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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 computationWed, 21 Dec 2016 07:46:21 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t14823027913tthijnm1cg1t3k.htm/, Retrieved Mon, 06 May 2024 20:13:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301854, Retrieved Mon, 06 May 2024 20:13:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-21 06:46:21] [672675941468e072e71d9fb024f2b817] [Current]
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Dataseries X:
1932.8
1861.4
2170.2
1999.6
2225.5
2195.7
2713.1
2412
2568.3
2623.7
3185.5
2722.6
3046.3
2854.2
3337.6
2920.3
3058.3
2933.7
3773.4
3193.5
3472.2
3345.5
4028.4
3463.1
3675.4
3500.8
4142.1
3598
3765.3
3557.7
4303.6
3620.1
3691.1
3678.1
4505.8
3695
3894.1
3718.9
4749.8
3855.9
4011.7
3907.6
4812.5
4071.3
4163.4
4077.6
5109.2
4207.6
4320.8
4396.9
5358.8




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301854&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301854&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301854&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.511090829155879
beta0.157471310081377
gamma0.676757938708097

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.511090829155879 \tabularnewline
beta & 0.157471310081377 \tabularnewline
gamma & 0.676757938708097 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301854&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]0.511090829155879[/C][/ROW]
[ROW][C]beta[/C][C]0.157471310081377[/C][/ROW]
[ROW][C]gamma[/C][C]0.676757938708097[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301854&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301854&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
alpha0.511090829155879
beta0.157471310081377
gamma0.676757938708097







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
52225.52043.3205156145182.179484385497
62195.72111.6606607671384.0393392328697
72713.12587.25607115576125.843928844243
824122480.74242247921-68.7424224792094
92568.32793.97812040236-225.678120402362
102623.72576.9174261085946.7825738914094
113185.53094.5863595466190.9136404533906
122722.62833.19469383351-110.59469383351
133046.33077.2950525245-30.9950525244985
142854.23027.62851922073-173.428519220731
153337.63472.1457744162-134.545774416201
162920.32958.51204105088-38.2120410508846
173058.33251.14934732664-192.849347326641
182933.73023.06210987458-89.3621098745766
193773.43497.79944943857275.600550561428
203193.53178.9793807706614.5206192293376
213472.23459.801448343412.3985516565981
223345.53365.09101892565-19.5910189256488
234028.44095.02489091979-66.6248909197857
243463.13455.899431537067.20056846294483
253675.43743.6835557354-68.2835557353974
263500.83573.51863338911-72.7186333891109
274142.14278.36582994631-136.265829946309
2835983581.0564221759716.943577824034
293765.33835.56229961961-70.262299619606
303557.73637.47733658389-79.7773365838907
314303.64309.37302239569-5.7730223956878
323620.13697.03856292337-76.9385629233675
333691.13858.04680981277-166.946809812774
343678.13581.7524229393296.3475770606838
354505.84366.23770710633139.562292893667
3636953781.92881744236-86.9288174423591
373894.13908.12498490641-14.0249849064089
383718.93799.71435927681-80.8143592768133
394749.84519.74147357383230.058526426169
403855.93880.95165475496-25.0516547549582
414011.74075.93210775509-64.2321077550946
423907.63915.62426805185-8.02426805184723
434812.54823.44317496971-10.9431749697123
444071.33949.25106634553122.048933654468
454163.44216.09943401534-52.6994340153369
464077.64078.83624293824-1.23624293823514
475109.25033.0271984911676.1728015088383
484207.64211.66584658485-4.06584658485372
494320.84360.71927606587-39.9192760658661
504396.94243.25724381824153.642756181757
515358.85375.16037085137-16.360370851372

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 2225.5 & 2043.3205156145 & 182.179484385497 \tabularnewline
6 & 2195.7 & 2111.66066076713 & 84.0393392328697 \tabularnewline
7 & 2713.1 & 2587.25607115576 & 125.843928844243 \tabularnewline
8 & 2412 & 2480.74242247921 & -68.7424224792094 \tabularnewline
9 & 2568.3 & 2793.97812040236 & -225.678120402362 \tabularnewline
10 & 2623.7 & 2576.91742610859 & 46.7825738914094 \tabularnewline
11 & 3185.5 & 3094.58635954661 & 90.9136404533906 \tabularnewline
12 & 2722.6 & 2833.19469383351 & -110.59469383351 \tabularnewline
13 & 3046.3 & 3077.2950525245 & -30.9950525244985 \tabularnewline
14 & 2854.2 & 3027.62851922073 & -173.428519220731 \tabularnewline
15 & 3337.6 & 3472.1457744162 & -134.545774416201 \tabularnewline
16 & 2920.3 & 2958.51204105088 & -38.2120410508846 \tabularnewline
17 & 3058.3 & 3251.14934732664 & -192.849347326641 \tabularnewline
18 & 2933.7 & 3023.06210987458 & -89.3621098745766 \tabularnewline
19 & 3773.4 & 3497.79944943857 & 275.600550561428 \tabularnewline
20 & 3193.5 & 3178.97938077066 & 14.5206192293376 \tabularnewline
21 & 3472.2 & 3459.8014483434 & 12.3985516565981 \tabularnewline
22 & 3345.5 & 3365.09101892565 & -19.5910189256488 \tabularnewline
23 & 4028.4 & 4095.02489091979 & -66.6248909197857 \tabularnewline
24 & 3463.1 & 3455.89943153706 & 7.20056846294483 \tabularnewline
25 & 3675.4 & 3743.6835557354 & -68.2835557353974 \tabularnewline
26 & 3500.8 & 3573.51863338911 & -72.7186333891109 \tabularnewline
27 & 4142.1 & 4278.36582994631 & -136.265829946309 \tabularnewline
28 & 3598 & 3581.05642217597 & 16.943577824034 \tabularnewline
29 & 3765.3 & 3835.56229961961 & -70.262299619606 \tabularnewline
30 & 3557.7 & 3637.47733658389 & -79.7773365838907 \tabularnewline
31 & 4303.6 & 4309.37302239569 & -5.7730223956878 \tabularnewline
32 & 3620.1 & 3697.03856292337 & -76.9385629233675 \tabularnewline
33 & 3691.1 & 3858.04680981277 & -166.946809812774 \tabularnewline
34 & 3678.1 & 3581.75242293932 & 96.3475770606838 \tabularnewline
35 & 4505.8 & 4366.23770710633 & 139.562292893667 \tabularnewline
36 & 3695 & 3781.92881744236 & -86.9288174423591 \tabularnewline
37 & 3894.1 & 3908.12498490641 & -14.0249849064089 \tabularnewline
38 & 3718.9 & 3799.71435927681 & -80.8143592768133 \tabularnewline
39 & 4749.8 & 4519.74147357383 & 230.058526426169 \tabularnewline
40 & 3855.9 & 3880.95165475496 & -25.0516547549582 \tabularnewline
41 & 4011.7 & 4075.93210775509 & -64.2321077550946 \tabularnewline
42 & 3907.6 & 3915.62426805185 & -8.02426805184723 \tabularnewline
43 & 4812.5 & 4823.44317496971 & -10.9431749697123 \tabularnewline
44 & 4071.3 & 3949.25106634553 & 122.048933654468 \tabularnewline
45 & 4163.4 & 4216.09943401534 & -52.6994340153369 \tabularnewline
46 & 4077.6 & 4078.83624293824 & -1.23624293823514 \tabularnewline
47 & 5109.2 & 5033.02719849116 & 76.1728015088383 \tabularnewline
48 & 4207.6 & 4211.66584658485 & -4.06584658485372 \tabularnewline
49 & 4320.8 & 4360.71927606587 & -39.9192760658661 \tabularnewline
50 & 4396.9 & 4243.25724381824 & 153.642756181757 \tabularnewline
51 & 5358.8 & 5375.16037085137 & -16.360370851372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301854&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]5[/C][C]2225.5[/C][C]2043.3205156145[/C][C]182.179484385497[/C][/ROW]
[ROW][C]6[/C][C]2195.7[/C][C]2111.66066076713[/C][C]84.0393392328697[/C][/ROW]
[ROW][C]7[/C][C]2713.1[/C][C]2587.25607115576[/C][C]125.843928844243[/C][/ROW]
[ROW][C]8[/C][C]2412[/C][C]2480.74242247921[/C][C]-68.7424224792094[/C][/ROW]
[ROW][C]9[/C][C]2568.3[/C][C]2793.97812040236[/C][C]-225.678120402362[/C][/ROW]
[ROW][C]10[/C][C]2623.7[/C][C]2576.91742610859[/C][C]46.7825738914094[/C][/ROW]
[ROW][C]11[/C][C]3185.5[/C][C]3094.58635954661[/C][C]90.9136404533906[/C][/ROW]
[ROW][C]12[/C][C]2722.6[/C][C]2833.19469383351[/C][C]-110.59469383351[/C][/ROW]
[ROW][C]13[/C][C]3046.3[/C][C]3077.2950525245[/C][C]-30.9950525244985[/C][/ROW]
[ROW][C]14[/C][C]2854.2[/C][C]3027.62851922073[/C][C]-173.428519220731[/C][/ROW]
[ROW][C]15[/C][C]3337.6[/C][C]3472.1457744162[/C][C]-134.545774416201[/C][/ROW]
[ROW][C]16[/C][C]2920.3[/C][C]2958.51204105088[/C][C]-38.2120410508846[/C][/ROW]
[ROW][C]17[/C][C]3058.3[/C][C]3251.14934732664[/C][C]-192.849347326641[/C][/ROW]
[ROW][C]18[/C][C]2933.7[/C][C]3023.06210987458[/C][C]-89.3621098745766[/C][/ROW]
[ROW][C]19[/C][C]3773.4[/C][C]3497.79944943857[/C][C]275.600550561428[/C][/ROW]
[ROW][C]20[/C][C]3193.5[/C][C]3178.97938077066[/C][C]14.5206192293376[/C][/ROW]
[ROW][C]21[/C][C]3472.2[/C][C]3459.8014483434[/C][C]12.3985516565981[/C][/ROW]
[ROW][C]22[/C][C]3345.5[/C][C]3365.09101892565[/C][C]-19.5910189256488[/C][/ROW]
[ROW][C]23[/C][C]4028.4[/C][C]4095.02489091979[/C][C]-66.6248909197857[/C][/ROW]
[ROW][C]24[/C][C]3463.1[/C][C]3455.89943153706[/C][C]7.20056846294483[/C][/ROW]
[ROW][C]25[/C][C]3675.4[/C][C]3743.6835557354[/C][C]-68.2835557353974[/C][/ROW]
[ROW][C]26[/C][C]3500.8[/C][C]3573.51863338911[/C][C]-72.7186333891109[/C][/ROW]
[ROW][C]27[/C][C]4142.1[/C][C]4278.36582994631[/C][C]-136.265829946309[/C][/ROW]
[ROW][C]28[/C][C]3598[/C][C]3581.05642217597[/C][C]16.943577824034[/C][/ROW]
[ROW][C]29[/C][C]3765.3[/C][C]3835.56229961961[/C][C]-70.262299619606[/C][/ROW]
[ROW][C]30[/C][C]3557.7[/C][C]3637.47733658389[/C][C]-79.7773365838907[/C][/ROW]
[ROW][C]31[/C][C]4303.6[/C][C]4309.37302239569[/C][C]-5.7730223956878[/C][/ROW]
[ROW][C]32[/C][C]3620.1[/C][C]3697.03856292337[/C][C]-76.9385629233675[/C][/ROW]
[ROW][C]33[/C][C]3691.1[/C][C]3858.04680981277[/C][C]-166.946809812774[/C][/ROW]
[ROW][C]34[/C][C]3678.1[/C][C]3581.75242293932[/C][C]96.3475770606838[/C][/ROW]
[ROW][C]35[/C][C]4505.8[/C][C]4366.23770710633[/C][C]139.562292893667[/C][/ROW]
[ROW][C]36[/C][C]3695[/C][C]3781.92881744236[/C][C]-86.9288174423591[/C][/ROW]
[ROW][C]37[/C][C]3894.1[/C][C]3908.12498490641[/C][C]-14.0249849064089[/C][/ROW]
[ROW][C]38[/C][C]3718.9[/C][C]3799.71435927681[/C][C]-80.8143592768133[/C][/ROW]
[ROW][C]39[/C][C]4749.8[/C][C]4519.74147357383[/C][C]230.058526426169[/C][/ROW]
[ROW][C]40[/C][C]3855.9[/C][C]3880.95165475496[/C][C]-25.0516547549582[/C][/ROW]
[ROW][C]41[/C][C]4011.7[/C][C]4075.93210775509[/C][C]-64.2321077550946[/C][/ROW]
[ROW][C]42[/C][C]3907.6[/C][C]3915.62426805185[/C][C]-8.02426805184723[/C][/ROW]
[ROW][C]43[/C][C]4812.5[/C][C]4823.44317496971[/C][C]-10.9431749697123[/C][/ROW]
[ROW][C]44[/C][C]4071.3[/C][C]3949.25106634553[/C][C]122.048933654468[/C][/ROW]
[ROW][C]45[/C][C]4163.4[/C][C]4216.09943401534[/C][C]-52.6994340153369[/C][/ROW]
[ROW][C]46[/C][C]4077.6[/C][C]4078.83624293824[/C][C]-1.23624293823514[/C][/ROW]
[ROW][C]47[/C][C]5109.2[/C][C]5033.02719849116[/C][C]76.1728015088383[/C][/ROW]
[ROW][C]48[/C][C]4207.6[/C][C]4211.66584658485[/C][C]-4.06584658485372[/C][/ROW]
[ROW][C]49[/C][C]4320.8[/C][C]4360.71927606587[/C][C]-39.9192760658661[/C][/ROW]
[ROW][C]50[/C][C]4396.9[/C][C]4243.25724381824[/C][C]153.642756181757[/C][/ROW]
[ROW][C]51[/C][C]5358.8[/C][C]5375.16037085137[/C][C]-16.360370851372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301854&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301854&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
52225.52043.3205156145182.179484385497
62195.72111.6606607671384.0393392328697
72713.12587.25607115576125.843928844243
824122480.74242247921-68.7424224792094
92568.32793.97812040236-225.678120402362
102623.72576.9174261085946.7825738914094
113185.53094.5863595466190.9136404533906
122722.62833.19469383351-110.59469383351
133046.33077.2950525245-30.9950525244985
142854.23027.62851922073-173.428519220731
153337.63472.1457744162-134.545774416201
162920.32958.51204105088-38.2120410508846
173058.33251.14934732664-192.849347326641
182933.73023.06210987458-89.3621098745766
193773.43497.79944943857275.600550561428
203193.53178.9793807706614.5206192293376
213472.23459.801448343412.3985516565981
223345.53365.09101892565-19.5910189256488
234028.44095.02489091979-66.6248909197857
243463.13455.899431537067.20056846294483
253675.43743.6835557354-68.2835557353974
263500.83573.51863338911-72.7186333891109
274142.14278.36582994631-136.265829946309
2835983581.0564221759716.943577824034
293765.33835.56229961961-70.262299619606
303557.73637.47733658389-79.7773365838907
314303.64309.37302239569-5.7730223956878
323620.13697.03856292337-76.9385629233675
333691.13858.04680981277-166.946809812774
343678.13581.7524229393296.3475770606838
354505.84366.23770710633139.562292893667
3636953781.92881744236-86.9288174423591
373894.13908.12498490641-14.0249849064089
383718.93799.71435927681-80.8143592768133
394749.84519.74147357383230.058526426169
403855.93880.95165475496-25.0516547549582
414011.74075.93210775509-64.2321077550946
423907.63915.62426805185-8.02426805184723
434812.54823.44317496971-10.9431749697123
444071.33949.25106634553122.048933654468
454163.44216.09943401534-52.6994340153369
464077.64078.83624293824-1.23624293823514
475109.25033.0271984911676.1728015088383
484207.64211.66584658485-4.06584658485372
494320.84360.71927606587-39.9192760658661
504396.94243.25724381824153.642756181757
515358.85375.16037085137-16.360370851372







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
524438.759306852544261.862061619444615.65655208563
534591.71295689174373.852511266424809.57340251697
544564.798365007624307.093602240334822.50312777491
555601.728241815175304.260017246695899.19646638365
564635.536790034664268.55946276665002.51411730272
574793.039838595474378.700102819245207.37957437171
584762.775050782334308.921485458045216.62861610662
595842.070955928845311.993752215926372.14815964177
604832.314273216784263.187490585555401.441055848
614994.366720299254367.973306114455620.76013448405
624960.751736557044292.939597062025628.56387605206
636082.413670042525296.499363736516868.32797634852

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
52 & 4438.75930685254 & 4261.86206161944 & 4615.65655208563 \tabularnewline
53 & 4591.7129568917 & 4373.85251126642 & 4809.57340251697 \tabularnewline
54 & 4564.79836500762 & 4307.09360224033 & 4822.50312777491 \tabularnewline
55 & 5601.72824181517 & 5304.26001724669 & 5899.19646638365 \tabularnewline
56 & 4635.53679003466 & 4268.5594627666 & 5002.51411730272 \tabularnewline
57 & 4793.03983859547 & 4378.70010281924 & 5207.37957437171 \tabularnewline
58 & 4762.77505078233 & 4308.92148545804 & 5216.62861610662 \tabularnewline
59 & 5842.07095592884 & 5311.99375221592 & 6372.14815964177 \tabularnewline
60 & 4832.31427321678 & 4263.18749058555 & 5401.441055848 \tabularnewline
61 & 4994.36672029925 & 4367.97330611445 & 5620.76013448405 \tabularnewline
62 & 4960.75173655704 & 4292.93959706202 & 5628.56387605206 \tabularnewline
63 & 6082.41367004252 & 5296.49936373651 & 6868.32797634852 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301854&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]52[/C][C]4438.75930685254[/C][C]4261.86206161944[/C][C]4615.65655208563[/C][/ROW]
[ROW][C]53[/C][C]4591.7129568917[/C][C]4373.85251126642[/C][C]4809.57340251697[/C][/ROW]
[ROW][C]54[/C][C]4564.79836500762[/C][C]4307.09360224033[/C][C]4822.50312777491[/C][/ROW]
[ROW][C]55[/C][C]5601.72824181517[/C][C]5304.26001724669[/C][C]5899.19646638365[/C][/ROW]
[ROW][C]56[/C][C]4635.53679003466[/C][C]4268.5594627666[/C][C]5002.51411730272[/C][/ROW]
[ROW][C]57[/C][C]4793.03983859547[/C][C]4378.70010281924[/C][C]5207.37957437171[/C][/ROW]
[ROW][C]58[/C][C]4762.77505078233[/C][C]4308.92148545804[/C][C]5216.62861610662[/C][/ROW]
[ROW][C]59[/C][C]5842.07095592884[/C][C]5311.99375221592[/C][C]6372.14815964177[/C][/ROW]
[ROW][C]60[/C][C]4832.31427321678[/C][C]4263.18749058555[/C][C]5401.441055848[/C][/ROW]
[ROW][C]61[/C][C]4994.36672029925[/C][C]4367.97330611445[/C][C]5620.76013448405[/C][/ROW]
[ROW][C]62[/C][C]4960.75173655704[/C][C]4292.93959706202[/C][C]5628.56387605206[/C][/ROW]
[ROW][C]63[/C][C]6082.41367004252[/C][C]5296.49936373651[/C][C]6868.32797634852[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301854&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301854&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
524438.759306852544261.862061619444615.65655208563
534591.71295689174373.852511266424809.57340251697
544564.798365007624307.093602240334822.50312777491
555601.728241815175304.260017246695899.19646638365
564635.536790034664268.55946276665002.51411730272
574793.039838595474378.700102819245207.37957437171
584762.775050782334308.921485458045216.62861610662
595842.070955928845311.993752215926372.14815964177
604832.314273216784263.187490585555401.441055848
614994.366720299254367.973306114455620.76013448405
624960.751736557044292.939597062025628.56387605206
636082.413670042525296.499363736516868.32797634852



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')