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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 07 May 2012 07:59:10 -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/2012/May/07/t1336392081sswmojngibe0wsi.htm/, Retrieved Sat, 04 May 2024 21:23:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166307, Retrieved Sat, 04 May 2024 21:23:19 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2012-05-07 11:59:10] [a05a60a2f3f20a69630af127f5d09cc4] [Current]
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Dataseries X:
98,01
99,2
100,7
106,41
107,51
107,1
99,75
98,96
107,26
107,11
107,2
107,65
104,78
105,56
107,95
107,11
107,47
107,06
99,71
99,6
107,19
107,26
113,24
113,52
110,48
111,41
115,5
118,32
118,42
117,5
110,23
109,19
118,41
118,3
116,1
114,11
113,41
114,33
116,61
123,64
123,77
123,39
116,03
114,95
123,4
123,53
114,45
114,26
114,35
112,77
115,31
114,93
116,38
115,07
105
103,43
114,52
115,04
117,16
115




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166307&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166307&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166307&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.940122076120127
beta0
gamma0.879523943587333

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.940122076120127 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.879523943587333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166307&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]0.940122076120127[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.879523943587333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166307&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166307&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
alpha0.940122076120127
beta0
gamma0.879523943587333







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13104.78103.7908497149840.989150285015697
14105.56105.612440022055-0.0524400220550092
15107.95108.069094236495-0.11909423649513
16107.11107.252741862916-0.142741862915869
17107.47107.3561428633820.113857136618449
18107.06106.6921860009810.367813999019177
1999.71102.036128650278-2.32612865027794
2099.698.67071674240530.929283257594719
21107.19107.452098207533-0.262098207533498
22107.26106.8591967162460.400803283753746
23113.24107.4373937045615.80260629543928
24113.52113.5098340844740.0101659155259313
25110.48110.687516440759-0.207516440759221
26111.41111.3674376438720.0425623561284425
27115.5114.0407389451561.45926105484389
28118.32114.6485926930063.67140730699427
29118.42118.362750002010.0572499979899419
30117.5117.567646049662-0.0676460496616613
31110.23111.842653584567-1.61265358456718
32109.19109.198130377866-0.00813037786647897
33118.41117.777957518770.632042481230044
34118.3118.0134723884720.286527611527688
35116.1118.788028931567-2.68802893156678
36114.11116.577847316553-2.46784731655293
37113.41111.3950456122222.0149543877782
38114.33114.1966194150670.13338058493288
39116.61117.096093266855-0.486093266855235
40123.64115.9780379306757.66196206932491
41123.77123.2507006433690.519299356630711
42123.39122.8387718258320.551228174167861
43116.03117.320236910911-1.29023691091105
44114.95115.000879063082-0.0508790630820499
45123.4124.021698274949-0.621698274948656
46123.53123.0383809765140.491619023486393
47114.45123.855080145326-9.40508014532602
48114.26115.337233133046-1.07723313304615
49114.35111.69132179632.65867820370019
50112.77115.003682512179-2.23368251217875
51115.31115.61267624144-0.302676241440437
52114.93115.076926195223-0.146926195223315
53116.38114.6632130709541.71678692904605
54115.07115.441353925412-0.371353925412421
55105109.37894488538-4.37894488537954
56103.43104.329832898748-0.899832898747903
57114.52111.6346575496662.88534245033419
58115.04114.0421162105670.997883789432521
59117.16114.7992586970732.36074130292704
60115117.794391373707-2.79439137370667

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.78 & 103.790849714984 & 0.989150285015697 \tabularnewline
14 & 105.56 & 105.612440022055 & -0.0524400220550092 \tabularnewline
15 & 107.95 & 108.069094236495 & -0.11909423649513 \tabularnewline
16 & 107.11 & 107.252741862916 & -0.142741862915869 \tabularnewline
17 & 107.47 & 107.356142863382 & 0.113857136618449 \tabularnewline
18 & 107.06 & 106.692186000981 & 0.367813999019177 \tabularnewline
19 & 99.71 & 102.036128650278 & -2.32612865027794 \tabularnewline
20 & 99.6 & 98.6707167424053 & 0.929283257594719 \tabularnewline
21 & 107.19 & 107.452098207533 & -0.262098207533498 \tabularnewline
22 & 107.26 & 106.859196716246 & 0.400803283753746 \tabularnewline
23 & 113.24 & 107.437393704561 & 5.80260629543928 \tabularnewline
24 & 113.52 & 113.509834084474 & 0.0101659155259313 \tabularnewline
25 & 110.48 & 110.687516440759 & -0.207516440759221 \tabularnewline
26 & 111.41 & 111.367437643872 & 0.0425623561284425 \tabularnewline
27 & 115.5 & 114.040738945156 & 1.45926105484389 \tabularnewline
28 & 118.32 & 114.648592693006 & 3.67140730699427 \tabularnewline
29 & 118.42 & 118.36275000201 & 0.0572499979899419 \tabularnewline
30 & 117.5 & 117.567646049662 & -0.0676460496616613 \tabularnewline
31 & 110.23 & 111.842653584567 & -1.61265358456718 \tabularnewline
32 & 109.19 & 109.198130377866 & -0.00813037786647897 \tabularnewline
33 & 118.41 & 117.77795751877 & 0.632042481230044 \tabularnewline
34 & 118.3 & 118.013472388472 & 0.286527611527688 \tabularnewline
35 & 116.1 & 118.788028931567 & -2.68802893156678 \tabularnewline
36 & 114.11 & 116.577847316553 & -2.46784731655293 \tabularnewline
37 & 113.41 & 111.395045612222 & 2.0149543877782 \tabularnewline
38 & 114.33 & 114.196619415067 & 0.13338058493288 \tabularnewline
39 & 116.61 & 117.096093266855 & -0.486093266855235 \tabularnewline
40 & 123.64 & 115.978037930675 & 7.66196206932491 \tabularnewline
41 & 123.77 & 123.250700643369 & 0.519299356630711 \tabularnewline
42 & 123.39 & 122.838771825832 & 0.551228174167861 \tabularnewline
43 & 116.03 & 117.320236910911 & -1.29023691091105 \tabularnewline
44 & 114.95 & 115.000879063082 & -0.0508790630820499 \tabularnewline
45 & 123.4 & 124.021698274949 & -0.621698274948656 \tabularnewline
46 & 123.53 & 123.038380976514 & 0.491619023486393 \tabularnewline
47 & 114.45 & 123.855080145326 & -9.40508014532602 \tabularnewline
48 & 114.26 & 115.337233133046 & -1.07723313304615 \tabularnewline
49 & 114.35 & 111.6913217963 & 2.65867820370019 \tabularnewline
50 & 112.77 & 115.003682512179 & -2.23368251217875 \tabularnewline
51 & 115.31 & 115.61267624144 & -0.302676241440437 \tabularnewline
52 & 114.93 & 115.076926195223 & -0.146926195223315 \tabularnewline
53 & 116.38 & 114.663213070954 & 1.71678692904605 \tabularnewline
54 & 115.07 & 115.441353925412 & -0.371353925412421 \tabularnewline
55 & 105 & 109.37894488538 & -4.37894488537954 \tabularnewline
56 & 103.43 & 104.329832898748 & -0.899832898747903 \tabularnewline
57 & 114.52 & 111.634657549666 & 2.88534245033419 \tabularnewline
58 & 115.04 & 114.042116210567 & 0.997883789432521 \tabularnewline
59 & 117.16 & 114.799258697073 & 2.36074130292704 \tabularnewline
60 & 115 & 117.794391373707 & -2.79439137370667 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166307&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]104.78[/C][C]103.790849714984[/C][C]0.989150285015697[/C][/ROW]
[ROW][C]14[/C][C]105.56[/C][C]105.612440022055[/C][C]-0.0524400220550092[/C][/ROW]
[ROW][C]15[/C][C]107.95[/C][C]108.069094236495[/C][C]-0.11909423649513[/C][/ROW]
[ROW][C]16[/C][C]107.11[/C][C]107.252741862916[/C][C]-0.142741862915869[/C][/ROW]
[ROW][C]17[/C][C]107.47[/C][C]107.356142863382[/C][C]0.113857136618449[/C][/ROW]
[ROW][C]18[/C][C]107.06[/C][C]106.692186000981[/C][C]0.367813999019177[/C][/ROW]
[ROW][C]19[/C][C]99.71[/C][C]102.036128650278[/C][C]-2.32612865027794[/C][/ROW]
[ROW][C]20[/C][C]99.6[/C][C]98.6707167424053[/C][C]0.929283257594719[/C][/ROW]
[ROW][C]21[/C][C]107.19[/C][C]107.452098207533[/C][C]-0.262098207533498[/C][/ROW]
[ROW][C]22[/C][C]107.26[/C][C]106.859196716246[/C][C]0.400803283753746[/C][/ROW]
[ROW][C]23[/C][C]113.24[/C][C]107.437393704561[/C][C]5.80260629543928[/C][/ROW]
[ROW][C]24[/C][C]113.52[/C][C]113.509834084474[/C][C]0.0101659155259313[/C][/ROW]
[ROW][C]25[/C][C]110.48[/C][C]110.687516440759[/C][C]-0.207516440759221[/C][/ROW]
[ROW][C]26[/C][C]111.41[/C][C]111.367437643872[/C][C]0.0425623561284425[/C][/ROW]
[ROW][C]27[/C][C]115.5[/C][C]114.040738945156[/C][C]1.45926105484389[/C][/ROW]
[ROW][C]28[/C][C]118.32[/C][C]114.648592693006[/C][C]3.67140730699427[/C][/ROW]
[ROW][C]29[/C][C]118.42[/C][C]118.36275000201[/C][C]0.0572499979899419[/C][/ROW]
[ROW][C]30[/C][C]117.5[/C][C]117.567646049662[/C][C]-0.0676460496616613[/C][/ROW]
[ROW][C]31[/C][C]110.23[/C][C]111.842653584567[/C][C]-1.61265358456718[/C][/ROW]
[ROW][C]32[/C][C]109.19[/C][C]109.198130377866[/C][C]-0.00813037786647897[/C][/ROW]
[ROW][C]33[/C][C]118.41[/C][C]117.77795751877[/C][C]0.632042481230044[/C][/ROW]
[ROW][C]34[/C][C]118.3[/C][C]118.013472388472[/C][C]0.286527611527688[/C][/ROW]
[ROW][C]35[/C][C]116.1[/C][C]118.788028931567[/C][C]-2.68802893156678[/C][/ROW]
[ROW][C]36[/C][C]114.11[/C][C]116.577847316553[/C][C]-2.46784731655293[/C][/ROW]
[ROW][C]37[/C][C]113.41[/C][C]111.395045612222[/C][C]2.0149543877782[/C][/ROW]
[ROW][C]38[/C][C]114.33[/C][C]114.196619415067[/C][C]0.13338058493288[/C][/ROW]
[ROW][C]39[/C][C]116.61[/C][C]117.096093266855[/C][C]-0.486093266855235[/C][/ROW]
[ROW][C]40[/C][C]123.64[/C][C]115.978037930675[/C][C]7.66196206932491[/C][/ROW]
[ROW][C]41[/C][C]123.77[/C][C]123.250700643369[/C][C]0.519299356630711[/C][/ROW]
[ROW][C]42[/C][C]123.39[/C][C]122.838771825832[/C][C]0.551228174167861[/C][/ROW]
[ROW][C]43[/C][C]116.03[/C][C]117.320236910911[/C][C]-1.29023691091105[/C][/ROW]
[ROW][C]44[/C][C]114.95[/C][C]115.000879063082[/C][C]-0.0508790630820499[/C][/ROW]
[ROW][C]45[/C][C]123.4[/C][C]124.021698274949[/C][C]-0.621698274948656[/C][/ROW]
[ROW][C]46[/C][C]123.53[/C][C]123.038380976514[/C][C]0.491619023486393[/C][/ROW]
[ROW][C]47[/C][C]114.45[/C][C]123.855080145326[/C][C]-9.40508014532602[/C][/ROW]
[ROW][C]48[/C][C]114.26[/C][C]115.337233133046[/C][C]-1.07723313304615[/C][/ROW]
[ROW][C]49[/C][C]114.35[/C][C]111.6913217963[/C][C]2.65867820370019[/C][/ROW]
[ROW][C]50[/C][C]112.77[/C][C]115.003682512179[/C][C]-2.23368251217875[/C][/ROW]
[ROW][C]51[/C][C]115.31[/C][C]115.61267624144[/C][C]-0.302676241440437[/C][/ROW]
[ROW][C]52[/C][C]114.93[/C][C]115.076926195223[/C][C]-0.146926195223315[/C][/ROW]
[ROW][C]53[/C][C]116.38[/C][C]114.663213070954[/C][C]1.71678692904605[/C][/ROW]
[ROW][C]54[/C][C]115.07[/C][C]115.441353925412[/C][C]-0.371353925412421[/C][/ROW]
[ROW][C]55[/C][C]105[/C][C]109.37894488538[/C][C]-4.37894488537954[/C][/ROW]
[ROW][C]56[/C][C]103.43[/C][C]104.329832898748[/C][C]-0.899832898747903[/C][/ROW]
[ROW][C]57[/C][C]114.52[/C][C]111.634657549666[/C][C]2.88534245033419[/C][/ROW]
[ROW][C]58[/C][C]115.04[/C][C]114.042116210567[/C][C]0.997883789432521[/C][/ROW]
[ROW][C]59[/C][C]117.16[/C][C]114.799258697073[/C][C]2.36074130292704[/C][/ROW]
[ROW][C]60[/C][C]115[/C][C]117.794391373707[/C][C]-2.79439137370667[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166307&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166307&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
13104.78103.7908497149840.989150285015697
14105.56105.612440022055-0.0524400220550092
15107.95108.069094236495-0.11909423649513
16107.11107.252741862916-0.142741862915869
17107.47107.3561428633820.113857136618449
18107.06106.6921860009810.367813999019177
1999.71102.036128650278-2.32612865027794
2099.698.67071674240530.929283257594719
21107.19107.452098207533-0.262098207533498
22107.26106.8591967162460.400803283753746
23113.24107.4373937045615.80260629543928
24113.52113.5098340844740.0101659155259313
25110.48110.687516440759-0.207516440759221
26111.41111.3674376438720.0425623561284425
27115.5114.0407389451561.45926105484389
28118.32114.6485926930063.67140730699427
29118.42118.362750002010.0572499979899419
30117.5117.567646049662-0.0676460496616613
31110.23111.842653584567-1.61265358456718
32109.19109.198130377866-0.00813037786647897
33118.41117.777957518770.632042481230044
34118.3118.0134723884720.286527611527688
35116.1118.788028931567-2.68802893156678
36114.11116.577847316553-2.46784731655293
37113.41111.3950456122222.0149543877782
38114.33114.1966194150670.13338058493288
39116.61117.096093266855-0.486093266855235
40123.64115.9780379306757.66196206932491
41123.77123.2507006433690.519299356630711
42123.39122.8387718258320.551228174167861
43116.03117.320236910911-1.29023691091105
44114.95115.000879063082-0.0508790630820499
45123.4124.021698274949-0.621698274948656
46123.53123.0383809765140.491619023486393
47114.45123.855080145326-9.40508014532602
48114.26115.337233133046-1.07723313304615
49114.35111.69132179632.65867820370019
50112.77115.003682512179-2.23368251217875
51115.31115.61267624144-0.302676241440437
52114.93115.076926195223-0.146926195223315
53116.38114.6632130709541.71678692904605
54115.07115.441353925412-0.371353925412421
55105109.37894488538-4.37894488537954
56103.43104.329832898748-0.899832898747903
57114.52111.6346575496662.88534245033419
58115.04114.0421162105670.997883789432521
59117.16114.7992586970732.36074130292704
60115117.794391373707-2.79439137370667







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61112.707546636338107.901799475681117.513293796995
62113.254677825702106.624732741806119.884622909597
63116.076355195318107.911923275539124.240787115098
64115.830814665446106.506547002196125.155082328695
65115.649636238913105.296635380989126.002637096838
66114.710446078231103.487640600831125.933251555631
67108.79616887747997.221150421409120.371187333549
68108.0151242473295.6661519389363120.364096555703
69116.724904960878102.654670690835130.795139230921
70116.309380438264101.584347945276131.034412931251
71116.195025509601100.813107287609131.576943731594
72116.69300066695178.0157801536927155.37022118021

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 112.707546636338 & 107.901799475681 & 117.513293796995 \tabularnewline
62 & 113.254677825702 & 106.624732741806 & 119.884622909597 \tabularnewline
63 & 116.076355195318 & 107.911923275539 & 124.240787115098 \tabularnewline
64 & 115.830814665446 & 106.506547002196 & 125.155082328695 \tabularnewline
65 & 115.649636238913 & 105.296635380989 & 126.002637096838 \tabularnewline
66 & 114.710446078231 & 103.487640600831 & 125.933251555631 \tabularnewline
67 & 108.796168877479 & 97.221150421409 & 120.371187333549 \tabularnewline
68 & 108.01512424732 & 95.6661519389363 & 120.364096555703 \tabularnewline
69 & 116.724904960878 & 102.654670690835 & 130.795139230921 \tabularnewline
70 & 116.309380438264 & 101.584347945276 & 131.034412931251 \tabularnewline
71 & 116.195025509601 & 100.813107287609 & 131.576943731594 \tabularnewline
72 & 116.693000666951 & 78.0157801536927 & 155.37022118021 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166307&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]112.707546636338[/C][C]107.901799475681[/C][C]117.513293796995[/C][/ROW]
[ROW][C]62[/C][C]113.254677825702[/C][C]106.624732741806[/C][C]119.884622909597[/C][/ROW]
[ROW][C]63[/C][C]116.076355195318[/C][C]107.911923275539[/C][C]124.240787115098[/C][/ROW]
[ROW][C]64[/C][C]115.830814665446[/C][C]106.506547002196[/C][C]125.155082328695[/C][/ROW]
[ROW][C]65[/C][C]115.649636238913[/C][C]105.296635380989[/C][C]126.002637096838[/C][/ROW]
[ROW][C]66[/C][C]114.710446078231[/C][C]103.487640600831[/C][C]125.933251555631[/C][/ROW]
[ROW][C]67[/C][C]108.796168877479[/C][C]97.221150421409[/C][C]120.371187333549[/C][/ROW]
[ROW][C]68[/C][C]108.01512424732[/C][C]95.6661519389363[/C][C]120.364096555703[/C][/ROW]
[ROW][C]69[/C][C]116.724904960878[/C][C]102.654670690835[/C][C]130.795139230921[/C][/ROW]
[ROW][C]70[/C][C]116.309380438264[/C][C]101.584347945276[/C][C]131.034412931251[/C][/ROW]
[ROW][C]71[/C][C]116.195025509601[/C][C]100.813107287609[/C][C]131.576943731594[/C][/ROW]
[ROW][C]72[/C][C]116.693000666951[/C][C]78.0157801536927[/C][C]155.37022118021[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166307&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166307&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
61112.707546636338107.901799475681117.513293796995
62113.254677825702106.624732741806119.884622909597
63116.076355195318107.911923275539124.240787115098
64115.830814665446106.506547002196125.155082328695
65115.649636238913105.296635380989126.002637096838
66114.710446078231103.487640600831125.933251555631
67108.79616887747997.221150421409120.371187333549
68108.0151242473295.6661519389363120.364096555703
69116.724904960878102.654670690835130.795139230921
70116.309380438264101.584347945276131.034412931251
71116.195025509601100.813107287609131.576943731594
72116.69300066695178.0157801536927155.37022118021



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=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')