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, 10 Dec 2016 12:24:03 +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/10/t1481369067ze0nrm3rska2jh2.htm/, Retrieved Mon, 06 May 2024 06:33:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298653, Retrieved Mon, 06 May 2024 06:33:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-10 11:24:03] [462f83e9ca944f1b841aaa868aea0854] [Current]
Feedback Forum

Post a new message
Dataseries X:
3891
3702
3712
3796
3856
3989
3922
4084
4169
4161
4205
4198
4228
4461
4326
4305
4351
4357
4449
4519
4422
4507
4549
4658
4468
4516
4548
4656
4640
4686
4734
4702
4723
4609
4731
4791
5111
4841
4875
4975
4973
4966
4937
4861
4980
4896
4924
4920
5088
5193
5169
5102
5041
4925
5091
4798
5098
5554
5173
5240
5101
5162
5207
5189
5258
5211
5149
5259
5327
5248
5421
5476
5507
5324
5123
5447
5290
5326
5118
5241
5178
5324
5292
5371
5453
5509
5437
5342
5390
5329
5258
5262
5147
5158
5125
5026
4917
4855
4668
4884
4923
4981
5148
5052
5061
4995
5058
5009
5145
5187
5327
5418
5482
5583
5735
5669




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298653&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298653&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298653&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.650440909511054
beta0.0224686836546399
gamma0.353261542070113

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.650440909511054 \tabularnewline
beta & 0.0224686836546399 \tabularnewline
gamma & 0.353261542070113 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298653&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]0.650440909511054[/C][/ROW]
[ROW][C]beta[/C][C]0.0224686836546399[/C][/ROW]
[ROW][C]gamma[/C][C]0.353261542070113[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298653&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298653&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
alpha0.650440909511054
beta0.0224686836546399
gamma0.353261542070113







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1342283977.44951923077250.550480769228
1444614374.7136629296786.2863370703271
1543264309.8113903441416.1886096558628
1643054317.25961077976-12.2596107797626
1743514369.23310946723-18.2331094672318
1843574372.30473152668-15.3047315266822
1944494390.2657519505858.7342480494153
2045194587.86812825467-68.8681282546686
2144224612.92455541824-190.924555418241
2245074473.2168790941433.7831209058559
2345494537.1203266102411.8796733897643
2446584541.82549189553116.174508104472
2544684682.67221166062-214.672211660615
2645164754.16997660606-238.169976606056
2745484461.9479670184386.0520329815699
2846564504.72228338667151.277716613329
2946404658.11655060325-18.1165506032548
3046864657.4143465409228.5856534590839
3147344709.4964147371524.5035852628462
3247024865.00660689366-163.006606893658
3347234808.31340995369-85.3134099536937
3446094761.14533313447-152.145333134475
3547314694.7888692047436.2111307952564
3647914721.9350581434769.0649418565308
3751114784.33235627703326.667643722971
3848415205.99694198822-364.996941988219
3948754870.423648149334.5763518506692
4049754866.17191614683108.828083853175
4149734968.331662645084.66833735492492
4249664985.84397179498-19.8439717949832
4349375002.84080758783-65.8408075878306
4448615072.03157946791-211.031579467914
4549804988.59222930346-8.59222930346459
4648964979.09244855896-83.0924485589649
4749244977.93782202059-53.9378220205936
4849204946.21460706804-26.2146070680383
4950884972.76617671927115.233823280733
5051935162.722518964130.2774810358978
5151695126.8933924515742.1066075484323
5251025157.47943314131-55.4794331413104
5350415135.05627261419-94.0562726141925
5449255079.03599077504-154.035990775039
5550914994.8165920918896.1834079081218
5647985145.58115672485-347.581156724848
5750984990.44275717072107.557242829277
5855545041.10909927131512.890900728691
5951735433.73410795213-260.734107952131
6052405270.43081829493-30.4308182949289
6151015311.15051055702-210.150510557019
6251625273.66097298585-111.660972985846
6352075139.5839342176867.4160657823249
6451895167.5656155496821.4343844503164
6552585184.5145404496273.4854595503766
6652115226.62004317338-15.6200431733805
6751495261.90989511984-112.909895119845
6852595217.3965192489341.6034807510669
6953275372.81412238683-45.8141223868261
7052485372.74421614616-124.744216146165
7154215244.74463597751176.255364022492
7254765390.1538297118385.8461702881668
7355075482.0488128460824.9511871539235
7453245610.8138084648-286.813808464798
7551235383.53660184857-260.536601848567
7654475186.34642018586260.653579814138
7752905362.63699736694-72.636997366938
7853265293.8758328983932.1241671016051
7951185344.08493840755-226.084938407552
8052415239.262466845791.73753315420618
8151785351.59654978412-173.596549784123
8253245250.4392521996373.5607478003703
8352925283.266911511578.73308848843317
8453715300.7726604542870.2273395457196
8554535366.9847368020286.0152631979818
8655095489.858069313119.1419306869002
8754375462.19156758455-25.1915675845494
8853425483.23817812857-141.238178128572
8953905351.8909753498338.1090246501744
9053295364.64428062436-35.6442806243631
9152585334.44266825716-76.4426682571566
9252625352.82724851342-90.827248513423
9351475379.69011252441-232.690112524407
9451585266.14069928859-108.140699288595
9551255165.64586727318-40.6458672731824
9650265150.77439528371-124.774395283707
9749175081.3962933882-164.396293388203
9848555018.77149035395-163.771490353953
9946684849.62055331594-181.620553315944
10048844735.26759950075148.73240049925
10149234799.59209726415123.40790273585
10249814844.88254633233136.117453667666
10351484910.03674103994237.963258960061
10450525124.41537811694-72.4153781169407
10550615139.27298091015-78.2729809101538
10649955137.33655806159-142.33655806159
10750585018.2279246414839.772075358519
10850095041.74409921489-32.7440992148895
10951455025.14771113009119.852288869908
11051875149.4553196287137.5446803712903
11153275113.95504657472213.044953425278
11254185307.78093270996110.219067290042
11354825354.04306798351127.956932016486
11455835414.04382310314168.956176896862
11557355523.796081515211.203918485004
11656695692.7128296061-23.7128296060964

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4228 & 3977.44951923077 & 250.550480769228 \tabularnewline
14 & 4461 & 4374.71366292967 & 86.2863370703271 \tabularnewline
15 & 4326 & 4309.81139034414 & 16.1886096558628 \tabularnewline
16 & 4305 & 4317.25961077976 & -12.2596107797626 \tabularnewline
17 & 4351 & 4369.23310946723 & -18.2331094672318 \tabularnewline
18 & 4357 & 4372.30473152668 & -15.3047315266822 \tabularnewline
19 & 4449 & 4390.26575195058 & 58.7342480494153 \tabularnewline
20 & 4519 & 4587.86812825467 & -68.8681282546686 \tabularnewline
21 & 4422 & 4612.92455541824 & -190.924555418241 \tabularnewline
22 & 4507 & 4473.21687909414 & 33.7831209058559 \tabularnewline
23 & 4549 & 4537.12032661024 & 11.8796733897643 \tabularnewline
24 & 4658 & 4541.82549189553 & 116.174508104472 \tabularnewline
25 & 4468 & 4682.67221166062 & -214.672211660615 \tabularnewline
26 & 4516 & 4754.16997660606 & -238.169976606056 \tabularnewline
27 & 4548 & 4461.94796701843 & 86.0520329815699 \tabularnewline
28 & 4656 & 4504.72228338667 & 151.277716613329 \tabularnewline
29 & 4640 & 4658.11655060325 & -18.1165506032548 \tabularnewline
30 & 4686 & 4657.41434654092 & 28.5856534590839 \tabularnewline
31 & 4734 & 4709.49641473715 & 24.5035852628462 \tabularnewline
32 & 4702 & 4865.00660689366 & -163.006606893658 \tabularnewline
33 & 4723 & 4808.31340995369 & -85.3134099536937 \tabularnewline
34 & 4609 & 4761.14533313447 & -152.145333134475 \tabularnewline
35 & 4731 & 4694.78886920474 & 36.2111307952564 \tabularnewline
36 & 4791 & 4721.93505814347 & 69.0649418565308 \tabularnewline
37 & 5111 & 4784.33235627703 & 326.667643722971 \tabularnewline
38 & 4841 & 5205.99694198822 & -364.996941988219 \tabularnewline
39 & 4875 & 4870.42364814933 & 4.5763518506692 \tabularnewline
40 & 4975 & 4866.17191614683 & 108.828083853175 \tabularnewline
41 & 4973 & 4968.33166264508 & 4.66833735492492 \tabularnewline
42 & 4966 & 4985.84397179498 & -19.8439717949832 \tabularnewline
43 & 4937 & 5002.84080758783 & -65.8408075878306 \tabularnewline
44 & 4861 & 5072.03157946791 & -211.031579467914 \tabularnewline
45 & 4980 & 4988.59222930346 & -8.59222930346459 \tabularnewline
46 & 4896 & 4979.09244855896 & -83.0924485589649 \tabularnewline
47 & 4924 & 4977.93782202059 & -53.9378220205936 \tabularnewline
48 & 4920 & 4946.21460706804 & -26.2146070680383 \tabularnewline
49 & 5088 & 4972.76617671927 & 115.233823280733 \tabularnewline
50 & 5193 & 5162.7225189641 & 30.2774810358978 \tabularnewline
51 & 5169 & 5126.89339245157 & 42.1066075484323 \tabularnewline
52 & 5102 & 5157.47943314131 & -55.4794331413104 \tabularnewline
53 & 5041 & 5135.05627261419 & -94.0562726141925 \tabularnewline
54 & 4925 & 5079.03599077504 & -154.035990775039 \tabularnewline
55 & 5091 & 4994.81659209188 & 96.1834079081218 \tabularnewline
56 & 4798 & 5145.58115672485 & -347.581156724848 \tabularnewline
57 & 5098 & 4990.44275717072 & 107.557242829277 \tabularnewline
58 & 5554 & 5041.10909927131 & 512.890900728691 \tabularnewline
59 & 5173 & 5433.73410795213 & -260.734107952131 \tabularnewline
60 & 5240 & 5270.43081829493 & -30.4308182949289 \tabularnewline
61 & 5101 & 5311.15051055702 & -210.150510557019 \tabularnewline
62 & 5162 & 5273.66097298585 & -111.660972985846 \tabularnewline
63 & 5207 & 5139.58393421768 & 67.4160657823249 \tabularnewline
64 & 5189 & 5167.56561554968 & 21.4343844503164 \tabularnewline
65 & 5258 & 5184.51454044962 & 73.4854595503766 \tabularnewline
66 & 5211 & 5226.62004317338 & -15.6200431733805 \tabularnewline
67 & 5149 & 5261.90989511984 & -112.909895119845 \tabularnewline
68 & 5259 & 5217.39651924893 & 41.6034807510669 \tabularnewline
69 & 5327 & 5372.81412238683 & -45.8141223868261 \tabularnewline
70 & 5248 & 5372.74421614616 & -124.744216146165 \tabularnewline
71 & 5421 & 5244.74463597751 & 176.255364022492 \tabularnewline
72 & 5476 & 5390.15382971183 & 85.8461702881668 \tabularnewline
73 & 5507 & 5482.04881284608 & 24.9511871539235 \tabularnewline
74 & 5324 & 5610.8138084648 & -286.813808464798 \tabularnewline
75 & 5123 & 5383.53660184857 & -260.536601848567 \tabularnewline
76 & 5447 & 5186.34642018586 & 260.653579814138 \tabularnewline
77 & 5290 & 5362.63699736694 & -72.636997366938 \tabularnewline
78 & 5326 & 5293.87583289839 & 32.1241671016051 \tabularnewline
79 & 5118 & 5344.08493840755 & -226.084938407552 \tabularnewline
80 & 5241 & 5239.26246684579 & 1.73753315420618 \tabularnewline
81 & 5178 & 5351.59654978412 & -173.596549784123 \tabularnewline
82 & 5324 & 5250.43925219963 & 73.5607478003703 \tabularnewline
83 & 5292 & 5283.26691151157 & 8.73308848843317 \tabularnewline
84 & 5371 & 5300.77266045428 & 70.2273395457196 \tabularnewline
85 & 5453 & 5366.98473680202 & 86.0152631979818 \tabularnewline
86 & 5509 & 5489.8580693131 & 19.1419306869002 \tabularnewline
87 & 5437 & 5462.19156758455 & -25.1915675845494 \tabularnewline
88 & 5342 & 5483.23817812857 & -141.238178128572 \tabularnewline
89 & 5390 & 5351.89097534983 & 38.1090246501744 \tabularnewline
90 & 5329 & 5364.64428062436 & -35.6442806243631 \tabularnewline
91 & 5258 & 5334.44266825716 & -76.4426682571566 \tabularnewline
92 & 5262 & 5352.82724851342 & -90.827248513423 \tabularnewline
93 & 5147 & 5379.69011252441 & -232.690112524407 \tabularnewline
94 & 5158 & 5266.14069928859 & -108.140699288595 \tabularnewline
95 & 5125 & 5165.64586727318 & -40.6458672731824 \tabularnewline
96 & 5026 & 5150.77439528371 & -124.774395283707 \tabularnewline
97 & 4917 & 5081.3962933882 & -164.396293388203 \tabularnewline
98 & 4855 & 5018.77149035395 & -163.771490353953 \tabularnewline
99 & 4668 & 4849.62055331594 & -181.620553315944 \tabularnewline
100 & 4884 & 4735.26759950075 & 148.73240049925 \tabularnewline
101 & 4923 & 4799.59209726415 & 123.40790273585 \tabularnewline
102 & 4981 & 4844.88254633233 & 136.117453667666 \tabularnewline
103 & 5148 & 4910.03674103994 & 237.963258960061 \tabularnewline
104 & 5052 & 5124.41537811694 & -72.4153781169407 \tabularnewline
105 & 5061 & 5139.27298091015 & -78.2729809101538 \tabularnewline
106 & 4995 & 5137.33655806159 & -142.33655806159 \tabularnewline
107 & 5058 & 5018.22792464148 & 39.772075358519 \tabularnewline
108 & 5009 & 5041.74409921489 & -32.7440992148895 \tabularnewline
109 & 5145 & 5025.14771113009 & 119.852288869908 \tabularnewline
110 & 5187 & 5149.45531962871 & 37.5446803712903 \tabularnewline
111 & 5327 & 5113.95504657472 & 213.044953425278 \tabularnewline
112 & 5418 & 5307.78093270996 & 110.219067290042 \tabularnewline
113 & 5482 & 5354.04306798351 & 127.956932016486 \tabularnewline
114 & 5583 & 5414.04382310314 & 168.956176896862 \tabularnewline
115 & 5735 & 5523.796081515 & 211.203918485004 \tabularnewline
116 & 5669 & 5692.7128296061 & -23.7128296060964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298653&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]4228[/C][C]3977.44951923077[/C][C]250.550480769228[/C][/ROW]
[ROW][C]14[/C][C]4461[/C][C]4374.71366292967[/C][C]86.2863370703271[/C][/ROW]
[ROW][C]15[/C][C]4326[/C][C]4309.81139034414[/C][C]16.1886096558628[/C][/ROW]
[ROW][C]16[/C][C]4305[/C][C]4317.25961077976[/C][C]-12.2596107797626[/C][/ROW]
[ROW][C]17[/C][C]4351[/C][C]4369.23310946723[/C][C]-18.2331094672318[/C][/ROW]
[ROW][C]18[/C][C]4357[/C][C]4372.30473152668[/C][C]-15.3047315266822[/C][/ROW]
[ROW][C]19[/C][C]4449[/C][C]4390.26575195058[/C][C]58.7342480494153[/C][/ROW]
[ROW][C]20[/C][C]4519[/C][C]4587.86812825467[/C][C]-68.8681282546686[/C][/ROW]
[ROW][C]21[/C][C]4422[/C][C]4612.92455541824[/C][C]-190.924555418241[/C][/ROW]
[ROW][C]22[/C][C]4507[/C][C]4473.21687909414[/C][C]33.7831209058559[/C][/ROW]
[ROW][C]23[/C][C]4549[/C][C]4537.12032661024[/C][C]11.8796733897643[/C][/ROW]
[ROW][C]24[/C][C]4658[/C][C]4541.82549189553[/C][C]116.174508104472[/C][/ROW]
[ROW][C]25[/C][C]4468[/C][C]4682.67221166062[/C][C]-214.672211660615[/C][/ROW]
[ROW][C]26[/C][C]4516[/C][C]4754.16997660606[/C][C]-238.169976606056[/C][/ROW]
[ROW][C]27[/C][C]4548[/C][C]4461.94796701843[/C][C]86.0520329815699[/C][/ROW]
[ROW][C]28[/C][C]4656[/C][C]4504.72228338667[/C][C]151.277716613329[/C][/ROW]
[ROW][C]29[/C][C]4640[/C][C]4658.11655060325[/C][C]-18.1165506032548[/C][/ROW]
[ROW][C]30[/C][C]4686[/C][C]4657.41434654092[/C][C]28.5856534590839[/C][/ROW]
[ROW][C]31[/C][C]4734[/C][C]4709.49641473715[/C][C]24.5035852628462[/C][/ROW]
[ROW][C]32[/C][C]4702[/C][C]4865.00660689366[/C][C]-163.006606893658[/C][/ROW]
[ROW][C]33[/C][C]4723[/C][C]4808.31340995369[/C][C]-85.3134099536937[/C][/ROW]
[ROW][C]34[/C][C]4609[/C][C]4761.14533313447[/C][C]-152.145333134475[/C][/ROW]
[ROW][C]35[/C][C]4731[/C][C]4694.78886920474[/C][C]36.2111307952564[/C][/ROW]
[ROW][C]36[/C][C]4791[/C][C]4721.93505814347[/C][C]69.0649418565308[/C][/ROW]
[ROW][C]37[/C][C]5111[/C][C]4784.33235627703[/C][C]326.667643722971[/C][/ROW]
[ROW][C]38[/C][C]4841[/C][C]5205.99694198822[/C][C]-364.996941988219[/C][/ROW]
[ROW][C]39[/C][C]4875[/C][C]4870.42364814933[/C][C]4.5763518506692[/C][/ROW]
[ROW][C]40[/C][C]4975[/C][C]4866.17191614683[/C][C]108.828083853175[/C][/ROW]
[ROW][C]41[/C][C]4973[/C][C]4968.33166264508[/C][C]4.66833735492492[/C][/ROW]
[ROW][C]42[/C][C]4966[/C][C]4985.84397179498[/C][C]-19.8439717949832[/C][/ROW]
[ROW][C]43[/C][C]4937[/C][C]5002.84080758783[/C][C]-65.8408075878306[/C][/ROW]
[ROW][C]44[/C][C]4861[/C][C]5072.03157946791[/C][C]-211.031579467914[/C][/ROW]
[ROW][C]45[/C][C]4980[/C][C]4988.59222930346[/C][C]-8.59222930346459[/C][/ROW]
[ROW][C]46[/C][C]4896[/C][C]4979.09244855896[/C][C]-83.0924485589649[/C][/ROW]
[ROW][C]47[/C][C]4924[/C][C]4977.93782202059[/C][C]-53.9378220205936[/C][/ROW]
[ROW][C]48[/C][C]4920[/C][C]4946.21460706804[/C][C]-26.2146070680383[/C][/ROW]
[ROW][C]49[/C][C]5088[/C][C]4972.76617671927[/C][C]115.233823280733[/C][/ROW]
[ROW][C]50[/C][C]5193[/C][C]5162.7225189641[/C][C]30.2774810358978[/C][/ROW]
[ROW][C]51[/C][C]5169[/C][C]5126.89339245157[/C][C]42.1066075484323[/C][/ROW]
[ROW][C]52[/C][C]5102[/C][C]5157.47943314131[/C][C]-55.4794331413104[/C][/ROW]
[ROW][C]53[/C][C]5041[/C][C]5135.05627261419[/C][C]-94.0562726141925[/C][/ROW]
[ROW][C]54[/C][C]4925[/C][C]5079.03599077504[/C][C]-154.035990775039[/C][/ROW]
[ROW][C]55[/C][C]5091[/C][C]4994.81659209188[/C][C]96.1834079081218[/C][/ROW]
[ROW][C]56[/C][C]4798[/C][C]5145.58115672485[/C][C]-347.581156724848[/C][/ROW]
[ROW][C]57[/C][C]5098[/C][C]4990.44275717072[/C][C]107.557242829277[/C][/ROW]
[ROW][C]58[/C][C]5554[/C][C]5041.10909927131[/C][C]512.890900728691[/C][/ROW]
[ROW][C]59[/C][C]5173[/C][C]5433.73410795213[/C][C]-260.734107952131[/C][/ROW]
[ROW][C]60[/C][C]5240[/C][C]5270.43081829493[/C][C]-30.4308182949289[/C][/ROW]
[ROW][C]61[/C][C]5101[/C][C]5311.15051055702[/C][C]-210.150510557019[/C][/ROW]
[ROW][C]62[/C][C]5162[/C][C]5273.66097298585[/C][C]-111.660972985846[/C][/ROW]
[ROW][C]63[/C][C]5207[/C][C]5139.58393421768[/C][C]67.4160657823249[/C][/ROW]
[ROW][C]64[/C][C]5189[/C][C]5167.56561554968[/C][C]21.4343844503164[/C][/ROW]
[ROW][C]65[/C][C]5258[/C][C]5184.51454044962[/C][C]73.4854595503766[/C][/ROW]
[ROW][C]66[/C][C]5211[/C][C]5226.62004317338[/C][C]-15.6200431733805[/C][/ROW]
[ROW][C]67[/C][C]5149[/C][C]5261.90989511984[/C][C]-112.909895119845[/C][/ROW]
[ROW][C]68[/C][C]5259[/C][C]5217.39651924893[/C][C]41.6034807510669[/C][/ROW]
[ROW][C]69[/C][C]5327[/C][C]5372.81412238683[/C][C]-45.8141223868261[/C][/ROW]
[ROW][C]70[/C][C]5248[/C][C]5372.74421614616[/C][C]-124.744216146165[/C][/ROW]
[ROW][C]71[/C][C]5421[/C][C]5244.74463597751[/C][C]176.255364022492[/C][/ROW]
[ROW][C]72[/C][C]5476[/C][C]5390.15382971183[/C][C]85.8461702881668[/C][/ROW]
[ROW][C]73[/C][C]5507[/C][C]5482.04881284608[/C][C]24.9511871539235[/C][/ROW]
[ROW][C]74[/C][C]5324[/C][C]5610.8138084648[/C][C]-286.813808464798[/C][/ROW]
[ROW][C]75[/C][C]5123[/C][C]5383.53660184857[/C][C]-260.536601848567[/C][/ROW]
[ROW][C]76[/C][C]5447[/C][C]5186.34642018586[/C][C]260.653579814138[/C][/ROW]
[ROW][C]77[/C][C]5290[/C][C]5362.63699736694[/C][C]-72.636997366938[/C][/ROW]
[ROW][C]78[/C][C]5326[/C][C]5293.87583289839[/C][C]32.1241671016051[/C][/ROW]
[ROW][C]79[/C][C]5118[/C][C]5344.08493840755[/C][C]-226.084938407552[/C][/ROW]
[ROW][C]80[/C][C]5241[/C][C]5239.26246684579[/C][C]1.73753315420618[/C][/ROW]
[ROW][C]81[/C][C]5178[/C][C]5351.59654978412[/C][C]-173.596549784123[/C][/ROW]
[ROW][C]82[/C][C]5324[/C][C]5250.43925219963[/C][C]73.5607478003703[/C][/ROW]
[ROW][C]83[/C][C]5292[/C][C]5283.26691151157[/C][C]8.73308848843317[/C][/ROW]
[ROW][C]84[/C][C]5371[/C][C]5300.77266045428[/C][C]70.2273395457196[/C][/ROW]
[ROW][C]85[/C][C]5453[/C][C]5366.98473680202[/C][C]86.0152631979818[/C][/ROW]
[ROW][C]86[/C][C]5509[/C][C]5489.8580693131[/C][C]19.1419306869002[/C][/ROW]
[ROW][C]87[/C][C]5437[/C][C]5462.19156758455[/C][C]-25.1915675845494[/C][/ROW]
[ROW][C]88[/C][C]5342[/C][C]5483.23817812857[/C][C]-141.238178128572[/C][/ROW]
[ROW][C]89[/C][C]5390[/C][C]5351.89097534983[/C][C]38.1090246501744[/C][/ROW]
[ROW][C]90[/C][C]5329[/C][C]5364.64428062436[/C][C]-35.6442806243631[/C][/ROW]
[ROW][C]91[/C][C]5258[/C][C]5334.44266825716[/C][C]-76.4426682571566[/C][/ROW]
[ROW][C]92[/C][C]5262[/C][C]5352.82724851342[/C][C]-90.827248513423[/C][/ROW]
[ROW][C]93[/C][C]5147[/C][C]5379.69011252441[/C][C]-232.690112524407[/C][/ROW]
[ROW][C]94[/C][C]5158[/C][C]5266.14069928859[/C][C]-108.140699288595[/C][/ROW]
[ROW][C]95[/C][C]5125[/C][C]5165.64586727318[/C][C]-40.6458672731824[/C][/ROW]
[ROW][C]96[/C][C]5026[/C][C]5150.77439528371[/C][C]-124.774395283707[/C][/ROW]
[ROW][C]97[/C][C]4917[/C][C]5081.3962933882[/C][C]-164.396293388203[/C][/ROW]
[ROW][C]98[/C][C]4855[/C][C]5018.77149035395[/C][C]-163.771490353953[/C][/ROW]
[ROW][C]99[/C][C]4668[/C][C]4849.62055331594[/C][C]-181.620553315944[/C][/ROW]
[ROW][C]100[/C][C]4884[/C][C]4735.26759950075[/C][C]148.73240049925[/C][/ROW]
[ROW][C]101[/C][C]4923[/C][C]4799.59209726415[/C][C]123.40790273585[/C][/ROW]
[ROW][C]102[/C][C]4981[/C][C]4844.88254633233[/C][C]136.117453667666[/C][/ROW]
[ROW][C]103[/C][C]5148[/C][C]4910.03674103994[/C][C]237.963258960061[/C][/ROW]
[ROW][C]104[/C][C]5052[/C][C]5124.41537811694[/C][C]-72.4153781169407[/C][/ROW]
[ROW][C]105[/C][C]5061[/C][C]5139.27298091015[/C][C]-78.2729809101538[/C][/ROW]
[ROW][C]106[/C][C]4995[/C][C]5137.33655806159[/C][C]-142.33655806159[/C][/ROW]
[ROW][C]107[/C][C]5058[/C][C]5018.22792464148[/C][C]39.772075358519[/C][/ROW]
[ROW][C]108[/C][C]5009[/C][C]5041.74409921489[/C][C]-32.7440992148895[/C][/ROW]
[ROW][C]109[/C][C]5145[/C][C]5025.14771113009[/C][C]119.852288869908[/C][/ROW]
[ROW][C]110[/C][C]5187[/C][C]5149.45531962871[/C][C]37.5446803712903[/C][/ROW]
[ROW][C]111[/C][C]5327[/C][C]5113.95504657472[/C][C]213.044953425278[/C][/ROW]
[ROW][C]112[/C][C]5418[/C][C]5307.78093270996[/C][C]110.219067290042[/C][/ROW]
[ROW][C]113[/C][C]5482[/C][C]5354.04306798351[/C][C]127.956932016486[/C][/ROW]
[ROW][C]114[/C][C]5583[/C][C]5414.04382310314[/C][C]168.956176896862[/C][/ROW]
[ROW][C]115[/C][C]5735[/C][C]5523.796081515[/C][C]211.203918485004[/C][/ROW]
[ROW][C]116[/C][C]5669[/C][C]5692.7128296061[/C][C]-23.7128296060964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298653&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298653&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
1342283977.44951923077250.550480769228
1444614374.7136629296786.2863370703271
1543264309.8113903441416.1886096558628
1643054317.25961077976-12.2596107797626
1743514369.23310946723-18.2331094672318
1843574372.30473152668-15.3047315266822
1944494390.2657519505858.7342480494153
2045194587.86812825467-68.8681282546686
2144224612.92455541824-190.924555418241
2245074473.2168790941433.7831209058559
2345494537.1203266102411.8796733897643
2446584541.82549189553116.174508104472
2544684682.67221166062-214.672211660615
2645164754.16997660606-238.169976606056
2745484461.9479670184386.0520329815699
2846564504.72228338667151.277716613329
2946404658.11655060325-18.1165506032548
3046864657.4143465409228.5856534590839
3147344709.4964147371524.5035852628462
3247024865.00660689366-163.006606893658
3347234808.31340995369-85.3134099536937
3446094761.14533313447-152.145333134475
3547314694.7888692047436.2111307952564
3647914721.9350581434769.0649418565308
3751114784.33235627703326.667643722971
3848415205.99694198822-364.996941988219
3948754870.423648149334.5763518506692
4049754866.17191614683108.828083853175
4149734968.331662645084.66833735492492
4249664985.84397179498-19.8439717949832
4349375002.84080758783-65.8408075878306
4448615072.03157946791-211.031579467914
4549804988.59222930346-8.59222930346459
4648964979.09244855896-83.0924485589649
4749244977.93782202059-53.9378220205936
4849204946.21460706804-26.2146070680383
4950884972.76617671927115.233823280733
5051935162.722518964130.2774810358978
5151695126.8933924515742.1066075484323
5251025157.47943314131-55.4794331413104
5350415135.05627261419-94.0562726141925
5449255079.03599077504-154.035990775039
5550914994.8165920918896.1834079081218
5647985145.58115672485-347.581156724848
5750984990.44275717072107.557242829277
5855545041.10909927131512.890900728691
5951735433.73410795213-260.734107952131
6052405270.43081829493-30.4308182949289
6151015311.15051055702-210.150510557019
6251625273.66097298585-111.660972985846
6352075139.5839342176867.4160657823249
6451895167.5656155496821.4343844503164
6552585184.5145404496273.4854595503766
6652115226.62004317338-15.6200431733805
6751495261.90989511984-112.909895119845
6852595217.3965192489341.6034807510669
6953275372.81412238683-45.8141223868261
7052485372.74421614616-124.744216146165
7154215244.74463597751176.255364022492
7254765390.1538297118385.8461702881668
7355075482.0488128460824.9511871539235
7453245610.8138084648-286.813808464798
7551235383.53660184857-260.536601848567
7654475186.34642018586260.653579814138
7752905362.63699736694-72.636997366938
7853265293.8758328983932.1241671016051
7951185344.08493840755-226.084938407552
8052415239.262466845791.73753315420618
8151785351.59654978412-173.596549784123
8253245250.4392521996373.5607478003703
8352925283.266911511578.73308848843317
8453715300.7726604542870.2273395457196
8554535366.9847368020286.0152631979818
8655095489.858069313119.1419306869002
8754375462.19156758455-25.1915675845494
8853425483.23817812857-141.238178128572
8953905351.8909753498338.1090246501744
9053295364.64428062436-35.6442806243631
9152585334.44266825716-76.4426682571566
9252625352.82724851342-90.827248513423
9351475379.69011252441-232.690112524407
9451585266.14069928859-108.140699288595
9551255165.64586727318-40.6458672731824
9650265150.77439528371-124.774395283707
9749175081.3962933882-164.396293388203
9848555018.77149035395-163.771490353953
9946684849.62055331594-181.620553315944
10048844735.26759950075148.73240049925
10149234799.59209726415123.40790273585
10249814844.88254633233136.117453667666
10351484910.03674103994237.963258960061
10450525124.41537811694-72.4153781169407
10550615139.27298091015-78.2729809101538
10649955137.33655806159-142.33655806159
10750585018.2279246414839.772075358519
10850095041.74409921489-32.7440992148895
10951455025.14771113009119.852288869908
11051875149.4553196287137.5446803712903
11153275113.95504657472213.044953425278
11254185307.78093270996110.219067290042
11354825354.04306798351127.956932016486
11455835414.04382310314168.956176896862
11557355523.796081515211.203918485004
11656695692.7128296061-23.7128296060964







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1175749.507827464735467.651077459276031.36457747019
1185802.698932760635464.200972659756141.19689286151
1195812.8663520275423.919346407726201.81335764628
1205815.183879234715379.78305715636250.58470131313
1215852.833071778925373.774502466976331.89164109087
1225901.372436030275380.715716248566422.02915581198
1235874.92706402085314.242899170256435.61122887134
1245926.172413837475326.688479781016525.65634789393
1255910.013282726825272.706355833276547.32020962037
1265897.057755234085222.715064817766571.40044565041
1275904.871097828885194.132919505986615.60927615179
1285907.056746069675160.44698396526653.66650817414

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 5749.50782746473 & 5467.65107745927 & 6031.36457747019 \tabularnewline
118 & 5802.69893276063 & 5464.20097265975 & 6141.19689286151 \tabularnewline
119 & 5812.866352027 & 5423.91934640772 & 6201.81335764628 \tabularnewline
120 & 5815.18387923471 & 5379.7830571563 & 6250.58470131313 \tabularnewline
121 & 5852.83307177892 & 5373.77450246697 & 6331.89164109087 \tabularnewline
122 & 5901.37243603027 & 5380.71571624856 & 6422.02915581198 \tabularnewline
123 & 5874.9270640208 & 5314.24289917025 & 6435.61122887134 \tabularnewline
124 & 5926.17241383747 & 5326.68847978101 & 6525.65634789393 \tabularnewline
125 & 5910.01328272682 & 5272.70635583327 & 6547.32020962037 \tabularnewline
126 & 5897.05775523408 & 5222.71506481776 & 6571.40044565041 \tabularnewline
127 & 5904.87109782888 & 5194.13291950598 & 6615.60927615179 \tabularnewline
128 & 5907.05674606967 & 5160.4469839652 & 6653.66650817414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298653&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]117[/C][C]5749.50782746473[/C][C]5467.65107745927[/C][C]6031.36457747019[/C][/ROW]
[ROW][C]118[/C][C]5802.69893276063[/C][C]5464.20097265975[/C][C]6141.19689286151[/C][/ROW]
[ROW][C]119[/C][C]5812.866352027[/C][C]5423.91934640772[/C][C]6201.81335764628[/C][/ROW]
[ROW][C]120[/C][C]5815.18387923471[/C][C]5379.7830571563[/C][C]6250.58470131313[/C][/ROW]
[ROW][C]121[/C][C]5852.83307177892[/C][C]5373.77450246697[/C][C]6331.89164109087[/C][/ROW]
[ROW][C]122[/C][C]5901.37243603027[/C][C]5380.71571624856[/C][C]6422.02915581198[/C][/ROW]
[ROW][C]123[/C][C]5874.9270640208[/C][C]5314.24289917025[/C][C]6435.61122887134[/C][/ROW]
[ROW][C]124[/C][C]5926.17241383747[/C][C]5326.68847978101[/C][C]6525.65634789393[/C][/ROW]
[ROW][C]125[/C][C]5910.01328272682[/C][C]5272.70635583327[/C][C]6547.32020962037[/C][/ROW]
[ROW][C]126[/C][C]5897.05775523408[/C][C]5222.71506481776[/C][C]6571.40044565041[/C][/ROW]
[ROW][C]127[/C][C]5904.87109782888[/C][C]5194.13291950598[/C][C]6615.60927615179[/C][/ROW]
[ROW][C]128[/C][C]5907.05674606967[/C][C]5160.4469839652[/C][C]6653.66650817414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298653&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298653&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
1175749.507827464735467.651077459276031.36457747019
1185802.698932760635464.200972659756141.19689286151
1195812.8663520275423.919346407726201.81335764628
1205815.183879234715379.78305715636250.58470131313
1215852.833071778925373.774502466976331.89164109087
1225901.372436030275380.715716248566422.02915581198
1235874.92706402085314.242899170256435.61122887134
1245926.172413837475326.688479781016525.65634789393
1255910.013282726825272.706355833276547.32020962037
1265897.057755234085222.715064817766571.40044565041
1275904.871097828885194.132919505986615.60927615179
1285907.056746069675160.44698396526653.66650817414



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')