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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 18 Dec 2016 16:49:54 +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/18/t1482076405p2p5dk1padpv36q.htm/, Retrieved Wed, 08 May 2024 11:31:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301152, Retrieved Wed, 08 May 2024 11:31:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Structural Time Series Models] [Structural time s...] [2016-12-12 12:07:55] [e37f5c813d0dfcb3787d64bb91655c98]
- RMP     [Exponential Smoothing] [ES F1] [2016-12-18 15:49:54] [10299735033611e1e2dae6371997f8c9] [Current]
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Dataseries X:
3567.2
3968.25
4285.35
4130.95
4219.4
4626.2
3860.75
4174.15
4668.65
4630.05
4553.7
4603.85
4310.7
4831.3
5145.3
4886.65
4934.05
5304.7
4419.45
4804.85
5105
5132.6
4982.5
4906.7
4506.4
5010.85
5392.25
5049.7
5143.9
5449.9
4520.4
4936.95
5358.55
5289.5
5123.55
4985.65
4682.65
5175.55
5374.7
5289
5176.15
5604.25
4608.8
4898.15
5448.65
5373.05
5078.6
5233.4
4629.2
5387.8
5736.65
5357.9
5337.95
5795.5
4804.05
5120.5
5850.45
5734.75
5539
5582.85
4983.1
5672
6185.8
5835.6
5930.4
6444.65
5171.05
5739.1
6413.9
6230.2
6015.45
6174.25
5579.25
6133.45
6478.7
6184.4
6185.65
6556
5123.25
6028.9
6499.95
6190.05
6027.95
6034
5128.75
6087.7
6628.15
6075.3
6352.1
6824
5412.35
6171.25
6521.35
6457.6
5930.95
5842.7
5120.1
5719.95
5946.7
5921.1
6072
6489.4
5291.15
5986.45
6538.15
6442.8
6169.55
5793
5254.85
6050.75
6606.15
6221.15
6293.4
6908.4
5498.95
6145.35




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=301152&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=301152&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301152&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
alpha0.543500420306629
beta0.0390683686433914
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.543500420306629 \tabularnewline
beta & 0.0390683686433914 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301152&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]0.543500420306629[/C][/ROW]
[ROW][C]beta[/C][C]0.0390683686433914[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301152&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301152&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
alpha0.543500420306629
beta0.0390683686433914
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134310.73941.39115918804369.308840811962
144831.34674.0106262878157.289373712202
155145.35093.2351719798252.0648280201831
164886.654889.06524382055-2.41524382055377
174934.054961.59867254905-27.5486725490528
185304.75351.45794597972-46.7579459797162
194419.454525.11329487546-105.663294875459
204804.854775.5766085153229.2733914846758
2151055276.24756624782-171.247566247821
225132.65135.67200071079-3.07200071078842
234982.55054.73886253109-72.2388625310932
244906.75064.39627603409-157.696276034094
254506.44856.0463252152-349.6463252152
265010.855086.31270407253-75.46270407253
275392.255311.2453991486181.00460085139
285049.75078.79257988332-29.0925798833186
295143.95105.6454678139238.2545321860844
305449.95504.18903149274-54.2890314927399
314520.44628.39029867808-107.990298678083
324936.954920.6673479837216.2826520162753
335358.555303.9441818953954.6058181046083
345289.55348.8918794398-59.3918794398032
355123.555190.57812093697-67.0281209369741
364985.655148.97084532043-163.320845320432
374682.654834.73393566182-152.083935661825
385175.555286.5303533216-110.980353321599
395374.75551.82236905595-177.12236905595
4052895111.5730513121177.426948687897
415176.155268.55342157037-92.4034215703723
425604.255538.2039894406266.0460105593793
434608.84690.21370670434-81.4137067043448
444898.155041.1509234325-143.000923432498
455448.655339.45462946828109.195370531722
465373.055347.2940606052925.7559393947058
475078.65218.84242740569-140.242427405693
485233.45079.00113948206154.39886051794
494629.24934.83660716666-305.636607166662
505387.85310.9423030426276.8576969573796
515736.655641.1205193970695.5294806029369
525357.95509.68855550091-151.78855550091
535337.955356.35159973182-18.4015997318229
545795.55731.9145081447263.5854918552832
554804.054808.5796077521-4.52960775210431
565120.55168.1293322237-47.6293322236952
575850.455630.36063591137220.089364088625
585734.755659.7012164559275.0487835440799
5955395482.6290308607956.3709691392141
605582.855588.69260637932-5.84260637932221
614983.15148.57003230319-165.470032303188
6256725779.58032155411-107.580321554112
636185.86018.23927376751167.56072623249
645835.65814.7844457119620.8155542880377
655930.45821.54270803539108.857291964613
666444.656311.79384697218132.856153027816
675171.055404.57983294058-233.529832940577
685739.15624.69708360027114.40291639973
696413.96305.35124586605108.548754133949
706230.26213.6348679309516.5651320690449
716015.456000.7849298864414.6650701135604
726174.256059.42984231736114.820157682639
735579.255618.22877390996-38.978773909962
746133.456353.31071365875-219.860713658752
756478.76663.05984268263-184.359842682632
766184.46200.3872057249-15.9872057248995
776185.656225.59298845302-39.9429884530227
7865566641.02582536359-85.0258253635857
795123.255438.61062376369-315.360623763691
806028.95761.819198518267.080801481997
816499.956514.75858490702-14.8085849070203
826190.056303.36477894851-113.314778948509
836027.956005.6576718062722.2923281937337
8460346100.93070692028-66.9307069202823
855128.755473.64153016242-344.891530162419
866087.75936.2942874462151.405712553798
876628.156448.32341699682179.826583003175
886075.36252.47171874921-177.171718749213
896352.16167.73873190306184.361268096935
9068246677.864419807146.135580192997
915412.355494.20989611724-81.8598961172429
926171.256213.44065431119-42.1906543111936
936521.356666.27169257184-144.921692571838
946457.66333.09374681108124.506253188917
955930.956225.49729753714-294.547297537138
965842.76100.06015482842-257.360154828424
975120.15230.56254710767-110.462547107669
985719.956040.34387969671-320.393879696708
995946.76292.06265065094-345.36265065094
1005921.15619.78791376367301.312086236335
10160725942.2978073725129.702192627505
1026489.46386.25271608625103.147283913753
1035291.155055.22785845302235.922141546975
1045986.455952.1036225929534.3463774070515
1056538.156388.0823991124150.0676008876
1066442.86332.93521418902109.864785810975
1076169.556020.48267116801149.067328831991
10857936156.94506776707-363.945067767071
1095254.855298.13291027614-43.2829102761425
1106050.756051.57500821584-0.825008215844719
1116606.156475.34915276514130.800847234859
1126221.156376.95471463064-155.804714630644
1136293.46382.85381297986-89.4538129798602
1146908.46701.09377096233207.306229037667
1155498.955495.021422747763.92857725224167
1166145.356176.5936719456-31.2436719455964

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4310.7 & 3941.39115918804 & 369.308840811962 \tabularnewline
14 & 4831.3 & 4674.0106262878 & 157.289373712202 \tabularnewline
15 & 5145.3 & 5093.23517197982 & 52.0648280201831 \tabularnewline
16 & 4886.65 & 4889.06524382055 & -2.41524382055377 \tabularnewline
17 & 4934.05 & 4961.59867254905 & -27.5486725490528 \tabularnewline
18 & 5304.7 & 5351.45794597972 & -46.7579459797162 \tabularnewline
19 & 4419.45 & 4525.11329487546 & -105.663294875459 \tabularnewline
20 & 4804.85 & 4775.57660851532 & 29.2733914846758 \tabularnewline
21 & 5105 & 5276.24756624782 & -171.247566247821 \tabularnewline
22 & 5132.6 & 5135.67200071079 & -3.07200071078842 \tabularnewline
23 & 4982.5 & 5054.73886253109 & -72.2388625310932 \tabularnewline
24 & 4906.7 & 5064.39627603409 & -157.696276034094 \tabularnewline
25 & 4506.4 & 4856.0463252152 & -349.6463252152 \tabularnewline
26 & 5010.85 & 5086.31270407253 & -75.46270407253 \tabularnewline
27 & 5392.25 & 5311.24539914861 & 81.00460085139 \tabularnewline
28 & 5049.7 & 5078.79257988332 & -29.0925798833186 \tabularnewline
29 & 5143.9 & 5105.64546781392 & 38.2545321860844 \tabularnewline
30 & 5449.9 & 5504.18903149274 & -54.2890314927399 \tabularnewline
31 & 4520.4 & 4628.39029867808 & -107.990298678083 \tabularnewline
32 & 4936.95 & 4920.66734798372 & 16.2826520162753 \tabularnewline
33 & 5358.55 & 5303.94418189539 & 54.6058181046083 \tabularnewline
34 & 5289.5 & 5348.8918794398 & -59.3918794398032 \tabularnewline
35 & 5123.55 & 5190.57812093697 & -67.0281209369741 \tabularnewline
36 & 4985.65 & 5148.97084532043 & -163.320845320432 \tabularnewline
37 & 4682.65 & 4834.73393566182 & -152.083935661825 \tabularnewline
38 & 5175.55 & 5286.5303533216 & -110.980353321599 \tabularnewline
39 & 5374.7 & 5551.82236905595 & -177.12236905595 \tabularnewline
40 & 5289 & 5111.5730513121 & 177.426948687897 \tabularnewline
41 & 5176.15 & 5268.55342157037 & -92.4034215703723 \tabularnewline
42 & 5604.25 & 5538.20398944062 & 66.0460105593793 \tabularnewline
43 & 4608.8 & 4690.21370670434 & -81.4137067043448 \tabularnewline
44 & 4898.15 & 5041.1509234325 & -143.000923432498 \tabularnewline
45 & 5448.65 & 5339.45462946828 & 109.195370531722 \tabularnewline
46 & 5373.05 & 5347.29406060529 & 25.7559393947058 \tabularnewline
47 & 5078.6 & 5218.84242740569 & -140.242427405693 \tabularnewline
48 & 5233.4 & 5079.00113948206 & 154.39886051794 \tabularnewline
49 & 4629.2 & 4934.83660716666 & -305.636607166662 \tabularnewline
50 & 5387.8 & 5310.94230304262 & 76.8576969573796 \tabularnewline
51 & 5736.65 & 5641.12051939706 & 95.5294806029369 \tabularnewline
52 & 5357.9 & 5509.68855550091 & -151.78855550091 \tabularnewline
53 & 5337.95 & 5356.35159973182 & -18.4015997318229 \tabularnewline
54 & 5795.5 & 5731.91450814472 & 63.5854918552832 \tabularnewline
55 & 4804.05 & 4808.5796077521 & -4.52960775210431 \tabularnewline
56 & 5120.5 & 5168.1293322237 & -47.6293322236952 \tabularnewline
57 & 5850.45 & 5630.36063591137 & 220.089364088625 \tabularnewline
58 & 5734.75 & 5659.70121645592 & 75.0487835440799 \tabularnewline
59 & 5539 & 5482.62903086079 & 56.3709691392141 \tabularnewline
60 & 5582.85 & 5588.69260637932 & -5.84260637932221 \tabularnewline
61 & 4983.1 & 5148.57003230319 & -165.470032303188 \tabularnewline
62 & 5672 & 5779.58032155411 & -107.580321554112 \tabularnewline
63 & 6185.8 & 6018.23927376751 & 167.56072623249 \tabularnewline
64 & 5835.6 & 5814.78444571196 & 20.8155542880377 \tabularnewline
65 & 5930.4 & 5821.54270803539 & 108.857291964613 \tabularnewline
66 & 6444.65 & 6311.79384697218 & 132.856153027816 \tabularnewline
67 & 5171.05 & 5404.57983294058 & -233.529832940577 \tabularnewline
68 & 5739.1 & 5624.69708360027 & 114.40291639973 \tabularnewline
69 & 6413.9 & 6305.35124586605 & 108.548754133949 \tabularnewline
70 & 6230.2 & 6213.63486793095 & 16.5651320690449 \tabularnewline
71 & 6015.45 & 6000.78492988644 & 14.6650701135604 \tabularnewline
72 & 6174.25 & 6059.42984231736 & 114.820157682639 \tabularnewline
73 & 5579.25 & 5618.22877390996 & -38.978773909962 \tabularnewline
74 & 6133.45 & 6353.31071365875 & -219.860713658752 \tabularnewline
75 & 6478.7 & 6663.05984268263 & -184.359842682632 \tabularnewline
76 & 6184.4 & 6200.3872057249 & -15.9872057248995 \tabularnewline
77 & 6185.65 & 6225.59298845302 & -39.9429884530227 \tabularnewline
78 & 6556 & 6641.02582536359 & -85.0258253635857 \tabularnewline
79 & 5123.25 & 5438.61062376369 & -315.360623763691 \tabularnewline
80 & 6028.9 & 5761.819198518 & 267.080801481997 \tabularnewline
81 & 6499.95 & 6514.75858490702 & -14.8085849070203 \tabularnewline
82 & 6190.05 & 6303.36477894851 & -113.314778948509 \tabularnewline
83 & 6027.95 & 6005.65767180627 & 22.2923281937337 \tabularnewline
84 & 6034 & 6100.93070692028 & -66.9307069202823 \tabularnewline
85 & 5128.75 & 5473.64153016242 & -344.891530162419 \tabularnewline
86 & 6087.7 & 5936.2942874462 & 151.405712553798 \tabularnewline
87 & 6628.15 & 6448.32341699682 & 179.826583003175 \tabularnewline
88 & 6075.3 & 6252.47171874921 & -177.171718749213 \tabularnewline
89 & 6352.1 & 6167.73873190306 & 184.361268096935 \tabularnewline
90 & 6824 & 6677.864419807 & 146.135580192997 \tabularnewline
91 & 5412.35 & 5494.20989611724 & -81.8598961172429 \tabularnewline
92 & 6171.25 & 6213.44065431119 & -42.1906543111936 \tabularnewline
93 & 6521.35 & 6666.27169257184 & -144.921692571838 \tabularnewline
94 & 6457.6 & 6333.09374681108 & 124.506253188917 \tabularnewline
95 & 5930.95 & 6225.49729753714 & -294.547297537138 \tabularnewline
96 & 5842.7 & 6100.06015482842 & -257.360154828424 \tabularnewline
97 & 5120.1 & 5230.56254710767 & -110.462547107669 \tabularnewline
98 & 5719.95 & 6040.34387969671 & -320.393879696708 \tabularnewline
99 & 5946.7 & 6292.06265065094 & -345.36265065094 \tabularnewline
100 & 5921.1 & 5619.78791376367 & 301.312086236335 \tabularnewline
101 & 6072 & 5942.2978073725 & 129.702192627505 \tabularnewline
102 & 6489.4 & 6386.25271608625 & 103.147283913753 \tabularnewline
103 & 5291.15 & 5055.22785845302 & 235.922141546975 \tabularnewline
104 & 5986.45 & 5952.10362259295 & 34.3463774070515 \tabularnewline
105 & 6538.15 & 6388.0823991124 & 150.0676008876 \tabularnewline
106 & 6442.8 & 6332.93521418902 & 109.864785810975 \tabularnewline
107 & 6169.55 & 6020.48267116801 & 149.067328831991 \tabularnewline
108 & 5793 & 6156.94506776707 & -363.945067767071 \tabularnewline
109 & 5254.85 & 5298.13291027614 & -43.2829102761425 \tabularnewline
110 & 6050.75 & 6051.57500821584 & -0.825008215844719 \tabularnewline
111 & 6606.15 & 6475.34915276514 & 130.800847234859 \tabularnewline
112 & 6221.15 & 6376.95471463064 & -155.804714630644 \tabularnewline
113 & 6293.4 & 6382.85381297986 & -89.4538129798602 \tabularnewline
114 & 6908.4 & 6701.09377096233 & 207.306229037667 \tabularnewline
115 & 5498.95 & 5495.02142274776 & 3.92857725224167 \tabularnewline
116 & 6145.35 & 6176.5936719456 & -31.2436719455964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301152&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]4310.7[/C][C]3941.39115918804[/C][C]369.308840811962[/C][/ROW]
[ROW][C]14[/C][C]4831.3[/C][C]4674.0106262878[/C][C]157.289373712202[/C][/ROW]
[ROW][C]15[/C][C]5145.3[/C][C]5093.23517197982[/C][C]52.0648280201831[/C][/ROW]
[ROW][C]16[/C][C]4886.65[/C][C]4889.06524382055[/C][C]-2.41524382055377[/C][/ROW]
[ROW][C]17[/C][C]4934.05[/C][C]4961.59867254905[/C][C]-27.5486725490528[/C][/ROW]
[ROW][C]18[/C][C]5304.7[/C][C]5351.45794597972[/C][C]-46.7579459797162[/C][/ROW]
[ROW][C]19[/C][C]4419.45[/C][C]4525.11329487546[/C][C]-105.663294875459[/C][/ROW]
[ROW][C]20[/C][C]4804.85[/C][C]4775.57660851532[/C][C]29.2733914846758[/C][/ROW]
[ROW][C]21[/C][C]5105[/C][C]5276.24756624782[/C][C]-171.247566247821[/C][/ROW]
[ROW][C]22[/C][C]5132.6[/C][C]5135.67200071079[/C][C]-3.07200071078842[/C][/ROW]
[ROW][C]23[/C][C]4982.5[/C][C]5054.73886253109[/C][C]-72.2388625310932[/C][/ROW]
[ROW][C]24[/C][C]4906.7[/C][C]5064.39627603409[/C][C]-157.696276034094[/C][/ROW]
[ROW][C]25[/C][C]4506.4[/C][C]4856.0463252152[/C][C]-349.6463252152[/C][/ROW]
[ROW][C]26[/C][C]5010.85[/C][C]5086.31270407253[/C][C]-75.46270407253[/C][/ROW]
[ROW][C]27[/C][C]5392.25[/C][C]5311.24539914861[/C][C]81.00460085139[/C][/ROW]
[ROW][C]28[/C][C]5049.7[/C][C]5078.79257988332[/C][C]-29.0925798833186[/C][/ROW]
[ROW][C]29[/C][C]5143.9[/C][C]5105.64546781392[/C][C]38.2545321860844[/C][/ROW]
[ROW][C]30[/C][C]5449.9[/C][C]5504.18903149274[/C][C]-54.2890314927399[/C][/ROW]
[ROW][C]31[/C][C]4520.4[/C][C]4628.39029867808[/C][C]-107.990298678083[/C][/ROW]
[ROW][C]32[/C][C]4936.95[/C][C]4920.66734798372[/C][C]16.2826520162753[/C][/ROW]
[ROW][C]33[/C][C]5358.55[/C][C]5303.94418189539[/C][C]54.6058181046083[/C][/ROW]
[ROW][C]34[/C][C]5289.5[/C][C]5348.8918794398[/C][C]-59.3918794398032[/C][/ROW]
[ROW][C]35[/C][C]5123.55[/C][C]5190.57812093697[/C][C]-67.0281209369741[/C][/ROW]
[ROW][C]36[/C][C]4985.65[/C][C]5148.97084532043[/C][C]-163.320845320432[/C][/ROW]
[ROW][C]37[/C][C]4682.65[/C][C]4834.73393566182[/C][C]-152.083935661825[/C][/ROW]
[ROW][C]38[/C][C]5175.55[/C][C]5286.5303533216[/C][C]-110.980353321599[/C][/ROW]
[ROW][C]39[/C][C]5374.7[/C][C]5551.82236905595[/C][C]-177.12236905595[/C][/ROW]
[ROW][C]40[/C][C]5289[/C][C]5111.5730513121[/C][C]177.426948687897[/C][/ROW]
[ROW][C]41[/C][C]5176.15[/C][C]5268.55342157037[/C][C]-92.4034215703723[/C][/ROW]
[ROW][C]42[/C][C]5604.25[/C][C]5538.20398944062[/C][C]66.0460105593793[/C][/ROW]
[ROW][C]43[/C][C]4608.8[/C][C]4690.21370670434[/C][C]-81.4137067043448[/C][/ROW]
[ROW][C]44[/C][C]4898.15[/C][C]5041.1509234325[/C][C]-143.000923432498[/C][/ROW]
[ROW][C]45[/C][C]5448.65[/C][C]5339.45462946828[/C][C]109.195370531722[/C][/ROW]
[ROW][C]46[/C][C]5373.05[/C][C]5347.29406060529[/C][C]25.7559393947058[/C][/ROW]
[ROW][C]47[/C][C]5078.6[/C][C]5218.84242740569[/C][C]-140.242427405693[/C][/ROW]
[ROW][C]48[/C][C]5233.4[/C][C]5079.00113948206[/C][C]154.39886051794[/C][/ROW]
[ROW][C]49[/C][C]4629.2[/C][C]4934.83660716666[/C][C]-305.636607166662[/C][/ROW]
[ROW][C]50[/C][C]5387.8[/C][C]5310.94230304262[/C][C]76.8576969573796[/C][/ROW]
[ROW][C]51[/C][C]5736.65[/C][C]5641.12051939706[/C][C]95.5294806029369[/C][/ROW]
[ROW][C]52[/C][C]5357.9[/C][C]5509.68855550091[/C][C]-151.78855550091[/C][/ROW]
[ROW][C]53[/C][C]5337.95[/C][C]5356.35159973182[/C][C]-18.4015997318229[/C][/ROW]
[ROW][C]54[/C][C]5795.5[/C][C]5731.91450814472[/C][C]63.5854918552832[/C][/ROW]
[ROW][C]55[/C][C]4804.05[/C][C]4808.5796077521[/C][C]-4.52960775210431[/C][/ROW]
[ROW][C]56[/C][C]5120.5[/C][C]5168.1293322237[/C][C]-47.6293322236952[/C][/ROW]
[ROW][C]57[/C][C]5850.45[/C][C]5630.36063591137[/C][C]220.089364088625[/C][/ROW]
[ROW][C]58[/C][C]5734.75[/C][C]5659.70121645592[/C][C]75.0487835440799[/C][/ROW]
[ROW][C]59[/C][C]5539[/C][C]5482.62903086079[/C][C]56.3709691392141[/C][/ROW]
[ROW][C]60[/C][C]5582.85[/C][C]5588.69260637932[/C][C]-5.84260637932221[/C][/ROW]
[ROW][C]61[/C][C]4983.1[/C][C]5148.57003230319[/C][C]-165.470032303188[/C][/ROW]
[ROW][C]62[/C][C]5672[/C][C]5779.58032155411[/C][C]-107.580321554112[/C][/ROW]
[ROW][C]63[/C][C]6185.8[/C][C]6018.23927376751[/C][C]167.56072623249[/C][/ROW]
[ROW][C]64[/C][C]5835.6[/C][C]5814.78444571196[/C][C]20.8155542880377[/C][/ROW]
[ROW][C]65[/C][C]5930.4[/C][C]5821.54270803539[/C][C]108.857291964613[/C][/ROW]
[ROW][C]66[/C][C]6444.65[/C][C]6311.79384697218[/C][C]132.856153027816[/C][/ROW]
[ROW][C]67[/C][C]5171.05[/C][C]5404.57983294058[/C][C]-233.529832940577[/C][/ROW]
[ROW][C]68[/C][C]5739.1[/C][C]5624.69708360027[/C][C]114.40291639973[/C][/ROW]
[ROW][C]69[/C][C]6413.9[/C][C]6305.35124586605[/C][C]108.548754133949[/C][/ROW]
[ROW][C]70[/C][C]6230.2[/C][C]6213.63486793095[/C][C]16.5651320690449[/C][/ROW]
[ROW][C]71[/C][C]6015.45[/C][C]6000.78492988644[/C][C]14.6650701135604[/C][/ROW]
[ROW][C]72[/C][C]6174.25[/C][C]6059.42984231736[/C][C]114.820157682639[/C][/ROW]
[ROW][C]73[/C][C]5579.25[/C][C]5618.22877390996[/C][C]-38.978773909962[/C][/ROW]
[ROW][C]74[/C][C]6133.45[/C][C]6353.31071365875[/C][C]-219.860713658752[/C][/ROW]
[ROW][C]75[/C][C]6478.7[/C][C]6663.05984268263[/C][C]-184.359842682632[/C][/ROW]
[ROW][C]76[/C][C]6184.4[/C][C]6200.3872057249[/C][C]-15.9872057248995[/C][/ROW]
[ROW][C]77[/C][C]6185.65[/C][C]6225.59298845302[/C][C]-39.9429884530227[/C][/ROW]
[ROW][C]78[/C][C]6556[/C][C]6641.02582536359[/C][C]-85.0258253635857[/C][/ROW]
[ROW][C]79[/C][C]5123.25[/C][C]5438.61062376369[/C][C]-315.360623763691[/C][/ROW]
[ROW][C]80[/C][C]6028.9[/C][C]5761.819198518[/C][C]267.080801481997[/C][/ROW]
[ROW][C]81[/C][C]6499.95[/C][C]6514.75858490702[/C][C]-14.8085849070203[/C][/ROW]
[ROW][C]82[/C][C]6190.05[/C][C]6303.36477894851[/C][C]-113.314778948509[/C][/ROW]
[ROW][C]83[/C][C]6027.95[/C][C]6005.65767180627[/C][C]22.2923281937337[/C][/ROW]
[ROW][C]84[/C][C]6034[/C][C]6100.93070692028[/C][C]-66.9307069202823[/C][/ROW]
[ROW][C]85[/C][C]5128.75[/C][C]5473.64153016242[/C][C]-344.891530162419[/C][/ROW]
[ROW][C]86[/C][C]6087.7[/C][C]5936.2942874462[/C][C]151.405712553798[/C][/ROW]
[ROW][C]87[/C][C]6628.15[/C][C]6448.32341699682[/C][C]179.826583003175[/C][/ROW]
[ROW][C]88[/C][C]6075.3[/C][C]6252.47171874921[/C][C]-177.171718749213[/C][/ROW]
[ROW][C]89[/C][C]6352.1[/C][C]6167.73873190306[/C][C]184.361268096935[/C][/ROW]
[ROW][C]90[/C][C]6824[/C][C]6677.864419807[/C][C]146.135580192997[/C][/ROW]
[ROW][C]91[/C][C]5412.35[/C][C]5494.20989611724[/C][C]-81.8598961172429[/C][/ROW]
[ROW][C]92[/C][C]6171.25[/C][C]6213.44065431119[/C][C]-42.1906543111936[/C][/ROW]
[ROW][C]93[/C][C]6521.35[/C][C]6666.27169257184[/C][C]-144.921692571838[/C][/ROW]
[ROW][C]94[/C][C]6457.6[/C][C]6333.09374681108[/C][C]124.506253188917[/C][/ROW]
[ROW][C]95[/C][C]5930.95[/C][C]6225.49729753714[/C][C]-294.547297537138[/C][/ROW]
[ROW][C]96[/C][C]5842.7[/C][C]6100.06015482842[/C][C]-257.360154828424[/C][/ROW]
[ROW][C]97[/C][C]5120.1[/C][C]5230.56254710767[/C][C]-110.462547107669[/C][/ROW]
[ROW][C]98[/C][C]5719.95[/C][C]6040.34387969671[/C][C]-320.393879696708[/C][/ROW]
[ROW][C]99[/C][C]5946.7[/C][C]6292.06265065094[/C][C]-345.36265065094[/C][/ROW]
[ROW][C]100[/C][C]5921.1[/C][C]5619.78791376367[/C][C]301.312086236335[/C][/ROW]
[ROW][C]101[/C][C]6072[/C][C]5942.2978073725[/C][C]129.702192627505[/C][/ROW]
[ROW][C]102[/C][C]6489.4[/C][C]6386.25271608625[/C][C]103.147283913753[/C][/ROW]
[ROW][C]103[/C][C]5291.15[/C][C]5055.22785845302[/C][C]235.922141546975[/C][/ROW]
[ROW][C]104[/C][C]5986.45[/C][C]5952.10362259295[/C][C]34.3463774070515[/C][/ROW]
[ROW][C]105[/C][C]6538.15[/C][C]6388.0823991124[/C][C]150.0676008876[/C][/ROW]
[ROW][C]106[/C][C]6442.8[/C][C]6332.93521418902[/C][C]109.864785810975[/C][/ROW]
[ROW][C]107[/C][C]6169.55[/C][C]6020.48267116801[/C][C]149.067328831991[/C][/ROW]
[ROW][C]108[/C][C]5793[/C][C]6156.94506776707[/C][C]-363.945067767071[/C][/ROW]
[ROW][C]109[/C][C]5254.85[/C][C]5298.13291027614[/C][C]-43.2829102761425[/C][/ROW]
[ROW][C]110[/C][C]6050.75[/C][C]6051.57500821584[/C][C]-0.825008215844719[/C][/ROW]
[ROW][C]111[/C][C]6606.15[/C][C]6475.34915276514[/C][C]130.800847234859[/C][/ROW]
[ROW][C]112[/C][C]6221.15[/C][C]6376.95471463064[/C][C]-155.804714630644[/C][/ROW]
[ROW][C]113[/C][C]6293.4[/C][C]6382.85381297986[/C][C]-89.4538129798602[/C][/ROW]
[ROW][C]114[/C][C]6908.4[/C][C]6701.09377096233[/C][C]207.306229037667[/C][/ROW]
[ROW][C]115[/C][C]5498.95[/C][C]5495.02142274776[/C][C]3.92857725224167[/C][/ROW]
[ROW][C]116[/C][C]6145.35[/C][C]6176.5936719456[/C][C]-31.2436719455964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301152&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301152&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
134310.73941.39115918804369.308840811962
144831.34674.0106262878157.289373712202
155145.35093.2351719798252.0648280201831
164886.654889.06524382055-2.41524382055377
174934.054961.59867254905-27.5486725490528
185304.75351.45794597972-46.7579459797162
194419.454525.11329487546-105.663294875459
204804.854775.5766085153229.2733914846758
2151055276.24756624782-171.247566247821
225132.65135.67200071079-3.07200071078842
234982.55054.73886253109-72.2388625310932
244906.75064.39627603409-157.696276034094
254506.44856.0463252152-349.6463252152
265010.855086.31270407253-75.46270407253
275392.255311.2453991486181.00460085139
285049.75078.79257988332-29.0925798833186
295143.95105.6454678139238.2545321860844
305449.95504.18903149274-54.2890314927399
314520.44628.39029867808-107.990298678083
324936.954920.6673479837216.2826520162753
335358.555303.9441818953954.6058181046083
345289.55348.8918794398-59.3918794398032
355123.555190.57812093697-67.0281209369741
364985.655148.97084532043-163.320845320432
374682.654834.73393566182-152.083935661825
385175.555286.5303533216-110.980353321599
395374.75551.82236905595-177.12236905595
4052895111.5730513121177.426948687897
415176.155268.55342157037-92.4034215703723
425604.255538.2039894406266.0460105593793
434608.84690.21370670434-81.4137067043448
444898.155041.1509234325-143.000923432498
455448.655339.45462946828109.195370531722
465373.055347.2940606052925.7559393947058
475078.65218.84242740569-140.242427405693
485233.45079.00113948206154.39886051794
494629.24934.83660716666-305.636607166662
505387.85310.9423030426276.8576969573796
515736.655641.1205193970695.5294806029369
525357.95509.68855550091-151.78855550091
535337.955356.35159973182-18.4015997318229
545795.55731.9145081447263.5854918552832
554804.054808.5796077521-4.52960775210431
565120.55168.1293322237-47.6293322236952
575850.455630.36063591137220.089364088625
585734.755659.7012164559275.0487835440799
5955395482.6290308607956.3709691392141
605582.855588.69260637932-5.84260637932221
614983.15148.57003230319-165.470032303188
6256725779.58032155411-107.580321554112
636185.86018.23927376751167.56072623249
645835.65814.7844457119620.8155542880377
655930.45821.54270803539108.857291964613
666444.656311.79384697218132.856153027816
675171.055404.57983294058-233.529832940577
685739.15624.69708360027114.40291639973
696413.96305.35124586605108.548754133949
706230.26213.6348679309516.5651320690449
716015.456000.7849298864414.6650701135604
726174.256059.42984231736114.820157682639
735579.255618.22877390996-38.978773909962
746133.456353.31071365875-219.860713658752
756478.76663.05984268263-184.359842682632
766184.46200.3872057249-15.9872057248995
776185.656225.59298845302-39.9429884530227
7865566641.02582536359-85.0258253635857
795123.255438.61062376369-315.360623763691
806028.95761.819198518267.080801481997
816499.956514.75858490702-14.8085849070203
826190.056303.36477894851-113.314778948509
836027.956005.6576718062722.2923281937337
8460346100.93070692028-66.9307069202823
855128.755473.64153016242-344.891530162419
866087.75936.2942874462151.405712553798
876628.156448.32341699682179.826583003175
886075.36252.47171874921-177.171718749213
896352.16167.73873190306184.361268096935
9068246677.864419807146.135580192997
915412.355494.20989611724-81.8598961172429
926171.256213.44065431119-42.1906543111936
936521.356666.27169257184-144.921692571838
946457.66333.09374681108124.506253188917
955930.956225.49729753714-294.547297537138
965842.76100.06015482842-257.360154828424
975120.15230.56254710767-110.462547107669
985719.956040.34387969671-320.393879696708
995946.76292.06265065094-345.36265065094
1005921.15619.78791376367301.312086236335
10160725942.2978073725129.702192627505
1026489.46386.25271608625103.147283913753
1035291.155055.22785845302235.922141546975
1045986.455952.1036225929534.3463774070515
1056538.156388.0823991124150.0676008876
1066442.86332.93521418902109.864785810975
1076169.556020.48267116801149.067328831991
10857936156.94506776707-363.945067767071
1095254.855298.13291027614-43.2829102761425
1106050.756051.57500821584-0.825008215844719
1116606.156475.34915276514130.800847234859
1126221.156376.95471463064-155.804714630644
1136293.46382.85381297986-89.4538129798602
1146908.46701.09377096233207.306229037667
1155498.955495.021422747763.92857725224167
1166145.356176.5936719456-31.2436719455964







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1176631.162537544556331.722906822946930.60216826617
1186474.32611223756130.436337601976818.21588687303
1196115.950255189935729.884093845136502.01641653473
1205929.931604135965503.193209488786356.66999878315
1215415.760826915414949.373905786635882.14774804418
1226213.483217325708.150413470176718.81602116984
1236699.184417920076155.383021897797242.98581394234
1246397.478479205335815.521641702276979.43531670839
1256520.269104195075900.346928951637140.19127943852
1267026.419954790586368.628164213027684.21174536814
1275614.254771565524918.6153366546309.89420647704
1286276.97230243095543.448677844487010.49592701732
1296762.784839975455938.627082483847586.94259746707
1306605.94841466845746.030828080297465.86600125651
1316247.572557620835351.558292382047143.58682285962
1326061.553906566865129.101877716746994.00593541698
1335547.38312934634578.14901056036516.61724813231
1346345.10551975095338.742568446857351.46847105496

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 6631.16253754455 & 6331.72290682294 & 6930.60216826617 \tabularnewline
118 & 6474.3261122375 & 6130.43633760197 & 6818.21588687303 \tabularnewline
119 & 6115.95025518993 & 5729.88409384513 & 6502.01641653473 \tabularnewline
120 & 5929.93160413596 & 5503.19320948878 & 6356.66999878315 \tabularnewline
121 & 5415.76082691541 & 4949.37390578663 & 5882.14774804418 \tabularnewline
122 & 6213.48321732 & 5708.15041347017 & 6718.81602116984 \tabularnewline
123 & 6699.18441792007 & 6155.38302189779 & 7242.98581394234 \tabularnewline
124 & 6397.47847920533 & 5815.52164170227 & 6979.43531670839 \tabularnewline
125 & 6520.26910419507 & 5900.34692895163 & 7140.19127943852 \tabularnewline
126 & 7026.41995479058 & 6368.62816421302 & 7684.21174536814 \tabularnewline
127 & 5614.25477156552 & 4918.615336654 & 6309.89420647704 \tabularnewline
128 & 6276.9723024309 & 5543.44867784448 & 7010.49592701732 \tabularnewline
129 & 6762.78483997545 & 5938.62708248384 & 7586.94259746707 \tabularnewline
130 & 6605.9484146684 & 5746.03082808029 & 7465.86600125651 \tabularnewline
131 & 6247.57255762083 & 5351.55829238204 & 7143.58682285962 \tabularnewline
132 & 6061.55390656686 & 5129.10187771674 & 6994.00593541698 \tabularnewline
133 & 5547.3831293463 & 4578.1490105603 & 6516.61724813231 \tabularnewline
134 & 6345.1055197509 & 5338.74256844685 & 7351.46847105496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301152&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]6631.16253754455[/C][C]6331.72290682294[/C][C]6930.60216826617[/C][/ROW]
[ROW][C]118[/C][C]6474.3261122375[/C][C]6130.43633760197[/C][C]6818.21588687303[/C][/ROW]
[ROW][C]119[/C][C]6115.95025518993[/C][C]5729.88409384513[/C][C]6502.01641653473[/C][/ROW]
[ROW][C]120[/C][C]5929.93160413596[/C][C]5503.19320948878[/C][C]6356.66999878315[/C][/ROW]
[ROW][C]121[/C][C]5415.76082691541[/C][C]4949.37390578663[/C][C]5882.14774804418[/C][/ROW]
[ROW][C]122[/C][C]6213.48321732[/C][C]5708.15041347017[/C][C]6718.81602116984[/C][/ROW]
[ROW][C]123[/C][C]6699.18441792007[/C][C]6155.38302189779[/C][C]7242.98581394234[/C][/ROW]
[ROW][C]124[/C][C]6397.47847920533[/C][C]5815.52164170227[/C][C]6979.43531670839[/C][/ROW]
[ROW][C]125[/C][C]6520.26910419507[/C][C]5900.34692895163[/C][C]7140.19127943852[/C][/ROW]
[ROW][C]126[/C][C]7026.41995479058[/C][C]6368.62816421302[/C][C]7684.21174536814[/C][/ROW]
[ROW][C]127[/C][C]5614.25477156552[/C][C]4918.615336654[/C][C]6309.89420647704[/C][/ROW]
[ROW][C]128[/C][C]6276.9723024309[/C][C]5543.44867784448[/C][C]7010.49592701732[/C][/ROW]
[ROW][C]129[/C][C]6762.78483997545[/C][C]5938.62708248384[/C][C]7586.94259746707[/C][/ROW]
[ROW][C]130[/C][C]6605.9484146684[/C][C]5746.03082808029[/C][C]7465.86600125651[/C][/ROW]
[ROW][C]131[/C][C]6247.57255762083[/C][C]5351.55829238204[/C][C]7143.58682285962[/C][/ROW]
[ROW][C]132[/C][C]6061.55390656686[/C][C]5129.10187771674[/C][C]6994.00593541698[/C][/ROW]
[ROW][C]133[/C][C]5547.3831293463[/C][C]4578.1490105603[/C][C]6516.61724813231[/C][/ROW]
[ROW][C]134[/C][C]6345.1055197509[/C][C]5338.74256844685[/C][C]7351.46847105496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301152&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301152&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
1176631.162537544556331.722906822946930.60216826617
1186474.32611223756130.436337601976818.21588687303
1196115.950255189935729.884093845136502.01641653473
1205929.931604135965503.193209488786356.66999878315
1215415.760826915414949.373905786635882.14774804418
1226213.483217325708.150413470176718.81602116984
1236699.184417920076155.383021897797242.98581394234
1246397.478479205335815.521641702276979.43531670839
1256520.269104195075900.346928951637140.19127943852
1267026.419954790586368.628164213027684.21174536814
1275614.254771565524918.6153366546309.89420647704
1286276.97230243095543.448677844487010.49592701732
1296762.784839975455938.627082483847586.94259746707
1306605.94841466845746.030828080297465.86600125651
1316247.572557620835351.558292382047143.58682285962
1326061.553906566865129.101877716746994.00593541698
1335547.38312934634578.14901056036516.61724813231
1346345.10551975095338.742568446857351.46847105496



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