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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 12 May 2014 08:25:39 -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/2014/May/12/t13998975888mwpd8524c77urc.htm/, Retrieved Wed, 15 May 2024 21:51:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234826, Retrieved Wed, 15 May 2024 21:51:11 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Buitenlandse reiz...] [2014-05-12 12:25:39] [0ade3821d8a7c4193aad47ee0feb583e] [Current]
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Dataseries X:
 107,00 
 116,14 
 117,18 
 102,28 
 109,43 
 114,28 
 117,39 
 116,66 
 114,29 
 114,18 
 114,12 
 122,62 
 115,70 
 127,91 
 119,55 
 115,08 
 116,63 
 121,38 
 123,41 
 120,70 
 119,40 
 116,83 
 116,40 
 121,67 
 116,54 
 129,61 
 119,93 
 117,64 
 121,01 
 124,20 
 125,23 
 123,24 
 121,58 
 120,89 
 117,77 
 110,91 
 124,23 
 127,70 
 129,45 
 120,13 
 122,02 
 126,59 
 126,34 
 125,15 
 125,02 
 124,40 
 127,55 
 126,63 
 130,18 
 136,95 
 136,81 
 129,59 
 133,37 
 140,02 
 139,67 
 139,99 
 134,57 
 134,41 
 134,99 
 135,70 




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234826&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234826&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234826&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.270437711727145
beta0
gamma0.619260149294389

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.270437711727145 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.619260149294389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234826&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]0.270437711727145[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.619260149294389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234826&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234826&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
alpha0.270437711727145
beta0
gamma0.619260149294389







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13115.7111.7374385683763.96256143162397
14127.91125.1095177031012.80048229689923
15119.55117.6352434824511.91475651754867
16115.08113.8693522754831.21064772451673
17116.63116.0509601643870.579039835612662
18121.38121.411757461107-0.0317574611073752
19123.41123.3573721345730.0526278654266576
20120.7122.29830778265-1.59830778265049
21119.4119.416518171853-0.0165181718529226
22116.83119.179587457167-2.34958745716651
23116.4118.160456823659-1.76045682365901
24121.67126.098149330586-4.42814933058565
25116.54119.733804925425-3.1938049254252
26129.61130.645518320575-1.03551832057462
27119.93121.733683838106-1.80368383810584
28117.64116.6440776271870.995922372813254
29121.01118.4822622805652.52773771943498
30124.2124.0941095646150.105890435384794
31125.23126.115073769996-0.885073769995515
32123.24124.05654521307-0.816545213069645
33121.58122.100808594368-0.520808594367949
34120.89120.673444038760.21655596124036
35117.77120.614458011618-2.84445801161824
36110.91127.053761983756-16.1437619837563
37124.23118.0787371424226.15126285757792
38127.7132.492799111275-4.79279911127479
39129.45122.2178055924837.2321944075172
40120.13120.836672492594-0.706672492593597
41122.02122.906468382818-0.886468382818038
42126.59126.5008219781060.0891780218935594
43126.34128.069559936343-1.72955993634346
44125.15125.813610911038-0.663610911037495
45125.02124.0328440023480.987155997651897
46124.4123.3464230261271.05357697387286
47127.55122.1308670589175.41913294108323
48126.63124.7964803908941.83351960910591
49130.18130.755834115074-0.575834115073661
50136.95138.406230183817-1.45623018381673
51136.81134.4663287426032.34367125739743
52129.59128.1764630688181.41353693118245
53133.37130.7384137652312.63158623476858
54140.02135.724968169744.29503183026011
55139.67137.6094420743382.06055792566167
56139.99136.8600677367693.12993226323121
57134.57136.851016049329-2.28101604932922
58134.41135.310766359758-0.900766359758109
59134.99135.538991770298-0.548991770298187
60135.7134.9706589826520.729341017348474

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 115.7 & 111.737438568376 & 3.96256143162397 \tabularnewline
14 & 127.91 & 125.109517703101 & 2.80048229689923 \tabularnewline
15 & 119.55 & 117.635243482451 & 1.91475651754867 \tabularnewline
16 & 115.08 & 113.869352275483 & 1.21064772451673 \tabularnewline
17 & 116.63 & 116.050960164387 & 0.579039835612662 \tabularnewline
18 & 121.38 & 121.411757461107 & -0.0317574611073752 \tabularnewline
19 & 123.41 & 123.357372134573 & 0.0526278654266576 \tabularnewline
20 & 120.7 & 122.29830778265 & -1.59830778265049 \tabularnewline
21 & 119.4 & 119.416518171853 & -0.0165181718529226 \tabularnewline
22 & 116.83 & 119.179587457167 & -2.34958745716651 \tabularnewline
23 & 116.4 & 118.160456823659 & -1.76045682365901 \tabularnewline
24 & 121.67 & 126.098149330586 & -4.42814933058565 \tabularnewline
25 & 116.54 & 119.733804925425 & -3.1938049254252 \tabularnewline
26 & 129.61 & 130.645518320575 & -1.03551832057462 \tabularnewline
27 & 119.93 & 121.733683838106 & -1.80368383810584 \tabularnewline
28 & 117.64 & 116.644077627187 & 0.995922372813254 \tabularnewline
29 & 121.01 & 118.482262280565 & 2.52773771943498 \tabularnewline
30 & 124.2 & 124.094109564615 & 0.105890435384794 \tabularnewline
31 & 125.23 & 126.115073769996 & -0.885073769995515 \tabularnewline
32 & 123.24 & 124.05654521307 & -0.816545213069645 \tabularnewline
33 & 121.58 & 122.100808594368 & -0.520808594367949 \tabularnewline
34 & 120.89 & 120.67344403876 & 0.21655596124036 \tabularnewline
35 & 117.77 & 120.614458011618 & -2.84445801161824 \tabularnewline
36 & 110.91 & 127.053761983756 & -16.1437619837563 \tabularnewline
37 & 124.23 & 118.078737142422 & 6.15126285757792 \tabularnewline
38 & 127.7 & 132.492799111275 & -4.79279911127479 \tabularnewline
39 & 129.45 & 122.217805592483 & 7.2321944075172 \tabularnewline
40 & 120.13 & 120.836672492594 & -0.706672492593597 \tabularnewline
41 & 122.02 & 122.906468382818 & -0.886468382818038 \tabularnewline
42 & 126.59 & 126.500821978106 & 0.0891780218935594 \tabularnewline
43 & 126.34 & 128.069559936343 & -1.72955993634346 \tabularnewline
44 & 125.15 & 125.813610911038 & -0.663610911037495 \tabularnewline
45 & 125.02 & 124.032844002348 & 0.987155997651897 \tabularnewline
46 & 124.4 & 123.346423026127 & 1.05357697387286 \tabularnewline
47 & 127.55 & 122.130867058917 & 5.41913294108323 \tabularnewline
48 & 126.63 & 124.796480390894 & 1.83351960910591 \tabularnewline
49 & 130.18 & 130.755834115074 & -0.575834115073661 \tabularnewline
50 & 136.95 & 138.406230183817 & -1.45623018381673 \tabularnewline
51 & 136.81 & 134.466328742603 & 2.34367125739743 \tabularnewline
52 & 129.59 & 128.176463068818 & 1.41353693118245 \tabularnewline
53 & 133.37 & 130.738413765231 & 2.63158623476858 \tabularnewline
54 & 140.02 & 135.72496816974 & 4.29503183026011 \tabularnewline
55 & 139.67 & 137.609442074338 & 2.06055792566167 \tabularnewline
56 & 139.99 & 136.860067736769 & 3.12993226323121 \tabularnewline
57 & 134.57 & 136.851016049329 & -2.28101604932922 \tabularnewline
58 & 134.41 & 135.310766359758 & -0.900766359758109 \tabularnewline
59 & 134.99 & 135.538991770298 & -0.548991770298187 \tabularnewline
60 & 135.7 & 134.970658982652 & 0.729341017348474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234826&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]115.7[/C][C]111.737438568376[/C][C]3.96256143162397[/C][/ROW]
[ROW][C]14[/C][C]127.91[/C][C]125.109517703101[/C][C]2.80048229689923[/C][/ROW]
[ROW][C]15[/C][C]119.55[/C][C]117.635243482451[/C][C]1.91475651754867[/C][/ROW]
[ROW][C]16[/C][C]115.08[/C][C]113.869352275483[/C][C]1.21064772451673[/C][/ROW]
[ROW][C]17[/C][C]116.63[/C][C]116.050960164387[/C][C]0.579039835612662[/C][/ROW]
[ROW][C]18[/C][C]121.38[/C][C]121.411757461107[/C][C]-0.0317574611073752[/C][/ROW]
[ROW][C]19[/C][C]123.41[/C][C]123.357372134573[/C][C]0.0526278654266576[/C][/ROW]
[ROW][C]20[/C][C]120.7[/C][C]122.29830778265[/C][C]-1.59830778265049[/C][/ROW]
[ROW][C]21[/C][C]119.4[/C][C]119.416518171853[/C][C]-0.0165181718529226[/C][/ROW]
[ROW][C]22[/C][C]116.83[/C][C]119.179587457167[/C][C]-2.34958745716651[/C][/ROW]
[ROW][C]23[/C][C]116.4[/C][C]118.160456823659[/C][C]-1.76045682365901[/C][/ROW]
[ROW][C]24[/C][C]121.67[/C][C]126.098149330586[/C][C]-4.42814933058565[/C][/ROW]
[ROW][C]25[/C][C]116.54[/C][C]119.733804925425[/C][C]-3.1938049254252[/C][/ROW]
[ROW][C]26[/C][C]129.61[/C][C]130.645518320575[/C][C]-1.03551832057462[/C][/ROW]
[ROW][C]27[/C][C]119.93[/C][C]121.733683838106[/C][C]-1.80368383810584[/C][/ROW]
[ROW][C]28[/C][C]117.64[/C][C]116.644077627187[/C][C]0.995922372813254[/C][/ROW]
[ROW][C]29[/C][C]121.01[/C][C]118.482262280565[/C][C]2.52773771943498[/C][/ROW]
[ROW][C]30[/C][C]124.2[/C][C]124.094109564615[/C][C]0.105890435384794[/C][/ROW]
[ROW][C]31[/C][C]125.23[/C][C]126.115073769996[/C][C]-0.885073769995515[/C][/ROW]
[ROW][C]32[/C][C]123.24[/C][C]124.05654521307[/C][C]-0.816545213069645[/C][/ROW]
[ROW][C]33[/C][C]121.58[/C][C]122.100808594368[/C][C]-0.520808594367949[/C][/ROW]
[ROW][C]34[/C][C]120.89[/C][C]120.67344403876[/C][C]0.21655596124036[/C][/ROW]
[ROW][C]35[/C][C]117.77[/C][C]120.614458011618[/C][C]-2.84445801161824[/C][/ROW]
[ROW][C]36[/C][C]110.91[/C][C]127.053761983756[/C][C]-16.1437619837563[/C][/ROW]
[ROW][C]37[/C][C]124.23[/C][C]118.078737142422[/C][C]6.15126285757792[/C][/ROW]
[ROW][C]38[/C][C]127.7[/C][C]132.492799111275[/C][C]-4.79279911127479[/C][/ROW]
[ROW][C]39[/C][C]129.45[/C][C]122.217805592483[/C][C]7.2321944075172[/C][/ROW]
[ROW][C]40[/C][C]120.13[/C][C]120.836672492594[/C][C]-0.706672492593597[/C][/ROW]
[ROW][C]41[/C][C]122.02[/C][C]122.906468382818[/C][C]-0.886468382818038[/C][/ROW]
[ROW][C]42[/C][C]126.59[/C][C]126.500821978106[/C][C]0.0891780218935594[/C][/ROW]
[ROW][C]43[/C][C]126.34[/C][C]128.069559936343[/C][C]-1.72955993634346[/C][/ROW]
[ROW][C]44[/C][C]125.15[/C][C]125.813610911038[/C][C]-0.663610911037495[/C][/ROW]
[ROW][C]45[/C][C]125.02[/C][C]124.032844002348[/C][C]0.987155997651897[/C][/ROW]
[ROW][C]46[/C][C]124.4[/C][C]123.346423026127[/C][C]1.05357697387286[/C][/ROW]
[ROW][C]47[/C][C]127.55[/C][C]122.130867058917[/C][C]5.41913294108323[/C][/ROW]
[ROW][C]48[/C][C]126.63[/C][C]124.796480390894[/C][C]1.83351960910591[/C][/ROW]
[ROW][C]49[/C][C]130.18[/C][C]130.755834115074[/C][C]-0.575834115073661[/C][/ROW]
[ROW][C]50[/C][C]136.95[/C][C]138.406230183817[/C][C]-1.45623018381673[/C][/ROW]
[ROW][C]51[/C][C]136.81[/C][C]134.466328742603[/C][C]2.34367125739743[/C][/ROW]
[ROW][C]52[/C][C]129.59[/C][C]128.176463068818[/C][C]1.41353693118245[/C][/ROW]
[ROW][C]53[/C][C]133.37[/C][C]130.738413765231[/C][C]2.63158623476858[/C][/ROW]
[ROW][C]54[/C][C]140.02[/C][C]135.72496816974[/C][C]4.29503183026011[/C][/ROW]
[ROW][C]55[/C][C]139.67[/C][C]137.609442074338[/C][C]2.06055792566167[/C][/ROW]
[ROW][C]56[/C][C]139.99[/C][C]136.860067736769[/C][C]3.12993226323121[/C][/ROW]
[ROW][C]57[/C][C]134.57[/C][C]136.851016049329[/C][C]-2.28101604932922[/C][/ROW]
[ROW][C]58[/C][C]134.41[/C][C]135.310766359758[/C][C]-0.900766359758109[/C][/ROW]
[ROW][C]59[/C][C]134.99[/C][C]135.538991770298[/C][C]-0.548991770298187[/C][/ROW]
[ROW][C]60[/C][C]135.7[/C][C]134.970658982652[/C][C]0.729341017348474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234826&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234826&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
13115.7111.7374385683763.96256143162397
14127.91125.1095177031012.80048229689923
15119.55117.6352434824511.91475651754867
16115.08113.8693522754831.21064772451673
17116.63116.0509601643870.579039835612662
18121.38121.411757461107-0.0317574611073752
19123.41123.3573721345730.0526278654266576
20120.7122.29830778265-1.59830778265049
21119.4119.416518171853-0.0165181718529226
22116.83119.179587457167-2.34958745716651
23116.4118.160456823659-1.76045682365901
24121.67126.098149330586-4.42814933058565
25116.54119.733804925425-3.1938049254252
26129.61130.645518320575-1.03551832057462
27119.93121.733683838106-1.80368383810584
28117.64116.6440776271870.995922372813254
29121.01118.4822622805652.52773771943498
30124.2124.0941095646150.105890435384794
31125.23126.115073769996-0.885073769995515
32123.24124.05654521307-0.816545213069645
33121.58122.100808594368-0.520808594367949
34120.89120.673444038760.21655596124036
35117.77120.614458011618-2.84445801161824
36110.91127.053761983756-16.1437619837563
37124.23118.0787371424226.15126285757792
38127.7132.492799111275-4.79279911127479
39129.45122.2178055924837.2321944075172
40120.13120.836672492594-0.706672492593597
41122.02122.906468382818-0.886468382818038
42126.59126.5008219781060.0891780218935594
43126.34128.069559936343-1.72955993634346
44125.15125.813610911038-0.663610911037495
45125.02124.0328440023480.987155997651897
46124.4123.3464230261271.05357697387286
47127.55122.1308670589175.41913294108323
48126.63124.7964803908941.83351960910591
49130.18130.755834115074-0.575834115073661
50136.95138.406230183817-1.45623018381673
51136.81134.4663287426032.34367125739743
52129.59128.1764630688181.41353693118245
53133.37130.7384137652312.63158623476858
54140.02135.724968169744.29503183026011
55139.67137.6094420743382.06055792566167
56139.99136.8600677367693.12993226323121
57134.57136.851016049329-2.28101604932922
58134.41135.310766359758-0.900766359758109
59134.99135.538991770298-0.548991770298187
60135.7134.9706589826520.729341017348474







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61139.5428820231132.771508687729146.314255358472
62146.951252223447139.936630536546153.965873910347
63145.121923449042137.872210491021152.371636407063
64137.778016364333130.300599795955145.255432932711
65140.507994463641132.809606379087148.206382548195
66145.534394883818137.621203387098153.447586380538
67145.247819809257137.125503623148153.370135995365
68144.424324305243136.098134252735152.750514357751
69141.124214774717132.599024961356149.649404588079
70140.824419268051132.104770082608149.544068453494
71141.455173709503132.545308251453150.365039167553
72141.612845502009132.516740673902150.708950330116

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 139.5428820231 & 132.771508687729 & 146.314255358472 \tabularnewline
62 & 146.951252223447 & 139.936630536546 & 153.965873910347 \tabularnewline
63 & 145.121923449042 & 137.872210491021 & 152.371636407063 \tabularnewline
64 & 137.778016364333 & 130.300599795955 & 145.255432932711 \tabularnewline
65 & 140.507994463641 & 132.809606379087 & 148.206382548195 \tabularnewline
66 & 145.534394883818 & 137.621203387098 & 153.447586380538 \tabularnewline
67 & 145.247819809257 & 137.125503623148 & 153.370135995365 \tabularnewline
68 & 144.424324305243 & 136.098134252735 & 152.750514357751 \tabularnewline
69 & 141.124214774717 & 132.599024961356 & 149.649404588079 \tabularnewline
70 & 140.824419268051 & 132.104770082608 & 149.544068453494 \tabularnewline
71 & 141.455173709503 & 132.545308251453 & 150.365039167553 \tabularnewline
72 & 141.612845502009 & 132.516740673902 & 150.708950330116 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234826&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]61[/C][C]139.5428820231[/C][C]132.771508687729[/C][C]146.314255358472[/C][/ROW]
[ROW][C]62[/C][C]146.951252223447[/C][C]139.936630536546[/C][C]153.965873910347[/C][/ROW]
[ROW][C]63[/C][C]145.121923449042[/C][C]137.872210491021[/C][C]152.371636407063[/C][/ROW]
[ROW][C]64[/C][C]137.778016364333[/C][C]130.300599795955[/C][C]145.255432932711[/C][/ROW]
[ROW][C]65[/C][C]140.507994463641[/C][C]132.809606379087[/C][C]148.206382548195[/C][/ROW]
[ROW][C]66[/C][C]145.534394883818[/C][C]137.621203387098[/C][C]153.447586380538[/C][/ROW]
[ROW][C]67[/C][C]145.247819809257[/C][C]137.125503623148[/C][C]153.370135995365[/C][/ROW]
[ROW][C]68[/C][C]144.424324305243[/C][C]136.098134252735[/C][C]152.750514357751[/C][/ROW]
[ROW][C]69[/C][C]141.124214774717[/C][C]132.599024961356[/C][C]149.649404588079[/C][/ROW]
[ROW][C]70[/C][C]140.824419268051[/C][C]132.104770082608[/C][C]149.544068453494[/C][/ROW]
[ROW][C]71[/C][C]141.455173709503[/C][C]132.545308251453[/C][C]150.365039167553[/C][/ROW]
[ROW][C]72[/C][C]141.612845502009[/C][C]132.516740673902[/C][C]150.708950330116[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234826&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234826&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
61139.5428820231132.771508687729146.314255358472
62146.951252223447139.936630536546153.965873910347
63145.121923449042137.872210491021152.371636407063
64137.778016364333130.300599795955145.255432932711
65140.507994463641132.809606379087148.206382548195
66145.534394883818137.621203387098153.447586380538
67145.247819809257137.125503623148153.370135995365
68144.424324305243136.098134252735152.750514357751
69141.124214774717132.599024961356149.649404588079
70140.824419268051132.104770082608149.544068453494
71141.455173709503132.545308251453150.365039167553
72141.612845502009132.516740673902150.708950330116



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')