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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 computationThu, 22 Dec 2011 14:18:23 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t132458155022ybv7sr9sp6h5g.htm/, Retrieved Thu, 02 May 2024 21:06:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159879, Retrieved Thu, 02 May 2024 21:06:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Classical Decompo...] [2011-11-30 17:01:51] [0b0939f48f9203aad97203a2adcb743b]
- RMP     [Exponential Smoothing] [Exponential smoot...] [2011-12-22 19:18:23] [586f91422d5bd41515f45f36c86ce0c0] [Current]
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Dataseries X:
235.1
280.7
264.6
240.7
201.4
240.8
241.1
223.8
206.1
174.7
203.3
220.5
299.5
347.4
338.3
327.7
351.6
396.6
438.8
395.6
363.5
378.8
357
369
464.8
479.1
431.3
366.5
326.3
355.1
331.6
261.3
249
205.5
235.6
240.9
264.9
253.8
232.3
193.8
177
213.2
207.2
180.6
188.6
175.4
199
179.6
225.8
234
200.2
183.6
178.2
203.2
208.5
191.8
172.8
148
159.4
154.5




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=159879&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=159879&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159879&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
alpha0.906413468950764
beta0.192868185527055
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.906413468950764 \tabularnewline
beta & 0.192868185527055 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159879&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]0.906413468950764[/C][/ROW]
[ROW][C]beta[/C][C]0.192868185527055[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159879&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159879&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
alpha0.906413468950764
beta0.192868185527055
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13299.5239.39449786324860.1055021367521
14347.4349.025775898395-1.62577589839515
15338.3347.097943320575-8.79794332057503
16327.7334.285286576006-6.58528657600624
17351.6356.981149630407-5.38114963040692
18396.6403.244401753485-6.64440175348449
19438.8386.33856197830752.4614380216931
20395.6437.869938652783-42.2699386527825
21363.5395.358459869247-31.858459869247
22378.8342.16880988649336.6311901135066
23357414.275404287143-57.2754042871429
24369376.984340015633-7.98434001563254
25464.8448.42145015744616.3785498425536
26479.1501.635734117548-22.5357341175475
27431.3465.423092324658-34.123092324658
28366.5410.7746310775-44.2746310774999
29326.3373.74444449936-47.4444444993601
30355.1348.7326904919596.36730950804105
31331.6318.39699135616213.203008643838
32261.3287.859965024123-26.5599650241227
33249225.69053040700823.3094695929919
34205.5203.6878465945251.81215340547504
35235.6204.13090229202631.4690977079738
36240.9236.0914920437144.80850795628649
37264.9307.840136848736-42.9401368487362
38253.8279.711204777489-25.9112047774892
39232.3214.83036953227817.4696304677221
40193.8190.4913522830343.30864771696574
41177189.108220025548-12.1082200255482
42213.2200.15275201334713.0472479866526
43207.2176.67034488862530.5296551113752
44180.6161.30493719524719.2950628047533
45188.6156.57031546981832.0296845301819
46175.4153.18843667186622.2115633281336
47199191.1920174068637.8079825931367
48179.6211.369119784056-31.769119784056
49225.8251.258578808775-25.458578808775
50234249.388840405279-15.3888404052788
51200.2208.764977232416-8.56497723241591
52183.6165.61073464010417.9892653598963
53178.2184.766112691054-6.566112691054
54203.2212.831772216964-9.63177221696398
55208.5176.10767913379432.3923208662064
56191.8167.38360392656124.4163960734392
57172.8175.382513289698-2.58251328969752
58148140.5576785441957.44232145580455
59159.4162.093154547394-2.69315454739393
60154.5165.479126079313-10.9791260793133

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 299.5 & 239.394497863248 & 60.1055021367521 \tabularnewline
14 & 347.4 & 349.025775898395 & -1.62577589839515 \tabularnewline
15 & 338.3 & 347.097943320575 & -8.79794332057503 \tabularnewline
16 & 327.7 & 334.285286576006 & -6.58528657600624 \tabularnewline
17 & 351.6 & 356.981149630407 & -5.38114963040692 \tabularnewline
18 & 396.6 & 403.244401753485 & -6.64440175348449 \tabularnewline
19 & 438.8 & 386.338561978307 & 52.4614380216931 \tabularnewline
20 & 395.6 & 437.869938652783 & -42.2699386527825 \tabularnewline
21 & 363.5 & 395.358459869247 & -31.858459869247 \tabularnewline
22 & 378.8 & 342.168809886493 & 36.6311901135066 \tabularnewline
23 & 357 & 414.275404287143 & -57.2754042871429 \tabularnewline
24 & 369 & 376.984340015633 & -7.98434001563254 \tabularnewline
25 & 464.8 & 448.421450157446 & 16.3785498425536 \tabularnewline
26 & 479.1 & 501.635734117548 & -22.5357341175475 \tabularnewline
27 & 431.3 & 465.423092324658 & -34.123092324658 \tabularnewline
28 & 366.5 & 410.7746310775 & -44.2746310774999 \tabularnewline
29 & 326.3 & 373.74444449936 & -47.4444444993601 \tabularnewline
30 & 355.1 & 348.732690491959 & 6.36730950804105 \tabularnewline
31 & 331.6 & 318.396991356162 & 13.203008643838 \tabularnewline
32 & 261.3 & 287.859965024123 & -26.5599650241227 \tabularnewline
33 & 249 & 225.690530407008 & 23.3094695929919 \tabularnewline
34 & 205.5 & 203.687846594525 & 1.81215340547504 \tabularnewline
35 & 235.6 & 204.130902292026 & 31.4690977079738 \tabularnewline
36 & 240.9 & 236.091492043714 & 4.80850795628649 \tabularnewline
37 & 264.9 & 307.840136848736 & -42.9401368487362 \tabularnewline
38 & 253.8 & 279.711204777489 & -25.9112047774892 \tabularnewline
39 & 232.3 & 214.830369532278 & 17.4696304677221 \tabularnewline
40 & 193.8 & 190.491352283034 & 3.30864771696574 \tabularnewline
41 & 177 & 189.108220025548 & -12.1082200255482 \tabularnewline
42 & 213.2 & 200.152752013347 & 13.0472479866526 \tabularnewline
43 & 207.2 & 176.670344888625 & 30.5296551113752 \tabularnewline
44 & 180.6 & 161.304937195247 & 19.2950628047533 \tabularnewline
45 & 188.6 & 156.570315469818 & 32.0296845301819 \tabularnewline
46 & 175.4 & 153.188436671866 & 22.2115633281336 \tabularnewline
47 & 199 & 191.192017406863 & 7.8079825931367 \tabularnewline
48 & 179.6 & 211.369119784056 & -31.769119784056 \tabularnewline
49 & 225.8 & 251.258578808775 & -25.458578808775 \tabularnewline
50 & 234 & 249.388840405279 & -15.3888404052788 \tabularnewline
51 & 200.2 & 208.764977232416 & -8.56497723241591 \tabularnewline
52 & 183.6 & 165.610734640104 & 17.9892653598963 \tabularnewline
53 & 178.2 & 184.766112691054 & -6.566112691054 \tabularnewline
54 & 203.2 & 212.831772216964 & -9.63177221696398 \tabularnewline
55 & 208.5 & 176.107679133794 & 32.3923208662064 \tabularnewline
56 & 191.8 & 167.383603926561 & 24.4163960734392 \tabularnewline
57 & 172.8 & 175.382513289698 & -2.58251328969752 \tabularnewline
58 & 148 & 140.557678544195 & 7.44232145580455 \tabularnewline
59 & 159.4 & 162.093154547394 & -2.69315454739393 \tabularnewline
60 & 154.5 & 165.479126079313 & -10.9791260793133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159879&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]299.5[/C][C]239.394497863248[/C][C]60.1055021367521[/C][/ROW]
[ROW][C]14[/C][C]347.4[/C][C]349.025775898395[/C][C]-1.62577589839515[/C][/ROW]
[ROW][C]15[/C][C]338.3[/C][C]347.097943320575[/C][C]-8.79794332057503[/C][/ROW]
[ROW][C]16[/C][C]327.7[/C][C]334.285286576006[/C][C]-6.58528657600624[/C][/ROW]
[ROW][C]17[/C][C]351.6[/C][C]356.981149630407[/C][C]-5.38114963040692[/C][/ROW]
[ROW][C]18[/C][C]396.6[/C][C]403.244401753485[/C][C]-6.64440175348449[/C][/ROW]
[ROW][C]19[/C][C]438.8[/C][C]386.338561978307[/C][C]52.4614380216931[/C][/ROW]
[ROW][C]20[/C][C]395.6[/C][C]437.869938652783[/C][C]-42.2699386527825[/C][/ROW]
[ROW][C]21[/C][C]363.5[/C][C]395.358459869247[/C][C]-31.858459869247[/C][/ROW]
[ROW][C]22[/C][C]378.8[/C][C]342.168809886493[/C][C]36.6311901135066[/C][/ROW]
[ROW][C]23[/C][C]357[/C][C]414.275404287143[/C][C]-57.2754042871429[/C][/ROW]
[ROW][C]24[/C][C]369[/C][C]376.984340015633[/C][C]-7.98434001563254[/C][/ROW]
[ROW][C]25[/C][C]464.8[/C][C]448.421450157446[/C][C]16.3785498425536[/C][/ROW]
[ROW][C]26[/C][C]479.1[/C][C]501.635734117548[/C][C]-22.5357341175475[/C][/ROW]
[ROW][C]27[/C][C]431.3[/C][C]465.423092324658[/C][C]-34.123092324658[/C][/ROW]
[ROW][C]28[/C][C]366.5[/C][C]410.7746310775[/C][C]-44.2746310774999[/C][/ROW]
[ROW][C]29[/C][C]326.3[/C][C]373.74444449936[/C][C]-47.4444444993601[/C][/ROW]
[ROW][C]30[/C][C]355.1[/C][C]348.732690491959[/C][C]6.36730950804105[/C][/ROW]
[ROW][C]31[/C][C]331.6[/C][C]318.396991356162[/C][C]13.203008643838[/C][/ROW]
[ROW][C]32[/C][C]261.3[/C][C]287.859965024123[/C][C]-26.5599650241227[/C][/ROW]
[ROW][C]33[/C][C]249[/C][C]225.690530407008[/C][C]23.3094695929919[/C][/ROW]
[ROW][C]34[/C][C]205.5[/C][C]203.687846594525[/C][C]1.81215340547504[/C][/ROW]
[ROW][C]35[/C][C]235.6[/C][C]204.130902292026[/C][C]31.4690977079738[/C][/ROW]
[ROW][C]36[/C][C]240.9[/C][C]236.091492043714[/C][C]4.80850795628649[/C][/ROW]
[ROW][C]37[/C][C]264.9[/C][C]307.840136848736[/C][C]-42.9401368487362[/C][/ROW]
[ROW][C]38[/C][C]253.8[/C][C]279.711204777489[/C][C]-25.9112047774892[/C][/ROW]
[ROW][C]39[/C][C]232.3[/C][C]214.830369532278[/C][C]17.4696304677221[/C][/ROW]
[ROW][C]40[/C][C]193.8[/C][C]190.491352283034[/C][C]3.30864771696574[/C][/ROW]
[ROW][C]41[/C][C]177[/C][C]189.108220025548[/C][C]-12.1082200255482[/C][/ROW]
[ROW][C]42[/C][C]213.2[/C][C]200.152752013347[/C][C]13.0472479866526[/C][/ROW]
[ROW][C]43[/C][C]207.2[/C][C]176.670344888625[/C][C]30.5296551113752[/C][/ROW]
[ROW][C]44[/C][C]180.6[/C][C]161.304937195247[/C][C]19.2950628047533[/C][/ROW]
[ROW][C]45[/C][C]188.6[/C][C]156.570315469818[/C][C]32.0296845301819[/C][/ROW]
[ROW][C]46[/C][C]175.4[/C][C]153.188436671866[/C][C]22.2115633281336[/C][/ROW]
[ROW][C]47[/C][C]199[/C][C]191.192017406863[/C][C]7.8079825931367[/C][/ROW]
[ROW][C]48[/C][C]179.6[/C][C]211.369119784056[/C][C]-31.769119784056[/C][/ROW]
[ROW][C]49[/C][C]225.8[/C][C]251.258578808775[/C][C]-25.458578808775[/C][/ROW]
[ROW][C]50[/C][C]234[/C][C]249.388840405279[/C][C]-15.3888404052788[/C][/ROW]
[ROW][C]51[/C][C]200.2[/C][C]208.764977232416[/C][C]-8.56497723241591[/C][/ROW]
[ROW][C]52[/C][C]183.6[/C][C]165.610734640104[/C][C]17.9892653598963[/C][/ROW]
[ROW][C]53[/C][C]178.2[/C][C]184.766112691054[/C][C]-6.566112691054[/C][/ROW]
[ROW][C]54[/C][C]203.2[/C][C]212.831772216964[/C][C]-9.63177221696398[/C][/ROW]
[ROW][C]55[/C][C]208.5[/C][C]176.107679133794[/C][C]32.3923208662064[/C][/ROW]
[ROW][C]56[/C][C]191.8[/C][C]167.383603926561[/C][C]24.4163960734392[/C][/ROW]
[ROW][C]57[/C][C]172.8[/C][C]175.382513289698[/C][C]-2.58251328969752[/C][/ROW]
[ROW][C]58[/C][C]148[/C][C]140.557678544195[/C][C]7.44232145580455[/C][/ROW]
[ROW][C]59[/C][C]159.4[/C][C]162.093154547394[/C][C]-2.69315454739393[/C][/ROW]
[ROW][C]60[/C][C]154.5[/C][C]165.479126079313[/C][C]-10.9791260793133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159879&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159879&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
13299.5239.39449786324860.1055021367521
14347.4349.025775898395-1.62577589839515
15338.3347.097943320575-8.79794332057503
16327.7334.285286576006-6.58528657600624
17351.6356.981149630407-5.38114963040692
18396.6403.244401753485-6.64440175348449
19438.8386.33856197830752.4614380216931
20395.6437.869938652783-42.2699386527825
21363.5395.358459869247-31.858459869247
22378.8342.16880988649336.6311901135066
23357414.275404287143-57.2754042871429
24369376.984340015633-7.98434001563254
25464.8448.42145015744616.3785498425536
26479.1501.635734117548-22.5357341175475
27431.3465.423092324658-34.123092324658
28366.5410.7746310775-44.2746310774999
29326.3373.74444449936-47.4444444993601
30355.1348.7326904919596.36730950804105
31331.6318.39699135616213.203008643838
32261.3287.859965024123-26.5599650241227
33249225.69053040700823.3094695929919
34205.5203.6878465945251.81215340547504
35235.6204.13090229202631.4690977079738
36240.9236.0914920437144.80850795628649
37264.9307.840136848736-42.9401368487362
38253.8279.711204777489-25.9112047774892
39232.3214.83036953227817.4696304677221
40193.8190.4913522830343.30864771696574
41177189.108220025548-12.1082200255482
42213.2200.15275201334713.0472479866526
43207.2176.67034488862530.5296551113752
44180.6161.30493719524719.2950628047533
45188.6156.57031546981832.0296845301819
46175.4153.18843667186622.2115633281336
47199191.1920174068637.8079825931367
48179.6211.369119784056-31.769119784056
49225.8251.258578808775-25.458578808775
50234249.388840405279-15.3888404052788
51200.2208.764977232416-8.56497723241591
52183.6165.61073464010417.9892653598963
53178.2184.766112691054-6.566112691054
54203.2212.831772216964-9.63177221696398
55208.5176.10767913379432.3923208662064
56191.8167.38360392656124.4163960734392
57172.8175.382513289698-2.58251328969752
58148140.5576785441957.44232145580455
59159.4162.093154547394-2.69315454739393
60154.5165.479126079313-10.9791260793133







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61224.869093870012173.019260795295276.71892694473
62251.533968903354175.170901703955327.897036102753
63232.703853689768132.340950071413333.066757308122
64208.50193027270183.6944326674244333.309427877978
65214.61247908826564.5850208139701364.639937362561
66255.04965978609578.893434086395431.205885485795
67239.37944674102636.1318947143431442.626998767708
68203.275948205296-28.0424816468563434.594378057449
69185.076191394575-75.2914039448527445.443786734003
70152.441259984032-137.94313464203442.825654610094
71163.892206395072-157.461142591032485.245555381175
72167.024481762407-186.232142501526520.281106026339

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 224.869093870012 & 173.019260795295 & 276.71892694473 \tabularnewline
62 & 251.533968903354 & 175.170901703955 & 327.897036102753 \tabularnewline
63 & 232.703853689768 & 132.340950071413 & 333.066757308122 \tabularnewline
64 & 208.501930272701 & 83.6944326674244 & 333.309427877978 \tabularnewline
65 & 214.612479088265 & 64.5850208139701 & 364.639937362561 \tabularnewline
66 & 255.049659786095 & 78.893434086395 & 431.205885485795 \tabularnewline
67 & 239.379446741026 & 36.1318947143431 & 442.626998767708 \tabularnewline
68 & 203.275948205296 & -28.0424816468563 & 434.594378057449 \tabularnewline
69 & 185.076191394575 & -75.2914039448527 & 445.443786734003 \tabularnewline
70 & 152.441259984032 & -137.94313464203 & 442.825654610094 \tabularnewline
71 & 163.892206395072 & -157.461142591032 & 485.245555381175 \tabularnewline
72 & 167.024481762407 & -186.232142501526 & 520.281106026339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159879&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]224.869093870012[/C][C]173.019260795295[/C][C]276.71892694473[/C][/ROW]
[ROW][C]62[/C][C]251.533968903354[/C][C]175.170901703955[/C][C]327.897036102753[/C][/ROW]
[ROW][C]63[/C][C]232.703853689768[/C][C]132.340950071413[/C][C]333.066757308122[/C][/ROW]
[ROW][C]64[/C][C]208.501930272701[/C][C]83.6944326674244[/C][C]333.309427877978[/C][/ROW]
[ROW][C]65[/C][C]214.612479088265[/C][C]64.5850208139701[/C][C]364.639937362561[/C][/ROW]
[ROW][C]66[/C][C]255.049659786095[/C][C]78.893434086395[/C][C]431.205885485795[/C][/ROW]
[ROW][C]67[/C][C]239.379446741026[/C][C]36.1318947143431[/C][C]442.626998767708[/C][/ROW]
[ROW][C]68[/C][C]203.275948205296[/C][C]-28.0424816468563[/C][C]434.594378057449[/C][/ROW]
[ROW][C]69[/C][C]185.076191394575[/C][C]-75.2914039448527[/C][C]445.443786734003[/C][/ROW]
[ROW][C]70[/C][C]152.441259984032[/C][C]-137.94313464203[/C][C]442.825654610094[/C][/ROW]
[ROW][C]71[/C][C]163.892206395072[/C][C]-157.461142591032[/C][C]485.245555381175[/C][/ROW]
[ROW][C]72[/C][C]167.024481762407[/C][C]-186.232142501526[/C][C]520.281106026339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159879&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159879&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
61224.869093870012173.019260795295276.71892694473
62251.533968903354175.170901703955327.897036102753
63232.703853689768132.340950071413333.066757308122
64208.50193027270183.6944326674244333.309427877978
65214.61247908826564.5850208139701364.639937362561
66255.04965978609578.893434086395431.205885485795
67239.37944674102636.1318947143431442.626998767708
68203.275948205296-28.0424816468563434.594378057449
69185.076191394575-75.2914039448527445.443786734003
70152.441259984032-137.94313464203442.825654610094
71163.892206395072-157.461142591032485.245555381175
72167.024481762407-186.232142501526520.281106026339



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')