Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 14 Aug 2011 13:29:53 -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/14/t131334306877rool5p9huwj9c.htm/, Retrieved Wed, 15 May 2024 15:31:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123693, Retrieved Wed, 15 May 2024 15:31:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSopracasa Erik
Estimated Impact192
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS A - STA...] [2011-08-14 17:29:53] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
5740
5639
5538
5336
7380
7279
5740
4718
4819
4819
4920
5133
4516
3898
3392
3392
5336
5538
3999
2258
3179
3179
3898
4313
4212
3179
3696
3493
5234
4819
3179
1954
3078
3392
3696
4100
3280
2572
2876
2977
5639
5639
4100
3898
4516
4212
5032
6054
6257
4819
4414
3999
6773
6976
6459
6976
6874
6054
6976
7998
8413
7178
6358
6976
9638
10458
10256
10660
10559
9537
11278
11693
12300
10458
9739
10559
12513
14254
13839
13839
14042
13333
15176
15176
14862
13120
13434
13637
14973
16714
15479
16097
15580
15277
17636
17119
16400
15378
16400
16917
17534
18354
17534
18040
17423
17322
19883
20096
19276
17838
19063
19579
20197
21118
20197
20916
20602
19478
21837
21837




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123693&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123693&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653576517001826
beta0.0529349454900191
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653576517001826 \tabularnewline
beta & 0.0529349454900191 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123693&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]0.653576517001826[/C][/ROW]
[ROW][C]beta[/C][C]0.0529349454900191[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123693&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
alpha0.653576517001826
beta0.0529349454900191
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1345165451.23530982906-935.23530982906
1438984212.20700581785-314.207005817851
1533923475.98925286797-83.9892528679734
1633923359.1639710620432.8360289379634
1753365238.0789793545797.9210206454345
1855385386.75312037352151.246879626484
1939993903.679151174295.3208488257974
2022582881.97606051683-623.976060516834
2131792529.98634478713649.013655212866
2231792939.90509661482239.094903385182
2338983186.93255366014711.067446339863
2443133870.57267508152442.427324918482
2542123227.33012282671984.669877173287
2631793540.63582461777-361.635824617773
2736962933.9219212744762.078078725599
2834933520.55819923458-27.5581992345769
2952345490.47926539314-256.47926539314
3048195521.6691693689-702.669169368901
3131793527.2488050042-348.248805004198
3219542017.23864077466-63.2386407746617
3330782542.90809583354535.091904166464
3433922802.60425947376589.395740526244
3536963520.44133572618175.558664273819
3641003820.85407465268279.145925347317
3732803312.92296353295-32.9229635329534
3825722513.7390488833358.260951116667
3928762604.24496493599271.755035064009
4029772613.40960439182363.590395608179
4156394789.745694544849.254305455997
4256395457.37466028556181.625339714445
4341004262.61015476808-162.610154768081
4438983078.00801059779819.991989402207
4545164524.11392289208-8.11392289207834
4642124564.70423283169-352.704232831695
4750324607.95873519209424.041264807907
4860545199.7704149978854.229585002204
4962575072.600167054251184.39983294575
5048195255.74153663318-436.741536633181
5144145234.68263699555-820.68263699555
5239994661.87230827785-662.872308277854
5367736400.27200946408372.727990535923
5469766573.37596234173402.624037658266
5564595459.64940527827999.35059472173
5669765470.924025389951505.07597461005
5768747197.66133190496-323.661331904962
5860547021.47800819964-967.47800819964
5969767019.5792554317-43.5792554316986
6079987526.17976301124471.82023698876
6184137321.61152456541091.38847543461
6271786937.30054993967240.69945006033
6363587304.37154325273-946.37154325273
6469766778.11122255401197.88877744599
6596389541.6483238862796.3516761137289
66104589638.7220041738819.277995826204
67102569112.691878312291143.30812168771
68106609506.890505098381153.10949490162
691055910471.537841127687.4621588723567
70953710456.7102185488-919.710218548757
711127810923.4324766185354.567523381535
721169311999.9144367891-306.914436789148
731230011605.1901574872694.809842512768
741045810757.4392681474-299.439268147426
75973910432.025033892-693.025033892038
761055910548.275749408610.7242505914292
771251313228.3673980385-715.367398038517
781425413091.33185475971162.66814524025
791383912959.8380414066879.161958593395
801383913233.5066200119605.493379988144
811404213500.8480212794541.151978720589
821333313479.0979316832-146.097931683236
831517614965.104124217210.895875783002
841517615785.7915482626-609.791548262587
851486215596.9148279677-734.91482796767
861312013477.6141033499-357.614103349872
871343412983.1340091634450.865990836581
881363714135.6787532563-498.678753256296
891497316258.5559667778-1285.55596677785
901671416406.9819474148307.018052585194
911547915595.9669365395-116.966936539548
921609715067.24554108721029.75445891282
931558015547.724526558432.2754734415521
941527714895.8394542397381.160545760325
951763616808.8962842573827.103715742662
961711917728.112091872-609.112091872012
971640017476.4521188065-1076.4521188065
981537815232.9386068328145.061393167205
991640015332.76512036521067.23487963484
1001691716566.227253273350.772746726951
1011753419008.0995345432-1474.09953454317
1021835419614.8861167578-1260.88611675784
1031753417607.8857753687-73.8857753686825
1041804017481.7012877134558.298712286603
1051742317269.3156046574153.68439534256
1061732216782.6608042038539.339195796223
1071988318924.0754538334958.924546166632
1082009619406.958770734689.04122926596
1091927619861.8074153111-585.807415311145
1101783818399.067229543-561.067229542994
1111906318369.355754563693.644245437023
1121957919110.0319315256468.968068474402
1132019721000.6479128167-803.647912816708
1142111822146.3563303659-1028.35633036595
1152019720737.4498959207-540.449895920661
1162091620544.1049776965371.895022303492
1172060220082.0446740116519.95532598842
1181947819993.3700757196-515.37007571958
1192183721579.3101595273257.689840472722
1202183721474.6328057808362.367194219183

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4516 & 5451.23530982906 & -935.23530982906 \tabularnewline
14 & 3898 & 4212.20700581785 & -314.207005817851 \tabularnewline
15 & 3392 & 3475.98925286797 & -83.9892528679734 \tabularnewline
16 & 3392 & 3359.16397106204 & 32.8360289379634 \tabularnewline
17 & 5336 & 5238.07897935457 & 97.9210206454345 \tabularnewline
18 & 5538 & 5386.75312037352 & 151.246879626484 \tabularnewline
19 & 3999 & 3903.6791511742 & 95.3208488257974 \tabularnewline
20 & 2258 & 2881.97606051683 & -623.976060516834 \tabularnewline
21 & 3179 & 2529.98634478713 & 649.013655212866 \tabularnewline
22 & 3179 & 2939.90509661482 & 239.094903385182 \tabularnewline
23 & 3898 & 3186.93255366014 & 711.067446339863 \tabularnewline
24 & 4313 & 3870.57267508152 & 442.427324918482 \tabularnewline
25 & 4212 & 3227.33012282671 & 984.669877173287 \tabularnewline
26 & 3179 & 3540.63582461777 & -361.635824617773 \tabularnewline
27 & 3696 & 2933.9219212744 & 762.078078725599 \tabularnewline
28 & 3493 & 3520.55819923458 & -27.5581992345769 \tabularnewline
29 & 5234 & 5490.47926539314 & -256.47926539314 \tabularnewline
30 & 4819 & 5521.6691693689 & -702.669169368901 \tabularnewline
31 & 3179 & 3527.2488050042 & -348.248805004198 \tabularnewline
32 & 1954 & 2017.23864077466 & -63.2386407746617 \tabularnewline
33 & 3078 & 2542.90809583354 & 535.091904166464 \tabularnewline
34 & 3392 & 2802.60425947376 & 589.395740526244 \tabularnewline
35 & 3696 & 3520.44133572618 & 175.558664273819 \tabularnewline
36 & 4100 & 3820.85407465268 & 279.145925347317 \tabularnewline
37 & 3280 & 3312.92296353295 & -32.9229635329534 \tabularnewline
38 & 2572 & 2513.73904888333 & 58.260951116667 \tabularnewline
39 & 2876 & 2604.24496493599 & 271.755035064009 \tabularnewline
40 & 2977 & 2613.40960439182 & 363.590395608179 \tabularnewline
41 & 5639 & 4789.745694544 & 849.254305455997 \tabularnewline
42 & 5639 & 5457.37466028556 & 181.625339714445 \tabularnewline
43 & 4100 & 4262.61015476808 & -162.610154768081 \tabularnewline
44 & 3898 & 3078.00801059779 & 819.991989402207 \tabularnewline
45 & 4516 & 4524.11392289208 & -8.11392289207834 \tabularnewline
46 & 4212 & 4564.70423283169 & -352.704232831695 \tabularnewline
47 & 5032 & 4607.95873519209 & 424.041264807907 \tabularnewline
48 & 6054 & 5199.7704149978 & 854.229585002204 \tabularnewline
49 & 6257 & 5072.60016705425 & 1184.39983294575 \tabularnewline
50 & 4819 & 5255.74153663318 & -436.741536633181 \tabularnewline
51 & 4414 & 5234.68263699555 & -820.68263699555 \tabularnewline
52 & 3999 & 4661.87230827785 & -662.872308277854 \tabularnewline
53 & 6773 & 6400.27200946408 & 372.727990535923 \tabularnewline
54 & 6976 & 6573.37596234173 & 402.624037658266 \tabularnewline
55 & 6459 & 5459.64940527827 & 999.35059472173 \tabularnewline
56 & 6976 & 5470.92402538995 & 1505.07597461005 \tabularnewline
57 & 6874 & 7197.66133190496 & -323.661331904962 \tabularnewline
58 & 6054 & 7021.47800819964 & -967.47800819964 \tabularnewline
59 & 6976 & 7019.5792554317 & -43.5792554316986 \tabularnewline
60 & 7998 & 7526.17976301124 & 471.82023698876 \tabularnewline
61 & 8413 & 7321.6115245654 & 1091.38847543461 \tabularnewline
62 & 7178 & 6937.30054993967 & 240.69945006033 \tabularnewline
63 & 6358 & 7304.37154325273 & -946.37154325273 \tabularnewline
64 & 6976 & 6778.11122255401 & 197.88877744599 \tabularnewline
65 & 9638 & 9541.64832388627 & 96.3516761137289 \tabularnewline
66 & 10458 & 9638.7220041738 & 819.277995826204 \tabularnewline
67 & 10256 & 9112.69187831229 & 1143.30812168771 \tabularnewline
68 & 10660 & 9506.89050509838 & 1153.10949490162 \tabularnewline
69 & 10559 & 10471.5378411276 & 87.4621588723567 \tabularnewline
70 & 9537 & 10456.7102185488 & -919.710218548757 \tabularnewline
71 & 11278 & 10923.4324766185 & 354.567523381535 \tabularnewline
72 & 11693 & 11999.9144367891 & -306.914436789148 \tabularnewline
73 & 12300 & 11605.1901574872 & 694.809842512768 \tabularnewline
74 & 10458 & 10757.4392681474 & -299.439268147426 \tabularnewline
75 & 9739 & 10432.025033892 & -693.025033892038 \tabularnewline
76 & 10559 & 10548.2757494086 & 10.7242505914292 \tabularnewline
77 & 12513 & 13228.3673980385 & -715.367398038517 \tabularnewline
78 & 14254 & 13091.3318547597 & 1162.66814524025 \tabularnewline
79 & 13839 & 12959.8380414066 & 879.161958593395 \tabularnewline
80 & 13839 & 13233.5066200119 & 605.493379988144 \tabularnewline
81 & 14042 & 13500.8480212794 & 541.151978720589 \tabularnewline
82 & 13333 & 13479.0979316832 & -146.097931683236 \tabularnewline
83 & 15176 & 14965.104124217 & 210.895875783002 \tabularnewline
84 & 15176 & 15785.7915482626 & -609.791548262587 \tabularnewline
85 & 14862 & 15596.9148279677 & -734.91482796767 \tabularnewline
86 & 13120 & 13477.6141033499 & -357.614103349872 \tabularnewline
87 & 13434 & 12983.1340091634 & 450.865990836581 \tabularnewline
88 & 13637 & 14135.6787532563 & -498.678753256296 \tabularnewline
89 & 14973 & 16258.5559667778 & -1285.55596677785 \tabularnewline
90 & 16714 & 16406.9819474148 & 307.018052585194 \tabularnewline
91 & 15479 & 15595.9669365395 & -116.966936539548 \tabularnewline
92 & 16097 & 15067.2455410872 & 1029.75445891282 \tabularnewline
93 & 15580 & 15547.7245265584 & 32.2754734415521 \tabularnewline
94 & 15277 & 14895.8394542397 & 381.160545760325 \tabularnewline
95 & 17636 & 16808.8962842573 & 827.103715742662 \tabularnewline
96 & 17119 & 17728.112091872 & -609.112091872012 \tabularnewline
97 & 16400 & 17476.4521188065 & -1076.4521188065 \tabularnewline
98 & 15378 & 15232.9386068328 & 145.061393167205 \tabularnewline
99 & 16400 & 15332.7651203652 & 1067.23487963484 \tabularnewline
100 & 16917 & 16566.227253273 & 350.772746726951 \tabularnewline
101 & 17534 & 19008.0995345432 & -1474.09953454317 \tabularnewline
102 & 18354 & 19614.8861167578 & -1260.88611675784 \tabularnewline
103 & 17534 & 17607.8857753687 & -73.8857753686825 \tabularnewline
104 & 18040 & 17481.7012877134 & 558.298712286603 \tabularnewline
105 & 17423 & 17269.3156046574 & 153.68439534256 \tabularnewline
106 & 17322 & 16782.6608042038 & 539.339195796223 \tabularnewline
107 & 19883 & 18924.0754538334 & 958.924546166632 \tabularnewline
108 & 20096 & 19406.958770734 & 689.04122926596 \tabularnewline
109 & 19276 & 19861.8074153111 & -585.807415311145 \tabularnewline
110 & 17838 & 18399.067229543 & -561.067229542994 \tabularnewline
111 & 19063 & 18369.355754563 & 693.644245437023 \tabularnewline
112 & 19579 & 19110.0319315256 & 468.968068474402 \tabularnewline
113 & 20197 & 21000.6479128167 & -803.647912816708 \tabularnewline
114 & 21118 & 22146.3563303659 & -1028.35633036595 \tabularnewline
115 & 20197 & 20737.4498959207 & -540.449895920661 \tabularnewline
116 & 20916 & 20544.1049776965 & 371.895022303492 \tabularnewline
117 & 20602 & 20082.0446740116 & 519.95532598842 \tabularnewline
118 & 19478 & 19993.3700757196 & -515.37007571958 \tabularnewline
119 & 21837 & 21579.3101595273 & 257.689840472722 \tabularnewline
120 & 21837 & 21474.6328057808 & 362.367194219183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123693&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]4516[/C][C]5451.23530982906[/C][C]-935.23530982906[/C][/ROW]
[ROW][C]14[/C][C]3898[/C][C]4212.20700581785[/C][C]-314.207005817851[/C][/ROW]
[ROW][C]15[/C][C]3392[/C][C]3475.98925286797[/C][C]-83.9892528679734[/C][/ROW]
[ROW][C]16[/C][C]3392[/C][C]3359.16397106204[/C][C]32.8360289379634[/C][/ROW]
[ROW][C]17[/C][C]5336[/C][C]5238.07897935457[/C][C]97.9210206454345[/C][/ROW]
[ROW][C]18[/C][C]5538[/C][C]5386.75312037352[/C][C]151.246879626484[/C][/ROW]
[ROW][C]19[/C][C]3999[/C][C]3903.6791511742[/C][C]95.3208488257974[/C][/ROW]
[ROW][C]20[/C][C]2258[/C][C]2881.97606051683[/C][C]-623.976060516834[/C][/ROW]
[ROW][C]21[/C][C]3179[/C][C]2529.98634478713[/C][C]649.013655212866[/C][/ROW]
[ROW][C]22[/C][C]3179[/C][C]2939.90509661482[/C][C]239.094903385182[/C][/ROW]
[ROW][C]23[/C][C]3898[/C][C]3186.93255366014[/C][C]711.067446339863[/C][/ROW]
[ROW][C]24[/C][C]4313[/C][C]3870.57267508152[/C][C]442.427324918482[/C][/ROW]
[ROW][C]25[/C][C]4212[/C][C]3227.33012282671[/C][C]984.669877173287[/C][/ROW]
[ROW][C]26[/C][C]3179[/C][C]3540.63582461777[/C][C]-361.635824617773[/C][/ROW]
[ROW][C]27[/C][C]3696[/C][C]2933.9219212744[/C][C]762.078078725599[/C][/ROW]
[ROW][C]28[/C][C]3493[/C][C]3520.55819923458[/C][C]-27.5581992345769[/C][/ROW]
[ROW][C]29[/C][C]5234[/C][C]5490.47926539314[/C][C]-256.47926539314[/C][/ROW]
[ROW][C]30[/C][C]4819[/C][C]5521.6691693689[/C][C]-702.669169368901[/C][/ROW]
[ROW][C]31[/C][C]3179[/C][C]3527.2488050042[/C][C]-348.248805004198[/C][/ROW]
[ROW][C]32[/C][C]1954[/C][C]2017.23864077466[/C][C]-63.2386407746617[/C][/ROW]
[ROW][C]33[/C][C]3078[/C][C]2542.90809583354[/C][C]535.091904166464[/C][/ROW]
[ROW][C]34[/C][C]3392[/C][C]2802.60425947376[/C][C]589.395740526244[/C][/ROW]
[ROW][C]35[/C][C]3696[/C][C]3520.44133572618[/C][C]175.558664273819[/C][/ROW]
[ROW][C]36[/C][C]4100[/C][C]3820.85407465268[/C][C]279.145925347317[/C][/ROW]
[ROW][C]37[/C][C]3280[/C][C]3312.92296353295[/C][C]-32.9229635329534[/C][/ROW]
[ROW][C]38[/C][C]2572[/C][C]2513.73904888333[/C][C]58.260951116667[/C][/ROW]
[ROW][C]39[/C][C]2876[/C][C]2604.24496493599[/C][C]271.755035064009[/C][/ROW]
[ROW][C]40[/C][C]2977[/C][C]2613.40960439182[/C][C]363.590395608179[/C][/ROW]
[ROW][C]41[/C][C]5639[/C][C]4789.745694544[/C][C]849.254305455997[/C][/ROW]
[ROW][C]42[/C][C]5639[/C][C]5457.37466028556[/C][C]181.625339714445[/C][/ROW]
[ROW][C]43[/C][C]4100[/C][C]4262.61015476808[/C][C]-162.610154768081[/C][/ROW]
[ROW][C]44[/C][C]3898[/C][C]3078.00801059779[/C][C]819.991989402207[/C][/ROW]
[ROW][C]45[/C][C]4516[/C][C]4524.11392289208[/C][C]-8.11392289207834[/C][/ROW]
[ROW][C]46[/C][C]4212[/C][C]4564.70423283169[/C][C]-352.704232831695[/C][/ROW]
[ROW][C]47[/C][C]5032[/C][C]4607.95873519209[/C][C]424.041264807907[/C][/ROW]
[ROW][C]48[/C][C]6054[/C][C]5199.7704149978[/C][C]854.229585002204[/C][/ROW]
[ROW][C]49[/C][C]6257[/C][C]5072.60016705425[/C][C]1184.39983294575[/C][/ROW]
[ROW][C]50[/C][C]4819[/C][C]5255.74153663318[/C][C]-436.741536633181[/C][/ROW]
[ROW][C]51[/C][C]4414[/C][C]5234.68263699555[/C][C]-820.68263699555[/C][/ROW]
[ROW][C]52[/C][C]3999[/C][C]4661.87230827785[/C][C]-662.872308277854[/C][/ROW]
[ROW][C]53[/C][C]6773[/C][C]6400.27200946408[/C][C]372.727990535923[/C][/ROW]
[ROW][C]54[/C][C]6976[/C][C]6573.37596234173[/C][C]402.624037658266[/C][/ROW]
[ROW][C]55[/C][C]6459[/C][C]5459.64940527827[/C][C]999.35059472173[/C][/ROW]
[ROW][C]56[/C][C]6976[/C][C]5470.92402538995[/C][C]1505.07597461005[/C][/ROW]
[ROW][C]57[/C][C]6874[/C][C]7197.66133190496[/C][C]-323.661331904962[/C][/ROW]
[ROW][C]58[/C][C]6054[/C][C]7021.47800819964[/C][C]-967.47800819964[/C][/ROW]
[ROW][C]59[/C][C]6976[/C][C]7019.5792554317[/C][C]-43.5792554316986[/C][/ROW]
[ROW][C]60[/C][C]7998[/C][C]7526.17976301124[/C][C]471.82023698876[/C][/ROW]
[ROW][C]61[/C][C]8413[/C][C]7321.6115245654[/C][C]1091.38847543461[/C][/ROW]
[ROW][C]62[/C][C]7178[/C][C]6937.30054993967[/C][C]240.69945006033[/C][/ROW]
[ROW][C]63[/C][C]6358[/C][C]7304.37154325273[/C][C]-946.37154325273[/C][/ROW]
[ROW][C]64[/C][C]6976[/C][C]6778.11122255401[/C][C]197.88877744599[/C][/ROW]
[ROW][C]65[/C][C]9638[/C][C]9541.64832388627[/C][C]96.3516761137289[/C][/ROW]
[ROW][C]66[/C][C]10458[/C][C]9638.7220041738[/C][C]819.277995826204[/C][/ROW]
[ROW][C]67[/C][C]10256[/C][C]9112.69187831229[/C][C]1143.30812168771[/C][/ROW]
[ROW][C]68[/C][C]10660[/C][C]9506.89050509838[/C][C]1153.10949490162[/C][/ROW]
[ROW][C]69[/C][C]10559[/C][C]10471.5378411276[/C][C]87.4621588723567[/C][/ROW]
[ROW][C]70[/C][C]9537[/C][C]10456.7102185488[/C][C]-919.710218548757[/C][/ROW]
[ROW][C]71[/C][C]11278[/C][C]10923.4324766185[/C][C]354.567523381535[/C][/ROW]
[ROW][C]72[/C][C]11693[/C][C]11999.9144367891[/C][C]-306.914436789148[/C][/ROW]
[ROW][C]73[/C][C]12300[/C][C]11605.1901574872[/C][C]694.809842512768[/C][/ROW]
[ROW][C]74[/C][C]10458[/C][C]10757.4392681474[/C][C]-299.439268147426[/C][/ROW]
[ROW][C]75[/C][C]9739[/C][C]10432.025033892[/C][C]-693.025033892038[/C][/ROW]
[ROW][C]76[/C][C]10559[/C][C]10548.2757494086[/C][C]10.7242505914292[/C][/ROW]
[ROW][C]77[/C][C]12513[/C][C]13228.3673980385[/C][C]-715.367398038517[/C][/ROW]
[ROW][C]78[/C][C]14254[/C][C]13091.3318547597[/C][C]1162.66814524025[/C][/ROW]
[ROW][C]79[/C][C]13839[/C][C]12959.8380414066[/C][C]879.161958593395[/C][/ROW]
[ROW][C]80[/C][C]13839[/C][C]13233.5066200119[/C][C]605.493379988144[/C][/ROW]
[ROW][C]81[/C][C]14042[/C][C]13500.8480212794[/C][C]541.151978720589[/C][/ROW]
[ROW][C]82[/C][C]13333[/C][C]13479.0979316832[/C][C]-146.097931683236[/C][/ROW]
[ROW][C]83[/C][C]15176[/C][C]14965.104124217[/C][C]210.895875783002[/C][/ROW]
[ROW][C]84[/C][C]15176[/C][C]15785.7915482626[/C][C]-609.791548262587[/C][/ROW]
[ROW][C]85[/C][C]14862[/C][C]15596.9148279677[/C][C]-734.91482796767[/C][/ROW]
[ROW][C]86[/C][C]13120[/C][C]13477.6141033499[/C][C]-357.614103349872[/C][/ROW]
[ROW][C]87[/C][C]13434[/C][C]12983.1340091634[/C][C]450.865990836581[/C][/ROW]
[ROW][C]88[/C][C]13637[/C][C]14135.6787532563[/C][C]-498.678753256296[/C][/ROW]
[ROW][C]89[/C][C]14973[/C][C]16258.5559667778[/C][C]-1285.55596677785[/C][/ROW]
[ROW][C]90[/C][C]16714[/C][C]16406.9819474148[/C][C]307.018052585194[/C][/ROW]
[ROW][C]91[/C][C]15479[/C][C]15595.9669365395[/C][C]-116.966936539548[/C][/ROW]
[ROW][C]92[/C][C]16097[/C][C]15067.2455410872[/C][C]1029.75445891282[/C][/ROW]
[ROW][C]93[/C][C]15580[/C][C]15547.7245265584[/C][C]32.2754734415521[/C][/ROW]
[ROW][C]94[/C][C]15277[/C][C]14895.8394542397[/C][C]381.160545760325[/C][/ROW]
[ROW][C]95[/C][C]17636[/C][C]16808.8962842573[/C][C]827.103715742662[/C][/ROW]
[ROW][C]96[/C][C]17119[/C][C]17728.112091872[/C][C]-609.112091872012[/C][/ROW]
[ROW][C]97[/C][C]16400[/C][C]17476.4521188065[/C][C]-1076.4521188065[/C][/ROW]
[ROW][C]98[/C][C]15378[/C][C]15232.9386068328[/C][C]145.061393167205[/C][/ROW]
[ROW][C]99[/C][C]16400[/C][C]15332.7651203652[/C][C]1067.23487963484[/C][/ROW]
[ROW][C]100[/C][C]16917[/C][C]16566.227253273[/C][C]350.772746726951[/C][/ROW]
[ROW][C]101[/C][C]17534[/C][C]19008.0995345432[/C][C]-1474.09953454317[/C][/ROW]
[ROW][C]102[/C][C]18354[/C][C]19614.8861167578[/C][C]-1260.88611675784[/C][/ROW]
[ROW][C]103[/C][C]17534[/C][C]17607.8857753687[/C][C]-73.8857753686825[/C][/ROW]
[ROW][C]104[/C][C]18040[/C][C]17481.7012877134[/C][C]558.298712286603[/C][/ROW]
[ROW][C]105[/C][C]17423[/C][C]17269.3156046574[/C][C]153.68439534256[/C][/ROW]
[ROW][C]106[/C][C]17322[/C][C]16782.6608042038[/C][C]539.339195796223[/C][/ROW]
[ROW][C]107[/C][C]19883[/C][C]18924.0754538334[/C][C]958.924546166632[/C][/ROW]
[ROW][C]108[/C][C]20096[/C][C]19406.958770734[/C][C]689.04122926596[/C][/ROW]
[ROW][C]109[/C][C]19276[/C][C]19861.8074153111[/C][C]-585.807415311145[/C][/ROW]
[ROW][C]110[/C][C]17838[/C][C]18399.067229543[/C][C]-561.067229542994[/C][/ROW]
[ROW][C]111[/C][C]19063[/C][C]18369.355754563[/C][C]693.644245437023[/C][/ROW]
[ROW][C]112[/C][C]19579[/C][C]19110.0319315256[/C][C]468.968068474402[/C][/ROW]
[ROW][C]113[/C][C]20197[/C][C]21000.6479128167[/C][C]-803.647912816708[/C][/ROW]
[ROW][C]114[/C][C]21118[/C][C]22146.3563303659[/C][C]-1028.35633036595[/C][/ROW]
[ROW][C]115[/C][C]20197[/C][C]20737.4498959207[/C][C]-540.449895920661[/C][/ROW]
[ROW][C]116[/C][C]20916[/C][C]20544.1049776965[/C][C]371.895022303492[/C][/ROW]
[ROW][C]117[/C][C]20602[/C][C]20082.0446740116[/C][C]519.95532598842[/C][/ROW]
[ROW][C]118[/C][C]19478[/C][C]19993.3700757196[/C][C]-515.37007571958[/C][/ROW]
[ROW][C]119[/C][C]21837[/C][C]21579.3101595273[/C][C]257.689840472722[/C][/ROW]
[ROW][C]120[/C][C]21837[/C][C]21474.6328057808[/C][C]362.367194219183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123693&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123693&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
1345165451.23530982906-935.23530982906
1438984212.20700581785-314.207005817851
1533923475.98925286797-83.9892528679734
1633923359.1639710620432.8360289379634
1753365238.0789793545797.9210206454345
1855385386.75312037352151.246879626484
1939993903.679151174295.3208488257974
2022582881.97606051683-623.976060516834
2131792529.98634478713649.013655212866
2231792939.90509661482239.094903385182
2338983186.93255366014711.067446339863
2443133870.57267508152442.427324918482
2542123227.33012282671984.669877173287
2631793540.63582461777-361.635824617773
2736962933.9219212744762.078078725599
2834933520.55819923458-27.5581992345769
2952345490.47926539314-256.47926539314
3048195521.6691693689-702.669169368901
3131793527.2488050042-348.248805004198
3219542017.23864077466-63.2386407746617
3330782542.90809583354535.091904166464
3433922802.60425947376589.395740526244
3536963520.44133572618175.558664273819
3641003820.85407465268279.145925347317
3732803312.92296353295-32.9229635329534
3825722513.7390488833358.260951116667
3928762604.24496493599271.755035064009
4029772613.40960439182363.590395608179
4156394789.745694544849.254305455997
4256395457.37466028556181.625339714445
4341004262.61015476808-162.610154768081
4438983078.00801059779819.991989402207
4545164524.11392289208-8.11392289207834
4642124564.70423283169-352.704232831695
4750324607.95873519209424.041264807907
4860545199.7704149978854.229585002204
4962575072.600167054251184.39983294575
5048195255.74153663318-436.741536633181
5144145234.68263699555-820.68263699555
5239994661.87230827785-662.872308277854
5367736400.27200946408372.727990535923
5469766573.37596234173402.624037658266
5564595459.64940527827999.35059472173
5669765470.924025389951505.07597461005
5768747197.66133190496-323.661331904962
5860547021.47800819964-967.47800819964
5969767019.5792554317-43.5792554316986
6079987526.17976301124471.82023698876
6184137321.61152456541091.38847543461
6271786937.30054993967240.69945006033
6363587304.37154325273-946.37154325273
6469766778.11122255401197.88877744599
6596389541.6483238862796.3516761137289
66104589638.7220041738819.277995826204
67102569112.691878312291143.30812168771
68106609506.890505098381153.10949490162
691055910471.537841127687.4621588723567
70953710456.7102185488-919.710218548757
711127810923.4324766185354.567523381535
721169311999.9144367891-306.914436789148
731230011605.1901574872694.809842512768
741045810757.4392681474-299.439268147426
75973910432.025033892-693.025033892038
761055910548.275749408610.7242505914292
771251313228.3673980385-715.367398038517
781425413091.33185475971162.66814524025
791383912959.8380414066879.161958593395
801383913233.5066200119605.493379988144
811404213500.8480212794541.151978720589
821333313479.0979316832-146.097931683236
831517614965.104124217210.895875783002
841517615785.7915482626-609.791548262587
851486215596.9148279677-734.91482796767
861312013477.6141033499-357.614103349872
871343412983.1340091634450.865990836581
881363714135.6787532563-498.678753256296
891497316258.5559667778-1285.55596677785
901671416406.9819474148307.018052585194
911547915595.9669365395-116.966936539548
921609715067.24554108721029.75445891282
931558015547.724526558432.2754734415521
941527714895.8394542397381.160545760325
951763616808.8962842573827.103715742662
961711917728.112091872-609.112091872012
971640017476.4521188065-1076.4521188065
981537815232.9386068328145.061393167205
991640015332.76512036521067.23487963484
1001691716566.227253273350.772746726951
1011753419008.0995345432-1474.09953454317
1021835419614.8861167578-1260.88611675784
1031753417607.8857753687-73.8857753686825
1041804017481.7012877134558.298712286603
1051742317269.3156046574153.68439534256
1061732216782.6608042038539.339195796223
1071988318924.0754538334958.924546166632
1082009619406.958770734689.04122926596
1091927619861.8074153111-585.807415311145
1101783818399.067229543-561.067229542994
1111906318369.355754563693.644245437023
1121957919110.0319315256468.968068474402
1132019721000.6479128167-803.647912816708
1142111822146.3563303659-1028.35633036595
1152019720737.4498959207-540.449895920661
1162091620544.1049776965371.895022303492
1172060220082.0446740116519.95532598842
1181947819993.3700757196-515.37007571958
1192183721579.3101595273257.689840472722
1202183721474.6328057808362.367194219183







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12121227.279295356319971.581026458322482.9775642544
12220129.188692812818604.881238713621653.496146912
12320893.459398478519119.419403647922667.499393309
12421071.575141503619058.699866343123084.4504166642
12522167.217899303919922.082092757424412.3537058504
12623740.528638803621267.090481573126213.9667960341
12723188.533272576220489.04700261625888.0195425364
12823698.948657600120774.500185332426623.3971298678
12923066.728839076619917.571933123826215.8857450295
13022283.184476756918908.962812325125657.4061411887
13124495.21658471220895.116391785328095.3167776387
13224270.918727373620443.777162391528098.0602923556

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 21227.2792953563 & 19971.5810264583 & 22482.9775642544 \tabularnewline
122 & 20129.1886928128 & 18604.8812387136 & 21653.496146912 \tabularnewline
123 & 20893.4593984785 & 19119.4194036479 & 22667.499393309 \tabularnewline
124 & 21071.5751415036 & 19058.6998663431 & 23084.4504166642 \tabularnewline
125 & 22167.2178993039 & 19922.0820927574 & 24412.3537058504 \tabularnewline
126 & 23740.5286388036 & 21267.0904815731 & 26213.9667960341 \tabularnewline
127 & 23188.5332725762 & 20489.047002616 & 25888.0195425364 \tabularnewline
128 & 23698.9486576001 & 20774.5001853324 & 26623.3971298678 \tabularnewline
129 & 23066.7288390766 & 19917.5719331238 & 26215.8857450295 \tabularnewline
130 & 22283.1844767569 & 18908.9628123251 & 25657.4061411887 \tabularnewline
131 & 24495.216584712 & 20895.1163917853 & 28095.3167776387 \tabularnewline
132 & 24270.9187273736 & 20443.7771623915 & 28098.0602923556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123693&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]21227.2792953563[/C][C]19971.5810264583[/C][C]22482.9775642544[/C][/ROW]
[ROW][C]122[/C][C]20129.1886928128[/C][C]18604.8812387136[/C][C]21653.496146912[/C][/ROW]
[ROW][C]123[/C][C]20893.4593984785[/C][C]19119.4194036479[/C][C]22667.499393309[/C][/ROW]
[ROW][C]124[/C][C]21071.5751415036[/C][C]19058.6998663431[/C][C]23084.4504166642[/C][/ROW]
[ROW][C]125[/C][C]22167.2178993039[/C][C]19922.0820927574[/C][C]24412.3537058504[/C][/ROW]
[ROW][C]126[/C][C]23740.5286388036[/C][C]21267.0904815731[/C][C]26213.9667960341[/C][/ROW]
[ROW][C]127[/C][C]23188.5332725762[/C][C]20489.047002616[/C][C]25888.0195425364[/C][/ROW]
[ROW][C]128[/C][C]23698.9486576001[/C][C]20774.5001853324[/C][C]26623.3971298678[/C][/ROW]
[ROW][C]129[/C][C]23066.7288390766[/C][C]19917.5719331238[/C][C]26215.8857450295[/C][/ROW]
[ROW][C]130[/C][C]22283.1844767569[/C][C]18908.9628123251[/C][C]25657.4061411887[/C][/ROW]
[ROW][C]131[/C][C]24495.216584712[/C][C]20895.1163917853[/C][C]28095.3167776387[/C][/ROW]
[ROW][C]132[/C][C]24270.9187273736[/C][C]20443.7771623915[/C][C]28098.0602923556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123693&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123693&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
12121227.279295356319971.581026458322482.9775642544
12220129.188692812818604.881238713621653.496146912
12320893.459398478519119.419403647922667.499393309
12421071.575141503619058.699866343123084.4504166642
12522167.217899303919922.082092757424412.3537058504
12623740.528638803621267.090481573126213.9667960341
12723188.533272576220489.04700261625888.0195425364
12823698.948657600120774.500185332426623.3971298678
12923066.728839076619917.571933123826215.8857450295
13022283.184476756918908.962812325125657.4061411887
13124495.21658471220895.116391785328095.3167776387
13224270.918727373620443.777162391528098.0602923556



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')