Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Aug 2011 09:55:15 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/15/t1313416533n8g32trj86ef6uc.htm/, Retrieved Tue, 14 May 2024 19:51:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123773, Retrieved Tue, 14 May 2024 19:51:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSébastien Delforge
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1 - sta...] [2011-08-15 13:55:15] [923770d86edf74ed976a539eae527e37] [Current]
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Dataseries X:
58109
57087
56064
54019
74712
73689
58109
47763
48785
48785
49808
51964
45718
39462
34339
34339
54019
56064
40484
22859
32183
32183
39462
43663
42640
32183
37417
35362
52987
48785
32183
19782
31160
34339
37417
41507
33205
26038
29116
30138
57087
57087
41507
39462
45718
42640
50942
61288
63343
48785
44685
40484
68567
70622
65388
70622
69589
61288
70622
80968
85169
72667
64365
70622
97570
105872
103827
107916
106894
96548
114173
118374
124519
105872
98593
106894
126675
144300
140099
140099
142154
134976
153634
153634
150455
132820
135999
138054
151579
169204
156701
162958
157724
154656
178538
173304
166025
155679
166025
171259
177505
185806
177505
182628
176381
175359
201285
203441
195140
180583
192984
198208
204464
213788
204464
211743
208564
197185
221066
221066




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123773&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123773&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123773&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.147614078116431
beta0.0992579978981152
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.147614078116431 \tabularnewline
beta & 0.0992579978981152 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123773&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]0.147614078116431[/C][/ROW]
[ROW][C]beta[/C][C]0.0992579978981152[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123773&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123773&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
alpha0.147614078116431
beta0.0992579978981152
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134571854595.085322342-8877.08532234195
143946246341.7410313703-6879.74103137029
153433939603.2949721112-5264.29497211119
163433938566.5689301931-4227.56893019312
175401958738.2212978255-4719.22129782545
185606458590.9694782133-2526.96947821329
194048440851.2514967908-367.251496790799
202285932521.2180422733-9662.21804227335
213218330719.30433497451463.69566502554
223218329906.8373028232276.16269717702
233946229775.41787963219686.58212036787
244366331475.743087328912187.2569126711
254264024365.630332618218274.3696673818
263218323478.26913844038704.73086155967
273741721816.963147802715600.0368521973
283536224735.960798725910626.0392012741
295298742719.462593498110267.5374065019
304878547488.94112879011296.05887120987
313218335555.7053416957-3372.70534169573
321978221368.0164375125-1586.01643751249
333116030759.8640785216400.135921478421
343433931816.50580287532522.49419712471
353741739460.5781226666-2043.57812266656
364150742741.7078778854-1234.70787788541
373320538784.6921752503-5579.69217525035
382603827692.4336764178-1654.43367641778
392911629200.8276352545-84.8276352544817
403013825894.79169096584243.20830903425
415708738124.586637418518962.4133625815
425708737444.987681179819642.0123188202
434150727157.930077493514349.0699225065
443946218492.851760251720969.1482397483
454571835080.37969358810637.620306412
464264041430.74442772911209.25557227089
475094247381.34273880853560.65726119148
486128855473.79316630725814.20683369278
496334347963.430688370615379.5693116294
504878541688.94358647087096.05641352919
514468550334.1440664718-5649.14406647178
524048452635.3015266549-12151.3015266549
536856793894.5319668584-25327.5319668584
547062286541.948704998-15919.948704998
556538858091.05922792257296.94077207749
567062248974.917318098221647.0826819018
576958958228.721650294711360.2783497053
586128855902.04323991155385.95676008852
597062267357.94227037223264.05772962778
608096880768.489765747199.51023425303
618516980011.60129824785157.39870175222
627266760707.43030440711959.569695593
636436558224.4263769356140.57362306499
647062255634.467204268214987.5327957318
6597570102927.680943284-5357.68094328391
66105872109353.733809501-3481.73380950067
67103827100222.8172670853604.18273291457
68107916103312.9216640944603.07833590619
69106894100208.3897491476685.61025085307
709654888251.39943130768296.60056869237
71114173102783.76070009211389.2392999084
72118374120265.879286517-1891.87928651691
73124519125538.313957147-1019.3139571467
74105872104283.2751203671588.72487963317
759859391243.21124462277349.7887553773
7610689497488.70123081489405.29876918516
77126675137491.042255798-10816.0422557984
78144300147929.747518004-3629.74751800418
79140099143586.557163357-3487.55716335698
80140099147440.861549395-7341.86154939464
81142154143130.14806424-976.148064239911
82134976126911.5734252688064.4265747321
83153634148480.0608313865153.9391686137
84153634154400.222315594-766.222315593506
85150455161814.676881965-11359.6768819649
86132820135208.468690236-2388.4686902363
87135999123496.96949985512502.0305001451
88138054133392.3930202944661.60697970603
89151579159969.554869551-8390.55486955078
90169204180663.584632421-11459.5846324213
91156701173553.163006368-16852.1630063677
92162958171380.886179055-8422.88617905477
93157724171879.399289662-14155.3992896623
94154656158735.887544314-4079.88754431388
95178538177818.372207719.627792999614
96173304176781.419171319-3477.41917131905
97166025173184.970793427-7159.97079342717
98155679151341.1003313214337.89966867934
99166025152428.84317678713596.1568232132
100171259155066.46123064816192.5387693516
101177505173412.6774143754092.32258562525
102185806195372.709809273-9566.70980927336
103177505181623.37770133-4118.3777013302
104182628189166.341148586-6538.34114858616
105176381184000.681230856-7619.68123085596
106175359179714.183736769-4355.18373676864
107201285206280.442051058-4995.44205105843
108203441199722.4369490893718.56305091083
109195140192778.0347118542361.9652881457
110180583180216.06067106366.939328939654
111192984189571.0795834673412.92041653328
112198208192737.152071365470.84792863953
113204464199361.9833967575102.01660324264
114213788210444.2465633113343.7534366886
115204464201838.1160136222625.88398637765
116211743208867.8716011192875.12839888051
117208564203253.7530390435310.24696095721
118197185203640.417664724-6455.41766472437
119221066233529.884268953-12463.8842689525
120221066233481.348183842-12415.3481838425

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 45718 & 54595.085322342 & -8877.08532234195 \tabularnewline
14 & 39462 & 46341.7410313703 & -6879.74103137029 \tabularnewline
15 & 34339 & 39603.2949721112 & -5264.29497211119 \tabularnewline
16 & 34339 & 38566.5689301931 & -4227.56893019312 \tabularnewline
17 & 54019 & 58738.2212978255 & -4719.22129782545 \tabularnewline
18 & 56064 & 58590.9694782133 & -2526.96947821329 \tabularnewline
19 & 40484 & 40851.2514967908 & -367.251496790799 \tabularnewline
20 & 22859 & 32521.2180422733 & -9662.21804227335 \tabularnewline
21 & 32183 & 30719.3043349745 & 1463.69566502554 \tabularnewline
22 & 32183 & 29906.837302823 & 2276.16269717702 \tabularnewline
23 & 39462 & 29775.4178796321 & 9686.58212036787 \tabularnewline
24 & 43663 & 31475.7430873289 & 12187.2569126711 \tabularnewline
25 & 42640 & 24365.6303326182 & 18274.3696673818 \tabularnewline
26 & 32183 & 23478.2691384403 & 8704.73086155967 \tabularnewline
27 & 37417 & 21816.9631478027 & 15600.0368521973 \tabularnewline
28 & 35362 & 24735.9607987259 & 10626.0392012741 \tabularnewline
29 & 52987 & 42719.4625934981 & 10267.5374065019 \tabularnewline
30 & 48785 & 47488.9411287901 & 1296.05887120987 \tabularnewline
31 & 32183 & 35555.7053416957 & -3372.70534169573 \tabularnewline
32 & 19782 & 21368.0164375125 & -1586.01643751249 \tabularnewline
33 & 31160 & 30759.8640785216 & 400.135921478421 \tabularnewline
34 & 34339 & 31816.5058028753 & 2522.49419712471 \tabularnewline
35 & 37417 & 39460.5781226666 & -2043.57812266656 \tabularnewline
36 & 41507 & 42741.7078778854 & -1234.70787788541 \tabularnewline
37 & 33205 & 38784.6921752503 & -5579.69217525035 \tabularnewline
38 & 26038 & 27692.4336764178 & -1654.43367641778 \tabularnewline
39 & 29116 & 29200.8276352545 & -84.8276352544817 \tabularnewline
40 & 30138 & 25894.7916909658 & 4243.20830903425 \tabularnewline
41 & 57087 & 38124.5866374185 & 18962.4133625815 \tabularnewline
42 & 57087 & 37444.9876811798 & 19642.0123188202 \tabularnewline
43 & 41507 & 27157.9300774935 & 14349.0699225065 \tabularnewline
44 & 39462 & 18492.8517602517 & 20969.1482397483 \tabularnewline
45 & 45718 & 35080.379693588 & 10637.620306412 \tabularnewline
46 & 42640 & 41430.7444277291 & 1209.25557227089 \tabularnewline
47 & 50942 & 47381.3427388085 & 3560.65726119148 \tabularnewline
48 & 61288 & 55473.7931663072 & 5814.20683369278 \tabularnewline
49 & 63343 & 47963.4306883706 & 15379.5693116294 \tabularnewline
50 & 48785 & 41688.9435864708 & 7096.05641352919 \tabularnewline
51 & 44685 & 50334.1440664718 & -5649.14406647178 \tabularnewline
52 & 40484 & 52635.3015266549 & -12151.3015266549 \tabularnewline
53 & 68567 & 93894.5319668584 & -25327.5319668584 \tabularnewline
54 & 70622 & 86541.948704998 & -15919.948704998 \tabularnewline
55 & 65388 & 58091.0592279225 & 7296.94077207749 \tabularnewline
56 & 70622 & 48974.9173180982 & 21647.0826819018 \tabularnewline
57 & 69589 & 58228.7216502947 & 11360.2783497053 \tabularnewline
58 & 61288 & 55902.0432399115 & 5385.95676008852 \tabularnewline
59 & 70622 & 67357.9422703722 & 3264.05772962778 \tabularnewline
60 & 80968 & 80768.489765747 & 199.51023425303 \tabularnewline
61 & 85169 & 80011.6012982478 & 5157.39870175222 \tabularnewline
62 & 72667 & 60707.430304407 & 11959.569695593 \tabularnewline
63 & 64365 & 58224.426376935 & 6140.57362306499 \tabularnewline
64 & 70622 & 55634.4672042682 & 14987.5327957318 \tabularnewline
65 & 97570 & 102927.680943284 & -5357.68094328391 \tabularnewline
66 & 105872 & 109353.733809501 & -3481.73380950067 \tabularnewline
67 & 103827 & 100222.817267085 & 3604.18273291457 \tabularnewline
68 & 107916 & 103312.921664094 & 4603.07833590619 \tabularnewline
69 & 106894 & 100208.389749147 & 6685.61025085307 \tabularnewline
70 & 96548 & 88251.3994313076 & 8296.60056869237 \tabularnewline
71 & 114173 & 102783.760700092 & 11389.2392999084 \tabularnewline
72 & 118374 & 120265.879286517 & -1891.87928651691 \tabularnewline
73 & 124519 & 125538.313957147 & -1019.3139571467 \tabularnewline
74 & 105872 & 104283.275120367 & 1588.72487963317 \tabularnewline
75 & 98593 & 91243.2112446227 & 7349.7887553773 \tabularnewline
76 & 106894 & 97488.7012308148 & 9405.29876918516 \tabularnewline
77 & 126675 & 137491.042255798 & -10816.0422557984 \tabularnewline
78 & 144300 & 147929.747518004 & -3629.74751800418 \tabularnewline
79 & 140099 & 143586.557163357 & -3487.55716335698 \tabularnewline
80 & 140099 & 147440.861549395 & -7341.86154939464 \tabularnewline
81 & 142154 & 143130.14806424 & -976.148064239911 \tabularnewline
82 & 134976 & 126911.573425268 & 8064.4265747321 \tabularnewline
83 & 153634 & 148480.060831386 & 5153.9391686137 \tabularnewline
84 & 153634 & 154400.222315594 & -766.222315593506 \tabularnewline
85 & 150455 & 161814.676881965 & -11359.6768819649 \tabularnewline
86 & 132820 & 135208.468690236 & -2388.4686902363 \tabularnewline
87 & 135999 & 123496.969499855 & 12502.0305001451 \tabularnewline
88 & 138054 & 133392.393020294 & 4661.60697970603 \tabularnewline
89 & 151579 & 159969.554869551 & -8390.55486955078 \tabularnewline
90 & 169204 & 180663.584632421 & -11459.5846324213 \tabularnewline
91 & 156701 & 173553.163006368 & -16852.1630063677 \tabularnewline
92 & 162958 & 171380.886179055 & -8422.88617905477 \tabularnewline
93 & 157724 & 171879.399289662 & -14155.3992896623 \tabularnewline
94 & 154656 & 158735.887544314 & -4079.88754431388 \tabularnewline
95 & 178538 & 177818.372207 & 719.627792999614 \tabularnewline
96 & 173304 & 176781.419171319 & -3477.41917131905 \tabularnewline
97 & 166025 & 173184.970793427 & -7159.97079342717 \tabularnewline
98 & 155679 & 151341.100331321 & 4337.89966867934 \tabularnewline
99 & 166025 & 152428.843176787 & 13596.1568232132 \tabularnewline
100 & 171259 & 155066.461230648 & 16192.5387693516 \tabularnewline
101 & 177505 & 173412.677414375 & 4092.32258562525 \tabularnewline
102 & 185806 & 195372.709809273 & -9566.70980927336 \tabularnewline
103 & 177505 & 181623.37770133 & -4118.3777013302 \tabularnewline
104 & 182628 & 189166.341148586 & -6538.34114858616 \tabularnewline
105 & 176381 & 184000.681230856 & -7619.68123085596 \tabularnewline
106 & 175359 & 179714.183736769 & -4355.18373676864 \tabularnewline
107 & 201285 & 206280.442051058 & -4995.44205105843 \tabularnewline
108 & 203441 & 199722.436949089 & 3718.56305091083 \tabularnewline
109 & 195140 & 192778.034711854 & 2361.9652881457 \tabularnewline
110 & 180583 & 180216.06067106 & 366.939328939654 \tabularnewline
111 & 192984 & 189571.079583467 & 3412.92041653328 \tabularnewline
112 & 198208 & 192737.15207136 & 5470.84792863953 \tabularnewline
113 & 204464 & 199361.983396757 & 5102.01660324264 \tabularnewline
114 & 213788 & 210444.246563311 & 3343.7534366886 \tabularnewline
115 & 204464 & 201838.116013622 & 2625.88398637765 \tabularnewline
116 & 211743 & 208867.871601119 & 2875.12839888051 \tabularnewline
117 & 208564 & 203253.753039043 & 5310.24696095721 \tabularnewline
118 & 197185 & 203640.417664724 & -6455.41766472437 \tabularnewline
119 & 221066 & 233529.884268953 & -12463.8842689525 \tabularnewline
120 & 221066 & 233481.348183842 & -12415.3481838425 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123773&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]45718[/C][C]54595.085322342[/C][C]-8877.08532234195[/C][/ROW]
[ROW][C]14[/C][C]39462[/C][C]46341.7410313703[/C][C]-6879.74103137029[/C][/ROW]
[ROW][C]15[/C][C]34339[/C][C]39603.2949721112[/C][C]-5264.29497211119[/C][/ROW]
[ROW][C]16[/C][C]34339[/C][C]38566.5689301931[/C][C]-4227.56893019312[/C][/ROW]
[ROW][C]17[/C][C]54019[/C][C]58738.2212978255[/C][C]-4719.22129782545[/C][/ROW]
[ROW][C]18[/C][C]56064[/C][C]58590.9694782133[/C][C]-2526.96947821329[/C][/ROW]
[ROW][C]19[/C][C]40484[/C][C]40851.2514967908[/C][C]-367.251496790799[/C][/ROW]
[ROW][C]20[/C][C]22859[/C][C]32521.2180422733[/C][C]-9662.21804227335[/C][/ROW]
[ROW][C]21[/C][C]32183[/C][C]30719.3043349745[/C][C]1463.69566502554[/C][/ROW]
[ROW][C]22[/C][C]32183[/C][C]29906.837302823[/C][C]2276.16269717702[/C][/ROW]
[ROW][C]23[/C][C]39462[/C][C]29775.4178796321[/C][C]9686.58212036787[/C][/ROW]
[ROW][C]24[/C][C]43663[/C][C]31475.7430873289[/C][C]12187.2569126711[/C][/ROW]
[ROW][C]25[/C][C]42640[/C][C]24365.6303326182[/C][C]18274.3696673818[/C][/ROW]
[ROW][C]26[/C][C]32183[/C][C]23478.2691384403[/C][C]8704.73086155967[/C][/ROW]
[ROW][C]27[/C][C]37417[/C][C]21816.9631478027[/C][C]15600.0368521973[/C][/ROW]
[ROW][C]28[/C][C]35362[/C][C]24735.9607987259[/C][C]10626.0392012741[/C][/ROW]
[ROW][C]29[/C][C]52987[/C][C]42719.4625934981[/C][C]10267.5374065019[/C][/ROW]
[ROW][C]30[/C][C]48785[/C][C]47488.9411287901[/C][C]1296.05887120987[/C][/ROW]
[ROW][C]31[/C][C]32183[/C][C]35555.7053416957[/C][C]-3372.70534169573[/C][/ROW]
[ROW][C]32[/C][C]19782[/C][C]21368.0164375125[/C][C]-1586.01643751249[/C][/ROW]
[ROW][C]33[/C][C]31160[/C][C]30759.8640785216[/C][C]400.135921478421[/C][/ROW]
[ROW][C]34[/C][C]34339[/C][C]31816.5058028753[/C][C]2522.49419712471[/C][/ROW]
[ROW][C]35[/C][C]37417[/C][C]39460.5781226666[/C][C]-2043.57812266656[/C][/ROW]
[ROW][C]36[/C][C]41507[/C][C]42741.7078778854[/C][C]-1234.70787788541[/C][/ROW]
[ROW][C]37[/C][C]33205[/C][C]38784.6921752503[/C][C]-5579.69217525035[/C][/ROW]
[ROW][C]38[/C][C]26038[/C][C]27692.4336764178[/C][C]-1654.43367641778[/C][/ROW]
[ROW][C]39[/C][C]29116[/C][C]29200.8276352545[/C][C]-84.8276352544817[/C][/ROW]
[ROW][C]40[/C][C]30138[/C][C]25894.7916909658[/C][C]4243.20830903425[/C][/ROW]
[ROW][C]41[/C][C]57087[/C][C]38124.5866374185[/C][C]18962.4133625815[/C][/ROW]
[ROW][C]42[/C][C]57087[/C][C]37444.9876811798[/C][C]19642.0123188202[/C][/ROW]
[ROW][C]43[/C][C]41507[/C][C]27157.9300774935[/C][C]14349.0699225065[/C][/ROW]
[ROW][C]44[/C][C]39462[/C][C]18492.8517602517[/C][C]20969.1482397483[/C][/ROW]
[ROW][C]45[/C][C]45718[/C][C]35080.379693588[/C][C]10637.620306412[/C][/ROW]
[ROW][C]46[/C][C]42640[/C][C]41430.7444277291[/C][C]1209.25557227089[/C][/ROW]
[ROW][C]47[/C][C]50942[/C][C]47381.3427388085[/C][C]3560.65726119148[/C][/ROW]
[ROW][C]48[/C][C]61288[/C][C]55473.7931663072[/C][C]5814.20683369278[/C][/ROW]
[ROW][C]49[/C][C]63343[/C][C]47963.4306883706[/C][C]15379.5693116294[/C][/ROW]
[ROW][C]50[/C][C]48785[/C][C]41688.9435864708[/C][C]7096.05641352919[/C][/ROW]
[ROW][C]51[/C][C]44685[/C][C]50334.1440664718[/C][C]-5649.14406647178[/C][/ROW]
[ROW][C]52[/C][C]40484[/C][C]52635.3015266549[/C][C]-12151.3015266549[/C][/ROW]
[ROW][C]53[/C][C]68567[/C][C]93894.5319668584[/C][C]-25327.5319668584[/C][/ROW]
[ROW][C]54[/C][C]70622[/C][C]86541.948704998[/C][C]-15919.948704998[/C][/ROW]
[ROW][C]55[/C][C]65388[/C][C]58091.0592279225[/C][C]7296.94077207749[/C][/ROW]
[ROW][C]56[/C][C]70622[/C][C]48974.9173180982[/C][C]21647.0826819018[/C][/ROW]
[ROW][C]57[/C][C]69589[/C][C]58228.7216502947[/C][C]11360.2783497053[/C][/ROW]
[ROW][C]58[/C][C]61288[/C][C]55902.0432399115[/C][C]5385.95676008852[/C][/ROW]
[ROW][C]59[/C][C]70622[/C][C]67357.9422703722[/C][C]3264.05772962778[/C][/ROW]
[ROW][C]60[/C][C]80968[/C][C]80768.489765747[/C][C]199.51023425303[/C][/ROW]
[ROW][C]61[/C][C]85169[/C][C]80011.6012982478[/C][C]5157.39870175222[/C][/ROW]
[ROW][C]62[/C][C]72667[/C][C]60707.430304407[/C][C]11959.569695593[/C][/ROW]
[ROW][C]63[/C][C]64365[/C][C]58224.426376935[/C][C]6140.57362306499[/C][/ROW]
[ROW][C]64[/C][C]70622[/C][C]55634.4672042682[/C][C]14987.5327957318[/C][/ROW]
[ROW][C]65[/C][C]97570[/C][C]102927.680943284[/C][C]-5357.68094328391[/C][/ROW]
[ROW][C]66[/C][C]105872[/C][C]109353.733809501[/C][C]-3481.73380950067[/C][/ROW]
[ROW][C]67[/C][C]103827[/C][C]100222.817267085[/C][C]3604.18273291457[/C][/ROW]
[ROW][C]68[/C][C]107916[/C][C]103312.921664094[/C][C]4603.07833590619[/C][/ROW]
[ROW][C]69[/C][C]106894[/C][C]100208.389749147[/C][C]6685.61025085307[/C][/ROW]
[ROW][C]70[/C][C]96548[/C][C]88251.3994313076[/C][C]8296.60056869237[/C][/ROW]
[ROW][C]71[/C][C]114173[/C][C]102783.760700092[/C][C]11389.2392999084[/C][/ROW]
[ROW][C]72[/C][C]118374[/C][C]120265.879286517[/C][C]-1891.87928651691[/C][/ROW]
[ROW][C]73[/C][C]124519[/C][C]125538.313957147[/C][C]-1019.3139571467[/C][/ROW]
[ROW][C]74[/C][C]105872[/C][C]104283.275120367[/C][C]1588.72487963317[/C][/ROW]
[ROW][C]75[/C][C]98593[/C][C]91243.2112446227[/C][C]7349.7887553773[/C][/ROW]
[ROW][C]76[/C][C]106894[/C][C]97488.7012308148[/C][C]9405.29876918516[/C][/ROW]
[ROW][C]77[/C][C]126675[/C][C]137491.042255798[/C][C]-10816.0422557984[/C][/ROW]
[ROW][C]78[/C][C]144300[/C][C]147929.747518004[/C][C]-3629.74751800418[/C][/ROW]
[ROW][C]79[/C][C]140099[/C][C]143586.557163357[/C][C]-3487.55716335698[/C][/ROW]
[ROW][C]80[/C][C]140099[/C][C]147440.861549395[/C][C]-7341.86154939464[/C][/ROW]
[ROW][C]81[/C][C]142154[/C][C]143130.14806424[/C][C]-976.148064239911[/C][/ROW]
[ROW][C]82[/C][C]134976[/C][C]126911.573425268[/C][C]8064.4265747321[/C][/ROW]
[ROW][C]83[/C][C]153634[/C][C]148480.060831386[/C][C]5153.9391686137[/C][/ROW]
[ROW][C]84[/C][C]153634[/C][C]154400.222315594[/C][C]-766.222315593506[/C][/ROW]
[ROW][C]85[/C][C]150455[/C][C]161814.676881965[/C][C]-11359.6768819649[/C][/ROW]
[ROW][C]86[/C][C]132820[/C][C]135208.468690236[/C][C]-2388.4686902363[/C][/ROW]
[ROW][C]87[/C][C]135999[/C][C]123496.969499855[/C][C]12502.0305001451[/C][/ROW]
[ROW][C]88[/C][C]138054[/C][C]133392.393020294[/C][C]4661.60697970603[/C][/ROW]
[ROW][C]89[/C][C]151579[/C][C]159969.554869551[/C][C]-8390.55486955078[/C][/ROW]
[ROW][C]90[/C][C]169204[/C][C]180663.584632421[/C][C]-11459.5846324213[/C][/ROW]
[ROW][C]91[/C][C]156701[/C][C]173553.163006368[/C][C]-16852.1630063677[/C][/ROW]
[ROW][C]92[/C][C]162958[/C][C]171380.886179055[/C][C]-8422.88617905477[/C][/ROW]
[ROW][C]93[/C][C]157724[/C][C]171879.399289662[/C][C]-14155.3992896623[/C][/ROW]
[ROW][C]94[/C][C]154656[/C][C]158735.887544314[/C][C]-4079.88754431388[/C][/ROW]
[ROW][C]95[/C][C]178538[/C][C]177818.372207[/C][C]719.627792999614[/C][/ROW]
[ROW][C]96[/C][C]173304[/C][C]176781.419171319[/C][C]-3477.41917131905[/C][/ROW]
[ROW][C]97[/C][C]166025[/C][C]173184.970793427[/C][C]-7159.97079342717[/C][/ROW]
[ROW][C]98[/C][C]155679[/C][C]151341.100331321[/C][C]4337.89966867934[/C][/ROW]
[ROW][C]99[/C][C]166025[/C][C]152428.843176787[/C][C]13596.1568232132[/C][/ROW]
[ROW][C]100[/C][C]171259[/C][C]155066.461230648[/C][C]16192.5387693516[/C][/ROW]
[ROW][C]101[/C][C]177505[/C][C]173412.677414375[/C][C]4092.32258562525[/C][/ROW]
[ROW][C]102[/C][C]185806[/C][C]195372.709809273[/C][C]-9566.70980927336[/C][/ROW]
[ROW][C]103[/C][C]177505[/C][C]181623.37770133[/C][C]-4118.3777013302[/C][/ROW]
[ROW][C]104[/C][C]182628[/C][C]189166.341148586[/C][C]-6538.34114858616[/C][/ROW]
[ROW][C]105[/C][C]176381[/C][C]184000.681230856[/C][C]-7619.68123085596[/C][/ROW]
[ROW][C]106[/C][C]175359[/C][C]179714.183736769[/C][C]-4355.18373676864[/C][/ROW]
[ROW][C]107[/C][C]201285[/C][C]206280.442051058[/C][C]-4995.44205105843[/C][/ROW]
[ROW][C]108[/C][C]203441[/C][C]199722.436949089[/C][C]3718.56305091083[/C][/ROW]
[ROW][C]109[/C][C]195140[/C][C]192778.034711854[/C][C]2361.9652881457[/C][/ROW]
[ROW][C]110[/C][C]180583[/C][C]180216.06067106[/C][C]366.939328939654[/C][/ROW]
[ROW][C]111[/C][C]192984[/C][C]189571.079583467[/C][C]3412.92041653328[/C][/ROW]
[ROW][C]112[/C][C]198208[/C][C]192737.15207136[/C][C]5470.84792863953[/C][/ROW]
[ROW][C]113[/C][C]204464[/C][C]199361.983396757[/C][C]5102.01660324264[/C][/ROW]
[ROW][C]114[/C][C]213788[/C][C]210444.246563311[/C][C]3343.7534366886[/C][/ROW]
[ROW][C]115[/C][C]204464[/C][C]201838.116013622[/C][C]2625.88398637765[/C][/ROW]
[ROW][C]116[/C][C]211743[/C][C]208867.871601119[/C][C]2875.12839888051[/C][/ROW]
[ROW][C]117[/C][C]208564[/C][C]203253.753039043[/C][C]5310.24696095721[/C][/ROW]
[ROW][C]118[/C][C]197185[/C][C]203640.417664724[/C][C]-6455.41766472437[/C][/ROW]
[ROW][C]119[/C][C]221066[/C][C]233529.884268953[/C][C]-12463.8842689525[/C][/ROW]
[ROW][C]120[/C][C]221066[/C][C]233481.348183842[/C][C]-12415.3481838425[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123773&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123773&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
134571854595.085322342-8877.08532234195
143946246341.7410313703-6879.74103137029
153433939603.2949721112-5264.29497211119
163433938566.5689301931-4227.56893019312
175401958738.2212978255-4719.22129782545
185606458590.9694782133-2526.96947821329
194048440851.2514967908-367.251496790799
202285932521.2180422733-9662.21804227335
213218330719.30433497451463.69566502554
223218329906.8373028232276.16269717702
233946229775.41787963219686.58212036787
244366331475.743087328912187.2569126711
254264024365.630332618218274.3696673818
263218323478.26913844038704.73086155967
273741721816.963147802715600.0368521973
283536224735.960798725910626.0392012741
295298742719.462593498110267.5374065019
304878547488.94112879011296.05887120987
313218335555.7053416957-3372.70534169573
321978221368.0164375125-1586.01643751249
333116030759.8640785216400.135921478421
343433931816.50580287532522.49419712471
353741739460.5781226666-2043.57812266656
364150742741.7078778854-1234.70787788541
373320538784.6921752503-5579.69217525035
382603827692.4336764178-1654.43367641778
392911629200.8276352545-84.8276352544817
403013825894.79169096584243.20830903425
415708738124.586637418518962.4133625815
425708737444.987681179819642.0123188202
434150727157.930077493514349.0699225065
443946218492.851760251720969.1482397483
454571835080.37969358810637.620306412
464264041430.74442772911209.25557227089
475094247381.34273880853560.65726119148
486128855473.79316630725814.20683369278
496334347963.430688370615379.5693116294
504878541688.94358647087096.05641352919
514468550334.1440664718-5649.14406647178
524048452635.3015266549-12151.3015266549
536856793894.5319668584-25327.5319668584
547062286541.948704998-15919.948704998
556538858091.05922792257296.94077207749
567062248974.917318098221647.0826819018
576958958228.721650294711360.2783497053
586128855902.04323991155385.95676008852
597062267357.94227037223264.05772962778
608096880768.489765747199.51023425303
618516980011.60129824785157.39870175222
627266760707.43030440711959.569695593
636436558224.4263769356140.57362306499
647062255634.467204268214987.5327957318
6597570102927.680943284-5357.68094328391
66105872109353.733809501-3481.73380950067
67103827100222.8172670853604.18273291457
68107916103312.9216640944603.07833590619
69106894100208.3897491476685.61025085307
709654888251.39943130768296.60056869237
71114173102783.76070009211389.2392999084
72118374120265.879286517-1891.87928651691
73124519125538.313957147-1019.3139571467
74105872104283.2751203671588.72487963317
759859391243.21124462277349.7887553773
7610689497488.70123081489405.29876918516
77126675137491.042255798-10816.0422557984
78144300147929.747518004-3629.74751800418
79140099143586.557163357-3487.55716335698
80140099147440.861549395-7341.86154939464
81142154143130.14806424-976.148064239911
82134976126911.5734252688064.4265747321
83153634148480.0608313865153.9391686137
84153634154400.222315594-766.222315593506
85150455161814.676881965-11359.6768819649
86132820135208.468690236-2388.4686902363
87135999123496.96949985512502.0305001451
88138054133392.3930202944661.60697970603
89151579159969.554869551-8390.55486955078
90169204180663.584632421-11459.5846324213
91156701173553.163006368-16852.1630063677
92162958171380.886179055-8422.88617905477
93157724171879.399289662-14155.3992896623
94154656158735.887544314-4079.88754431388
95178538177818.372207719.627792999614
96173304176781.419171319-3477.41917131905
97166025173184.970793427-7159.97079342717
98155679151341.1003313214337.89966867934
99166025152428.84317678713596.1568232132
100171259155066.46123064816192.5387693516
101177505173412.6774143754092.32258562525
102185806195372.709809273-9566.70980927336
103177505181623.37770133-4118.3777013302
104182628189166.341148586-6538.34114858616
105176381184000.681230856-7619.68123085596
106175359179714.183736769-4355.18373676864
107201285206280.442051058-4995.44205105843
108203441199722.4369490893718.56305091083
109195140192778.0347118542361.9652881457
110180583180216.06067106366.939328939654
111192984189571.0795834673412.92041653328
112198208192737.152071365470.84792863953
113204464199361.9833967575102.01660324264
114213788210444.2465633113343.7534366886
115204464201838.1160136222625.88398637765
116211743208867.8716011192875.12839888051
117208564203253.7530390435310.24696095721
118197185203640.417664724-6455.41766472437
119221066233529.884268953-12463.8842689525
120221066233481.348183842-12415.3481838425







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121221541.457653081204107.281057781238975.634248381
122204690.456862211187064.90242515222316.011299272
123217886.876572917199949.895654641235823.857491192
124222518.323383494204251.821751258240784.825015731
125228258.755593473209597.726476088246919.784710857
126237602.96400053218436.135639022256769.792362038
127226285.322541171206882.199894575245688.445187767
128233301.585328502213315.335098013253287.835558992
129228333.812907957207978.173027124248689.45278879
130216277.482702733195738.528604536236816.436800929
131243817.992707225221888.949726061265747.035688388
132245347.234659759230966.248997929259728.220321589

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 221541.457653081 & 204107.281057781 & 238975.634248381 \tabularnewline
122 & 204690.456862211 & 187064.90242515 & 222316.011299272 \tabularnewline
123 & 217886.876572917 & 199949.895654641 & 235823.857491192 \tabularnewline
124 & 222518.323383494 & 204251.821751258 & 240784.825015731 \tabularnewline
125 & 228258.755593473 & 209597.726476088 & 246919.784710857 \tabularnewline
126 & 237602.96400053 & 218436.135639022 & 256769.792362038 \tabularnewline
127 & 226285.322541171 & 206882.199894575 & 245688.445187767 \tabularnewline
128 & 233301.585328502 & 213315.335098013 & 253287.835558992 \tabularnewline
129 & 228333.812907957 & 207978.173027124 & 248689.45278879 \tabularnewline
130 & 216277.482702733 & 195738.528604536 & 236816.436800929 \tabularnewline
131 & 243817.992707225 & 221888.949726061 & 265747.035688388 \tabularnewline
132 & 245347.234659759 & 230966.248997929 & 259728.220321589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123773&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]121[/C][C]221541.457653081[/C][C]204107.281057781[/C][C]238975.634248381[/C][/ROW]
[ROW][C]122[/C][C]204690.456862211[/C][C]187064.90242515[/C][C]222316.011299272[/C][/ROW]
[ROW][C]123[/C][C]217886.876572917[/C][C]199949.895654641[/C][C]235823.857491192[/C][/ROW]
[ROW][C]124[/C][C]222518.323383494[/C][C]204251.821751258[/C][C]240784.825015731[/C][/ROW]
[ROW][C]125[/C][C]228258.755593473[/C][C]209597.726476088[/C][C]246919.784710857[/C][/ROW]
[ROW][C]126[/C][C]237602.96400053[/C][C]218436.135639022[/C][C]256769.792362038[/C][/ROW]
[ROW][C]127[/C][C]226285.322541171[/C][C]206882.199894575[/C][C]245688.445187767[/C][/ROW]
[ROW][C]128[/C][C]233301.585328502[/C][C]213315.335098013[/C][C]253287.835558992[/C][/ROW]
[ROW][C]129[/C][C]228333.812907957[/C][C]207978.173027124[/C][C]248689.45278879[/C][/ROW]
[ROW][C]130[/C][C]216277.482702733[/C][C]195738.528604536[/C][C]236816.436800929[/C][/ROW]
[ROW][C]131[/C][C]243817.992707225[/C][C]221888.949726061[/C][C]265747.035688388[/C][/ROW]
[ROW][C]132[/C][C]245347.234659759[/C][C]230966.248997929[/C][C]259728.220321589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123773&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123773&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
121221541.457653081204107.281057781238975.634248381
122204690.456862211187064.90242515222316.011299272
123217886.876572917199949.895654641235823.857491192
124222518.323383494204251.821751258240784.825015731
125228258.755593473209597.726476088246919.784710857
126237602.96400053218436.135639022256769.792362038
127226285.322541171206882.199894575245688.445187767
128233301.585328502213315.335098013253287.835558992
129228333.812907957207978.173027124248689.45278879
130216277.482702733195738.528604536236816.436800929
131243817.992707225221888.949726061265747.035688388
132245347.234659759230966.248997929259728.220321589



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')