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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2011 07:28:53 -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/19/t1324298074dr2gew4ire7nntw.htm/, Retrieved Wed, 29 May 2024 04:03:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157323, Retrieved Wed, 29 May 2024 04:03:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact84

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [gemiddelde consum...] [2011-12-19 12:28:53] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15,14
14,2
13,83
14,31
14,04
14,9
14,92
15,36
15,5
15,65
16,18
15,44
15,58
15,24
15,33
16,07
15,82
15,87
15,72
17,07
16,83
17,52
17,76
17,36
17,95
16,71
17,14
16,72
17,26
17,24
17,69
18,13
18,08
18,18
18,18
17,64
17,89
16,82
16,61
16,66
17,02
16,91
17,18
18,06
17,58
17,48
17,54
17,44
17,79
16,79
16,19
16,62
16,39
16,54
17,26
18
17,29
18,16
17,82
17,48
18,31
17,04
17,03
16,97
17,11
17,12
17,69
18,5
18,27
18,45
18,35
18,03
18,49
18,07
17,8
17,88
18,12
18,68
18,8
19,64
19,56
19,3
20,07
19,82
20,29
19,36
18,74
18,87
18,87
18,91
19,31
20,06
20,72
20,42
20,58
20,58
21,18
19,87
19,83
19,48
19,49
19,4
19,89
20,44
20,07
19,75
19,54
19,07
19,55
18,01
17,5
17,41
17,47
17,6
17,64
18,3
18,27
17,99
18,04
17,62
18,22
17,67
17,73
17,99
18,15
18,41
18,36
19,52
19,96
19,6
19,48
19,13

Tables (Output of Computation)





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=157323&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=157323&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157323&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.615330042873785
beta0.0453371563588558
gamma0.91156455241003

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.615330042873785 \tabularnewline
beta & 0.0453371563588558 \tabularnewline
gamma & 0.91156455241003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157323&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]0.615330042873785[/C][/ROW]
[ROW][C]beta[/C][C]0.0453371563588558[/C][/ROW]
[ROW][C]gamma[/C][C]0.91156455241003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157323&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157323&T=1

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


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.615330042873785
beta0.0453371563588558
gamma0.91156455241003






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315.5814.89583867521370.684161324786324
1415.2415.00895191412370.23104808587634
1515.3315.25761325206050.0723867479394791
1616.0716.05399823131880.0160017686811784
1715.8215.81571757857730.00428242142267976
1815.8715.86826179410810.00173820589186491
1915.7216.3584556353302-0.638455635330155
2017.0716.47190777521790.598092224782093
2116.8317.018763463032-0.188763463031997
2217.5217.05617721305890.463822786941069
2317.7617.8764196316914-0.1164196316914
2417.3617.09929032959260.260709670407437
2517.9517.72222864301660.227771356983354
2616.7117.4216328698516-0.71163286985157
2717.1417.03430747425260.105692525747365
2816.7217.832052178628-1.11205217862803
2917.2616.86470411670370.395295883296264
3017.2417.13703423621780.102965763782187
3117.6917.44793118970870.242068810291332
3218.1318.5442577840765-0.414257784076515
3318.0818.1714940769861-0.091494076986109
3418.1818.4795266073413-0.299526607341331
3518.1818.5872345987286-0.407234598728564
3617.6417.7159263695436-0.0759263695435806
3717.8918.0633086083128-0.17330860831283
3816.8217.1184597934866-0.298459793486636
3916.6117.215442006907-0.605442006906973
4016.6617.0722349497735-0.412234949773545
4117.0217.00721701424090.0127829857591024
4216.9116.87415608555130.0358439144487406
4317.1817.1231417443680.0568582556320401
4418.0617.80080804431830.259191955681676
4517.5817.8998504378799-0.319850437879872
4617.4817.9322856577037-0.452285657703712
4717.5417.8418310174442-0.301831017444151
4817.4417.08809755173410.351902448265882
4917.7917.61306680915460.176933190845375
5016.7916.7980969724068-0.00809697240680052
5116.1916.9324538503481-0.742453850348149
5216.6216.7352148412742-0.115214841274241
5316.3916.9728087483367-0.582808748336664
5416.5416.43554654273150.104453457268534
5517.2616.6902303078450.569769692154999
561817.72487577365490.275124226345145
5717.2917.6015448920295-0.311544892029474
5818.1617.56374906035680.596250939643181
5917.8218.1715958942046-0.351595894204607
6017.4817.61543317674-0.135433176739973
6118.3117.76454154931840.545458450681643
6217.0417.1071007360238-0.067100736023793
6317.0316.94164690353570.0883530964642709
6416.9717.4927473656936-0.52274736569359
6517.1117.3214193997851-0.211419399785065
6617.1217.2698421411735-0.149842141173494
6717.6917.54028825681920.149711743180813
6818.518.21049732201210.289502677987873
6918.2717.8880543979560.38194560204396
7018.4518.6124074607472-0.162407460747218
7118.3518.417003936571-0.0670039365709805
7218.0318.115635191953-0.0856351919529565
7318.4918.5394088701481-0.0494088701480528
7418.0717.28980576702160.780194232978399
7517.817.71253759756690.0874624024331148
7617.8818.0610913432132-0.181091343213225
7718.1218.2309781414621-0.110978141462105
7818.6818.28741553773220.392584462267813
7918.819.036422275235-0.236422275235018
8019.6419.54702749545690.0929725045430878
8119.5619.15956435359020.400435646409846
8219.319.7284279547368-0.428427954736755
8320.0719.41937743492640.650622565073579
8419.8219.58966262858870.230337371411309
8520.2920.26599118751130.0240088124886668
8619.3619.3999385724158-0.0399385724158279
8718.7419.0997039043141-0.359703904314113
8818.8719.091052584472-0.221052584471988
8918.8719.2719390885167-0.401939088516677
9018.9119.3288011836505-0.418801183650462
9119.3119.3382270520245-0.0282270520245262
9220.0620.0785031576661-0.0185031576661352
9320.7219.71320756832371.00679243167625
9420.4220.36440364468060.0555963553194267
9520.5820.7449266744236-0.164926674423619
9620.5820.25662282328510.323377176714867
9721.1820.91106424832330.268935751676672
9819.8720.1733441916236-0.303344191623562
9919.8319.59159853145310.238401468546908
10019.4820.0089798341558-0.528979834155827
10119.4919.9377531085957-0.44775310859573
10219.419.960025435392-0.560025435391964
10319.8920.0150810991069-0.125081099106922
10420.4420.6920416462832-0.252041646283164
10520.0720.5289210940271-0.45892109402708
10619.7519.8901486561095-0.140148656109492
10719.5420.0129037896225-0.472903789622542
10819.0719.4377317297321-0.367731729732064
10919.5519.5599579183187-0.00995791831874371
11018.0118.3543098081151-0.344309808115074
11117.517.8405322890028-0.340532289002798
11217.4117.5196557467516-0.109655746751589
11317.4717.6336929103852-0.16369291038524
11417.617.6980709758531-0.0980709758531333
11517.6418.1094656927238-0.469465692723805
11618.318.4399604549135-0.139960454913542
11718.2718.18635431080120.0836456891988142
11817.9917.92144377559930.068556224400691
11918.0417.98998874012740.0500112598726368
12017.6217.7220972195997-0.102097219599742
12118.2218.08927717405860.130722825941412
12217.6716.81292472511920.857075274880767
12317.7317.03320711434970.696792885650332
12417.9917.45401068900140.535989310998563
12518.1517.98682177198840.163178228011617
12618.4118.32490005618850.085099943811489
12718.3618.77344136361-0.41344136361004
12819.5219.31018014621890.209819853781141
12919.9619.41619915749910.543800842500925
13019.619.50796885586130.0920311441387227
13119.4819.6639347981737-0.183934798173748
13219.1319.2717046809088-0.141704680908838

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15.58 & 14.8958386752137 & 0.684161324786324 \tabularnewline
14 & 15.24 & 15.0089519141237 & 0.23104808587634 \tabularnewline
15 & 15.33 & 15.2576132520605 & 0.0723867479394791 \tabularnewline
16 & 16.07 & 16.0539982313188 & 0.0160017686811784 \tabularnewline
17 & 15.82 & 15.8157175785773 & 0.00428242142267976 \tabularnewline
18 & 15.87 & 15.8682617941081 & 0.00173820589186491 \tabularnewline
19 & 15.72 & 16.3584556353302 & -0.638455635330155 \tabularnewline
20 & 17.07 & 16.4719077752179 & 0.598092224782093 \tabularnewline
21 & 16.83 & 17.018763463032 & -0.188763463031997 \tabularnewline
22 & 17.52 & 17.0561772130589 & 0.463822786941069 \tabularnewline
23 & 17.76 & 17.8764196316914 & -0.1164196316914 \tabularnewline
24 & 17.36 & 17.0992903295926 & 0.260709670407437 \tabularnewline
25 & 17.95 & 17.7222286430166 & 0.227771356983354 \tabularnewline
26 & 16.71 & 17.4216328698516 & -0.71163286985157 \tabularnewline
27 & 17.14 & 17.0343074742526 & 0.105692525747365 \tabularnewline
28 & 16.72 & 17.832052178628 & -1.11205217862803 \tabularnewline
29 & 17.26 & 16.8647041167037 & 0.395295883296264 \tabularnewline
30 & 17.24 & 17.1370342362178 & 0.102965763782187 \tabularnewline
31 & 17.69 & 17.4479311897087 & 0.242068810291332 \tabularnewline
32 & 18.13 & 18.5442577840765 & -0.414257784076515 \tabularnewline
33 & 18.08 & 18.1714940769861 & -0.091494076986109 \tabularnewline
34 & 18.18 & 18.4795266073413 & -0.299526607341331 \tabularnewline
35 & 18.18 & 18.5872345987286 & -0.407234598728564 \tabularnewline
36 & 17.64 & 17.7159263695436 & -0.0759263695435806 \tabularnewline
37 & 17.89 & 18.0633086083128 & -0.17330860831283 \tabularnewline
38 & 16.82 & 17.1184597934866 & -0.298459793486636 \tabularnewline
39 & 16.61 & 17.215442006907 & -0.605442006906973 \tabularnewline
40 & 16.66 & 17.0722349497735 & -0.412234949773545 \tabularnewline
41 & 17.02 & 17.0072170142409 & 0.0127829857591024 \tabularnewline
42 & 16.91 & 16.8741560855513 & 0.0358439144487406 \tabularnewline
43 & 17.18 & 17.123141744368 & 0.0568582556320401 \tabularnewline
44 & 18.06 & 17.8008080443183 & 0.259191955681676 \tabularnewline
45 & 17.58 & 17.8998504378799 & -0.319850437879872 \tabularnewline
46 & 17.48 & 17.9322856577037 & -0.452285657703712 \tabularnewline
47 & 17.54 & 17.8418310174442 & -0.301831017444151 \tabularnewline
48 & 17.44 & 17.0880975517341 & 0.351902448265882 \tabularnewline
49 & 17.79 & 17.6130668091546 & 0.176933190845375 \tabularnewline
50 & 16.79 & 16.7980969724068 & -0.00809697240680052 \tabularnewline
51 & 16.19 & 16.9324538503481 & -0.742453850348149 \tabularnewline
52 & 16.62 & 16.7352148412742 & -0.115214841274241 \tabularnewline
53 & 16.39 & 16.9728087483367 & -0.582808748336664 \tabularnewline
54 & 16.54 & 16.4355465427315 & 0.104453457268534 \tabularnewline
55 & 17.26 & 16.690230307845 & 0.569769692154999 \tabularnewline
56 & 18 & 17.7248757736549 & 0.275124226345145 \tabularnewline
57 & 17.29 & 17.6015448920295 & -0.311544892029474 \tabularnewline
58 & 18.16 & 17.5637490603568 & 0.596250939643181 \tabularnewline
59 & 17.82 & 18.1715958942046 & -0.351595894204607 \tabularnewline
60 & 17.48 & 17.61543317674 & -0.135433176739973 \tabularnewline
61 & 18.31 & 17.7645415493184 & 0.545458450681643 \tabularnewline
62 & 17.04 & 17.1071007360238 & -0.067100736023793 \tabularnewline
63 & 17.03 & 16.9416469035357 & 0.0883530964642709 \tabularnewline
64 & 16.97 & 17.4927473656936 & -0.52274736569359 \tabularnewline
65 & 17.11 & 17.3214193997851 & -0.211419399785065 \tabularnewline
66 & 17.12 & 17.2698421411735 & -0.149842141173494 \tabularnewline
67 & 17.69 & 17.5402882568192 & 0.149711743180813 \tabularnewline
68 & 18.5 & 18.2104973220121 & 0.289502677987873 \tabularnewline
69 & 18.27 & 17.888054397956 & 0.38194560204396 \tabularnewline
70 & 18.45 & 18.6124074607472 & -0.162407460747218 \tabularnewline
71 & 18.35 & 18.417003936571 & -0.0670039365709805 \tabularnewline
72 & 18.03 & 18.115635191953 & -0.0856351919529565 \tabularnewline
73 & 18.49 & 18.5394088701481 & -0.0494088701480528 \tabularnewline
74 & 18.07 & 17.2898057670216 & 0.780194232978399 \tabularnewline
75 & 17.8 & 17.7125375975669 & 0.0874624024331148 \tabularnewline
76 & 17.88 & 18.0610913432132 & -0.181091343213225 \tabularnewline
77 & 18.12 & 18.2309781414621 & -0.110978141462105 \tabularnewline
78 & 18.68 & 18.2874155377322 & 0.392584462267813 \tabularnewline
79 & 18.8 & 19.036422275235 & -0.236422275235018 \tabularnewline
80 & 19.64 & 19.5470274954569 & 0.0929725045430878 \tabularnewline
81 & 19.56 & 19.1595643535902 & 0.400435646409846 \tabularnewline
82 & 19.3 & 19.7284279547368 & -0.428427954736755 \tabularnewline
83 & 20.07 & 19.4193774349264 & 0.650622565073579 \tabularnewline
84 & 19.82 & 19.5896626285887 & 0.230337371411309 \tabularnewline
85 & 20.29 & 20.2659911875113 & 0.0240088124886668 \tabularnewline
86 & 19.36 & 19.3999385724158 & -0.0399385724158279 \tabularnewline
87 & 18.74 & 19.0997039043141 & -0.359703904314113 \tabularnewline
88 & 18.87 & 19.091052584472 & -0.221052584471988 \tabularnewline
89 & 18.87 & 19.2719390885167 & -0.401939088516677 \tabularnewline
90 & 18.91 & 19.3288011836505 & -0.418801183650462 \tabularnewline
91 & 19.31 & 19.3382270520245 & -0.0282270520245262 \tabularnewline
92 & 20.06 & 20.0785031576661 & -0.0185031576661352 \tabularnewline
93 & 20.72 & 19.7132075683237 & 1.00679243167625 \tabularnewline
94 & 20.42 & 20.3644036446806 & 0.0555963553194267 \tabularnewline
95 & 20.58 & 20.7449266744236 & -0.164926674423619 \tabularnewline
96 & 20.58 & 20.2566228232851 & 0.323377176714867 \tabularnewline
97 & 21.18 & 20.9110642483233 & 0.268935751676672 \tabularnewline
98 & 19.87 & 20.1733441916236 & -0.303344191623562 \tabularnewline
99 & 19.83 & 19.5915985314531 & 0.238401468546908 \tabularnewline
100 & 19.48 & 20.0089798341558 & -0.528979834155827 \tabularnewline
101 & 19.49 & 19.9377531085957 & -0.44775310859573 \tabularnewline
102 & 19.4 & 19.960025435392 & -0.560025435391964 \tabularnewline
103 & 19.89 & 20.0150810991069 & -0.125081099106922 \tabularnewline
104 & 20.44 & 20.6920416462832 & -0.252041646283164 \tabularnewline
105 & 20.07 & 20.5289210940271 & -0.45892109402708 \tabularnewline
106 & 19.75 & 19.8901486561095 & -0.140148656109492 \tabularnewline
107 & 19.54 & 20.0129037896225 & -0.472903789622542 \tabularnewline
108 & 19.07 & 19.4377317297321 & -0.367731729732064 \tabularnewline
109 & 19.55 & 19.5599579183187 & -0.00995791831874371 \tabularnewline
110 & 18.01 & 18.3543098081151 & -0.344309808115074 \tabularnewline
111 & 17.5 & 17.8405322890028 & -0.340532289002798 \tabularnewline
112 & 17.41 & 17.5196557467516 & -0.109655746751589 \tabularnewline
113 & 17.47 & 17.6336929103852 & -0.16369291038524 \tabularnewline
114 & 17.6 & 17.6980709758531 & -0.0980709758531333 \tabularnewline
115 & 17.64 & 18.1094656927238 & -0.469465692723805 \tabularnewline
116 & 18.3 & 18.4399604549135 & -0.139960454913542 \tabularnewline
117 & 18.27 & 18.1863543108012 & 0.0836456891988142 \tabularnewline
118 & 17.99 & 17.9214437755993 & 0.068556224400691 \tabularnewline
119 & 18.04 & 17.9899887401274 & 0.0500112598726368 \tabularnewline
120 & 17.62 & 17.7220972195997 & -0.102097219599742 \tabularnewline
121 & 18.22 & 18.0892771740586 & 0.130722825941412 \tabularnewline
122 & 17.67 & 16.8129247251192 & 0.857075274880767 \tabularnewline
123 & 17.73 & 17.0332071143497 & 0.696792885650332 \tabularnewline
124 & 17.99 & 17.4540106890014 & 0.535989310998563 \tabularnewline
125 & 18.15 & 17.9868217719884 & 0.163178228011617 \tabularnewline
126 & 18.41 & 18.3249000561885 & 0.085099943811489 \tabularnewline
127 & 18.36 & 18.77344136361 & -0.41344136361004 \tabularnewline
128 & 19.52 & 19.3101801462189 & 0.209819853781141 \tabularnewline
129 & 19.96 & 19.4161991574991 & 0.543800842500925 \tabularnewline
130 & 19.6 & 19.5079688558613 & 0.0920311441387227 \tabularnewline
131 & 19.48 & 19.6639347981737 & -0.183934798173748 \tabularnewline
132 & 19.13 & 19.2717046809088 & -0.141704680908838 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157323&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]15.58[/C][C]14.8958386752137[/C][C]0.684161324786324[/C][/ROW]
[ROW][C]14[/C][C]15.24[/C][C]15.0089519141237[/C][C]0.23104808587634[/C][/ROW]
[ROW][C]15[/C][C]15.33[/C][C]15.2576132520605[/C][C]0.0723867479394791[/C][/ROW]
[ROW][C]16[/C][C]16.07[/C][C]16.0539982313188[/C][C]0.0160017686811784[/C][/ROW]
[ROW][C]17[/C][C]15.82[/C][C]15.8157175785773[/C][C]0.00428242142267976[/C][/ROW]
[ROW][C]18[/C][C]15.87[/C][C]15.8682617941081[/C][C]0.00173820589186491[/C][/ROW]
[ROW][C]19[/C][C]15.72[/C][C]16.3584556353302[/C][C]-0.638455635330155[/C][/ROW]
[ROW][C]20[/C][C]17.07[/C][C]16.4719077752179[/C][C]0.598092224782093[/C][/ROW]
[ROW][C]21[/C][C]16.83[/C][C]17.018763463032[/C][C]-0.188763463031997[/C][/ROW]
[ROW][C]22[/C][C]17.52[/C][C]17.0561772130589[/C][C]0.463822786941069[/C][/ROW]
[ROW][C]23[/C][C]17.76[/C][C]17.8764196316914[/C][C]-0.1164196316914[/C][/ROW]
[ROW][C]24[/C][C]17.36[/C][C]17.0992903295926[/C][C]0.260709670407437[/C][/ROW]
[ROW][C]25[/C][C]17.95[/C][C]17.7222286430166[/C][C]0.227771356983354[/C][/ROW]
[ROW][C]26[/C][C]16.71[/C][C]17.4216328698516[/C][C]-0.71163286985157[/C][/ROW]
[ROW][C]27[/C][C]17.14[/C][C]17.0343074742526[/C][C]0.105692525747365[/C][/ROW]
[ROW][C]28[/C][C]16.72[/C][C]17.832052178628[/C][C]-1.11205217862803[/C][/ROW]
[ROW][C]29[/C][C]17.26[/C][C]16.8647041167037[/C][C]0.395295883296264[/C][/ROW]
[ROW][C]30[/C][C]17.24[/C][C]17.1370342362178[/C][C]0.102965763782187[/C][/ROW]
[ROW][C]31[/C][C]17.69[/C][C]17.4479311897087[/C][C]0.242068810291332[/C][/ROW]
[ROW][C]32[/C][C]18.13[/C][C]18.5442577840765[/C][C]-0.414257784076515[/C][/ROW]
[ROW][C]33[/C][C]18.08[/C][C]18.1714940769861[/C][C]-0.091494076986109[/C][/ROW]
[ROW][C]34[/C][C]18.18[/C][C]18.4795266073413[/C][C]-0.299526607341331[/C][/ROW]
[ROW][C]35[/C][C]18.18[/C][C]18.5872345987286[/C][C]-0.407234598728564[/C][/ROW]
[ROW][C]36[/C][C]17.64[/C][C]17.7159263695436[/C][C]-0.0759263695435806[/C][/ROW]
[ROW][C]37[/C][C]17.89[/C][C]18.0633086083128[/C][C]-0.17330860831283[/C][/ROW]
[ROW][C]38[/C][C]16.82[/C][C]17.1184597934866[/C][C]-0.298459793486636[/C][/ROW]
[ROW][C]39[/C][C]16.61[/C][C]17.215442006907[/C][C]-0.605442006906973[/C][/ROW]
[ROW][C]40[/C][C]16.66[/C][C]17.0722349497735[/C][C]-0.412234949773545[/C][/ROW]
[ROW][C]41[/C][C]17.02[/C][C]17.0072170142409[/C][C]0.0127829857591024[/C][/ROW]
[ROW][C]42[/C][C]16.91[/C][C]16.8741560855513[/C][C]0.0358439144487406[/C][/ROW]
[ROW][C]43[/C][C]17.18[/C][C]17.123141744368[/C][C]0.0568582556320401[/C][/ROW]
[ROW][C]44[/C][C]18.06[/C][C]17.8008080443183[/C][C]0.259191955681676[/C][/ROW]
[ROW][C]45[/C][C]17.58[/C][C]17.8998504378799[/C][C]-0.319850437879872[/C][/ROW]
[ROW][C]46[/C][C]17.48[/C][C]17.9322856577037[/C][C]-0.452285657703712[/C][/ROW]
[ROW][C]47[/C][C]17.54[/C][C]17.8418310174442[/C][C]-0.301831017444151[/C][/ROW]
[ROW][C]48[/C][C]17.44[/C][C]17.0880975517341[/C][C]0.351902448265882[/C][/ROW]
[ROW][C]49[/C][C]17.79[/C][C]17.6130668091546[/C][C]0.176933190845375[/C][/ROW]
[ROW][C]50[/C][C]16.79[/C][C]16.7980969724068[/C][C]-0.00809697240680052[/C][/ROW]
[ROW][C]51[/C][C]16.19[/C][C]16.9324538503481[/C][C]-0.742453850348149[/C][/ROW]
[ROW][C]52[/C][C]16.62[/C][C]16.7352148412742[/C][C]-0.115214841274241[/C][/ROW]
[ROW][C]53[/C][C]16.39[/C][C]16.9728087483367[/C][C]-0.582808748336664[/C][/ROW]
[ROW][C]54[/C][C]16.54[/C][C]16.4355465427315[/C][C]0.104453457268534[/C][/ROW]
[ROW][C]55[/C][C]17.26[/C][C]16.690230307845[/C][C]0.569769692154999[/C][/ROW]
[ROW][C]56[/C][C]18[/C][C]17.7248757736549[/C][C]0.275124226345145[/C][/ROW]
[ROW][C]57[/C][C]17.29[/C][C]17.6015448920295[/C][C]-0.311544892029474[/C][/ROW]
[ROW][C]58[/C][C]18.16[/C][C]17.5637490603568[/C][C]0.596250939643181[/C][/ROW]
[ROW][C]59[/C][C]17.82[/C][C]18.1715958942046[/C][C]-0.351595894204607[/C][/ROW]
[ROW][C]60[/C][C]17.48[/C][C]17.61543317674[/C][C]-0.135433176739973[/C][/ROW]
[ROW][C]61[/C][C]18.31[/C][C]17.7645415493184[/C][C]0.545458450681643[/C][/ROW]
[ROW][C]62[/C][C]17.04[/C][C]17.1071007360238[/C][C]-0.067100736023793[/C][/ROW]
[ROW][C]63[/C][C]17.03[/C][C]16.9416469035357[/C][C]0.0883530964642709[/C][/ROW]
[ROW][C]64[/C][C]16.97[/C][C]17.4927473656936[/C][C]-0.52274736569359[/C][/ROW]
[ROW][C]65[/C][C]17.11[/C][C]17.3214193997851[/C][C]-0.211419399785065[/C][/ROW]
[ROW][C]66[/C][C]17.12[/C][C]17.2698421411735[/C][C]-0.149842141173494[/C][/ROW]
[ROW][C]67[/C][C]17.69[/C][C]17.5402882568192[/C][C]0.149711743180813[/C][/ROW]
[ROW][C]68[/C][C]18.5[/C][C]18.2104973220121[/C][C]0.289502677987873[/C][/ROW]
[ROW][C]69[/C][C]18.27[/C][C]17.888054397956[/C][C]0.38194560204396[/C][/ROW]
[ROW][C]70[/C][C]18.45[/C][C]18.6124074607472[/C][C]-0.162407460747218[/C][/ROW]
[ROW][C]71[/C][C]18.35[/C][C]18.417003936571[/C][C]-0.0670039365709805[/C][/ROW]
[ROW][C]72[/C][C]18.03[/C][C]18.115635191953[/C][C]-0.0856351919529565[/C][/ROW]
[ROW][C]73[/C][C]18.49[/C][C]18.5394088701481[/C][C]-0.0494088701480528[/C][/ROW]
[ROW][C]74[/C][C]18.07[/C][C]17.2898057670216[/C][C]0.780194232978399[/C][/ROW]
[ROW][C]75[/C][C]17.8[/C][C]17.7125375975669[/C][C]0.0874624024331148[/C][/ROW]
[ROW][C]76[/C][C]17.88[/C][C]18.0610913432132[/C][C]-0.181091343213225[/C][/ROW]
[ROW][C]77[/C][C]18.12[/C][C]18.2309781414621[/C][C]-0.110978141462105[/C][/ROW]
[ROW][C]78[/C][C]18.68[/C][C]18.2874155377322[/C][C]0.392584462267813[/C][/ROW]
[ROW][C]79[/C][C]18.8[/C][C]19.036422275235[/C][C]-0.236422275235018[/C][/ROW]
[ROW][C]80[/C][C]19.64[/C][C]19.5470274954569[/C][C]0.0929725045430878[/C][/ROW]
[ROW][C]81[/C][C]19.56[/C][C]19.1595643535902[/C][C]0.400435646409846[/C][/ROW]
[ROW][C]82[/C][C]19.3[/C][C]19.7284279547368[/C][C]-0.428427954736755[/C][/ROW]
[ROW][C]83[/C][C]20.07[/C][C]19.4193774349264[/C][C]0.650622565073579[/C][/ROW]
[ROW][C]84[/C][C]19.82[/C][C]19.5896626285887[/C][C]0.230337371411309[/C][/ROW]
[ROW][C]85[/C][C]20.29[/C][C]20.2659911875113[/C][C]0.0240088124886668[/C][/ROW]
[ROW][C]86[/C][C]19.36[/C][C]19.3999385724158[/C][C]-0.0399385724158279[/C][/ROW]
[ROW][C]87[/C][C]18.74[/C][C]19.0997039043141[/C][C]-0.359703904314113[/C][/ROW]
[ROW][C]88[/C][C]18.87[/C][C]19.091052584472[/C][C]-0.221052584471988[/C][/ROW]
[ROW][C]89[/C][C]18.87[/C][C]19.2719390885167[/C][C]-0.401939088516677[/C][/ROW]
[ROW][C]90[/C][C]18.91[/C][C]19.3288011836505[/C][C]-0.418801183650462[/C][/ROW]
[ROW][C]91[/C][C]19.31[/C][C]19.3382270520245[/C][C]-0.0282270520245262[/C][/ROW]
[ROW][C]92[/C][C]20.06[/C][C]20.0785031576661[/C][C]-0.0185031576661352[/C][/ROW]
[ROW][C]93[/C][C]20.72[/C][C]19.7132075683237[/C][C]1.00679243167625[/C][/ROW]
[ROW][C]94[/C][C]20.42[/C][C]20.3644036446806[/C][C]0.0555963553194267[/C][/ROW]
[ROW][C]95[/C][C]20.58[/C][C]20.7449266744236[/C][C]-0.164926674423619[/C][/ROW]
[ROW][C]96[/C][C]20.58[/C][C]20.2566228232851[/C][C]0.323377176714867[/C][/ROW]
[ROW][C]97[/C][C]21.18[/C][C]20.9110642483233[/C][C]0.268935751676672[/C][/ROW]
[ROW][C]98[/C][C]19.87[/C][C]20.1733441916236[/C][C]-0.303344191623562[/C][/ROW]
[ROW][C]99[/C][C]19.83[/C][C]19.5915985314531[/C][C]0.238401468546908[/C][/ROW]
[ROW][C]100[/C][C]19.48[/C][C]20.0089798341558[/C][C]-0.528979834155827[/C][/ROW]
[ROW][C]101[/C][C]19.49[/C][C]19.9377531085957[/C][C]-0.44775310859573[/C][/ROW]
[ROW][C]102[/C][C]19.4[/C][C]19.960025435392[/C][C]-0.560025435391964[/C][/ROW]
[ROW][C]103[/C][C]19.89[/C][C]20.0150810991069[/C][C]-0.125081099106922[/C][/ROW]
[ROW][C]104[/C][C]20.44[/C][C]20.6920416462832[/C][C]-0.252041646283164[/C][/ROW]
[ROW][C]105[/C][C]20.07[/C][C]20.5289210940271[/C][C]-0.45892109402708[/C][/ROW]
[ROW][C]106[/C][C]19.75[/C][C]19.8901486561095[/C][C]-0.140148656109492[/C][/ROW]
[ROW][C]107[/C][C]19.54[/C][C]20.0129037896225[/C][C]-0.472903789622542[/C][/ROW]
[ROW][C]108[/C][C]19.07[/C][C]19.4377317297321[/C][C]-0.367731729732064[/C][/ROW]
[ROW][C]109[/C][C]19.55[/C][C]19.5599579183187[/C][C]-0.00995791831874371[/C][/ROW]
[ROW][C]110[/C][C]18.01[/C][C]18.3543098081151[/C][C]-0.344309808115074[/C][/ROW]
[ROW][C]111[/C][C]17.5[/C][C]17.8405322890028[/C][C]-0.340532289002798[/C][/ROW]
[ROW][C]112[/C][C]17.41[/C][C]17.5196557467516[/C][C]-0.109655746751589[/C][/ROW]
[ROW][C]113[/C][C]17.47[/C][C]17.6336929103852[/C][C]-0.16369291038524[/C][/ROW]
[ROW][C]114[/C][C]17.6[/C][C]17.6980709758531[/C][C]-0.0980709758531333[/C][/ROW]
[ROW][C]115[/C][C]17.64[/C][C]18.1094656927238[/C][C]-0.469465692723805[/C][/ROW]
[ROW][C]116[/C][C]18.3[/C][C]18.4399604549135[/C][C]-0.139960454913542[/C][/ROW]
[ROW][C]117[/C][C]18.27[/C][C]18.1863543108012[/C][C]0.0836456891988142[/C][/ROW]
[ROW][C]118[/C][C]17.99[/C][C]17.9214437755993[/C][C]0.068556224400691[/C][/ROW]
[ROW][C]119[/C][C]18.04[/C][C]17.9899887401274[/C][C]0.0500112598726368[/C][/ROW]
[ROW][C]120[/C][C]17.62[/C][C]17.7220972195997[/C][C]-0.102097219599742[/C][/ROW]
[ROW][C]121[/C][C]18.22[/C][C]18.0892771740586[/C][C]0.130722825941412[/C][/ROW]
[ROW][C]122[/C][C]17.67[/C][C]16.8129247251192[/C][C]0.857075274880767[/C][/ROW]
[ROW][C]123[/C][C]17.73[/C][C]17.0332071143497[/C][C]0.696792885650332[/C][/ROW]
[ROW][C]124[/C][C]17.99[/C][C]17.4540106890014[/C][C]0.535989310998563[/C][/ROW]
[ROW][C]125[/C][C]18.15[/C][C]17.9868217719884[/C][C]0.163178228011617[/C][/ROW]
[ROW][C]126[/C][C]18.41[/C][C]18.3249000561885[/C][C]0.085099943811489[/C][/ROW]
[ROW][C]127[/C][C]18.36[/C][C]18.77344136361[/C][C]-0.41344136361004[/C][/ROW]
[ROW][C]128[/C][C]19.52[/C][C]19.3101801462189[/C][C]0.209819853781141[/C][/ROW]
[ROW][C]129[/C][C]19.96[/C][C]19.4161991574991[/C][C]0.543800842500925[/C][/ROW]
[ROW][C]130[/C][C]19.6[/C][C]19.5079688558613[/C][C]0.0920311441387227[/C][/ROW]
[ROW][C]131[/C][C]19.48[/C][C]19.6639347981737[/C][C]-0.183934798173748[/C][/ROW]
[ROW][C]132[/C][C]19.13[/C][C]19.2717046809088[/C][C]-0.141704680908838[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157323&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157323&T=2

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


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315.5814.89583867521370.684161324786324
1415.2415.00895191412370.23104808587634
1515.3315.25761325206050.0723867479394791
1616.0716.05399823131880.0160017686811784
1715.8215.81571757857730.00428242142267976
1815.8715.86826179410810.00173820589186491
1915.7216.3584556353302-0.638455635330155
2017.0716.47190777521790.598092224782093
2116.8317.018763463032-0.188763463031997
2217.5217.05617721305890.463822786941069
2317.7617.8764196316914-0.1164196316914
2417.3617.09929032959260.260709670407437
2517.9517.72222864301660.227771356983354
2616.7117.4216328698516-0.71163286985157
2717.1417.03430747425260.105692525747365
2816.7217.832052178628-1.11205217862803
2917.2616.86470411670370.395295883296264
3017.2417.13703423621780.102965763782187
3117.6917.44793118970870.242068810291332
3218.1318.5442577840765-0.414257784076515
3318.0818.1714940769861-0.091494076986109
3418.1818.4795266073413-0.299526607341331
3518.1818.5872345987286-0.407234598728564
3617.6417.7159263695436-0.0759263695435806
3717.8918.0633086083128-0.17330860831283
3816.8217.1184597934866-0.298459793486636
3916.6117.215442006907-0.605442006906973
4016.6617.0722349497735-0.412234949773545
4117.0217.00721701424090.0127829857591024
4216.9116.87415608555130.0358439144487406
4317.1817.1231417443680.0568582556320401
4418.0617.80080804431830.259191955681676
4517.5817.8998504378799-0.319850437879872
4617.4817.9322856577037-0.452285657703712
4717.5417.8418310174442-0.301831017444151
4817.4417.08809755173410.351902448265882
4917.7917.61306680915460.176933190845375
5016.7916.7980969724068-0.00809697240680052
5116.1916.9324538503481-0.742453850348149
5216.6216.7352148412742-0.115214841274241
5316.3916.9728087483367-0.582808748336664
5416.5416.43554654273150.104453457268534
5517.2616.6902303078450.569769692154999
561817.72487577365490.275124226345145
5717.2917.6015448920295-0.311544892029474
5818.1617.56374906035680.596250939643181
5917.8218.1715958942046-0.351595894204607
6017.4817.61543317674-0.135433176739973
6118.3117.76454154931840.545458450681643
6217.0417.1071007360238-0.067100736023793
6317.0316.94164690353570.0883530964642709
6416.9717.4927473656936-0.52274736569359
6517.1117.3214193997851-0.211419399785065
6617.1217.2698421411735-0.149842141173494
6717.6917.54028825681920.149711743180813
6818.518.21049732201210.289502677987873
6918.2717.8880543979560.38194560204396
7018.4518.6124074607472-0.162407460747218
7118.3518.417003936571-0.0670039365709805
7218.0318.115635191953-0.0856351919529565
7318.4918.5394088701481-0.0494088701480528
7418.0717.28980576702160.780194232978399
7517.817.71253759756690.0874624024331148
7617.8818.0610913432132-0.181091343213225
7718.1218.2309781414621-0.110978141462105
7818.6818.28741553773220.392584462267813
7918.819.036422275235-0.236422275235018
8019.6419.54702749545690.0929725045430878
8119.5619.15956435359020.400435646409846
8219.319.7284279547368-0.428427954736755
8320.0719.41937743492640.650622565073579
8419.8219.58966262858870.230337371411309
8520.2920.26599118751130.0240088124886668
8619.3619.3999385724158-0.0399385724158279
8718.7419.0997039043141-0.359703904314113
8818.8719.091052584472-0.221052584471988
8918.8719.2719390885167-0.401939088516677
9018.9119.3288011836505-0.418801183650462
9119.3119.3382270520245-0.0282270520245262
9220.0620.0785031576661-0.0185031576661352
9320.7219.71320756832371.00679243167625
9420.4220.36440364468060.0555963553194267
9520.5820.7449266744236-0.164926674423619
9620.5820.25662282328510.323377176714867
9721.1820.91106424832330.268935751676672
9819.8720.1733441916236-0.303344191623562
9919.8319.59159853145310.238401468546908
10019.4820.0089798341558-0.528979834155827
10119.4919.9377531085957-0.44775310859573
10219.419.960025435392-0.560025435391964
10319.8920.0150810991069-0.125081099106922
10420.4420.6920416462832-0.252041646283164
10520.0720.5289210940271-0.45892109402708
10619.7519.8901486561095-0.140148656109492
10719.5420.0129037896225-0.472903789622542
10819.0719.4377317297321-0.367731729732064
10919.5519.5599579183187-0.00995791831874371
11018.0118.3543098081151-0.344309808115074
11117.517.8405322890028-0.340532289002798
11217.4117.5196557467516-0.109655746751589
11317.4717.6336929103852-0.16369291038524
11417.617.6980709758531-0.0980709758531333
11517.6418.1094656927238-0.469465692723805
11618.318.4399604549135-0.139960454913542
11718.2718.18635431080120.0836456891988142
11817.9917.92144377559930.068556224400691
11918.0417.98998874012740.0500112598726368
12017.6217.7220972195997-0.102097219599742
12118.2218.08927717405860.130722825941412
12217.6716.81292472511920.857075274880767
12317.7317.03320711434970.696792885650332
12417.9917.45401068900140.535989310998563
12518.1517.98682177198840.163178228011617
12618.4118.32490005618850.085099943811489
12718.3618.77344136361-0.41344136361004
12819.5219.31018014621890.209819853781141
12919.9619.41619915749910.543800842500925
13019.619.50796885586130.0920311441387227
13119.4819.6639347981737-0.183934798173748
13219.1319.2717046809088-0.141704680908838






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13319.767999237540319.052627152197820.4833713228828
13418.734106429992217.883522873666419.5846899863179
13518.415092045131117.438366854150919.3918172361113
13618.37560401050117.278310559231519.4728974617705
13718.457777342149917.243499200493819.672055483806
13818.673415997561717.344490070163520.0023419249598
13918.897751541625117.455680938526220.339822144724
14019.921947643631518.367650864622521.4762444226404
14120.024622666948218.358593483602621.6906518502938
14219.616844603258617.839259591961521.3944296145556
14319.610328679910617.721122302718121.4995350571032
14419.342134043711317.341052688550721.343215398872

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 19.7679992375403 & 19.0526271521978 & 20.4833713228828 \tabularnewline
134 & 18.7341064299922 & 17.8835228736664 & 19.5846899863179 \tabularnewline
135 & 18.4150920451311 & 17.4383668541509 & 19.3918172361113 \tabularnewline
136 & 18.375604010501 & 17.2783105592315 & 19.4728974617705 \tabularnewline
137 & 18.4577773421499 & 17.2434992004938 & 19.672055483806 \tabularnewline
138 & 18.6734159975617 & 17.3444900701635 & 20.0023419249598 \tabularnewline
139 & 18.8977515416251 & 17.4556809385262 & 20.339822144724 \tabularnewline
140 & 19.9219476436315 & 18.3676508646225 & 21.4762444226404 \tabularnewline
141 & 20.0246226669482 & 18.3585934836026 & 21.6906518502938 \tabularnewline
142 & 19.6168446032586 & 17.8392595919615 & 21.3944296145556 \tabularnewline
143 & 19.6103286799106 & 17.7211223027181 & 21.4995350571032 \tabularnewline
144 & 19.3421340437113 & 17.3410526885507 & 21.343215398872 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157323&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]19.7679992375403[/C][C]19.0526271521978[/C][C]20.4833713228828[/C][/ROW]
[ROW][C]134[/C][C]18.7341064299922[/C][C]17.8835228736664[/C][C]19.5846899863179[/C][/ROW]
[ROW][C]135[/C][C]18.4150920451311[/C][C]17.4383668541509[/C][C]19.3918172361113[/C][/ROW]
[ROW][C]136[/C][C]18.375604010501[/C][C]17.2783105592315[/C][C]19.4728974617705[/C][/ROW]
[ROW][C]137[/C][C]18.4577773421499[/C][C]17.2434992004938[/C][C]19.672055483806[/C][/ROW]
[ROW][C]138[/C][C]18.6734159975617[/C][C]17.3444900701635[/C][C]20.0023419249598[/C][/ROW]
[ROW][C]139[/C][C]18.8977515416251[/C][C]17.4556809385262[/C][C]20.339822144724[/C][/ROW]
[ROW][C]140[/C][C]19.9219476436315[/C][C]18.3676508646225[/C][C]21.4762444226404[/C][/ROW]
[ROW][C]141[/C][C]20.0246226669482[/C][C]18.3585934836026[/C][C]21.6906518502938[/C][/ROW]
[ROW][C]142[/C][C]19.6168446032586[/C][C]17.8392595919615[/C][C]21.3944296145556[/C][/ROW]
[ROW][C]143[/C][C]19.6103286799106[/C][C]17.7211223027181[/C][C]21.4995350571032[/C][/ROW]
[ROW][C]144[/C][C]19.3421340437113[/C][C]17.3410526885507[/C][C]21.343215398872[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157323&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157323&T=3

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


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13319.767999237540319.052627152197820.4833713228828
13418.734106429992217.883522873666419.5846899863179
13518.415092045131117.438366854150919.3918172361113
13618.37560401050117.278310559231519.4728974617705
13718.457777342149917.243499200493819.672055483806
13818.673415997561717.344490070163520.0023419249598
13918.897751541625117.455680938526220.339822144724
14019.921947643631518.367650864622521.4762444226404
14120.024622666948218.358593483602621.6906518502938
14219.616844603258617.839259591961521.3944296145556
14319.610328679910617.721122302718121.4995350571032
14419.342134043711317.341052688550721.343215398872


Figures (Output of Computation)

Input Parameters & R Code

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')