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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 23:50:37 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/16/t15029202550jxasuihk5qdrzi.htm/, Retrieved Sun, 12 May 2024 00:18:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307519, Retrieved Sun, 12 May 2024 00:18:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-16 21:50:37] [b4406e95441bfa154caa3f19e1e15192] [Current]
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Dataseries X:
1684800
1622400
1716000
1372800
1778400
1747200
1872000
1934400
2152800
1872000
1778400
2215200
1872000
1404000
1653600
1248000
1747200
1435200
1903200
1716000
1809600
2028000
1996800
2371200
1716000
1435200
1591200
1154400
1653600
1279200
1809600
1716000
1528800
2184000
1965600
2246400
1684800
1560000
1404000
1154400
1528800
1372800
1872000
1809600
1560000
2090400
1934400
2496000
1996800
1216800
1216800
1216800
1435200
1435200
1934400
1778400
1591200
1996800
1840800
2652000
2090400
1216800
1279200
1060800
1466400
1684800
2121600
2090400
1684800
1965600
1747200
2496000
1903200
1528800
1372800
1029600
1528800
1840800
2152800
2028000
1497600
2152800
1684800
2589600
2152800
1560000
1435200
967200
1528800
1466400
2215200
2215200
1684800
2184000
1622400
2527200
2152800
1591200
1216800
842400
1653600
1591200
2090400
2402400
1778400
1996800
1497600
2589600




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307519&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307519&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307519&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00926118605786535
beta1
gamma0.929768627343191

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605786535 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627343191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307519&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]0.00926118605786535[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627343191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307519&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307519&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
alpha0.00926118605786535
beta1
gamma0.929768627343191







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1318720001936016.66666667-64016.6666666674
1414040001466458.19887233-62458.1988723313
1516536001729535.72733761-75935.7273376081
1612480001320985.18300485-72985.1830048547
1717472001793186.03485286-45986.034852864
1814352001454011.04561048-18811.045610477
1919032001818213.5164062484986.4835937573
2017160001872164.35106928-156164.351069281
2118096002088835.57587364-279235.575873638
2220280001798680.96254457229319.03745543
2319968001701259.93438262295540.065617385
2423712002145389.24301865225810.756981353
2517160001749394.59486281-33394.5948628134
2614352001282395.17515454152804.824845456
2715912001537884.8105853553315.1894146539
2811544001137279.6643795817120.3356204182
2916536001640050.4261127813549.5738872222
3012792001331875.58088575-52675.5808857456
3118096001796481.0293059913118.9706940132
3217160001632065.4114207483934.5885792614
3315288001744252.92555484-215452.925554837
3421840001930399.51644369253600.483556314
3519656001901679.6776311363920.3223688747
3622464002284763.43127703-38363.431277032
3716848001650437.8212225534362.1787774488
3815600001359097.13145651200902.868543494
3914040001527344.1579214-123344.157921404
4011544001094083.2936995160316.7063004931
4115288001596686.45081174-67886.4508117402
4213728001228720.97592813144079.02407187
4318720001759545.34199519112454.658004815
4418096001665991.58804574143608.411954256
4515600001508210.7731127251789.2268872836
4620904002136641.74499072-46241.7449907199
4719344001935379.90793802-979.90793802496
4824960002228002.34015692267997.659843076
4919968001670702.24810284326097.751897155
5012168001545371.94284458-328571.942844581
5112168001415027.44103294-198227.44103294
5212168001154554.9465062562245.0534937524
5314352001543399.70217979-108199.702179795
5414352001374260.281534160939.7184658975
5519344001878359.4148686956040.5851313123
5617784001815634.03344899-37234.033448993
5715912001572576.9309880818623.0690119159
5819968002111070.07866473-114270.078664733
5918408001950912.82750346-110112.827503464
6026520002489325.97347617162674.026523827
6120904001982625.00616112107774.99383888
6212168001248251.89550595-31451.8955059499
6312792001239511.8869963939688.1130036146
6410608001222167.38637453-161367.386374528
6514664001450852.1078312515547.8921687519
6616848001438726.30392746246073.696072541
6721216001941805.14175627179794.858243732
6820904001797229.35382365293170.646176349
6916848001614669.4699963470130.5300036597
7019656002037685.15962313-72085.1596231286
7117472001888599.84807855-141399.848078547
7224960002684565.01346091-188565.013460914
7319032002127349.60779324-224149.607793243
7415288001261887.64932227266912.350677733
7513728001324440.345018548359.6549815005
7610296001125050.92585428-95450.9258542773
7715288001521002.104829467797.89517054101
7818408001724772.50270559116027.497294412
7921528002168006.62167028-15206.6216702829
8020280002126668.87882254-98668.8788225418
8114976001732003.03089312-234403.030893123
8221528002015353.02759315137446.972406848
8316848001800456.72795788-115656.727957882
8425896002549550.4202711640049.5797288399
8521528001960127.14840359192672.851596411
8615600001553185.237441666814.76255833544
8714352001411912.9646921523287.0353078451
889672001079492.27195445-112292.271954451
8915288001569913.14953608-41113.1495360842
9014664001871991.35398141-405591.353981406
9122152002183740.7447702231459.2552297842
9222152002060618.87205088154581.127949123
9316848001540276.83651312144523.163486883
9421840002170189.0000817913810.999918208
9516224001720374.50913685-97974.5091368454
9625272002612601.09758554-85401.0975855449
9721528002160983.35670825-8183.35670824535
9815912001577493.6969051913706.3030948099
9912168001448039.69422153-231239.694221535
100842400982595.499780769-140195.499780769
10116536001532290.41517765121309.584822349
10215912001495600.3547506995599.6452493125
10320904002214695.0720958-124295.072095795
10424024002202214.03790245200185.962097545
10517784001672120.36564556106279.634354442
10619968002180008.61205841-183208.612058408
10714976001622309.55053232-124709.550532318
10825896002522535.2053581267064.7946418831

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1872000 & 1936016.66666667 & -64016.6666666674 \tabularnewline
14 & 1404000 & 1466458.19887233 & -62458.1988723313 \tabularnewline
15 & 1653600 & 1729535.72733761 & -75935.7273376081 \tabularnewline
16 & 1248000 & 1320985.18300485 & -72985.1830048547 \tabularnewline
17 & 1747200 & 1793186.03485286 & -45986.034852864 \tabularnewline
18 & 1435200 & 1454011.04561048 & -18811.045610477 \tabularnewline
19 & 1903200 & 1818213.51640624 & 84986.4835937573 \tabularnewline
20 & 1716000 & 1872164.35106928 & -156164.351069281 \tabularnewline
21 & 1809600 & 2088835.57587364 & -279235.575873638 \tabularnewline
22 & 2028000 & 1798680.96254457 & 229319.03745543 \tabularnewline
23 & 1996800 & 1701259.93438262 & 295540.065617385 \tabularnewline
24 & 2371200 & 2145389.24301865 & 225810.756981353 \tabularnewline
25 & 1716000 & 1749394.59486281 & -33394.5948628134 \tabularnewline
26 & 1435200 & 1282395.17515454 & 152804.824845456 \tabularnewline
27 & 1591200 & 1537884.81058535 & 53315.1894146539 \tabularnewline
28 & 1154400 & 1137279.66437958 & 17120.3356204182 \tabularnewline
29 & 1653600 & 1640050.42611278 & 13549.5738872222 \tabularnewline
30 & 1279200 & 1331875.58088575 & -52675.5808857456 \tabularnewline
31 & 1809600 & 1796481.02930599 & 13118.9706940132 \tabularnewline
32 & 1716000 & 1632065.41142074 & 83934.5885792614 \tabularnewline
33 & 1528800 & 1744252.92555484 & -215452.925554837 \tabularnewline
34 & 2184000 & 1930399.51644369 & 253600.483556314 \tabularnewline
35 & 1965600 & 1901679.67763113 & 63920.3223688747 \tabularnewline
36 & 2246400 & 2284763.43127703 & -38363.431277032 \tabularnewline
37 & 1684800 & 1650437.82122255 & 34362.1787774488 \tabularnewline
38 & 1560000 & 1359097.13145651 & 200902.868543494 \tabularnewline
39 & 1404000 & 1527344.1579214 & -123344.157921404 \tabularnewline
40 & 1154400 & 1094083.29369951 & 60316.7063004931 \tabularnewline
41 & 1528800 & 1596686.45081174 & -67886.4508117402 \tabularnewline
42 & 1372800 & 1228720.97592813 & 144079.02407187 \tabularnewline
43 & 1872000 & 1759545.34199519 & 112454.658004815 \tabularnewline
44 & 1809600 & 1665991.58804574 & 143608.411954256 \tabularnewline
45 & 1560000 & 1508210.77311272 & 51789.2268872836 \tabularnewline
46 & 2090400 & 2136641.74499072 & -46241.7449907199 \tabularnewline
47 & 1934400 & 1935379.90793802 & -979.90793802496 \tabularnewline
48 & 2496000 & 2228002.34015692 & 267997.659843076 \tabularnewline
49 & 1996800 & 1670702.24810284 & 326097.751897155 \tabularnewline
50 & 1216800 & 1545371.94284458 & -328571.942844581 \tabularnewline
51 & 1216800 & 1415027.44103294 & -198227.44103294 \tabularnewline
52 & 1216800 & 1154554.94650625 & 62245.0534937524 \tabularnewline
53 & 1435200 & 1543399.70217979 & -108199.702179795 \tabularnewline
54 & 1435200 & 1374260.2815341 & 60939.7184658975 \tabularnewline
55 & 1934400 & 1878359.41486869 & 56040.5851313123 \tabularnewline
56 & 1778400 & 1815634.03344899 & -37234.033448993 \tabularnewline
57 & 1591200 & 1572576.93098808 & 18623.0690119159 \tabularnewline
58 & 1996800 & 2111070.07866473 & -114270.078664733 \tabularnewline
59 & 1840800 & 1950912.82750346 & -110112.827503464 \tabularnewline
60 & 2652000 & 2489325.97347617 & 162674.026523827 \tabularnewline
61 & 2090400 & 1982625.00616112 & 107774.99383888 \tabularnewline
62 & 1216800 & 1248251.89550595 & -31451.8955059499 \tabularnewline
63 & 1279200 & 1239511.88699639 & 39688.1130036146 \tabularnewline
64 & 1060800 & 1222167.38637453 & -161367.386374528 \tabularnewline
65 & 1466400 & 1450852.10783125 & 15547.8921687519 \tabularnewline
66 & 1684800 & 1438726.30392746 & 246073.696072541 \tabularnewline
67 & 2121600 & 1941805.14175627 & 179794.858243732 \tabularnewline
68 & 2090400 & 1797229.35382365 & 293170.646176349 \tabularnewline
69 & 1684800 & 1614669.46999634 & 70130.5300036597 \tabularnewline
70 & 1965600 & 2037685.15962313 & -72085.1596231286 \tabularnewline
71 & 1747200 & 1888599.84807855 & -141399.848078547 \tabularnewline
72 & 2496000 & 2684565.01346091 & -188565.013460914 \tabularnewline
73 & 1903200 & 2127349.60779324 & -224149.607793243 \tabularnewline
74 & 1528800 & 1261887.64932227 & 266912.350677733 \tabularnewline
75 & 1372800 & 1324440.3450185 & 48359.6549815005 \tabularnewline
76 & 1029600 & 1125050.92585428 & -95450.9258542773 \tabularnewline
77 & 1528800 & 1521002.10482946 & 7797.89517054101 \tabularnewline
78 & 1840800 & 1724772.50270559 & 116027.497294412 \tabularnewline
79 & 2152800 & 2168006.62167028 & -15206.6216702829 \tabularnewline
80 & 2028000 & 2126668.87882254 & -98668.8788225418 \tabularnewline
81 & 1497600 & 1732003.03089312 & -234403.030893123 \tabularnewline
82 & 2152800 & 2015353.02759315 & 137446.972406848 \tabularnewline
83 & 1684800 & 1800456.72795788 & -115656.727957882 \tabularnewline
84 & 2589600 & 2549550.42027116 & 40049.5797288399 \tabularnewline
85 & 2152800 & 1960127.14840359 & 192672.851596411 \tabularnewline
86 & 1560000 & 1553185.23744166 & 6814.76255833544 \tabularnewline
87 & 1435200 & 1411912.96469215 & 23287.0353078451 \tabularnewline
88 & 967200 & 1079492.27195445 & -112292.271954451 \tabularnewline
89 & 1528800 & 1569913.14953608 & -41113.1495360842 \tabularnewline
90 & 1466400 & 1871991.35398141 & -405591.353981406 \tabularnewline
91 & 2215200 & 2183740.74477022 & 31459.2552297842 \tabularnewline
92 & 2215200 & 2060618.87205088 & 154581.127949123 \tabularnewline
93 & 1684800 & 1540276.83651312 & 144523.163486883 \tabularnewline
94 & 2184000 & 2170189.00008179 & 13810.999918208 \tabularnewline
95 & 1622400 & 1720374.50913685 & -97974.5091368454 \tabularnewline
96 & 2527200 & 2612601.09758554 & -85401.0975855449 \tabularnewline
97 & 2152800 & 2160983.35670825 & -8183.35670824535 \tabularnewline
98 & 1591200 & 1577493.69690519 & 13706.3030948099 \tabularnewline
99 & 1216800 & 1448039.69422153 & -231239.694221535 \tabularnewline
100 & 842400 & 982595.499780769 & -140195.499780769 \tabularnewline
101 & 1653600 & 1532290.41517765 & 121309.584822349 \tabularnewline
102 & 1591200 & 1495600.35475069 & 95599.6452493125 \tabularnewline
103 & 2090400 & 2214695.0720958 & -124295.072095795 \tabularnewline
104 & 2402400 & 2202214.03790245 & 200185.962097545 \tabularnewline
105 & 1778400 & 1672120.36564556 & 106279.634354442 \tabularnewline
106 & 1996800 & 2180008.61205841 & -183208.612058408 \tabularnewline
107 & 1497600 & 1622309.55053232 & -124709.550532318 \tabularnewline
108 & 2589600 & 2522535.20535812 & 67064.7946418831 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307519&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]1872000[/C][C]1936016.66666667[/C][C]-64016.6666666674[/C][/ROW]
[ROW][C]14[/C][C]1404000[/C][C]1466458.19887233[/C][C]-62458.1988723313[/C][/ROW]
[ROW][C]15[/C][C]1653600[/C][C]1729535.72733761[/C][C]-75935.7273376081[/C][/ROW]
[ROW][C]16[/C][C]1248000[/C][C]1320985.18300485[/C][C]-72985.1830048547[/C][/ROW]
[ROW][C]17[/C][C]1747200[/C][C]1793186.03485286[/C][C]-45986.034852864[/C][/ROW]
[ROW][C]18[/C][C]1435200[/C][C]1454011.04561048[/C][C]-18811.045610477[/C][/ROW]
[ROW][C]19[/C][C]1903200[/C][C]1818213.51640624[/C][C]84986.4835937573[/C][/ROW]
[ROW][C]20[/C][C]1716000[/C][C]1872164.35106928[/C][C]-156164.351069281[/C][/ROW]
[ROW][C]21[/C][C]1809600[/C][C]2088835.57587364[/C][C]-279235.575873638[/C][/ROW]
[ROW][C]22[/C][C]2028000[/C][C]1798680.96254457[/C][C]229319.03745543[/C][/ROW]
[ROW][C]23[/C][C]1996800[/C][C]1701259.93438262[/C][C]295540.065617385[/C][/ROW]
[ROW][C]24[/C][C]2371200[/C][C]2145389.24301865[/C][C]225810.756981353[/C][/ROW]
[ROW][C]25[/C][C]1716000[/C][C]1749394.59486281[/C][C]-33394.5948628134[/C][/ROW]
[ROW][C]26[/C][C]1435200[/C][C]1282395.17515454[/C][C]152804.824845456[/C][/ROW]
[ROW][C]27[/C][C]1591200[/C][C]1537884.81058535[/C][C]53315.1894146539[/C][/ROW]
[ROW][C]28[/C][C]1154400[/C][C]1137279.66437958[/C][C]17120.3356204182[/C][/ROW]
[ROW][C]29[/C][C]1653600[/C][C]1640050.42611278[/C][C]13549.5738872222[/C][/ROW]
[ROW][C]30[/C][C]1279200[/C][C]1331875.58088575[/C][C]-52675.5808857456[/C][/ROW]
[ROW][C]31[/C][C]1809600[/C][C]1796481.02930599[/C][C]13118.9706940132[/C][/ROW]
[ROW][C]32[/C][C]1716000[/C][C]1632065.41142074[/C][C]83934.5885792614[/C][/ROW]
[ROW][C]33[/C][C]1528800[/C][C]1744252.92555484[/C][C]-215452.925554837[/C][/ROW]
[ROW][C]34[/C][C]2184000[/C][C]1930399.51644369[/C][C]253600.483556314[/C][/ROW]
[ROW][C]35[/C][C]1965600[/C][C]1901679.67763113[/C][C]63920.3223688747[/C][/ROW]
[ROW][C]36[/C][C]2246400[/C][C]2284763.43127703[/C][C]-38363.431277032[/C][/ROW]
[ROW][C]37[/C][C]1684800[/C][C]1650437.82122255[/C][C]34362.1787774488[/C][/ROW]
[ROW][C]38[/C][C]1560000[/C][C]1359097.13145651[/C][C]200902.868543494[/C][/ROW]
[ROW][C]39[/C][C]1404000[/C][C]1527344.1579214[/C][C]-123344.157921404[/C][/ROW]
[ROW][C]40[/C][C]1154400[/C][C]1094083.29369951[/C][C]60316.7063004931[/C][/ROW]
[ROW][C]41[/C][C]1528800[/C][C]1596686.45081174[/C][C]-67886.4508117402[/C][/ROW]
[ROW][C]42[/C][C]1372800[/C][C]1228720.97592813[/C][C]144079.02407187[/C][/ROW]
[ROW][C]43[/C][C]1872000[/C][C]1759545.34199519[/C][C]112454.658004815[/C][/ROW]
[ROW][C]44[/C][C]1809600[/C][C]1665991.58804574[/C][C]143608.411954256[/C][/ROW]
[ROW][C]45[/C][C]1560000[/C][C]1508210.77311272[/C][C]51789.2268872836[/C][/ROW]
[ROW][C]46[/C][C]2090400[/C][C]2136641.74499072[/C][C]-46241.7449907199[/C][/ROW]
[ROW][C]47[/C][C]1934400[/C][C]1935379.90793802[/C][C]-979.90793802496[/C][/ROW]
[ROW][C]48[/C][C]2496000[/C][C]2228002.34015692[/C][C]267997.659843076[/C][/ROW]
[ROW][C]49[/C][C]1996800[/C][C]1670702.24810284[/C][C]326097.751897155[/C][/ROW]
[ROW][C]50[/C][C]1216800[/C][C]1545371.94284458[/C][C]-328571.942844581[/C][/ROW]
[ROW][C]51[/C][C]1216800[/C][C]1415027.44103294[/C][C]-198227.44103294[/C][/ROW]
[ROW][C]52[/C][C]1216800[/C][C]1154554.94650625[/C][C]62245.0534937524[/C][/ROW]
[ROW][C]53[/C][C]1435200[/C][C]1543399.70217979[/C][C]-108199.702179795[/C][/ROW]
[ROW][C]54[/C][C]1435200[/C][C]1374260.2815341[/C][C]60939.7184658975[/C][/ROW]
[ROW][C]55[/C][C]1934400[/C][C]1878359.41486869[/C][C]56040.5851313123[/C][/ROW]
[ROW][C]56[/C][C]1778400[/C][C]1815634.03344899[/C][C]-37234.033448993[/C][/ROW]
[ROW][C]57[/C][C]1591200[/C][C]1572576.93098808[/C][C]18623.0690119159[/C][/ROW]
[ROW][C]58[/C][C]1996800[/C][C]2111070.07866473[/C][C]-114270.078664733[/C][/ROW]
[ROW][C]59[/C][C]1840800[/C][C]1950912.82750346[/C][C]-110112.827503464[/C][/ROW]
[ROW][C]60[/C][C]2652000[/C][C]2489325.97347617[/C][C]162674.026523827[/C][/ROW]
[ROW][C]61[/C][C]2090400[/C][C]1982625.00616112[/C][C]107774.99383888[/C][/ROW]
[ROW][C]62[/C][C]1216800[/C][C]1248251.89550595[/C][C]-31451.8955059499[/C][/ROW]
[ROW][C]63[/C][C]1279200[/C][C]1239511.88699639[/C][C]39688.1130036146[/C][/ROW]
[ROW][C]64[/C][C]1060800[/C][C]1222167.38637453[/C][C]-161367.386374528[/C][/ROW]
[ROW][C]65[/C][C]1466400[/C][C]1450852.10783125[/C][C]15547.8921687519[/C][/ROW]
[ROW][C]66[/C][C]1684800[/C][C]1438726.30392746[/C][C]246073.696072541[/C][/ROW]
[ROW][C]67[/C][C]2121600[/C][C]1941805.14175627[/C][C]179794.858243732[/C][/ROW]
[ROW][C]68[/C][C]2090400[/C][C]1797229.35382365[/C][C]293170.646176349[/C][/ROW]
[ROW][C]69[/C][C]1684800[/C][C]1614669.46999634[/C][C]70130.5300036597[/C][/ROW]
[ROW][C]70[/C][C]1965600[/C][C]2037685.15962313[/C][C]-72085.1596231286[/C][/ROW]
[ROW][C]71[/C][C]1747200[/C][C]1888599.84807855[/C][C]-141399.848078547[/C][/ROW]
[ROW][C]72[/C][C]2496000[/C][C]2684565.01346091[/C][C]-188565.013460914[/C][/ROW]
[ROW][C]73[/C][C]1903200[/C][C]2127349.60779324[/C][C]-224149.607793243[/C][/ROW]
[ROW][C]74[/C][C]1528800[/C][C]1261887.64932227[/C][C]266912.350677733[/C][/ROW]
[ROW][C]75[/C][C]1372800[/C][C]1324440.3450185[/C][C]48359.6549815005[/C][/ROW]
[ROW][C]76[/C][C]1029600[/C][C]1125050.92585428[/C][C]-95450.9258542773[/C][/ROW]
[ROW][C]77[/C][C]1528800[/C][C]1521002.10482946[/C][C]7797.89517054101[/C][/ROW]
[ROW][C]78[/C][C]1840800[/C][C]1724772.50270559[/C][C]116027.497294412[/C][/ROW]
[ROW][C]79[/C][C]2152800[/C][C]2168006.62167028[/C][C]-15206.6216702829[/C][/ROW]
[ROW][C]80[/C][C]2028000[/C][C]2126668.87882254[/C][C]-98668.8788225418[/C][/ROW]
[ROW][C]81[/C][C]1497600[/C][C]1732003.03089312[/C][C]-234403.030893123[/C][/ROW]
[ROW][C]82[/C][C]2152800[/C][C]2015353.02759315[/C][C]137446.972406848[/C][/ROW]
[ROW][C]83[/C][C]1684800[/C][C]1800456.72795788[/C][C]-115656.727957882[/C][/ROW]
[ROW][C]84[/C][C]2589600[/C][C]2549550.42027116[/C][C]40049.5797288399[/C][/ROW]
[ROW][C]85[/C][C]2152800[/C][C]1960127.14840359[/C][C]192672.851596411[/C][/ROW]
[ROW][C]86[/C][C]1560000[/C][C]1553185.23744166[/C][C]6814.76255833544[/C][/ROW]
[ROW][C]87[/C][C]1435200[/C][C]1411912.96469215[/C][C]23287.0353078451[/C][/ROW]
[ROW][C]88[/C][C]967200[/C][C]1079492.27195445[/C][C]-112292.271954451[/C][/ROW]
[ROW][C]89[/C][C]1528800[/C][C]1569913.14953608[/C][C]-41113.1495360842[/C][/ROW]
[ROW][C]90[/C][C]1466400[/C][C]1871991.35398141[/C][C]-405591.353981406[/C][/ROW]
[ROW][C]91[/C][C]2215200[/C][C]2183740.74477022[/C][C]31459.2552297842[/C][/ROW]
[ROW][C]92[/C][C]2215200[/C][C]2060618.87205088[/C][C]154581.127949123[/C][/ROW]
[ROW][C]93[/C][C]1684800[/C][C]1540276.83651312[/C][C]144523.163486883[/C][/ROW]
[ROW][C]94[/C][C]2184000[/C][C]2170189.00008179[/C][C]13810.999918208[/C][/ROW]
[ROW][C]95[/C][C]1622400[/C][C]1720374.50913685[/C][C]-97974.5091368454[/C][/ROW]
[ROW][C]96[/C][C]2527200[/C][C]2612601.09758554[/C][C]-85401.0975855449[/C][/ROW]
[ROW][C]97[/C][C]2152800[/C][C]2160983.35670825[/C][C]-8183.35670824535[/C][/ROW]
[ROW][C]98[/C][C]1591200[/C][C]1577493.69690519[/C][C]13706.3030948099[/C][/ROW]
[ROW][C]99[/C][C]1216800[/C][C]1448039.69422153[/C][C]-231239.694221535[/C][/ROW]
[ROW][C]100[/C][C]842400[/C][C]982595.499780769[/C][C]-140195.499780769[/C][/ROW]
[ROW][C]101[/C][C]1653600[/C][C]1532290.41517765[/C][C]121309.584822349[/C][/ROW]
[ROW][C]102[/C][C]1591200[/C][C]1495600.35475069[/C][C]95599.6452493125[/C][/ROW]
[ROW][C]103[/C][C]2090400[/C][C]2214695.0720958[/C][C]-124295.072095795[/C][/ROW]
[ROW][C]104[/C][C]2402400[/C][C]2202214.03790245[/C][C]200185.962097545[/C][/ROW]
[ROW][C]105[/C][C]1778400[/C][C]1672120.36564556[/C][C]106279.634354442[/C][/ROW]
[ROW][C]106[/C][C]1996800[/C][C]2180008.61205841[/C][C]-183208.612058408[/C][/ROW]
[ROW][C]107[/C][C]1497600[/C][C]1622309.55053232[/C][C]-124709.550532318[/C][/ROW]
[ROW][C]108[/C][C]2589600[/C][C]2522535.20535812[/C][C]67064.7946418831[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307519&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307519&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
1318720001936016.66666667-64016.6666666674
1414040001466458.19887233-62458.1988723313
1516536001729535.72733761-75935.7273376081
1612480001320985.18300485-72985.1830048547
1717472001793186.03485286-45986.034852864
1814352001454011.04561048-18811.045610477
1919032001818213.5164062484986.4835937573
2017160001872164.35106928-156164.351069281
2118096002088835.57587364-279235.575873638
2220280001798680.96254457229319.03745543
2319968001701259.93438262295540.065617385
2423712002145389.24301865225810.756981353
2517160001749394.59486281-33394.5948628134
2614352001282395.17515454152804.824845456
2715912001537884.8105853553315.1894146539
2811544001137279.6643795817120.3356204182
2916536001640050.4261127813549.5738872222
3012792001331875.58088575-52675.5808857456
3118096001796481.0293059913118.9706940132
3217160001632065.4114207483934.5885792614
3315288001744252.92555484-215452.925554837
3421840001930399.51644369253600.483556314
3519656001901679.6776311363920.3223688747
3622464002284763.43127703-38363.431277032
3716848001650437.8212225534362.1787774488
3815600001359097.13145651200902.868543494
3914040001527344.1579214-123344.157921404
4011544001094083.2936995160316.7063004931
4115288001596686.45081174-67886.4508117402
4213728001228720.97592813144079.02407187
4318720001759545.34199519112454.658004815
4418096001665991.58804574143608.411954256
4515600001508210.7731127251789.2268872836
4620904002136641.74499072-46241.7449907199
4719344001935379.90793802-979.90793802496
4824960002228002.34015692267997.659843076
4919968001670702.24810284326097.751897155
5012168001545371.94284458-328571.942844581
5112168001415027.44103294-198227.44103294
5212168001154554.9465062562245.0534937524
5314352001543399.70217979-108199.702179795
5414352001374260.281534160939.7184658975
5519344001878359.4148686956040.5851313123
5617784001815634.03344899-37234.033448993
5715912001572576.9309880818623.0690119159
5819968002111070.07866473-114270.078664733
5918408001950912.82750346-110112.827503464
6026520002489325.97347617162674.026523827
6120904001982625.00616112107774.99383888
6212168001248251.89550595-31451.8955059499
6312792001239511.8869963939688.1130036146
6410608001222167.38637453-161367.386374528
6514664001450852.1078312515547.8921687519
6616848001438726.30392746246073.696072541
6721216001941805.14175627179794.858243732
6820904001797229.35382365293170.646176349
6916848001614669.4699963470130.5300036597
7019656002037685.15962313-72085.1596231286
7117472001888599.84807855-141399.848078547
7224960002684565.01346091-188565.013460914
7319032002127349.60779324-224149.607793243
7415288001261887.64932227266912.350677733
7513728001324440.345018548359.6549815005
7610296001125050.92585428-95450.9258542773
7715288001521002.104829467797.89517054101
7818408001724772.50270559116027.497294412
7921528002168006.62167028-15206.6216702829
8020280002126668.87882254-98668.8788225418
8114976001732003.03089312-234403.030893123
8221528002015353.02759315137446.972406848
8316848001800456.72795788-115656.727957882
8425896002549550.4202711640049.5797288399
8521528001960127.14840359192672.851596411
8615600001553185.237441666814.76255833544
8714352001411912.9646921523287.0353078451
889672001079492.27195445-112292.271954451
8915288001569913.14953608-41113.1495360842
9014664001871991.35398141-405591.353981406
9122152002183740.7447702231459.2552297842
9222152002060618.87205088154581.127949123
9316848001540276.83651312144523.163486883
9421840002170189.0000817913810.999918208
9516224001720374.50913685-97974.5091368454
9625272002612601.09758554-85401.0975855449
9721528002160983.35670825-8183.35670824535
9815912001577493.6969051913706.3030948099
9912168001448039.69422153-231239.694221535
100842400982595.499780769-140195.499780769
10116536001532290.41517765121309.584822349
10215912001495600.3547506995599.6452493125
10320904002214695.0720958-124295.072095795
10424024002202214.03790245200185.962097545
10517784001672120.36564556106279.634354442
10619968002180008.61205841-183208.612058408
10714976001622309.55053232-124709.550532318
10825896002522535.2053581267064.7946418831







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092141535.791563041855548.274391032427523.30873504
1101576438.121872121290401.550855941862474.6928883
1111219248.68368841933101.772269131505395.59510768
112839979.106438694553636.1392878611126322.07358953
1131633325.228415371346676.192633291919974.26419744
1141572170.677621341285081.476258441859259.87898423
1152087278.807316821799591.573849362374966.04078428
1162375454.797338262086988.327903832663921.2667727
1171755758.300684361466308.618368342045207.98300039
1181993767.308161441703108.370392372284426.24593051
1191491117.987611871199002.543797611783233.43142614
1202569774.147093592275934.749101472863613.54508571

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2141535.79156304 & 1855548.27439103 & 2427523.30873504 \tabularnewline
110 & 1576438.12187212 & 1290401.55085594 & 1862474.6928883 \tabularnewline
111 & 1219248.68368841 & 933101.77226913 & 1505395.59510768 \tabularnewline
112 & 839979.106438694 & 553636.139287861 & 1126322.07358953 \tabularnewline
113 & 1633325.22841537 & 1346676.19263329 & 1919974.26419744 \tabularnewline
114 & 1572170.67762134 & 1285081.47625844 & 1859259.87898423 \tabularnewline
115 & 2087278.80731682 & 1799591.57384936 & 2374966.04078428 \tabularnewline
116 & 2375454.79733826 & 2086988.32790383 & 2663921.2667727 \tabularnewline
117 & 1755758.30068436 & 1466308.61836834 & 2045207.98300039 \tabularnewline
118 & 1993767.30816144 & 1703108.37039237 & 2284426.24593051 \tabularnewline
119 & 1491117.98761187 & 1199002.54379761 & 1783233.43142614 \tabularnewline
120 & 2569774.14709359 & 2275934.74910147 & 2863613.54508571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307519&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]109[/C][C]2141535.79156304[/C][C]1855548.27439103[/C][C]2427523.30873504[/C][/ROW]
[ROW][C]110[/C][C]1576438.12187212[/C][C]1290401.55085594[/C][C]1862474.6928883[/C][/ROW]
[ROW][C]111[/C][C]1219248.68368841[/C][C]933101.77226913[/C][C]1505395.59510768[/C][/ROW]
[ROW][C]112[/C][C]839979.106438694[/C][C]553636.139287861[/C][C]1126322.07358953[/C][/ROW]
[ROW][C]113[/C][C]1633325.22841537[/C][C]1346676.19263329[/C][C]1919974.26419744[/C][/ROW]
[ROW][C]114[/C][C]1572170.67762134[/C][C]1285081.47625844[/C][C]1859259.87898423[/C][/ROW]
[ROW][C]115[/C][C]2087278.80731682[/C][C]1799591.57384936[/C][C]2374966.04078428[/C][/ROW]
[ROW][C]116[/C][C]2375454.79733826[/C][C]2086988.32790383[/C][C]2663921.2667727[/C][/ROW]
[ROW][C]117[/C][C]1755758.30068436[/C][C]1466308.61836834[/C][C]2045207.98300039[/C][/ROW]
[ROW][C]118[/C][C]1993767.30816144[/C][C]1703108.37039237[/C][C]2284426.24593051[/C][/ROW]
[ROW][C]119[/C][C]1491117.98761187[/C][C]1199002.54379761[/C][C]1783233.43142614[/C][/ROW]
[ROW][C]120[/C][C]2569774.14709359[/C][C]2275934.74910147[/C][C]2863613.54508571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307519&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307519&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
1092141535.791563041855548.274391032427523.30873504
1101576438.121872121290401.550855941862474.6928883
1111219248.68368841933101.772269131505395.59510768
112839979.106438694553636.1392878611126322.07358953
1131633325.228415371346676.192633291919974.26419744
1141572170.677621341285081.476258441859259.87898423
1152087278.807316821799591.573849362374966.04078428
1162375454.797338262086988.327903832663921.2667727
1171755758.300684361466308.618368342045207.98300039
1181993767.308161441703108.370392372284426.24593051
1191491117.987611871199002.543797611783233.43142614
1202569774.147093592275934.749101472863613.54508571



Parameters (Session):
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')