44382 & 42652.1608178754 & 1729.83918212465 \tabularnewline
94 & 42142 & 42748.8402027503 & -606.84020275026 \tabularnewline
95 & 43452 & 41266.1706928582 & 2185.82930714175 \tabularnewline
96 & 36912 & 42032.0562119294 & -5120.05621192943 \tabularnewline
97 & 42413 & 38595.0438517550 & 3817.95614824496 \tabularnewline
98 & 45344 & 44311.4750405502 & 1032.52495944980 \tabularnewline
99 & 44873 & 47813.8719279095 & -2940.87192790951 \tabularnewline
100 & 47510 & 45845.4858058215 & 1664.51419417854 \tabularnewline
101 & 49554 & 49191.2271995566 & 362.772800443418 \tabularnewline
102 & 47369 & 50117.2841589157 & -2748.28415891575 \tabularnewline
103 & 45998 & 46818.7952928201 & -820.795292820098 \tabularnewline
104 & 48140 & 46352.8461654387 & 1787.15383456134 \tabularnewline
105 & 48441 & 47061.9581884764 & 1379.04181152360 \tabularnewline
106 & 44928 & 46731.3736734092 & -1803.37367340922 \tabularnewline
107 & 40454 & 44232.5967428259 & -3778.59674282591 \tabularnewline
108 & 38661 & 38929.7351696376 & -268.735169637628 \tabularnewline
109 & 37246 & 40253.0966116523 & -3007.09661165235 \tabularnewline
110 & 36843 & 39241.0996663667 & -2398.09966636668 \tabularnewline
111 & 36424 & 38940.5066795011 & -2516.50667950107 \tabularnewline
112 & 37594 & 37105.0737663897 & 488.926233610327 \tabularnewline
113 & 38144 & 38806.0182783147 & -662.018278314725 \tabularnewline
114 & 38737 & 38104.5573333210 & 632.442666678951 \tabularnewline
115 & 34560 & 37571.8648115244 & -3011.86481152441 \tabularnewline
116 & 36080 & 34713.6333482769 & 1366.36665172310 \tabularnewline
117 & 33508 & 34500.1350615145 & -992.13506151447 \tabularnewline
118 & 35462 & 31243.9913207504 & 4218.00867924961 \tabularnewline
119 & 33374 & 33793.8255223271 & -419.825522327112 \tabularnewline
120 & 32110 & 31476.0730985790 & 633.926901421037 \tabularnewline
121 & 35533 & 33286.3035515304 & 2246.69644846962 \tabularnewline
122 & 35532 & 37099.7813944856 & -1567.78139448558 \tabularnewline
123 & 37903 & 37570.5120480186 & 332.487951981377 \tabularnewline
124 & 36763 & 38605.9608480421 & -1842.96084804205 \tabularnewline
125 & 40399 & 38153.9636423554 & 2245.03635764461 \tabularnewline
126 & 44164 & 40321.2421541632 & 3842.75784583678 \tabularnewline
127 & 44496 & 42834.6117060323 & 1661.38829396766 \tabularnewline
128 & 43110 & 44903.8144325821 & -1793.81443258212 \tabularnewline
129 & 43880 & 42015.3117884113 & 1864.68821158871 \tabularnewline
130 & 43930 & 42048.3056966335 & 1881.69430336646 \tabularnewline
131 & 44327 & 42594.8939984711 & 1732.10600152887 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113960&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]29812[/C][C]30527.3862179487[/C][C]-715.386217948708[/C][/ROW]
[ROW][C]14[/C][C]30951[/C][C]31047.1674454637[/C][C]-96.1674454637323[/C][/ROW]
[ROW][C]15[/C][C]32974[/C][C]33169.383341243[/C][C]-195.383341243003[/C][/ROW]
[ROW][C]16[/C][C]32936[/C][C]33227.9392475456[/C][C]-291.939247545641[/C][/ROW]
[ROW][C]17[/C][C]34012[/C][C]34322.0847316208[/C][C]-310.084731620802[/C][/ROW]
[ROW][C]18[/C][C]32946[/C][C]33220.2617826689[/C][C]-274.261782668931[/C][/ROW]
[ROW][C]19[/C][C]31948[/C][C]31908.495301961[/C][C]39.5046980390071[/C][/ROW]
[ROW][C]20[/C][C]30599[/C][C]31745.7252381622[/C][C]-1146.72523816215[/C][/ROW]
[ROW][C]21[/C][C]27691[/C][C]29406.3215077756[/C][C]-1715.32150777561[/C][/ROW]
[ROW][C]22[/C][C]25073[/C][C]24987.1818719044[/C][C]85.8181280955978[/C][/ROW]
[ROW][C]23[/C][C]23406[/C][C]23310.4422823264[/C][C]95.5577176736297[/C][/ROW]
[ROW][C]24[/C][C]22248[/C][C]21091.8594159644[/C][C]1156.14058403558[/C][/ROW]
[ROW][C]25[/C][C]22896[/C][C]22791.8229862359[/C][C]104.177013764132[/C][/ROW]
[ROW][C]26[/C][C]25317[/C][C]23993.1658906221[/C][C]1323.83410937788[/C][/ROW]
[ROW][C]27[/C][C]26558[/C][C]27368.8649921360[/C][C]-810.864992136041[/C][/ROW]
[ROW][C]28[/C][C]26471[/C][C]26792.5121484789[/C][C]-321.512148478851[/C][/ROW]
[ROW][C]29[/C][C]27543[/C][C]27790.9994892360[/C][C]-247.999489236041[/C][/ROW]
[ROW][C]30[/C][C]26198[/C][C]26682.3094967578[/C][C]-484.309496757764[/C][/ROW]
[ROW][C]31[/C][C]24725[/C][C]25118.8710407817[/C][C]-393.871040781738[/C][/ROW]
[ROW][C]32[/C][C]25005[/C][C]24415.4801313731[/C][C]589.519868626885[/C][/ROW]
[ROW][C]33[/C][C]23462[/C][C]23617.5811942989[/C][C]-155.581194298909[/C][/ROW]
[ROW][C]34[/C][C]20780[/C][C]20744.8645018595[/C][C]35.1354981404584[/C][/ROW]
[ROW][C]35[/C][C]19815[/C][C]19056.1264748894[/C][C]758.873525110637[/C][/ROW]
[ROW][C]36[/C][C]19761[/C][C]17552.5573290717[/C][C]2208.44267092833[/C][/ROW]
[ROW][C]37[/C][C]21454[/C][C]20268.6810542379[/C][C]1185.31894576205[/C][/ROW]
[ROW][C]38[/C][C]23899[/C][C]22656.5370918102[/C][C]1242.46290818983[/C][/ROW]
[ROW][C]39[/C][C]24939[/C][C]25998.9335164244[/C][C]-1059.93351642441[/C][/ROW]
[ROW][C]40[/C][C]23580[/C][C]25344.6750313823[/C][C]-1764.67503138226[/C][/ROW]
[ROW][C]41[/C][C]24562[/C][C]25097.2654055416[/C][C]-535.265405541566[/C][/ROW]
[ROW][C]42[/C][C]24696[/C][C]23776.7960171806[/C][C]919.203982819385[/C][/ROW]
[ROW][C]43[/C][C]23785[/C][C]23619.1160900398[/C][C]165.883909960183[/C][/ROW]
[ROW][C]44[/C][C]23812[/C][C]23610.1162954216[/C][C]201.883704578398[/C][/ROW]
[ROW][C]45[/C][C]21917[/C][C]22545.6616580007[/C][C]-628.661658000696[/C][/ROW]
[ROW][C]46[/C][C]19713[/C][C]19352.3161063817[/C][C]360.683893618301[/C][/ROW]
[ROW][C]47[/C][C]19282[/C][C]18111.2072668002[/C][C]1170.79273319976[/C][/ROW]
[ROW][C]48[/C][C]18788[/C][C]17182.9312166205[/C][C]1605.06878337952[/C][/ROW]
[ROW][C]49[/C][C]21453[/C][C]19409.3218519604[/C][C]2043.67814803963[/C][/ROW]
[ROW][C]50[/C][C]24482[/C][C]22728.3452717110[/C][C]1753.65472828905[/C][/ROW]
[ROW][C]51[/C][C]27474[/C][C]26596.7309766793[/C][C]877.26902332074[/C][/ROW]
[ROW][C]52[/C][C]27264[/C][C]27921.2115785828[/C][C]-657.211578582781[/C][/ROW]
[ROW][C]53[/C][C]27349[/C][C]29021.9809662332[/C][C]-1672.98096623325[/C][/ROW]
[ROW][C]54[/C][C]30632[/C][C]26959.2690108566[/C][C]3672.7309891434[/C][/ROW]
[ROW][C]55[/C][C]29429[/C][C]29630.0949590114[/C][C]-201.094959011432[/C][/ROW]
[ROW][C]56[/C][C]30084[/C][C]29612.0942239926[/C][C]471.905776007392[/C][/ROW]
[ROW][C]57[/C][C]26290[/C][C]29093.4487988619[/C][C]-2803.44879886193[/C][/ROW]
[ROW][C]58[/C][C]24379[/C][C]24205.0313594758[/C][C]173.968640524181[/C][/ROW]
[ROW][C]59[/C][C]23335[/C][C]23075.1865792973[/C][C]259.813420702729[/C][/ROW]
[ROW][C]60[/C][C]21346[/C][C]21542.7966352568[/C][C]-196.796635256756[/C][/ROW]
[ROW][C]61[/C][C]21106[/C][C]22280.1808332974[/C][C]-1174.18083329741[/C][/ROW]
[ROW][C]62[/C][C]24514[/C][C]22656.9803867172[/C][C]1857.01961328281[/C][/ROW]
[ROW][C]63[/C][C]28353[/C][C]26603.6586168924[/C][C]1749.34138310758[/C][/ROW]
[ROW][C]64[/C][C]30805[/C][C]28714.3293399193[/C][C]2090.67066008069[/C][/ROW]
[ROW][C]65[/C][C]31348[/C][C]32448.3776406776[/C][C]-1100.37764067759[/C][/ROW]
[ROW][C]66[/C][C]34556[/C][C]31335.1486473814[/C][C]3220.85135261857[/C][/ROW]
[ROW][C]67[/C][C]33855[/C][C]33582.9567129103[/C][C]272.043287089655[/C][/ROW]
[ROW][C]68[/C][C]34787[/C][C]34212.9907907347[/C][C]574.009209265343[/C][/ROW]
[ROW][C]69[/C][C]32529[/C][C]33827.9229410715[/C][C]-1298.92294107154[/C][/ROW]
[ROW][C]70[/C][C]29998[/C][C]30698.0259899003[/C][C]-700.02598990026[/C][/ROW]
[ROW][C]71[/C][C]29257[/C][C]28983.3606357208[/C][C]273.639364279239[/C][/ROW]
[ROW][C]72[/C][C]28155[/C][C]27655.6317350005[/C][C]499.368264999532[/C][/ROW]
[ROW][C]73[/C][C]30466[/C][C]29225.9259566508[/C][C]1240.07404334917[/C][/ROW]
[ROW][C]74[/C][C]35704[/C][C]32283.1537982069[/C][C]3420.84620179306[/C][/ROW]
[ROW][C]75[/C][C]39327[/C][C]38048.9602302758[/C][C]1278.03976972422[/C][/ROW]
[ROW][C]76[/C][C]39351[/C][C]40116.3661225652[/C][C]-765.366122565225[/C][/ROW]
[ROW][C]77[/C][C]42234[/C][C]41353.4633928287[/C][C]880.536607171263[/C][/ROW]
[ROW][C]78[/C][C]43630[/C][C]42590.2054303953[/C][C]1039.79456960472[/C][/ROW]
[ROW][C]79[/C][C]43722[/C][C]42962.8122646198[/C][C]759.187735380183[/C][/ROW]
[ROW][C]80[/C][C]43121[/C][C]44327.8605201136[/C][C]-1206.86052011357[/C][/ROW]
[ROW][C]81[/C][C]37985[/C][C]42433.4629753998[/C][C]-4448.4629753998[/C][/ROW]
[ROW][C]82[/C][C]37135[/C][C]36531.5932570855[/C][C]603.406742914478[/C][/ROW]
[ROW][C]83[/C][C]34646[/C][C]36191.6924389163[/C][C]-1545.69243891629[/C][/ROW]
[ROW][C]84[/C][C]33026[/C][C]33274.2265354958[/C][C]-248.226535495778[/C][/ROW]
[ROW][C]85[/C][C]35087[/C][C]34231.4758443396[/C][C]855.524155660401[/C][/ROW]
[ROW][C]86[/C][C]38846[/C][C]37058.677029755[/C][C]1787.32297024497[/C][/ROW]
[ROW][C]87[/C][C]42013[/C][C]41192.3506086852[/C][C]820.649391314837[/C][/ROW]
[ROW][C]88[/C][C]43908[/C][C]42692.2747261073[/C][C]1215.72527389266[/C][/ROW]
[ROW][C]89[/C][C]42868[/C][C]45838.4964479147[/C][C]-2970.49644791472[/C][/ROW]
[ROW][C]90[/C][C]44423[/C][C]43426.4468771271[/C][C]996.553122872894[/C][/ROW]
[ROW][C]91[/C][C]44167[/C][C]43617.6148199731[/C][C]549.385180026882[/C][/ROW]
[ROW][C]92[/C][C]43636[/C][C]44564.4476014687[/C][C]-928.447601468695[/C][/ROW]
[ROW][C]93[/C][C]44382[/C][C]42652.1608178754[/C][C]1729.83918212465[/C][/ROW]
[ROW][C]94[/C][C]42142[/C][C]42748.8402027503[/C][C]-606.84020275026[/C][/ROW]
[ROW][C]95[/C][C]43452[/C][C]41266.1706928582[/C][C]2185.82930714175[/C][/ROW]
[ROW][C]96[/C][C]36912[/C][C]42032.0562119294[/C][C]-5120.05621192943[/C][/ROW]
[ROW][C]97[/C][C]42413[/C][C]38595.0438517550[/C][C]3817.95614824496[/C][/ROW]
[ROW][C]98[/C][C]45344[/C][C]44311.4750405502[/C][C]1032.52495944980[/C][/ROW]
[ROW][C]99[/C][C]44873[/C][C]47813.8719279095[/C][C]-2940.87192790951[/C][/ROW]
[ROW][C]100[/C][C]47510[/C][C]45845.4858058215[/C][C]1664.51419417854[/C][/ROW]
[ROW][C]101[/C][C]49554[/C][C]49191.2271995566[/C][C]362.772800443418[/C][/ROW]
[ROW][C]102[/C][C]47369[/C][C]50117.2841589157[/C][C]-2748.28415891575[/C][/ROW]
[ROW][C]103[/C][C]45998[/C][C]46818.7952928201[/C][C]-820.795292820098[/C][/ROW]
[ROW][C]104[/C][C]48140[/C][C]46352.8461654387[/C][C]1787.15383456134[/C][/ROW]
[ROW][C]105[/C][C]48441[/C][C]47061.9581884764[/C][C]1379.04181152360[/C][/ROW]
[ROW][C]106[/C][C]44928[/C][C]46731.3736734092[/C][C]-1803.37367340922[/C][/ROW]
[ROW][C]107[/C][C]40454[/C][C]44232.5967428259[/C][C]-3778.59674282591[/C][/ROW]
[ROW][C]108[/C][C]38661[/C][C]38929.7351696376[/C][C]-268.735169637628[/C][/ROW]
[ROW][C]109[/C][C]37246[/C][C]40253.0966116523[/C][C]-3007.09661165235[/C][/ROW]
[ROW][C]110[/C][C]36843[/C][C]39241.0996663667[/C][C]-2398.09966636668[/C][/ROW]
[ROW][C]111[/C][C]36424[/C][C]38940.5066795011[/C][C]-2516.50667950107[/C][/ROW]
[ROW][C]112[/C][C]37594[/C][C]37105.0737663897[/C][C]488.926233610327[/C][/ROW]
[ROW][C]113[/C][C]38144[/C][C]38806.0182783147[/C][C]-662.018278314725[/C][/ROW]
[ROW][C]114[/C][C]38737[/C][C]38104.5573333210[/C][C]632.442666678951[/C][/ROW]
[ROW][C]115[/C][C]34560[/C][C]37571.8648115244[/C][C]-3011.86481152441[/C][/ROW]
[ROW][C]116[/C][C]36080[/C][C]34713.6333482769[/C][C]1366.36665172310[/C][/ROW]
[ROW][C]117[/C][C]33508[/C][C]34500.1350615145[/C][C]-992.13506151447[/C][/ROW]
[ROW][C]118[/C][C]35462[/C][C]31243.9913207504[/C][C]4218.00867924961[/C][/ROW]
[ROW][C]119[/C][C]33374[/C][C]33793.8255223271[/C][C]-419.825522327112[/C][/ROW]
[ROW][C]120[/C][C]32110[/C][C]31476.0730985790[/C][C]633.926901421037[/C][/ROW]
[ROW][C]121[/C][C]35533[/C][C]33286.3035515304[/C][C]2246.69644846962[/C][/ROW]
[ROW][C]122[/C][C]35532[/C][C]37099.7813944856[/C][C]-1567.78139448558[/C][/ROW]
[ROW][C]123[/C][C]37903[/C][C]37570.5120480186[/C][C]332.487951981377[/C][/ROW]
[ROW][C]124[/C][C]36763[/C][C]38605.9608480421[/C][C]-1842.96084804205[/C][/ROW]
[ROW][C]125[/C][C]40399[/C][C]38153.9636423554[/C][C]2245.03635764461[/C][/ROW]
[ROW][C]126[/C][C]44164[/C][C]40321.2421541632[/C][C]3842.75784583678[/C][/ROW]
[ROW][C]127[/C][C]44496[/C][C]42834.6117060323[/C][C]1661.38829396766[/C][/ROW]
[ROW][C]128[/C][C]43110[/C][C]44903.8144325821[/C][C]-1793.81443258212[/C][/ROW]
[ROW][C]129[/C][C]43880[/C][C]42015.3117884113[/C][C]1864.68821158871[/C][/ROW]
[ROW][C]130[/C][C]43930[/C][C]42048.3056966335[/C][C]1881.69430336646[/C][/ROW]
[ROW][C]131[/C][C]44327[/C][C]42594.8939984711[/C][C]1732.10600152887[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113960&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113960&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
132981230527.3862179487-715.386217948708
143095131047.1674454637-96.1674454637323
153297433169.383341243-195.383341243003
163293633227.9392475456-291.939247545641
173401234322.0847316208-310.084731620802
183294633220.2617826689-274.261782668931
193194831908.49530196139.5046980390071
203059931745.7252381622-1146.72523816215
212769129406.3215077756-1715.32150777561
222507324987.181871904485.8181280955978
232340623310.442282326495.5577176736297
242224821091.85941596441156.14058403558
252289622791.8229862359104.177013764132
262531723993.16589062211323.83410937788
272655827368.8649921360-810.864992136041
282647126792.5121484789-321.512148478851
292754327790.9994892360-247.999489236041
302619826682.3094967578-484.309496757764
312472525118.8710407817-393.871040781738
322500524415.4801313731589.519868626885
332346223617.5811942989-155.581194298909
342078020744.864501859535.1354981404584
351981519056.1264748894758.873525110637
361976117552.55732907172208.44267092833
372145420268.68105423791185.31894576205
382389922656.53709181021242.46290818983
392493925998.9335164244-1059.93351642441
402358025344.6750313823-1764.67503138226
412456225097.2654055416-535.265405541566
422469623776.7960171806919.203982819385
432378523619.1160900398165.883909960183
442381223610.1162954216201.883704578398
452191722545.6616580007-628.661658000696
461971319352.3161063817360.683893618301
471928218111.20726680021170.79273319976
481878817182.93121662051605.06878337952
492145319409.32185196042043.67814803963
502448222728.34527171101753.65472828905
512747426596.7309766793877.26902332074
522726427921.2115785828-657.211578582781
532734929021.9809662332-1672.98096623325
543063226959.26901085663672.7309891434
552942929630.0949590114-201.094959011432
563008429612.0942239926471.905776007392
572629029093.4487988619-2803.44879886193
582437924205.0313594758173.968640524181
592333523075.1865792973259.813420702729
602134621542.7966352568-196.796635256756
612110622280.1808332974-1174.18083329741
622451422656.98038671721857.01961328281
632835326603.65861689241749.34138310758
643080528714.32933991932090.67066008069
653134832448.3776406776-1100.37764067759
663455631335.14864738143220.85135261857
673385533582.9567129103272.043287089655
683478734212.9907907347574.009209265343
693252933827.9229410715-1298.92294107154
702999830698.0259899003-700.02598990026
712925728983.3606357208273.639364279239
722815527655.6317350005499.368264999532
733046629225.92595665081240.07404334917
743570432283.15379820693420.84620179306
753932738048.96023027581278.03976972422
763935140116.3661225652-765.366122565225
774223441353.4633928287880.536607171263
784363042590.20543039531039.79456960472
794372242962.8122646198759.187735380183
804312144327.8605201136-1206.86052011357
813798542433.4629753998-4448.4629753998
823713536531.5932570855603.406742914478
833464636191.6924389163-1545.69243891629
843302633274.2265354958-248.226535495778
853508734231.4758443396855.524155660401
863884637058.6770297551787.32297024497
874201341192.3506086852820.649391314837
884390842692.27472610731215.72527389266
894286845838.4964479147-2970.49644791472
904442343426.4468771271996.553122872894
914416743617.6148199731549.385180026882
924363644564.4476014687-928.447601468695
934438242652.16081787541729.83918212465
944214242748.8402027503-606.84020275026
954345241266.17069285822185.82930714175
963691242032.0562119294-5120.05621192943
974241338595.04385175503817.95614824496
984534444311.47504055021032.52495944980
994487347813.8719279095-2940.87192790951
1004751045845.48580582151664.51419417854
1014955449191.2271995566362.772800443418
1024736950117.2841589157-2748.28415891575
1034599846818.7952928201-820.795292820098
1044814046352.84616543871787.15383456134
1054844147061.95818847641379.04181152360
1064492846731.3736734092-1803.37367340922
1074045444232.5967428259-3778.59674282591
1083866138929.7351696376-268.735169637628
1093724640253.0966116523-3007.09661165235
1103684339241.0996663667-2398.09966636668
1113642438940.5066795011-2516.50667950107
1123759437105.0737663897488.926233610327
1133814438806.0182783147-662.018278314725
1143873738104.5573333210632.442666678951
1153456037571.8648115244-3011.86481152441
1163608034713.63334827691366.36665172310
1173350834500.1350615145-992.13506151447
1183546231243.99132075044218.00867924961
1193337433793.8255223271-419.825522327112
1203211031476.0730985790633.926901421037
1213553333286.30355153042246.69644846962
1223553237099.7813944856-1567.78139448558
1233790337570.5120480186332.487951981377
1243676338605.9608480421-1842.96084804205
1254039938153.96364235542245.03635764461
1264416440321.24215416323842.75784583678
1274449642834.61170603231661.38829396766
1284311044903.8144325821-1793.81443258212
1294388042015.31178841131864.68821158871
1304393042048.30569663351881.69430336646
1314432742594.89399847111732.10600152887







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13242725.585465146439416.205016849046034.9659134437
13344432.771881200839857.975317735749007.5684446659
13446334.487389815240702.441477832651966.5333017978
13548706.544126483642121.904346032555291.1839069347
13649705.352493917542230.505829141557180.1991586935
13751563.348738037243238.719891086559887.9775849879
13852096.745514545342949.736780266461243.7542488242
13951194.814433408641244.424887649661145.2039791675
14051726.383787054640985.860297225562466.9072768836
14150855.992596074639334.469416885262377.515775264
14249319.256931978937022.828339684361615.6855242735
14348201.141471381535133.594895228161268.6880475349

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
132 & 42725.5854651464 & 39416.2050168490 & 46034.9659134437 \tabularnewline
133 & 44432.7718812008 & 39857.9753177357 & 49007.5684446659 \tabularnewline
134 & 46334.4873898152 & 40702.4414778326 & 51966.5333017978 \tabularnewline
135 & 48706.5441264836 & 42121.9043460325 & 55291.1839069347 \tabularnewline
136 & 49705.3524939175 & 42230.5058291415 & 57180.1991586935 \tabularnewline
137 & 51563.3487380372 & 43238.7198910865 & 59887.9775849879 \tabularnewline
138 & 52096.7455145453 & 42949.7367802664 & 61243.7542488242 \tabularnewline
139 & 51194.8144334086 & 41244.4248876496 & 61145.2039791675 \tabularnewline
140 & 51726.3837870546 & 40985.8602972255 & 62466.9072768836 \tabularnewline
141 & 50855.9925960746 & 39334.4694168852 & 62377.515775264 \tabularnewline
142 & 49319.2569319789 & 37022.8283396843 & 61615.6855242735 \tabularnewline
143 & 48201.1414713815 & 35133.5948952281 & 61268.6880475349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113960&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]132[/C][C]42725.5854651464[/C][C]39416.2050168490[/C][C]46034.9659134437[/C][/ROW]
[ROW][C]133[/C][C]44432.7718812008[/C][C]39857.9753177357[/C][C]49007.5684446659[/C][/ROW]
[ROW][C]134[/C][C]46334.4873898152[/C][C]40702.4414778326[/C][C]51966.5333017978[/C][/ROW]
[ROW][C]135[/C][C]48706.5441264836[/C][C]42121.9043460325[/C][C]55291.1839069347[/C][/ROW]
[ROW][C]136[/C][C]49705.3524939175[/C][C]42230.5058291415[/C][C]57180.1991586935[/C][/ROW]
[ROW][C]137[/C][C]51563.3487380372[/C][C]43238.7198910865[/C][C]59887.9775849879[/C][/ROW]
[ROW][C]138[/C][C]52096.7455145453[/C][C]42949.7367802664[/C][C]61243.7542488242[/C][/ROW]
[ROW][C]139[/C][C]51194.8144334086[/C][C]41244.4248876496[/C][C]61145.2039791675[/C][/ROW]
[ROW][C]140[/C][C]51726.3837870546[/C][C]40985.8602972255[/C][C]62466.9072768836[/C][/ROW]
[ROW][C]141[/C][C]50855.9925960746[/C][C]39334.4694168852[/C][C]62377.515775264[/C][/ROW]
[ROW][C]142[/C][C]49319.2569319789[/C][C]37022.8283396843[/C][C]61615.6855242735[/C][/ROW]
[ROW][C]143[/C][C]48201.1414713815[/C][C]35133.5948952281[/C][C]61268.6880475349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113960&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113960&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
13242725.585465146439416.205016849046034.9659134437
13344432.771881200839857.975317735749007.5684446659
13446334.487389815240702.441477832651966.5333017978
13548706.544126483642121.904346032555291.1839069347
13649705.352493917542230.505829141557180.1991586935
13751563.348738037243238.719891086559887.9775849879
13852096.745514545342949.736780266461243.7542488242
13951194.814433408641244.424887649661145.2039791675
14051726.383787054640985.860297225562466.9072768836
14150855.992596074639334.469416885262377.515775264
14249319.256931978937022.828339684361615.6855242735
14348201.141471381535133.594895228161268.6880475349



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')