Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 18 Aug 2009 16:41:31 -0600
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/Aug/19/t1250635372nc2pag2njq9j05v.htm/, Retrieved Tue, 07 May 2024 20:26:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42907, Retrieved Tue, 07 May 2024 20:26:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Triple Smoothing ...] [2009-08-18 22:41:31] [b3f4824a747975de0748bc1b396f9742] [Current]
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Dataseries X:
15.22
15.27
15.31
15.33
15.42
15.49
15.65
15.67
15.69
15.83
15.92
15.99
15.94
15.96
16.03
16.09
16.04
16.23
16.2
16.2
16.26
16.28
16.27
16.29
16.3
16.37
16.39
16.42
16.43
16.37
16.37
16.39
16.48
16.51
16.5
16.54
16.52
16.56
16.61
16.75
16.75
16.79
16.82
16.84
17.14
17.25
17.28
17.3
17.34
17.44
17.48
17.55
17.59
17.66
17.67
17.64
17.68
17.72
17.78
17.83
17.88
18.11
18.16
18.27
18.29
18.35
18.35
18.38
18.41
18.41
18.42
18.43
18.48
18.54
18.65
18.66
18.69
18.72
18.72
18.73
18.84
18.83
18.91
18.91
18.94
18.97
19
19.08
19.18
19.24
19.23
19.25
19.3
19.33
19.35
19.35
19.31
19.47
19.7
19.76
19.9
19.97
20.1
20.26
20.44
20.43
20.57
20.6
20.69
20.93
20.98
21.11
21.14
21.16
21.32
21.32
21.48
21.58
21.74
21.75
21.81
21.89
22.21
22.37
22.47
22.51
22.55
22.61
22.58
22.85
22.93
22.98




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time40 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 40 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42907&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]40 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42907&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42907&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 time40 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.78099895625679
beta0.0460781151747984
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.78099895625679 \tabularnewline
beta & 0.0460781151747984 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42907&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]0.78099895625679[/C][/ROW]
[ROW][C]beta[/C][C]0.0460781151747984[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42907&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42907&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
alpha0.78099895625679
beta0.0460781151747984
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315.9415.59144230769230.348557692307683
1415.9615.90155285610490.0584471438950818
1516.0316.036357370696-0.0063573706960156
1616.0916.1136541779200-0.023654177920033
1716.0416.0757576214709-0.035757621470907
1816.2316.2733714801529-0.043371480152949
1916.216.2613947821027-0.0613947821026599
2016.216.233549159149-0.0335491591490076
2116.2616.22624360641490.0337563935850831
2216.2816.3898017434307-0.109801743430666
2316.2716.3914563610085-0.121456361008452
2416.2916.3604712225677-0.0704712225676651
2516.316.3260205440628-0.0260205440628347
2616.3716.26423038747710.105769612522860
2716.3916.4076834556650-0.0176834556650469
2816.4216.4578210034749-0.0378210034749067
2916.4316.39117410326150.0388258967385156
3016.3716.6330188018747-0.263018801874679
3116.3716.4252948465807-0.0552948465806722
3216.3916.38827519923250.00172480076753345
3316.4816.40449167309330.075508326906732
3416.5116.5519542841776-0.0419542841776277
3516.516.5892225865623-0.0892225865623253
3616.5416.5809150497607-0.0409150497607378
3716.5216.5666833520677-0.0466833520677064
3816.5616.5042750499130.055724950087015
3916.6116.56646328699640.0435367130035935
4016.7516.64706305521250.102936944787491
4116.7516.69925864402000.050741355979973
4216.7916.8768587281696-0.0868587281696271
4316.8216.8511005634444-0.0311005634443582
4416.8416.8452278608033-0.00522786080325588
4517.1416.87168664986390.268313350136115
4617.2517.15045748244880.0995425175511997
4717.2817.2994270054886-0.019427005488609
4817.317.3702650501609-0.0702650501609341
4917.3417.3448474558009-0.00484745580092394
5017.4417.35204570398160.0879542960183919
5117.4817.45240086009100.0275991399089754
5217.5517.54865363844640.00134636155355494
5317.5917.52151178844660.0684882115534435
5417.6617.6949118306985-0.0349118306985403
5517.6717.7358788903356-0.0658788903356111
5617.6417.7212025887058-0.0812025887057928
5717.6817.7581889949228-0.078188994922769
5817.7217.726869292852-0.00686929285200577
5917.7817.76033583943010.0196641605698673
6017.8317.8456362174876-0.0156362174876001
6117.8817.87424188981920.00575811018079264
6218.1117.90746010049720.202539899502785
6318.1618.08562558468510.0743744153149173
6418.2718.21588065194690.0541193480531277
6518.2918.24977795739400.0402220426060325
6618.3518.3825595933806-0.0325595933805616
6718.3518.4227687387518-0.072768738751801
6818.3818.4032944312908-0.0232944312908465
6918.4118.4921898312556-0.0821898312556293
7018.4118.4792433945053-0.0692433945052784
7118.4218.4734408576235-0.0534408576234568
7218.4318.4949188166158-0.0649188166157728
7318.4818.4889500231198-0.00895002311979098
7418.5418.5524771258536-0.0124771258536320
7518.6518.52560886535240.124391134647638
7618.6618.6832537095085-0.0232537095084737
7718.6918.64365744441440.0463425555856141
7818.7218.7554784301133-0.0354784301132547
7918.7218.774695571888-0.0546955718879865
8018.7318.7709151618363-0.0409151618363097
8118.8418.82326036702980.0167396329701965
8218.8318.8840829238590-0.0540829238589566
8318.9118.88779695216280.0222030478372339
8418.9118.9627767129206-0.0527767129205934
8518.9418.9759227468811-0.0359227468811305
8618.9719.0140157079538-0.0440157079537542
871918.98775912859150.0122408714085473
8819.0819.01671340115510.0632865988449147
8919.1819.05429404577280.125705954227175
9019.2419.20738229366610.0326177063338591
9119.2319.2752278577121-0.0452278577120993
9219.2519.2818543458718-0.0318543458717926
9319.319.3542232694736-0.0542232694735603
9419.3319.3418806909311-0.0118806909311360
9519.3519.3945470878261-0.0445470878260821
9619.3519.3978580432810-0.0478580432810354
9719.3119.4155972240627-0.105597224062727
9819.4719.39205538645610.077944613543913
9919.719.47231218387910.227687816120863
10019.7619.6874048869230.0725951130769964
10119.919.75295588449080.147044115509186
10219.9719.91012119525050.0598788047495376
10320.119.99098883760850.109011162391489
10420.2620.13533469463960.124665305360434
10520.4420.34500919338190.0949908066181209
10620.4320.4838081908987-0.0538081908986747
10720.5720.52039890528420.0496010947158467
10820.620.6237261234222-0.0237261234221826
10920.6920.67574753508610.0142524649139268
11020.9320.81839722694650.111602773053491
11120.9820.9913393777712-0.0113393777712325
11221.1121.01078921429070.0992107857093316
11321.1421.13939183705110.000608162948857682
11421.1621.1837921463301-0.0237921463300665
11521.3221.22775245633520.092247543664751
11621.3221.3795105021167-0.0595105021167086
11721.4821.4492934976940.0307065023059891
11821.5821.51343434463600.0665656553640375
11921.7421.67915049732970.0608495026703118
12021.7521.7880756175723-0.0380756175723462
12121.8121.8495626896373-0.0395626896373393
12221.8921.9819212271168-0.0919212271168348
12322.2121.97208128292360.237918717076436
12422.3722.22247646963820.147523530361788
12522.4722.38102028414060.0889797158593701
12622.5122.50607828022770.00392171977229339
12722.5522.6150765311661-0.065076531166099
12822.6122.6230484803313-0.0130484803313493
12922.5822.7628669235168-0.182866923516777
13022.8522.67436552040890.175634479591139
13122.9322.9342427036316-0.00424270363162904
13222.9822.97855393954490.00144606045514450

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15.94 & 15.5914423076923 & 0.348557692307683 \tabularnewline
14 & 15.96 & 15.9015528561049 & 0.0584471438950818 \tabularnewline
15 & 16.03 & 16.036357370696 & -0.0063573706960156 \tabularnewline
16 & 16.09 & 16.1136541779200 & -0.023654177920033 \tabularnewline
17 & 16.04 & 16.0757576214709 & -0.035757621470907 \tabularnewline
18 & 16.23 & 16.2733714801529 & -0.043371480152949 \tabularnewline
19 & 16.2 & 16.2613947821027 & -0.0613947821026599 \tabularnewline
20 & 16.2 & 16.233549159149 & -0.0335491591490076 \tabularnewline
21 & 16.26 & 16.2262436064149 & 0.0337563935850831 \tabularnewline
22 & 16.28 & 16.3898017434307 & -0.109801743430666 \tabularnewline
23 & 16.27 & 16.3914563610085 & -0.121456361008452 \tabularnewline
24 & 16.29 & 16.3604712225677 & -0.0704712225676651 \tabularnewline
25 & 16.3 & 16.3260205440628 & -0.0260205440628347 \tabularnewline
26 & 16.37 & 16.2642303874771 & 0.105769612522860 \tabularnewline
27 & 16.39 & 16.4076834556650 & -0.0176834556650469 \tabularnewline
28 & 16.42 & 16.4578210034749 & -0.0378210034749067 \tabularnewline
29 & 16.43 & 16.3911741032615 & 0.0388258967385156 \tabularnewline
30 & 16.37 & 16.6330188018747 & -0.263018801874679 \tabularnewline
31 & 16.37 & 16.4252948465807 & -0.0552948465806722 \tabularnewline
32 & 16.39 & 16.3882751992325 & 0.00172480076753345 \tabularnewline
33 & 16.48 & 16.4044916730933 & 0.075508326906732 \tabularnewline
34 & 16.51 & 16.5519542841776 & -0.0419542841776277 \tabularnewline
35 & 16.5 & 16.5892225865623 & -0.0892225865623253 \tabularnewline
36 & 16.54 & 16.5809150497607 & -0.0409150497607378 \tabularnewline
37 & 16.52 & 16.5666833520677 & -0.0466833520677064 \tabularnewline
38 & 16.56 & 16.504275049913 & 0.055724950087015 \tabularnewline
39 & 16.61 & 16.5664632869964 & 0.0435367130035935 \tabularnewline
40 & 16.75 & 16.6470630552125 & 0.102936944787491 \tabularnewline
41 & 16.75 & 16.6992586440200 & 0.050741355979973 \tabularnewline
42 & 16.79 & 16.8768587281696 & -0.0868587281696271 \tabularnewline
43 & 16.82 & 16.8511005634444 & -0.0311005634443582 \tabularnewline
44 & 16.84 & 16.8452278608033 & -0.00522786080325588 \tabularnewline
45 & 17.14 & 16.8716866498639 & 0.268313350136115 \tabularnewline
46 & 17.25 & 17.1504574824488 & 0.0995425175511997 \tabularnewline
47 & 17.28 & 17.2994270054886 & -0.019427005488609 \tabularnewline
48 & 17.3 & 17.3702650501609 & -0.0702650501609341 \tabularnewline
49 & 17.34 & 17.3448474558009 & -0.00484745580092394 \tabularnewline
50 & 17.44 & 17.3520457039816 & 0.0879542960183919 \tabularnewline
51 & 17.48 & 17.4524008600910 & 0.0275991399089754 \tabularnewline
52 & 17.55 & 17.5486536384464 & 0.00134636155355494 \tabularnewline
53 & 17.59 & 17.5215117884466 & 0.0684882115534435 \tabularnewline
54 & 17.66 & 17.6949118306985 & -0.0349118306985403 \tabularnewline
55 & 17.67 & 17.7358788903356 & -0.0658788903356111 \tabularnewline
56 & 17.64 & 17.7212025887058 & -0.0812025887057928 \tabularnewline
57 & 17.68 & 17.7581889949228 & -0.078188994922769 \tabularnewline
58 & 17.72 & 17.726869292852 & -0.00686929285200577 \tabularnewline
59 & 17.78 & 17.7603358394301 & 0.0196641605698673 \tabularnewline
60 & 17.83 & 17.8456362174876 & -0.0156362174876001 \tabularnewline
61 & 17.88 & 17.8742418898192 & 0.00575811018079264 \tabularnewline
62 & 18.11 & 17.9074601004972 & 0.202539899502785 \tabularnewline
63 & 18.16 & 18.0856255846851 & 0.0743744153149173 \tabularnewline
64 & 18.27 & 18.2158806519469 & 0.0541193480531277 \tabularnewline
65 & 18.29 & 18.2497779573940 & 0.0402220426060325 \tabularnewline
66 & 18.35 & 18.3825595933806 & -0.0325595933805616 \tabularnewline
67 & 18.35 & 18.4227687387518 & -0.072768738751801 \tabularnewline
68 & 18.38 & 18.4032944312908 & -0.0232944312908465 \tabularnewline
69 & 18.41 & 18.4921898312556 & -0.0821898312556293 \tabularnewline
70 & 18.41 & 18.4792433945053 & -0.0692433945052784 \tabularnewline
71 & 18.42 & 18.4734408576235 & -0.0534408576234568 \tabularnewline
72 & 18.43 & 18.4949188166158 & -0.0649188166157728 \tabularnewline
73 & 18.48 & 18.4889500231198 & -0.00895002311979098 \tabularnewline
74 & 18.54 & 18.5524771258536 & -0.0124771258536320 \tabularnewline
75 & 18.65 & 18.5256088653524 & 0.124391134647638 \tabularnewline
76 & 18.66 & 18.6832537095085 & -0.0232537095084737 \tabularnewline
77 & 18.69 & 18.6436574444144 & 0.0463425555856141 \tabularnewline
78 & 18.72 & 18.7554784301133 & -0.0354784301132547 \tabularnewline
79 & 18.72 & 18.774695571888 & -0.0546955718879865 \tabularnewline
80 & 18.73 & 18.7709151618363 & -0.0409151618363097 \tabularnewline
81 & 18.84 & 18.8232603670298 & 0.0167396329701965 \tabularnewline
82 & 18.83 & 18.8840829238590 & -0.0540829238589566 \tabularnewline
83 & 18.91 & 18.8877969521628 & 0.0222030478372339 \tabularnewline
84 & 18.91 & 18.9627767129206 & -0.0527767129205934 \tabularnewline
85 & 18.94 & 18.9759227468811 & -0.0359227468811305 \tabularnewline
86 & 18.97 & 19.0140157079538 & -0.0440157079537542 \tabularnewline
87 & 19 & 18.9877591285915 & 0.0122408714085473 \tabularnewline
88 & 19.08 & 19.0167134011551 & 0.0632865988449147 \tabularnewline
89 & 19.18 & 19.0542940457728 & 0.125705954227175 \tabularnewline
90 & 19.24 & 19.2073822936661 & 0.0326177063338591 \tabularnewline
91 & 19.23 & 19.2752278577121 & -0.0452278577120993 \tabularnewline
92 & 19.25 & 19.2818543458718 & -0.0318543458717926 \tabularnewline
93 & 19.3 & 19.3542232694736 & -0.0542232694735603 \tabularnewline
94 & 19.33 & 19.3418806909311 & -0.0118806909311360 \tabularnewline
95 & 19.35 & 19.3945470878261 & -0.0445470878260821 \tabularnewline
96 & 19.35 & 19.3978580432810 & -0.0478580432810354 \tabularnewline
97 & 19.31 & 19.4155972240627 & -0.105597224062727 \tabularnewline
98 & 19.47 & 19.3920553864561 & 0.077944613543913 \tabularnewline
99 & 19.7 & 19.4723121838791 & 0.227687816120863 \tabularnewline
100 & 19.76 & 19.687404886923 & 0.0725951130769964 \tabularnewline
101 & 19.9 & 19.7529558844908 & 0.147044115509186 \tabularnewline
102 & 19.97 & 19.9101211952505 & 0.0598788047495376 \tabularnewline
103 & 20.1 & 19.9909888376085 & 0.109011162391489 \tabularnewline
104 & 20.26 & 20.1353346946396 & 0.124665305360434 \tabularnewline
105 & 20.44 & 20.3450091933819 & 0.0949908066181209 \tabularnewline
106 & 20.43 & 20.4838081908987 & -0.0538081908986747 \tabularnewline
107 & 20.57 & 20.5203989052842 & 0.0496010947158467 \tabularnewline
108 & 20.6 & 20.6237261234222 & -0.0237261234221826 \tabularnewline
109 & 20.69 & 20.6757475350861 & 0.0142524649139268 \tabularnewline
110 & 20.93 & 20.8183972269465 & 0.111602773053491 \tabularnewline
111 & 20.98 & 20.9913393777712 & -0.0113393777712325 \tabularnewline
112 & 21.11 & 21.0107892142907 & 0.0992107857093316 \tabularnewline
113 & 21.14 & 21.1393918370511 & 0.000608162948857682 \tabularnewline
114 & 21.16 & 21.1837921463301 & -0.0237921463300665 \tabularnewline
115 & 21.32 & 21.2277524563352 & 0.092247543664751 \tabularnewline
116 & 21.32 & 21.3795105021167 & -0.0595105021167086 \tabularnewline
117 & 21.48 & 21.449293497694 & 0.0307065023059891 \tabularnewline
118 & 21.58 & 21.5134343446360 & 0.0665656553640375 \tabularnewline
119 & 21.74 & 21.6791504973297 & 0.0608495026703118 \tabularnewline
120 & 21.75 & 21.7880756175723 & -0.0380756175723462 \tabularnewline
121 & 21.81 & 21.8495626896373 & -0.0395626896373393 \tabularnewline
122 & 21.89 & 21.9819212271168 & -0.0919212271168348 \tabularnewline
123 & 22.21 & 21.9720812829236 & 0.237918717076436 \tabularnewline
124 & 22.37 & 22.2224764696382 & 0.147523530361788 \tabularnewline
125 & 22.47 & 22.3810202841406 & 0.0889797158593701 \tabularnewline
126 & 22.51 & 22.5060782802277 & 0.00392171977229339 \tabularnewline
127 & 22.55 & 22.6150765311661 & -0.065076531166099 \tabularnewline
128 & 22.61 & 22.6230484803313 & -0.0130484803313493 \tabularnewline
129 & 22.58 & 22.7628669235168 & -0.182866923516777 \tabularnewline
130 & 22.85 & 22.6743655204089 & 0.175634479591139 \tabularnewline
131 & 22.93 & 22.9342427036316 & -0.00424270363162904 \tabularnewline
132 & 22.98 & 22.9785539395449 & 0.00144606045514450 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42907&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]15.94[/C][C]15.5914423076923[/C][C]0.348557692307683[/C][/ROW]
[ROW][C]14[/C][C]15.96[/C][C]15.9015528561049[/C][C]0.0584471438950818[/C][/ROW]
[ROW][C]15[/C][C]16.03[/C][C]16.036357370696[/C][C]-0.0063573706960156[/C][/ROW]
[ROW][C]16[/C][C]16.09[/C][C]16.1136541779200[/C][C]-0.023654177920033[/C][/ROW]
[ROW][C]17[/C][C]16.04[/C][C]16.0757576214709[/C][C]-0.035757621470907[/C][/ROW]
[ROW][C]18[/C][C]16.23[/C][C]16.2733714801529[/C][C]-0.043371480152949[/C][/ROW]
[ROW][C]19[/C][C]16.2[/C][C]16.2613947821027[/C][C]-0.0613947821026599[/C][/ROW]
[ROW][C]20[/C][C]16.2[/C][C]16.233549159149[/C][C]-0.0335491591490076[/C][/ROW]
[ROW][C]21[/C][C]16.26[/C][C]16.2262436064149[/C][C]0.0337563935850831[/C][/ROW]
[ROW][C]22[/C][C]16.28[/C][C]16.3898017434307[/C][C]-0.109801743430666[/C][/ROW]
[ROW][C]23[/C][C]16.27[/C][C]16.3914563610085[/C][C]-0.121456361008452[/C][/ROW]
[ROW][C]24[/C][C]16.29[/C][C]16.3604712225677[/C][C]-0.0704712225676651[/C][/ROW]
[ROW][C]25[/C][C]16.3[/C][C]16.3260205440628[/C][C]-0.0260205440628347[/C][/ROW]
[ROW][C]26[/C][C]16.37[/C][C]16.2642303874771[/C][C]0.105769612522860[/C][/ROW]
[ROW][C]27[/C][C]16.39[/C][C]16.4076834556650[/C][C]-0.0176834556650469[/C][/ROW]
[ROW][C]28[/C][C]16.42[/C][C]16.4578210034749[/C][C]-0.0378210034749067[/C][/ROW]
[ROW][C]29[/C][C]16.43[/C][C]16.3911741032615[/C][C]0.0388258967385156[/C][/ROW]
[ROW][C]30[/C][C]16.37[/C][C]16.6330188018747[/C][C]-0.263018801874679[/C][/ROW]
[ROW][C]31[/C][C]16.37[/C][C]16.4252948465807[/C][C]-0.0552948465806722[/C][/ROW]
[ROW][C]32[/C][C]16.39[/C][C]16.3882751992325[/C][C]0.00172480076753345[/C][/ROW]
[ROW][C]33[/C][C]16.48[/C][C]16.4044916730933[/C][C]0.075508326906732[/C][/ROW]
[ROW][C]34[/C][C]16.51[/C][C]16.5519542841776[/C][C]-0.0419542841776277[/C][/ROW]
[ROW][C]35[/C][C]16.5[/C][C]16.5892225865623[/C][C]-0.0892225865623253[/C][/ROW]
[ROW][C]36[/C][C]16.54[/C][C]16.5809150497607[/C][C]-0.0409150497607378[/C][/ROW]
[ROW][C]37[/C][C]16.52[/C][C]16.5666833520677[/C][C]-0.0466833520677064[/C][/ROW]
[ROW][C]38[/C][C]16.56[/C][C]16.504275049913[/C][C]0.055724950087015[/C][/ROW]
[ROW][C]39[/C][C]16.61[/C][C]16.5664632869964[/C][C]0.0435367130035935[/C][/ROW]
[ROW][C]40[/C][C]16.75[/C][C]16.6470630552125[/C][C]0.102936944787491[/C][/ROW]
[ROW][C]41[/C][C]16.75[/C][C]16.6992586440200[/C][C]0.050741355979973[/C][/ROW]
[ROW][C]42[/C][C]16.79[/C][C]16.8768587281696[/C][C]-0.0868587281696271[/C][/ROW]
[ROW][C]43[/C][C]16.82[/C][C]16.8511005634444[/C][C]-0.0311005634443582[/C][/ROW]
[ROW][C]44[/C][C]16.84[/C][C]16.8452278608033[/C][C]-0.00522786080325588[/C][/ROW]
[ROW][C]45[/C][C]17.14[/C][C]16.8716866498639[/C][C]0.268313350136115[/C][/ROW]
[ROW][C]46[/C][C]17.25[/C][C]17.1504574824488[/C][C]0.0995425175511997[/C][/ROW]
[ROW][C]47[/C][C]17.28[/C][C]17.2994270054886[/C][C]-0.019427005488609[/C][/ROW]
[ROW][C]48[/C][C]17.3[/C][C]17.3702650501609[/C][C]-0.0702650501609341[/C][/ROW]
[ROW][C]49[/C][C]17.34[/C][C]17.3448474558009[/C][C]-0.00484745580092394[/C][/ROW]
[ROW][C]50[/C][C]17.44[/C][C]17.3520457039816[/C][C]0.0879542960183919[/C][/ROW]
[ROW][C]51[/C][C]17.48[/C][C]17.4524008600910[/C][C]0.0275991399089754[/C][/ROW]
[ROW][C]52[/C][C]17.55[/C][C]17.5486536384464[/C][C]0.00134636155355494[/C][/ROW]
[ROW][C]53[/C][C]17.59[/C][C]17.5215117884466[/C][C]0.0684882115534435[/C][/ROW]
[ROW][C]54[/C][C]17.66[/C][C]17.6949118306985[/C][C]-0.0349118306985403[/C][/ROW]
[ROW][C]55[/C][C]17.67[/C][C]17.7358788903356[/C][C]-0.0658788903356111[/C][/ROW]
[ROW][C]56[/C][C]17.64[/C][C]17.7212025887058[/C][C]-0.0812025887057928[/C][/ROW]
[ROW][C]57[/C][C]17.68[/C][C]17.7581889949228[/C][C]-0.078188994922769[/C][/ROW]
[ROW][C]58[/C][C]17.72[/C][C]17.726869292852[/C][C]-0.00686929285200577[/C][/ROW]
[ROW][C]59[/C][C]17.78[/C][C]17.7603358394301[/C][C]0.0196641605698673[/C][/ROW]
[ROW][C]60[/C][C]17.83[/C][C]17.8456362174876[/C][C]-0.0156362174876001[/C][/ROW]
[ROW][C]61[/C][C]17.88[/C][C]17.8742418898192[/C][C]0.00575811018079264[/C][/ROW]
[ROW][C]62[/C][C]18.11[/C][C]17.9074601004972[/C][C]0.202539899502785[/C][/ROW]
[ROW][C]63[/C][C]18.16[/C][C]18.0856255846851[/C][C]0.0743744153149173[/C][/ROW]
[ROW][C]64[/C][C]18.27[/C][C]18.2158806519469[/C][C]0.0541193480531277[/C][/ROW]
[ROW][C]65[/C][C]18.29[/C][C]18.2497779573940[/C][C]0.0402220426060325[/C][/ROW]
[ROW][C]66[/C][C]18.35[/C][C]18.3825595933806[/C][C]-0.0325595933805616[/C][/ROW]
[ROW][C]67[/C][C]18.35[/C][C]18.4227687387518[/C][C]-0.072768738751801[/C][/ROW]
[ROW][C]68[/C][C]18.38[/C][C]18.4032944312908[/C][C]-0.0232944312908465[/C][/ROW]
[ROW][C]69[/C][C]18.41[/C][C]18.4921898312556[/C][C]-0.0821898312556293[/C][/ROW]
[ROW][C]70[/C][C]18.41[/C][C]18.4792433945053[/C][C]-0.0692433945052784[/C][/ROW]
[ROW][C]71[/C][C]18.42[/C][C]18.4734408576235[/C][C]-0.0534408576234568[/C][/ROW]
[ROW][C]72[/C][C]18.43[/C][C]18.4949188166158[/C][C]-0.0649188166157728[/C][/ROW]
[ROW][C]73[/C][C]18.48[/C][C]18.4889500231198[/C][C]-0.00895002311979098[/C][/ROW]
[ROW][C]74[/C][C]18.54[/C][C]18.5524771258536[/C][C]-0.0124771258536320[/C][/ROW]
[ROW][C]75[/C][C]18.65[/C][C]18.5256088653524[/C][C]0.124391134647638[/C][/ROW]
[ROW][C]76[/C][C]18.66[/C][C]18.6832537095085[/C][C]-0.0232537095084737[/C][/ROW]
[ROW][C]77[/C][C]18.69[/C][C]18.6436574444144[/C][C]0.0463425555856141[/C][/ROW]
[ROW][C]78[/C][C]18.72[/C][C]18.7554784301133[/C][C]-0.0354784301132547[/C][/ROW]
[ROW][C]79[/C][C]18.72[/C][C]18.774695571888[/C][C]-0.0546955718879865[/C][/ROW]
[ROW][C]80[/C][C]18.73[/C][C]18.7709151618363[/C][C]-0.0409151618363097[/C][/ROW]
[ROW][C]81[/C][C]18.84[/C][C]18.8232603670298[/C][C]0.0167396329701965[/C][/ROW]
[ROW][C]82[/C][C]18.83[/C][C]18.8840829238590[/C][C]-0.0540829238589566[/C][/ROW]
[ROW][C]83[/C][C]18.91[/C][C]18.8877969521628[/C][C]0.0222030478372339[/C][/ROW]
[ROW][C]84[/C][C]18.91[/C][C]18.9627767129206[/C][C]-0.0527767129205934[/C][/ROW]
[ROW][C]85[/C][C]18.94[/C][C]18.9759227468811[/C][C]-0.0359227468811305[/C][/ROW]
[ROW][C]86[/C][C]18.97[/C][C]19.0140157079538[/C][C]-0.0440157079537542[/C][/ROW]
[ROW][C]87[/C][C]19[/C][C]18.9877591285915[/C][C]0.0122408714085473[/C][/ROW]
[ROW][C]88[/C][C]19.08[/C][C]19.0167134011551[/C][C]0.0632865988449147[/C][/ROW]
[ROW][C]89[/C][C]19.18[/C][C]19.0542940457728[/C][C]0.125705954227175[/C][/ROW]
[ROW][C]90[/C][C]19.24[/C][C]19.2073822936661[/C][C]0.0326177063338591[/C][/ROW]
[ROW][C]91[/C][C]19.23[/C][C]19.2752278577121[/C][C]-0.0452278577120993[/C][/ROW]
[ROW][C]92[/C][C]19.25[/C][C]19.2818543458718[/C][C]-0.0318543458717926[/C][/ROW]
[ROW][C]93[/C][C]19.3[/C][C]19.3542232694736[/C][C]-0.0542232694735603[/C][/ROW]
[ROW][C]94[/C][C]19.33[/C][C]19.3418806909311[/C][C]-0.0118806909311360[/C][/ROW]
[ROW][C]95[/C][C]19.35[/C][C]19.3945470878261[/C][C]-0.0445470878260821[/C][/ROW]
[ROW][C]96[/C][C]19.35[/C][C]19.3978580432810[/C][C]-0.0478580432810354[/C][/ROW]
[ROW][C]97[/C][C]19.31[/C][C]19.4155972240627[/C][C]-0.105597224062727[/C][/ROW]
[ROW][C]98[/C][C]19.47[/C][C]19.3920553864561[/C][C]0.077944613543913[/C][/ROW]
[ROW][C]99[/C][C]19.7[/C][C]19.4723121838791[/C][C]0.227687816120863[/C][/ROW]
[ROW][C]100[/C][C]19.76[/C][C]19.687404886923[/C][C]0.0725951130769964[/C][/ROW]
[ROW][C]101[/C][C]19.9[/C][C]19.7529558844908[/C][C]0.147044115509186[/C][/ROW]
[ROW][C]102[/C][C]19.97[/C][C]19.9101211952505[/C][C]0.0598788047495376[/C][/ROW]
[ROW][C]103[/C][C]20.1[/C][C]19.9909888376085[/C][C]0.109011162391489[/C][/ROW]
[ROW][C]104[/C][C]20.26[/C][C]20.1353346946396[/C][C]0.124665305360434[/C][/ROW]
[ROW][C]105[/C][C]20.44[/C][C]20.3450091933819[/C][C]0.0949908066181209[/C][/ROW]
[ROW][C]106[/C][C]20.43[/C][C]20.4838081908987[/C][C]-0.0538081908986747[/C][/ROW]
[ROW][C]107[/C][C]20.57[/C][C]20.5203989052842[/C][C]0.0496010947158467[/C][/ROW]
[ROW][C]108[/C][C]20.6[/C][C]20.6237261234222[/C][C]-0.0237261234221826[/C][/ROW]
[ROW][C]109[/C][C]20.69[/C][C]20.6757475350861[/C][C]0.0142524649139268[/C][/ROW]
[ROW][C]110[/C][C]20.93[/C][C]20.8183972269465[/C][C]0.111602773053491[/C][/ROW]
[ROW][C]111[/C][C]20.98[/C][C]20.9913393777712[/C][C]-0.0113393777712325[/C][/ROW]
[ROW][C]112[/C][C]21.11[/C][C]21.0107892142907[/C][C]0.0992107857093316[/C][/ROW]
[ROW][C]113[/C][C]21.14[/C][C]21.1393918370511[/C][C]0.000608162948857682[/C][/ROW]
[ROW][C]114[/C][C]21.16[/C][C]21.1837921463301[/C][C]-0.0237921463300665[/C][/ROW]
[ROW][C]115[/C][C]21.32[/C][C]21.2277524563352[/C][C]0.092247543664751[/C][/ROW]
[ROW][C]116[/C][C]21.32[/C][C]21.3795105021167[/C][C]-0.0595105021167086[/C][/ROW]
[ROW][C]117[/C][C]21.48[/C][C]21.449293497694[/C][C]0.0307065023059891[/C][/ROW]
[ROW][C]118[/C][C]21.58[/C][C]21.5134343446360[/C][C]0.0665656553640375[/C][/ROW]
[ROW][C]119[/C][C]21.74[/C][C]21.6791504973297[/C][C]0.0608495026703118[/C][/ROW]
[ROW][C]120[/C][C]21.75[/C][C]21.7880756175723[/C][C]-0.0380756175723462[/C][/ROW]
[ROW][C]121[/C][C]21.81[/C][C]21.8495626896373[/C][C]-0.0395626896373393[/C][/ROW]
[ROW][C]122[/C][C]21.89[/C][C]21.9819212271168[/C][C]-0.0919212271168348[/C][/ROW]
[ROW][C]123[/C][C]22.21[/C][C]21.9720812829236[/C][C]0.237918717076436[/C][/ROW]
[ROW][C]124[/C][C]22.37[/C][C]22.2224764696382[/C][C]0.147523530361788[/C][/ROW]
[ROW][C]125[/C][C]22.47[/C][C]22.3810202841406[/C][C]0.0889797158593701[/C][/ROW]
[ROW][C]126[/C][C]22.51[/C][C]22.5060782802277[/C][C]0.00392171977229339[/C][/ROW]
[ROW][C]127[/C][C]22.55[/C][C]22.6150765311661[/C][C]-0.065076531166099[/C][/ROW]
[ROW][C]128[/C][C]22.61[/C][C]22.6230484803313[/C][C]-0.0130484803313493[/C][/ROW]
[ROW][C]129[/C][C]22.58[/C][C]22.7628669235168[/C][C]-0.182866923516777[/C][/ROW]
[ROW][C]130[/C][C]22.85[/C][C]22.6743655204089[/C][C]0.175634479591139[/C][/ROW]
[ROW][C]131[/C][C]22.93[/C][C]22.9342427036316[/C][C]-0.00424270363162904[/C][/ROW]
[ROW][C]132[/C][C]22.98[/C][C]22.9785539395449[/C][C]0.00144606045514450[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42907&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42907&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
1315.9415.59144230769230.348557692307683
1415.9615.90155285610490.0584471438950818
1516.0316.036357370696-0.0063573706960156
1616.0916.1136541779200-0.023654177920033
1716.0416.0757576214709-0.035757621470907
1816.2316.2733714801529-0.043371480152949
1916.216.2613947821027-0.0613947821026599
2016.216.233549159149-0.0335491591490076
2116.2616.22624360641490.0337563935850831
2216.2816.3898017434307-0.109801743430666
2316.2716.3914563610085-0.121456361008452
2416.2916.3604712225677-0.0704712225676651
2516.316.3260205440628-0.0260205440628347
2616.3716.26423038747710.105769612522860
2716.3916.4076834556650-0.0176834556650469
2816.4216.4578210034749-0.0378210034749067
2916.4316.39117410326150.0388258967385156
3016.3716.6330188018747-0.263018801874679
3116.3716.4252948465807-0.0552948465806722
3216.3916.38827519923250.00172480076753345
3316.4816.40449167309330.075508326906732
3416.5116.5519542841776-0.0419542841776277
3516.516.5892225865623-0.0892225865623253
3616.5416.5809150497607-0.0409150497607378
3716.5216.5666833520677-0.0466833520677064
3816.5616.5042750499130.055724950087015
3916.6116.56646328699640.0435367130035935
4016.7516.64706305521250.102936944787491
4116.7516.69925864402000.050741355979973
4216.7916.8768587281696-0.0868587281696271
4316.8216.8511005634444-0.0311005634443582
4416.8416.8452278608033-0.00522786080325588
4517.1416.87168664986390.268313350136115
4617.2517.15045748244880.0995425175511997
4717.2817.2994270054886-0.019427005488609
4817.317.3702650501609-0.0702650501609341
4917.3417.3448474558009-0.00484745580092394
5017.4417.35204570398160.0879542960183919
5117.4817.45240086009100.0275991399089754
5217.5517.54865363844640.00134636155355494
5317.5917.52151178844660.0684882115534435
5417.6617.6949118306985-0.0349118306985403
5517.6717.7358788903356-0.0658788903356111
5617.6417.7212025887058-0.0812025887057928
5717.6817.7581889949228-0.078188994922769
5817.7217.726869292852-0.00686929285200577
5917.7817.76033583943010.0196641605698673
6017.8317.8456362174876-0.0156362174876001
6117.8817.87424188981920.00575811018079264
6218.1117.90746010049720.202539899502785
6318.1618.08562558468510.0743744153149173
6418.2718.21588065194690.0541193480531277
6518.2918.24977795739400.0402220426060325
6618.3518.3825595933806-0.0325595933805616
6718.3518.4227687387518-0.072768738751801
6818.3818.4032944312908-0.0232944312908465
6918.4118.4921898312556-0.0821898312556293
7018.4118.4792433945053-0.0692433945052784
7118.4218.4734408576235-0.0534408576234568
7218.4318.4949188166158-0.0649188166157728
7318.4818.4889500231198-0.00895002311979098
7418.5418.5524771258536-0.0124771258536320
7518.6518.52560886535240.124391134647638
7618.6618.6832537095085-0.0232537095084737
7718.6918.64365744441440.0463425555856141
7818.7218.7554784301133-0.0354784301132547
7918.7218.774695571888-0.0546955718879865
8018.7318.7709151618363-0.0409151618363097
8118.8418.82326036702980.0167396329701965
8218.8318.8840829238590-0.0540829238589566
8318.9118.88779695216280.0222030478372339
8418.9118.9627767129206-0.0527767129205934
8518.9418.9759227468811-0.0359227468811305
8618.9719.0140157079538-0.0440157079537542
871918.98775912859150.0122408714085473
8819.0819.01671340115510.0632865988449147
8919.1819.05429404577280.125705954227175
9019.2419.20738229366610.0326177063338591
9119.2319.2752278577121-0.0452278577120993
9219.2519.2818543458718-0.0318543458717926
9319.319.3542232694736-0.0542232694735603
9419.3319.3418806909311-0.0118806909311360
9519.3519.3945470878261-0.0445470878260821
9619.3519.3978580432810-0.0478580432810354
9719.3119.4155972240627-0.105597224062727
9819.4719.39205538645610.077944613543913
9919.719.47231218387910.227687816120863
10019.7619.6874048869230.0725951130769964
10119.919.75295588449080.147044115509186
10219.9719.91012119525050.0598788047495376
10320.119.99098883760850.109011162391489
10420.2620.13533469463960.124665305360434
10520.4420.34500919338190.0949908066181209
10620.4320.4838081908987-0.0538081908986747
10720.5720.52039890528420.0496010947158467
10820.620.6237261234222-0.0237261234221826
10920.6920.67574753508610.0142524649139268
11020.9320.81839722694650.111602773053491
11120.9820.9913393777712-0.0113393777712325
11221.1121.01078921429070.0992107857093316
11321.1421.13939183705110.000608162948857682
11421.1621.1837921463301-0.0237921463300665
11521.3221.22775245633520.092247543664751
11621.3221.3795105021167-0.0595105021167086
11721.4821.4492934976940.0307065023059891
11821.5821.51343434463600.0665656553640375
11921.7421.67915049732970.0608495026703118
12021.7521.7880756175723-0.0380756175723462
12121.8121.8495626896373-0.0395626896373393
12221.8921.9819212271168-0.0919212271168348
12322.2121.97208128292360.237918717076436
12422.3722.22247646963820.147523530361788
12522.4722.38102028414060.0889797158593701
12622.5122.50607828022770.00392171977229339
12722.5522.6150765311661-0.065076531166099
12822.6122.6230484803313-0.0130484803313493
12922.5822.7628669235168-0.182866923516777
13022.8522.67436552040890.175634479591139
13122.9322.9342427036316-0.00424270363162904
13222.9822.97855393954490.00144606045514450







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13323.079891761043622.909017643980223.2507658781069
13423.242415914882623.021765486224623.4630663435406
13523.390643382085223.126200643678323.6550861204921
13623.440907424441723.135942441411523.7458724074720
13723.471585201454823.128098265884523.8150721370250
13823.505491075170323.124775314661823.8862068356787
13923.593143380080223.176054764369224.0102319957912
14023.662503738106923.209608418655424.1153990575584
14123.774961698152423.286623815451824.263299580853
14223.9140112611923.390448761044224.4375737613358
14323.997224165612323.438546075544924.5559022556796
14424.046146833225723.452379147785824.6399145186656

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 23.0798917610436 & 22.9090176439802 & 23.2507658781069 \tabularnewline
134 & 23.2424159148826 & 23.0217654862246 & 23.4630663435406 \tabularnewline
135 & 23.3906433820852 & 23.1262006436783 & 23.6550861204921 \tabularnewline
136 & 23.4409074244417 & 23.1359424414115 & 23.7458724074720 \tabularnewline
137 & 23.4715852014548 & 23.1280982658845 & 23.8150721370250 \tabularnewline
138 & 23.5054910751703 & 23.1247753146618 & 23.8862068356787 \tabularnewline
139 & 23.5931433800802 & 23.1760547643692 & 24.0102319957912 \tabularnewline
140 & 23.6625037381069 & 23.2096084186554 & 24.1153990575584 \tabularnewline
141 & 23.7749616981524 & 23.2866238154518 & 24.263299580853 \tabularnewline
142 & 23.91401126119 & 23.3904487610442 & 24.4375737613358 \tabularnewline
143 & 23.9972241656123 & 23.4385460755449 & 24.5559022556796 \tabularnewline
144 & 24.0461468332257 & 23.4523791477858 & 24.6399145186656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42907&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]133[/C][C]23.0798917610436[/C][C]22.9090176439802[/C][C]23.2507658781069[/C][/ROW]
[ROW][C]134[/C][C]23.2424159148826[/C][C]23.0217654862246[/C][C]23.4630663435406[/C][/ROW]
[ROW][C]135[/C][C]23.3906433820852[/C][C]23.1262006436783[/C][C]23.6550861204921[/C][/ROW]
[ROW][C]136[/C][C]23.4409074244417[/C][C]23.1359424414115[/C][C]23.7458724074720[/C][/ROW]
[ROW][C]137[/C][C]23.4715852014548[/C][C]23.1280982658845[/C][C]23.8150721370250[/C][/ROW]
[ROW][C]138[/C][C]23.5054910751703[/C][C]23.1247753146618[/C][C]23.8862068356787[/C][/ROW]
[ROW][C]139[/C][C]23.5931433800802[/C][C]23.1760547643692[/C][C]24.0102319957912[/C][/ROW]
[ROW][C]140[/C][C]23.6625037381069[/C][C]23.2096084186554[/C][C]24.1153990575584[/C][/ROW]
[ROW][C]141[/C][C]23.7749616981524[/C][C]23.2866238154518[/C][C]24.263299580853[/C][/ROW]
[ROW][C]142[/C][C]23.91401126119[/C][C]23.3904487610442[/C][C]24.4375737613358[/C][/ROW]
[ROW][C]143[/C][C]23.9972241656123[/C][C]23.4385460755449[/C][C]24.5559022556796[/C][/ROW]
[ROW][C]144[/C][C]24.0461468332257[/C][C]23.4523791477858[/C][C]24.6399145186656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42907&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42907&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
13323.079891761043622.909017643980223.2507658781069
13423.242415914882623.021765486224623.4630663435406
13523.390643382085223.126200643678323.6550861204921
13623.440907424441723.135942441411523.7458724074720
13723.471585201454823.128098265884523.8150721370250
13823.505491075170323.124775314661823.8862068356787
13923.593143380080223.176054764369224.0102319957912
14023.662503738106923.209608418655424.1153990575584
14123.774961698152423.286623815451824.263299580853
14223.9140112611923.390448761044224.4375737613358
14323.997224165612323.438546075544924.5559022556796
14424.046146833225723.452379147785824.6399145186656



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=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')