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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 computationTue, 15 Dec 2015 11:10:12 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/15/t1450178371dq4hu0abzslrao9.htm/, Retrieved Sat, 18 May 2024 16:47:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286467, Retrieved Sat, 18 May 2024 16:47:27 +0000
QR Codes:

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] [Triple exponentia...] [2015-12-15 11:10:12] [6c9172abf40f1c7e1d0d83ef980264f4] [Current]
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Dataseries X:
20.7
20.7
20.7
18
18
18
16.9
16.9
16.9
24.4
24.4
24.4
15.5
15.5
15.5
18.4
18.4
18.4
16.2
16.2
16.2
20.6
20.6
20.6
19.8
19.8
19.8
21.6
21.6
21.6
22.3
22.3
22.3
23.7
23.7
23.7
22.1
22.1
22.1
26.6
26.6
26.6
23.5
23.5
23.5
19.6
19.6
19.6
20
20
20
20.1
20.1
20.1
16
16
16
18.9
18.9
18.9




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=286467&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=286467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286467&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
alpha0.406419506680217
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.406419506680217 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286467&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]0.406419506680217[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286467&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
alpha0.406419506680217
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315.516.0995993589744-0.599599358974384
1415.515.7889378725716-0.288937872571625
1515.515.6045352742172-0.104535274217225
1618.418.5242441555832-0.124244155583234
1718.418.6651096297739-0.265109629773917
1818.418.7487246274357-0.348724627435743
1916.215.03169019233011.16830980766988
2016.215.81454147729040.385458522709643
2116.216.2792267292131-0.0792267292130866
2220.623.8217214969545-3.22172149695447
2320.622.3537117581119-1.7537117581119
2420.621.4823298131315-0.882329813131491
2519.811.75501733839928.04498266160084
2619.815.14208521060974.65791478939033
2719.817.07763781605022.72236218394978
2821.621.1345541602760.465445839723994
2921.621.43146615379190.168533846208117
3021.621.6416900874764-0.0416900874763826
3122.318.94992252700793.35007747299208
3222.320.15480149827652.14519850172347
3322.321.05885130328081.24114869671921
3423.727.2726488057715-3.5726488057715
3523.726.5333973081793-2.83339730817931
3623.725.7404454193422-2.04044541934217
3722.120.84153071402651.2584692859735
3822.119.45992974954152.64007025045845
3922.119.42648470252822.67351529747176
4026.622.12388720226174.47611279773826
4126.623.87457131472872.72542868527129
4226.624.99918236127441.60081763872561
4323.524.9882490423763-1.48824904237629
4423.523.5115450839548-0.0115450839548252
4523.523.00242589559190.497574104408088
4619.626.0566438828256-6.45664388282561
4719.624.5840857973771-4.98408579737708
4819.623.3877329270922-3.78773292709216
492019.73685791304940.263142086950602
502018.77082794142221.22917205857778
512018.1838186747941.81618132520598
5220.121.6027706379243-1.50277063792427
5320.119.88434795484550.215652045154499
5420.119.32138963763590.778610362364081
551617.1426855186239-1.14268551862391
561616.6829679811797-0.682967981179651
571616.2031726491398-0.203172649139848
5818.914.84470534297334.05529465702665
5918.918.51848588794690.38151411205309
6018.920.2129492128243-1.31294921282428

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15.5 & 16.0995993589744 & -0.599599358974384 \tabularnewline
14 & 15.5 & 15.7889378725716 & -0.288937872571625 \tabularnewline
15 & 15.5 & 15.6045352742172 & -0.104535274217225 \tabularnewline
16 & 18.4 & 18.5242441555832 & -0.124244155583234 \tabularnewline
17 & 18.4 & 18.6651096297739 & -0.265109629773917 \tabularnewline
18 & 18.4 & 18.7487246274357 & -0.348724627435743 \tabularnewline
19 & 16.2 & 15.0316901923301 & 1.16830980766988 \tabularnewline
20 & 16.2 & 15.8145414772904 & 0.385458522709643 \tabularnewline
21 & 16.2 & 16.2792267292131 & -0.0792267292130866 \tabularnewline
22 & 20.6 & 23.8217214969545 & -3.22172149695447 \tabularnewline
23 & 20.6 & 22.3537117581119 & -1.7537117581119 \tabularnewline
24 & 20.6 & 21.4823298131315 & -0.882329813131491 \tabularnewline
25 & 19.8 & 11.7550173383992 & 8.04498266160084 \tabularnewline
26 & 19.8 & 15.1420852106097 & 4.65791478939033 \tabularnewline
27 & 19.8 & 17.0776378160502 & 2.72236218394978 \tabularnewline
28 & 21.6 & 21.134554160276 & 0.465445839723994 \tabularnewline
29 & 21.6 & 21.4314661537919 & 0.168533846208117 \tabularnewline
30 & 21.6 & 21.6416900874764 & -0.0416900874763826 \tabularnewline
31 & 22.3 & 18.9499225270079 & 3.35007747299208 \tabularnewline
32 & 22.3 & 20.1548014982765 & 2.14519850172347 \tabularnewline
33 & 22.3 & 21.0588513032808 & 1.24114869671921 \tabularnewline
34 & 23.7 & 27.2726488057715 & -3.5726488057715 \tabularnewline
35 & 23.7 & 26.5333973081793 & -2.83339730817931 \tabularnewline
36 & 23.7 & 25.7404454193422 & -2.04044541934217 \tabularnewline
37 & 22.1 & 20.8415307140265 & 1.2584692859735 \tabularnewline
38 & 22.1 & 19.4599297495415 & 2.64007025045845 \tabularnewline
39 & 22.1 & 19.4264847025282 & 2.67351529747176 \tabularnewline
40 & 26.6 & 22.1238872022617 & 4.47611279773826 \tabularnewline
41 & 26.6 & 23.8745713147287 & 2.72542868527129 \tabularnewline
42 & 26.6 & 24.9991823612744 & 1.60081763872561 \tabularnewline
43 & 23.5 & 24.9882490423763 & -1.48824904237629 \tabularnewline
44 & 23.5 & 23.5115450839548 & -0.0115450839548252 \tabularnewline
45 & 23.5 & 23.0024258955919 & 0.497574104408088 \tabularnewline
46 & 19.6 & 26.0566438828256 & -6.45664388282561 \tabularnewline
47 & 19.6 & 24.5840857973771 & -4.98408579737708 \tabularnewline
48 & 19.6 & 23.3877329270922 & -3.78773292709216 \tabularnewline
49 & 20 & 19.7368579130494 & 0.263142086950602 \tabularnewline
50 & 20 & 18.7708279414222 & 1.22917205857778 \tabularnewline
51 & 20 & 18.183818674794 & 1.81618132520598 \tabularnewline
52 & 20.1 & 21.6027706379243 & -1.50277063792427 \tabularnewline
53 & 20.1 & 19.8843479548455 & 0.215652045154499 \tabularnewline
54 & 20.1 & 19.3213896376359 & 0.778610362364081 \tabularnewline
55 & 16 & 17.1426855186239 & -1.14268551862391 \tabularnewline
56 & 16 & 16.6829679811797 & -0.682967981179651 \tabularnewline
57 & 16 & 16.2031726491398 & -0.203172649139848 \tabularnewline
58 & 18.9 & 14.8447053429733 & 4.05529465702665 \tabularnewline
59 & 18.9 & 18.5184858879469 & 0.38151411205309 \tabularnewline
60 & 18.9 & 20.2129492128243 & -1.31294921282428 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286467&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]15.5[/C][C]16.0995993589744[/C][C]-0.599599358974384[/C][/ROW]
[ROW][C]14[/C][C]15.5[/C][C]15.7889378725716[/C][C]-0.288937872571625[/C][/ROW]
[ROW][C]15[/C][C]15.5[/C][C]15.6045352742172[/C][C]-0.104535274217225[/C][/ROW]
[ROW][C]16[/C][C]18.4[/C][C]18.5242441555832[/C][C]-0.124244155583234[/C][/ROW]
[ROW][C]17[/C][C]18.4[/C][C]18.6651096297739[/C][C]-0.265109629773917[/C][/ROW]
[ROW][C]18[/C][C]18.4[/C][C]18.7487246274357[/C][C]-0.348724627435743[/C][/ROW]
[ROW][C]19[/C][C]16.2[/C][C]15.0316901923301[/C][C]1.16830980766988[/C][/ROW]
[ROW][C]20[/C][C]16.2[/C][C]15.8145414772904[/C][C]0.385458522709643[/C][/ROW]
[ROW][C]21[/C][C]16.2[/C][C]16.2792267292131[/C][C]-0.0792267292130866[/C][/ROW]
[ROW][C]22[/C][C]20.6[/C][C]23.8217214969545[/C][C]-3.22172149695447[/C][/ROW]
[ROW][C]23[/C][C]20.6[/C][C]22.3537117581119[/C][C]-1.7537117581119[/C][/ROW]
[ROW][C]24[/C][C]20.6[/C][C]21.4823298131315[/C][C]-0.882329813131491[/C][/ROW]
[ROW][C]25[/C][C]19.8[/C][C]11.7550173383992[/C][C]8.04498266160084[/C][/ROW]
[ROW][C]26[/C][C]19.8[/C][C]15.1420852106097[/C][C]4.65791478939033[/C][/ROW]
[ROW][C]27[/C][C]19.8[/C][C]17.0776378160502[/C][C]2.72236218394978[/C][/ROW]
[ROW][C]28[/C][C]21.6[/C][C]21.134554160276[/C][C]0.465445839723994[/C][/ROW]
[ROW][C]29[/C][C]21.6[/C][C]21.4314661537919[/C][C]0.168533846208117[/C][/ROW]
[ROW][C]30[/C][C]21.6[/C][C]21.6416900874764[/C][C]-0.0416900874763826[/C][/ROW]
[ROW][C]31[/C][C]22.3[/C][C]18.9499225270079[/C][C]3.35007747299208[/C][/ROW]
[ROW][C]32[/C][C]22.3[/C][C]20.1548014982765[/C][C]2.14519850172347[/C][/ROW]
[ROW][C]33[/C][C]22.3[/C][C]21.0588513032808[/C][C]1.24114869671921[/C][/ROW]
[ROW][C]34[/C][C]23.7[/C][C]27.2726488057715[/C][C]-3.5726488057715[/C][/ROW]
[ROW][C]35[/C][C]23.7[/C][C]26.5333973081793[/C][C]-2.83339730817931[/C][/ROW]
[ROW][C]36[/C][C]23.7[/C][C]25.7404454193422[/C][C]-2.04044541934217[/C][/ROW]
[ROW][C]37[/C][C]22.1[/C][C]20.8415307140265[/C][C]1.2584692859735[/C][/ROW]
[ROW][C]38[/C][C]22.1[/C][C]19.4599297495415[/C][C]2.64007025045845[/C][/ROW]
[ROW][C]39[/C][C]22.1[/C][C]19.4264847025282[/C][C]2.67351529747176[/C][/ROW]
[ROW][C]40[/C][C]26.6[/C][C]22.1238872022617[/C][C]4.47611279773826[/C][/ROW]
[ROW][C]41[/C][C]26.6[/C][C]23.8745713147287[/C][C]2.72542868527129[/C][/ROW]
[ROW][C]42[/C][C]26.6[/C][C]24.9991823612744[/C][C]1.60081763872561[/C][/ROW]
[ROW][C]43[/C][C]23.5[/C][C]24.9882490423763[/C][C]-1.48824904237629[/C][/ROW]
[ROW][C]44[/C][C]23.5[/C][C]23.5115450839548[/C][C]-0.0115450839548252[/C][/ROW]
[ROW][C]45[/C][C]23.5[/C][C]23.0024258955919[/C][C]0.497574104408088[/C][/ROW]
[ROW][C]46[/C][C]19.6[/C][C]26.0566438828256[/C][C]-6.45664388282561[/C][/ROW]
[ROW][C]47[/C][C]19.6[/C][C]24.5840857973771[/C][C]-4.98408579737708[/C][/ROW]
[ROW][C]48[/C][C]19.6[/C][C]23.3877329270922[/C][C]-3.78773292709216[/C][/ROW]
[ROW][C]49[/C][C]20[/C][C]19.7368579130494[/C][C]0.263142086950602[/C][/ROW]
[ROW][C]50[/C][C]20[/C][C]18.7708279414222[/C][C]1.22917205857778[/C][/ROW]
[ROW][C]51[/C][C]20[/C][C]18.183818674794[/C][C]1.81618132520598[/C][/ROW]
[ROW][C]52[/C][C]20.1[/C][C]21.6027706379243[/C][C]-1.50277063792427[/C][/ROW]
[ROW][C]53[/C][C]20.1[/C][C]19.8843479548455[/C][C]0.215652045154499[/C][/ROW]
[ROW][C]54[/C][C]20.1[/C][C]19.3213896376359[/C][C]0.778610362364081[/C][/ROW]
[ROW][C]55[/C][C]16[/C][C]17.1426855186239[/C][C]-1.14268551862391[/C][/ROW]
[ROW][C]56[/C][C]16[/C][C]16.6829679811797[/C][C]-0.682967981179651[/C][/ROW]
[ROW][C]57[/C][C]16[/C][C]16.2031726491398[/C][C]-0.203172649139848[/C][/ROW]
[ROW][C]58[/C][C]18.9[/C][C]14.8447053429733[/C][C]4.05529465702665[/C][/ROW]
[ROW][C]59[/C][C]18.9[/C][C]18.5184858879469[/C][C]0.38151411205309[/C][/ROW]
[ROW][C]60[/C][C]18.9[/C][C]20.2129492128243[/C][C]-1.31294921282428[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286467&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286467&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
1315.516.0995993589744-0.599599358974384
1415.515.7889378725716-0.288937872571625
1515.515.6045352742172-0.104535274217225
1618.418.5242441555832-0.124244155583234
1718.418.6651096297739-0.265109629773917
1818.418.7487246274357-0.348724627435743
1916.215.03169019233011.16830980766988
2016.215.81454147729040.385458522709643
2116.216.2792267292131-0.0792267292130866
2220.623.8217214969545-3.22172149695447
2320.622.3537117581119-1.7537117581119
2420.621.4823298131315-0.882329813131491
2519.811.75501733839928.04498266160084
2619.815.14208521060974.65791478939033
2719.817.07763781605022.72236218394978
2821.621.1345541602760.465445839723994
2921.621.43146615379190.168533846208117
3021.621.6416900874764-0.0416900874763826
3122.318.94992252700793.35007747299208
3222.320.15480149827652.14519850172347
3322.321.05885130328081.24114869671921
3423.727.2726488057715-3.5726488057715
3523.726.5333973081793-2.83339730817931
3623.725.7404454193422-2.04044541934217
3722.120.84153071402651.2584692859735
3822.119.45992974954152.64007025045845
3922.119.42648470252822.67351529747176
4026.622.12388720226174.47611279773826
4126.623.87457131472872.72542868527129
4226.624.99918236127441.60081763872561
4323.524.9882490423763-1.48824904237629
4423.523.5115450839548-0.0115450839548252
4523.523.00242589559190.497574104408088
4619.626.0566438828256-6.45664388282561
4719.624.5840857973771-4.98408579737708
4819.623.3877329270922-3.78773292709216
492019.73685791304940.263142086950602
502018.77082794142221.22917205857778
512018.1838186747941.81618132520598
5220.121.6027706379243-1.50277063792427
5320.119.88434795484550.215652045154499
5420.119.32138963763590.778610362364081
551617.1426855186239-1.14268551862391
561616.6829679811797-0.682967981179651
571616.2031726491398-0.203172649139848
5818.914.84470534297334.05529465702665
5918.918.51848588794690.38151411205309
6018.920.2129492128243-1.31294921282428







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6119.972394964286814.961829688857924.9829602397156
6219.472835462614514.064263138243724.8814077869853
6318.734703944382512.955470016207624.5139378725573
6419.445459245701213.317944659412225.5729738319901
6519.357814047894912.900777172221925.8148509235679
6619.041371608526812.270831347778225.8119118692754
6715.40578129329658.3356253097955622.4759372767975
6815.6833528032868.325771961755823.0409336448161
6915.76592613112038.131734225733823.4001180365068
7017.01777527716869.1166502777216524.9189002766155
7116.86272049995648.7033904744272325.0220505254856
7217.39632867132878.9867177008901825.8059396417671

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 19.9723949642868 & 14.9618296888579 & 24.9829602397156 \tabularnewline
62 & 19.4728354626145 & 14.0642631382437 & 24.8814077869853 \tabularnewline
63 & 18.7347039443825 & 12.9554700162076 & 24.5139378725573 \tabularnewline
64 & 19.4454592457012 & 13.3179446594122 & 25.5729738319901 \tabularnewline
65 & 19.3578140478949 & 12.9007771722219 & 25.8148509235679 \tabularnewline
66 & 19.0413716085268 & 12.2708313477782 & 25.8119118692754 \tabularnewline
67 & 15.4057812932965 & 8.33562530979556 & 22.4759372767975 \tabularnewline
68 & 15.683352803286 & 8.3257719617558 & 23.0409336448161 \tabularnewline
69 & 15.7659261311203 & 8.1317342257338 & 23.4001180365068 \tabularnewline
70 & 17.0177752771686 & 9.11665027772165 & 24.9189002766155 \tabularnewline
71 & 16.8627204999564 & 8.70339047442723 & 25.0220505254856 \tabularnewline
72 & 17.3963286713287 & 8.98671770089018 & 25.8059396417671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286467&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]19.9723949642868[/C][C]14.9618296888579[/C][C]24.9829602397156[/C][/ROW]
[ROW][C]62[/C][C]19.4728354626145[/C][C]14.0642631382437[/C][C]24.8814077869853[/C][/ROW]
[ROW][C]63[/C][C]18.7347039443825[/C][C]12.9554700162076[/C][C]24.5139378725573[/C][/ROW]
[ROW][C]64[/C][C]19.4454592457012[/C][C]13.3179446594122[/C][C]25.5729738319901[/C][/ROW]
[ROW][C]65[/C][C]19.3578140478949[/C][C]12.9007771722219[/C][C]25.8148509235679[/C][/ROW]
[ROW][C]66[/C][C]19.0413716085268[/C][C]12.2708313477782[/C][C]25.8119118692754[/C][/ROW]
[ROW][C]67[/C][C]15.4057812932965[/C][C]8.33562530979556[/C][C]22.4759372767975[/C][/ROW]
[ROW][C]68[/C][C]15.683352803286[/C][C]8.3257719617558[/C][C]23.0409336448161[/C][/ROW]
[ROW][C]69[/C][C]15.7659261311203[/C][C]8.1317342257338[/C][C]23.4001180365068[/C][/ROW]
[ROW][C]70[/C][C]17.0177752771686[/C][C]9.11665027772165[/C][C]24.9189002766155[/C][/ROW]
[ROW][C]71[/C][C]16.8627204999564[/C][C]8.70339047442723[/C][C]25.0220505254856[/C][/ROW]
[ROW][C]72[/C][C]17.3963286713287[/C][C]8.98671770089018[/C][C]25.8059396417671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286467&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286467&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
6119.972394964286814.961829688857924.9829602397156
6219.472835462614514.064263138243724.8814077869853
6318.734703944382512.955470016207624.5139378725573
6419.445459245701213.317944659412225.5729738319901
6519.357814047894912.900777172221925.8148509235679
6619.041371608526812.270831347778225.8119118692754
6715.40578129329658.3356253097955622.4759372767975
6815.6833528032868.325771961755823.0409336448161
6915.76592613112038.131734225733823.4001180365068
7017.01777527716869.1166502777216524.9189002766155
7116.86272049995648.7033904744272325.0220505254856
7217.39632867132878.9867177008901825.8059396417671



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')