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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Dec 2009 05:11:55 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259928760vzopm2w8phoynd9.htm/, Retrieved Sun, 28 Apr 2024 07:39:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63365, Retrieved Sun, 28 Apr 2024 07:39:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [] [2009-12-04 12:11:55] [2f6049721194fa571920c3539d7b729e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17
14
15
16
16
15
13
12
13
13
12
10
14
14
15
16
16
15
15
13
15
15
15
13
16
16
14
16
15
14
15
15
14
13
12
13
12
9
10
8
11
8
8
8
4
6
8
10
5
6
5
9
8
6
9
11
11
8
11
11
13

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63365&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63365&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63365&T=0

As an alternative you can also use a QR Code:  
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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.27909312390333
beta0.261615313687514
gamma0.364635897888864

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.27909312390333 \tabularnewline
beta & 0.261615313687514 \tabularnewline
gamma & 0.364635897888864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63365&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]0.27909312390333[/C][/ROW]
[ROW][C]beta[/C][C]0.261615313687514[/C][/ROW]
[ROW][C]gamma[/C][C]0.364635897888864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63365&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63365&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.27909312390333
beta0.261615313687514
gamma0.364635897888864






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131414.0102512035019-0.0102512035018787
141413.95719333846260.0428066615374423
151514.91732369169090.0826763083090931
161615.84359587715740.156404122842602
171615.76128001377600.238719986224041
181514.69693631136870.30306368863131
191513.71399375246701.28600624753303
201313.3134495246946-0.313449524694612
211514.5238272704860.476172729513991
221514.88718693335640.112813066643646
231513.99142073493201.00857926506798
241312.13907362445470.860926375545342
251617.6503731751283-1.65037317512833
261617.3562525620149-1.35625256201488
271418.257879186246-4.257879186246
281617.9155792109460-1.91557921094597
291516.9175619900258-1.91756199002584
301414.7711881886316-0.771188188631637
311513.25455660616841.74544339383157
321512.19896468284552.8010353171545
331414.2497661341261-0.24976613412608
341314.0482751376354-1.04827513763537
351212.7987471649270-0.798747164927015
361310.33740501560262.66259498439742
371214.8295877213844-2.82958772138442
38913.8541932204021-4.85419322040207
391012.1817400869882-2.18174008698822
40811.9738044342622-3.97380443426224
41119.709637003918811.29036299608119
4288.61034823859755-0.610348238597554
4387.411977315897060.588022684102945
4486.23888887266141.76111112733860
4546.31100840793949-2.31100840793949
4664.732461790159541.26753820984046
4784.11376580643483.8862341935652
48104.329891901586515.67010809841349
4957.08645151102966-2.08645151102966
5066.06859837485366-0.0685983748536616
5156.40780863830277-1.40780863830277
5296.075598777547332.92440122245267
5387.781879979356830.218120020643167
5467.01780839356718-1.01780839356718
5596.829164448497232.17083555150277
56117.309916011393813.69008398860619
57117.543221442314183.45677855768582
58810.6103616524784-2.61036165247845
591110.96402440535540.0359755946446274
601110.83276638509010.167233614909858
61139.872678259200923.12732174079908

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14 & 14.0102512035019 & -0.0102512035018787 \tabularnewline
14 & 14 & 13.9571933384626 & 0.0428066615374423 \tabularnewline
15 & 15 & 14.9173236916909 & 0.0826763083090931 \tabularnewline
16 & 16 & 15.8435958771574 & 0.156404122842602 \tabularnewline
17 & 16 & 15.7612800137760 & 0.238719986224041 \tabularnewline
18 & 15 & 14.6969363113687 & 0.30306368863131 \tabularnewline
19 & 15 & 13.7139937524670 & 1.28600624753303 \tabularnewline
20 & 13 & 13.3134495246946 & -0.313449524694612 \tabularnewline
21 & 15 & 14.523827270486 & 0.476172729513991 \tabularnewline
22 & 15 & 14.8871869333564 & 0.112813066643646 \tabularnewline
23 & 15 & 13.9914207349320 & 1.00857926506798 \tabularnewline
24 & 13 & 12.1390736244547 & 0.860926375545342 \tabularnewline
25 & 16 & 17.6503731751283 & -1.65037317512833 \tabularnewline
26 & 16 & 17.3562525620149 & -1.35625256201488 \tabularnewline
27 & 14 & 18.257879186246 & -4.257879186246 \tabularnewline
28 & 16 & 17.9155792109460 & -1.91557921094597 \tabularnewline
29 & 15 & 16.9175619900258 & -1.91756199002584 \tabularnewline
30 & 14 & 14.7711881886316 & -0.771188188631637 \tabularnewline
31 & 15 & 13.2545566061684 & 1.74544339383157 \tabularnewline
32 & 15 & 12.1989646828455 & 2.8010353171545 \tabularnewline
33 & 14 & 14.2497661341261 & -0.24976613412608 \tabularnewline
34 & 13 & 14.0482751376354 & -1.04827513763537 \tabularnewline
35 & 12 & 12.7987471649270 & -0.798747164927015 \tabularnewline
36 & 13 & 10.3374050156026 & 2.66259498439742 \tabularnewline
37 & 12 & 14.8295877213844 & -2.82958772138442 \tabularnewline
38 & 9 & 13.8541932204021 & -4.85419322040207 \tabularnewline
39 & 10 & 12.1817400869882 & -2.18174008698822 \tabularnewline
40 & 8 & 11.9738044342622 & -3.97380443426224 \tabularnewline
41 & 11 & 9.70963700391881 & 1.29036299608119 \tabularnewline
42 & 8 & 8.61034823859755 & -0.610348238597554 \tabularnewline
43 & 8 & 7.41197731589706 & 0.588022684102945 \tabularnewline
44 & 8 & 6.2388888726614 & 1.76111112733860 \tabularnewline
45 & 4 & 6.31100840793949 & -2.31100840793949 \tabularnewline
46 & 6 & 4.73246179015954 & 1.26753820984046 \tabularnewline
47 & 8 & 4.1137658064348 & 3.8862341935652 \tabularnewline
48 & 10 & 4.32989190158651 & 5.67010809841349 \tabularnewline
49 & 5 & 7.08645151102966 & -2.08645151102966 \tabularnewline
50 & 6 & 6.06859837485366 & -0.0685983748536616 \tabularnewline
51 & 5 & 6.40780863830277 & -1.40780863830277 \tabularnewline
52 & 9 & 6.07559877754733 & 2.92440122245267 \tabularnewline
53 & 8 & 7.78187997935683 & 0.218120020643167 \tabularnewline
54 & 6 & 7.01780839356718 & -1.01780839356718 \tabularnewline
55 & 9 & 6.82916444849723 & 2.17083555150277 \tabularnewline
56 & 11 & 7.30991601139381 & 3.69008398860619 \tabularnewline
57 & 11 & 7.54322144231418 & 3.45677855768582 \tabularnewline
58 & 8 & 10.6103616524784 & -2.61036165247845 \tabularnewline
59 & 11 & 10.9640244053554 & 0.0359755946446274 \tabularnewline
60 & 11 & 10.8327663850901 & 0.167233614909858 \tabularnewline
61 & 13 & 9.87267825920092 & 3.12732174079908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63365&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]14[/C][C]14.0102512035019[/C][C]-0.0102512035018787[/C][/ROW]
[ROW][C]14[/C][C]14[/C][C]13.9571933384626[/C][C]0.0428066615374423[/C][/ROW]
[ROW][C]15[/C][C]15[/C][C]14.9173236916909[/C][C]0.0826763083090931[/C][/ROW]
[ROW][C]16[/C][C]16[/C][C]15.8435958771574[/C][C]0.156404122842602[/C][/ROW]
[ROW][C]17[/C][C]16[/C][C]15.7612800137760[/C][C]0.238719986224041[/C][/ROW]
[ROW][C]18[/C][C]15[/C][C]14.6969363113687[/C][C]0.30306368863131[/C][/ROW]
[ROW][C]19[/C][C]15[/C][C]13.7139937524670[/C][C]1.28600624753303[/C][/ROW]
[ROW][C]20[/C][C]13[/C][C]13.3134495246946[/C][C]-0.313449524694612[/C][/ROW]
[ROW][C]21[/C][C]15[/C][C]14.523827270486[/C][C]0.476172729513991[/C][/ROW]
[ROW][C]22[/C][C]15[/C][C]14.8871869333564[/C][C]0.112813066643646[/C][/ROW]
[ROW][C]23[/C][C]15[/C][C]13.9914207349320[/C][C]1.00857926506798[/C][/ROW]
[ROW][C]24[/C][C]13[/C][C]12.1390736244547[/C][C]0.860926375545342[/C][/ROW]
[ROW][C]25[/C][C]16[/C][C]17.6503731751283[/C][C]-1.65037317512833[/C][/ROW]
[ROW][C]26[/C][C]16[/C][C]17.3562525620149[/C][C]-1.35625256201488[/C][/ROW]
[ROW][C]27[/C][C]14[/C][C]18.257879186246[/C][C]-4.257879186246[/C][/ROW]
[ROW][C]28[/C][C]16[/C][C]17.9155792109460[/C][C]-1.91557921094597[/C][/ROW]
[ROW][C]29[/C][C]15[/C][C]16.9175619900258[/C][C]-1.91756199002584[/C][/ROW]
[ROW][C]30[/C][C]14[/C][C]14.7711881886316[/C][C]-0.771188188631637[/C][/ROW]
[ROW][C]31[/C][C]15[/C][C]13.2545566061684[/C][C]1.74544339383157[/C][/ROW]
[ROW][C]32[/C][C]15[/C][C]12.1989646828455[/C][C]2.8010353171545[/C][/ROW]
[ROW][C]33[/C][C]14[/C][C]14.2497661341261[/C][C]-0.24976613412608[/C][/ROW]
[ROW][C]34[/C][C]13[/C][C]14.0482751376354[/C][C]-1.04827513763537[/C][/ROW]
[ROW][C]35[/C][C]12[/C][C]12.7987471649270[/C][C]-0.798747164927015[/C][/ROW]
[ROW][C]36[/C][C]13[/C][C]10.3374050156026[/C][C]2.66259498439742[/C][/ROW]
[ROW][C]37[/C][C]12[/C][C]14.8295877213844[/C][C]-2.82958772138442[/C][/ROW]
[ROW][C]38[/C][C]9[/C][C]13.8541932204021[/C][C]-4.85419322040207[/C][/ROW]
[ROW][C]39[/C][C]10[/C][C]12.1817400869882[/C][C]-2.18174008698822[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]11.9738044342622[/C][C]-3.97380443426224[/C][/ROW]
[ROW][C]41[/C][C]11[/C][C]9.70963700391881[/C][C]1.29036299608119[/C][/ROW]
[ROW][C]42[/C][C]8[/C][C]8.61034823859755[/C][C]-0.610348238597554[/C][/ROW]
[ROW][C]43[/C][C]8[/C][C]7.41197731589706[/C][C]0.588022684102945[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]6.2388888726614[/C][C]1.76111112733860[/C][/ROW]
[ROW][C]45[/C][C]4[/C][C]6.31100840793949[/C][C]-2.31100840793949[/C][/ROW]
[ROW][C]46[/C][C]6[/C][C]4.73246179015954[/C][C]1.26753820984046[/C][/ROW]
[ROW][C]47[/C][C]8[/C][C]4.1137658064348[/C][C]3.8862341935652[/C][/ROW]
[ROW][C]48[/C][C]10[/C][C]4.32989190158651[/C][C]5.67010809841349[/C][/ROW]
[ROW][C]49[/C][C]5[/C][C]7.08645151102966[/C][C]-2.08645151102966[/C][/ROW]
[ROW][C]50[/C][C]6[/C][C]6.06859837485366[/C][C]-0.0685983748536616[/C][/ROW]
[ROW][C]51[/C][C]5[/C][C]6.40780863830277[/C][C]-1.40780863830277[/C][/ROW]
[ROW][C]52[/C][C]9[/C][C]6.07559877754733[/C][C]2.92440122245267[/C][/ROW]
[ROW][C]53[/C][C]8[/C][C]7.78187997935683[/C][C]0.218120020643167[/C][/ROW]
[ROW][C]54[/C][C]6[/C][C]7.01780839356718[/C][C]-1.01780839356718[/C][/ROW]
[ROW][C]55[/C][C]9[/C][C]6.82916444849723[/C][C]2.17083555150277[/C][/ROW]
[ROW][C]56[/C][C]11[/C][C]7.30991601139381[/C][C]3.69008398860619[/C][/ROW]
[ROW][C]57[/C][C]11[/C][C]7.54322144231418[/C][C]3.45677855768582[/C][/ROW]
[ROW][C]58[/C][C]8[/C][C]10.6103616524784[/C][C]-2.61036165247845[/C][/ROW]
[ROW][C]59[/C][C]11[/C][C]10.9640244053554[/C][C]0.0359755946446274[/C][/ROW]
[ROW][C]60[/C][C]11[/C][C]10.8327663850901[/C][C]0.167233614909858[/C][/ROW]
[ROW][C]61[/C][C]13[/C][C]9.87267825920092[/C][C]3.12732174079908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63365&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63365&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131414.0102512035019-0.0102512035018787
141413.95719333846260.0428066615374423
151514.91732369169090.0826763083090931
161615.84359587715740.156404122842602
171615.76128001377600.238719986224041
181514.69693631136870.30306368863131
191513.71399375246701.28600624753303
201313.3134495246946-0.313449524694612
211514.5238272704860.476172729513991
221514.88718693335640.112813066643646
231513.99142073493201.00857926506798
241312.13907362445470.860926375545342
251617.6503731751283-1.65037317512833
261617.3562525620149-1.35625256201488
271418.257879186246-4.257879186246
281617.9155792109460-1.91557921094597
291516.9175619900258-1.91756199002584
301414.7711881886316-0.771188188631637
311513.25455660616841.74544339383157
321512.19896468284552.8010353171545
331414.2497661341261-0.24976613412608
341314.0482751376354-1.04827513763537
351212.7987471649270-0.798747164927015
361310.33740501560262.66259498439742
371214.8295877213844-2.82958772138442
38913.8541932204021-4.85419322040207
391012.1817400869882-2.18174008698822
40811.9738044342622-3.97380443426224
41119.709637003918811.29036299608119
4288.61034823859755-0.610348238597554
4387.411977315897060.588022684102945
4486.23888887266141.76111112733860
4546.31100840793949-2.31100840793949
4664.732461790159541.26753820984046
4784.11376580643483.8862341935652
48104.329891901586515.67010809841349
4957.08645151102966-2.08645151102966
5066.06859837485366-0.0685983748536616
5156.40780863830277-1.40780863830277
5296.075598777547332.92440122245267
5387.781879979356830.218120020643167
5467.01780839356718-1.01780839356718
5596.829164448497232.17083555150277
56117.309916011393813.69008398860619
57117.543221442314183.45677855768582
58810.6103616524784-2.61036165247845
591110.96402440535540.0359755946446274
601110.83276638509010.167233614909858
61139.872678259200923.12732174079908






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6211.73338040376779.4145735752861514.0521872322493
6312.54442816708029.7706287031289215.3182276310314
6416.344772104412112.604181151581220.0853630572430
6517.553211779887113.039535386333922.0668881734404
6615.644901320814110.986727894444120.3030747471841
6718.750838545172112.703831784047524.7978453062966
6819.670925068189412.718886501558326.6229636348205
6917.598593529597710.734376560398724.4628104987967
7017.986123799725110.391147905262625.5810996941876
7121.265040498464011.696452011001230.8336289859267
7220.875179829970910.817054239642530.9333054202994
7320.13028094505649.6311298713929130.6294320187199

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 11.7333804037677 & 9.41457357528615 & 14.0521872322493 \tabularnewline
63 & 12.5444281670802 & 9.77062870312892 & 15.3182276310314 \tabularnewline
64 & 16.3447721044121 & 12.6041811515812 & 20.0853630572430 \tabularnewline
65 & 17.5532117798871 & 13.0395353863339 & 22.0668881734404 \tabularnewline
66 & 15.6449013208141 & 10.9867278944441 & 20.3030747471841 \tabularnewline
67 & 18.7508385451721 & 12.7038317840475 & 24.7978453062966 \tabularnewline
68 & 19.6709250681894 & 12.7188865015583 & 26.6229636348205 \tabularnewline
69 & 17.5985935295977 & 10.7343765603987 & 24.4628104987967 \tabularnewline
70 & 17.9861237997251 & 10.3911479052626 & 25.5810996941876 \tabularnewline
71 & 21.2650404984640 & 11.6964520110012 & 30.8336289859267 \tabularnewline
72 & 20.8751798299709 & 10.8170542396425 & 30.9333054202994 \tabularnewline
73 & 20.1302809450564 & 9.63112987139291 & 30.6294320187199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63365&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]62[/C][C]11.7333804037677[/C][C]9.41457357528615[/C][C]14.0521872322493[/C][/ROW]
[ROW][C]63[/C][C]12.5444281670802[/C][C]9.77062870312892[/C][C]15.3182276310314[/C][/ROW]
[ROW][C]64[/C][C]16.3447721044121[/C][C]12.6041811515812[/C][C]20.0853630572430[/C][/ROW]
[ROW][C]65[/C][C]17.5532117798871[/C][C]13.0395353863339[/C][C]22.0668881734404[/C][/ROW]
[ROW][C]66[/C][C]15.6449013208141[/C][C]10.9867278944441[/C][C]20.3030747471841[/C][/ROW]
[ROW][C]67[/C][C]18.7508385451721[/C][C]12.7038317840475[/C][C]24.7978453062966[/C][/ROW]
[ROW][C]68[/C][C]19.6709250681894[/C][C]12.7188865015583[/C][C]26.6229636348205[/C][/ROW]
[ROW][C]69[/C][C]17.5985935295977[/C][C]10.7343765603987[/C][C]24.4628104987967[/C][/ROW]
[ROW][C]70[/C][C]17.9861237997251[/C][C]10.3911479052626[/C][C]25.5810996941876[/C][/ROW]
[ROW][C]71[/C][C]21.2650404984640[/C][C]11.6964520110012[/C][C]30.8336289859267[/C][/ROW]
[ROW][C]72[/C][C]20.8751798299709[/C][C]10.8170542396425[/C][C]30.9333054202994[/C][/ROW]
[ROW][C]73[/C][C]20.1302809450564[/C][C]9.63112987139291[/C][C]30.6294320187199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63365&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63365&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6211.73338040376779.4145735752861514.0521872322493
6312.54442816708029.7706287031289215.3182276310314
6416.344772104412112.604181151581220.0853630572430
6517.553211779887113.039535386333922.0668881734404
6615.644901320814110.986727894444120.3030747471841
6718.750838545172112.703831784047524.7978453062966
6819.670925068189412.718886501558326.6229636348205
6917.598593529597710.734376560398724.4628104987967
7017.986123799725110.391147905262625.5810996941876
7121.265040498464011.696452011001230.8336289859267
7220.875179829970910.817054239642530.9333054202994
7320.13028094505649.6311298713929130.6294320187199


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')