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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 computationSun, 24 Jan 2010 07:31:51 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/24/t1264343582q7sasr7r3edl3kp.htm/, Retrieved Thu, 02 May 2024 19:38:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72413, Retrieved Thu, 02 May 2024 19:38:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact205

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [KDGP2W52] [2010-01-12 16:57:41] [6871f93be6d0be6de9fd7f767f34808c]
- RMPD    [Exponential Smoothing] [oef 10] [2010-01-24 14:31:51] [e2fca4e96a317e1c60e38968a8de4457] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104,65
109,2
103,93
101,93
101,58
102,63
106,83
105,57
105
104,16
106,93
106,5
106,47
112,33
106,81
103,49
104,13
103,2
105,55
102,8
106,68
105,43
109,01
112,24
112,87
110,98
112,85
112,08
110,72
109,69
112,53
112,99
111,74
111,15
114,82
117,38
117,81
122,85
116,96
119,16
117,74
118,84
123,81
120,33
119,2
117,32
128,58
129,2
126,19
132,1
128,12
122,28
122,36
123,13
125,97
126,14
122,7
122,67
129,19
133,01
123,96
128,96
127,32
131,38
125,25
127,91
130,42
128,44
125,86
125,71
130,63
131,78
125,61
131,84
122,14
127,13
124,49
125,48
129,86
126,32
125,56
125,64
128,26
125,47
134,4
134,5
131,22
121,62
124,16
127,5
132,86
127,87
124,07
124,25
131,16
129,24
129,24
135,51
128,97
126,89
127,52
130,31
132,39
132,69
128,73
129,66
127,72
132,63
129,74
138,46
134,31
128,8
129,95
134,15
136,01
135,1
132,27
132,49
130,06
136,11
131,47
140,61
141,65
126,75
133,9
138,75
141,86
141,13
138,76
138,65
138,59
147,09
140,17
152,38
144,02
139,55
141,1
145,85
147,88
145,17

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72413&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72413&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72413&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.192470581329793
beta0.127574015048930
gamma0.278645614438447

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.192470581329793 \tabularnewline
beta & 0.127574015048930 \tabularnewline
gamma & 0.278645614438447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72413&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]0.192470581329793[/C][/ROW]
[ROW][C]beta[/C][C]0.127574015048930[/C][/ROW]
[ROW][C]gamma[/C][C]0.278645614438447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72413&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72413&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
alpha0.192470581329793
beta0.127574015048930
gamma0.278645614438447






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13106.47105.5514823717950.918517628205095
14112.33111.8619933721840.46800662781601
15106.81106.5939524744250.216047525574922
16103.49103.3143884122930.175611587706996
17104.13103.9746869649470.155313035052657
18103.2102.8786422376620.321357762338479
19105.55107.995780266074-2.44578026607390
20102.8106.136521342062-3.33652134206226
21106.68104.6697285367302.01027146326953
22105.43104.0768134152601.35318658474043
23109.01107.0144052599501.99559474005021
24112.24106.9658920975905.27410790240981
25112.87108.4441611529294.42583884707123
26110.98115.588951832551-4.60895183255118
27112.85109.4229854950423.42701450495809
28112.08106.9671164755845.11288352441589
29110.72108.9091351778631.81086482213715
30109.69108.5457567849141.14424321508602
31112.53113.595493962886-1.06549396288563
32112.99112.2322259222870.757774077712995
33111.74113.287859006119-1.54785900611947
34111.15112.306175986157-1.15617598615718
35114.82115.287646212105-0.46764621210518
36117.38115.8245673962781.55543260372221
37117.81116.6267413904591.18325860954052
38122.85121.2653658688941.58463413110579
39116.96118.402664935398-1.44266493539767
40119.16115.5722727248753.58772727512513
41117.74116.6236942823821.11630571761812
42118.84116.1055325271522.73446747284784
43123.81121.1320632540332.67793674596714
44120.33121.159419551819-0.829419551819441
45119.2121.611653517556-2.41165351755623
46117.32120.751529924536-3.43152992453589
47128.58123.5938011494054.98619885059472
48129.2125.9133747312233.28662526877739
49126.19127.285241492775-1.09524149277451
50132.1131.8399238728360.260076127164268
51128.12128.272861505131-0.152861505130772
52122.28127.086063298654-4.806063298654
53122.36126.023151597029-3.66315159702911
54123.13124.889169112345-1.75916911234523
55125.97128.867723195293-2.89772319529294
56126.14126.725453167908-0.58545316790817
57122.7126.567338579470-3.86733857947016
58122.67124.860528905382-2.19052890538217
59129.19129.529216933957-0.339216933957431
60133.01130.0040636517103.00593634828965
61123.96129.891718014941-5.9317180149407
62128.96133.257526732992-4.29752673299203
63127.32128.045474056270-0.725474056269633
64131.38125.0124978216326.36750217836797
65125.25125.942770027757-0.692770027757291
66127.91125.4672873370012.44271266299889
67130.42129.7599278693980.660072130601662
68128.44128.671621144527-0.231621144526656
69125.86127.700722994668-1.84072299466835
70125.71126.668631848210-0.958631848209578
71130.63131.928592321967-1.29859232196711
72131.78132.885535267363-1.10553526736291
73125.61129.783835781963-4.17383578196264
74131.84133.711950959510-1.87195095950980
75122.14129.686321260562-7.54632126056227
76127.13126.6848818089030.44511819109718
77124.49124.4895123086100.000487691390347322
78125.48124.4729197430571.00708025694263
79129.86127.6728016204092.18719837959097
80126.32126.2999536322640.0200463677359011
81125.56124.6437780862540.916221913745801
82125.64124.0368510646291.60314893537115
83128.26129.472335531010-1.21233553100973
84125.47130.250391586619-4.78039158661872
85134.4125.4218154188548.97818458114577
86134.5132.3930403144082.10695968559151
87131.22127.9478924135233.27210758647696
88121.62129.183984927775-7.56398492777458
89124.16125.507505568038-1.34750556803806
90127.5125.5853181509251.91468184907498
91132.86129.3750720726043.48492792739628
92127.87127.945864632671-0.0758646326710419
93124.07126.65203302007-2.58203302007001
94124.25125.619617850366-1.36961785036640
95131.16129.8696676560141.29033234398639
96129.24130.408260719601-1.16826071960111
97129.24129.541197716841-0.301197716840733
98135.51133.1228455076482.38715449235212
99128.97128.9432384925940.0267615074057801
100126.89126.986168482726-0.0961684827264833
101127.52126.1989382744671.32106172553317
102130.31127.6430517733632.66694822663679
103132.39132.0680350056630.321964994336554
104132.69129.2882679956443.40173200435555
105128.73128.2446846966830.485315303317236
106129.66128.2956088661861.36439113381445
107127.72133.957687935371-6.23768793537073
108132.63132.5965800606210.0334199393790016
109129.74132.287854035257-2.54785403525716
110138.46136.1187869681672.34121303183309
111134.31131.4748688731742.83513112682562
112128.8130.175277777956-1.37527777795646
113129.95129.5739579034310.376042096568767
114134.15131.2290265541892.92097344581143
115136.01135.2714838725380.738516127462276
116135.1133.3713481360161.72865186398420
117132.27131.4148938793860.855106120613897
118132.49131.8092605583510.680739441649138
119130.06135.686855801320-5.62685580131964
120136.11135.9270813309370.182918669063412
121131.47135.142651879377-3.67265187937747
122140.61139.9059335083180.704066491682426
123141.65135.0665807761846.58341922381572
124126.75133.641587229086-6.89158722908567
125133.9132.3377292194141.56227078058606
126138.75134.7880022096383.96199779036246
127141.86138.559546726373.30045327363004
128141.13137.4580151296903.67198487030984
129138.76135.8094635747252.95053642527520
130138.65136.7497843688191.90021563118111
131138.59139.654616096987-1.06461609698732
132147.09142.4040683629784.68593163702161
133140.17142.053191249567-1.88319124956735
134152.38148.6240697057253.75593029427472
135144.02146.248340050457-2.22834005045721
136139.55140.432192999611-0.88219299961051
137141.1142.67168680762-1.57168680762013
138145.85145.4662659661260.383734033874106
139147.88148.719908643336-0.839908643336287
140145.17147.123081524382-1.95308152438204

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 106.47 & 105.551482371795 & 0.918517628205095 \tabularnewline
14 & 112.33 & 111.861993372184 & 0.46800662781601 \tabularnewline
15 & 106.81 & 106.593952474425 & 0.216047525574922 \tabularnewline
16 & 103.49 & 103.314388412293 & 0.175611587706996 \tabularnewline
17 & 104.13 & 103.974686964947 & 0.155313035052657 \tabularnewline
18 & 103.2 & 102.878642237662 & 0.321357762338479 \tabularnewline
19 & 105.55 & 107.995780266074 & -2.44578026607390 \tabularnewline
20 & 102.8 & 106.136521342062 & -3.33652134206226 \tabularnewline
21 & 106.68 & 104.669728536730 & 2.01027146326953 \tabularnewline
22 & 105.43 & 104.076813415260 & 1.35318658474043 \tabularnewline
23 & 109.01 & 107.014405259950 & 1.99559474005021 \tabularnewline
24 & 112.24 & 106.965892097590 & 5.27410790240981 \tabularnewline
25 & 112.87 & 108.444161152929 & 4.42583884707123 \tabularnewline
26 & 110.98 & 115.588951832551 & -4.60895183255118 \tabularnewline
27 & 112.85 & 109.422985495042 & 3.42701450495809 \tabularnewline
28 & 112.08 & 106.967116475584 & 5.11288352441589 \tabularnewline
29 & 110.72 & 108.909135177863 & 1.81086482213715 \tabularnewline
30 & 109.69 & 108.545756784914 & 1.14424321508602 \tabularnewline
31 & 112.53 & 113.595493962886 & -1.06549396288563 \tabularnewline
32 & 112.99 & 112.232225922287 & 0.757774077712995 \tabularnewline
33 & 111.74 & 113.287859006119 & -1.54785900611947 \tabularnewline
34 & 111.15 & 112.306175986157 & -1.15617598615718 \tabularnewline
35 & 114.82 & 115.287646212105 & -0.46764621210518 \tabularnewline
36 & 117.38 & 115.824567396278 & 1.55543260372221 \tabularnewline
37 & 117.81 & 116.626741390459 & 1.18325860954052 \tabularnewline
38 & 122.85 & 121.265365868894 & 1.58463413110579 \tabularnewline
39 & 116.96 & 118.402664935398 & -1.44266493539767 \tabularnewline
40 & 119.16 & 115.572272724875 & 3.58772727512513 \tabularnewline
41 & 117.74 & 116.623694282382 & 1.11630571761812 \tabularnewline
42 & 118.84 & 116.105532527152 & 2.73446747284784 \tabularnewline
43 & 123.81 & 121.132063254033 & 2.67793674596714 \tabularnewline
44 & 120.33 & 121.159419551819 & -0.829419551819441 \tabularnewline
45 & 119.2 & 121.611653517556 & -2.41165351755623 \tabularnewline
46 & 117.32 & 120.751529924536 & -3.43152992453589 \tabularnewline
47 & 128.58 & 123.593801149405 & 4.98619885059472 \tabularnewline
48 & 129.2 & 125.913374731223 & 3.28662526877739 \tabularnewline
49 & 126.19 & 127.285241492775 & -1.09524149277451 \tabularnewline
50 & 132.1 & 131.839923872836 & 0.260076127164268 \tabularnewline
51 & 128.12 & 128.272861505131 & -0.152861505130772 \tabularnewline
52 & 122.28 & 127.086063298654 & -4.806063298654 \tabularnewline
53 & 122.36 & 126.023151597029 & -3.66315159702911 \tabularnewline
54 & 123.13 & 124.889169112345 & -1.75916911234523 \tabularnewline
55 & 125.97 & 128.867723195293 & -2.89772319529294 \tabularnewline
56 & 126.14 & 126.725453167908 & -0.58545316790817 \tabularnewline
57 & 122.7 & 126.567338579470 & -3.86733857947016 \tabularnewline
58 & 122.67 & 124.860528905382 & -2.19052890538217 \tabularnewline
59 & 129.19 & 129.529216933957 & -0.339216933957431 \tabularnewline
60 & 133.01 & 130.004063651710 & 3.00593634828965 \tabularnewline
61 & 123.96 & 129.891718014941 & -5.9317180149407 \tabularnewline
62 & 128.96 & 133.257526732992 & -4.29752673299203 \tabularnewline
63 & 127.32 & 128.045474056270 & -0.725474056269633 \tabularnewline
64 & 131.38 & 125.012497821632 & 6.36750217836797 \tabularnewline
65 & 125.25 & 125.942770027757 & -0.692770027757291 \tabularnewline
66 & 127.91 & 125.467287337001 & 2.44271266299889 \tabularnewline
67 & 130.42 & 129.759927869398 & 0.660072130601662 \tabularnewline
68 & 128.44 & 128.671621144527 & -0.231621144526656 \tabularnewline
69 & 125.86 & 127.700722994668 & -1.84072299466835 \tabularnewline
70 & 125.71 & 126.668631848210 & -0.958631848209578 \tabularnewline
71 & 130.63 & 131.928592321967 & -1.29859232196711 \tabularnewline
72 & 131.78 & 132.885535267363 & -1.10553526736291 \tabularnewline
73 & 125.61 & 129.783835781963 & -4.17383578196264 \tabularnewline
74 & 131.84 & 133.711950959510 & -1.87195095950980 \tabularnewline
75 & 122.14 & 129.686321260562 & -7.54632126056227 \tabularnewline
76 & 127.13 & 126.684881808903 & 0.44511819109718 \tabularnewline
77 & 124.49 & 124.489512308610 & 0.000487691390347322 \tabularnewline
78 & 125.48 & 124.472919743057 & 1.00708025694263 \tabularnewline
79 & 129.86 & 127.672801620409 & 2.18719837959097 \tabularnewline
80 & 126.32 & 126.299953632264 & 0.0200463677359011 \tabularnewline
81 & 125.56 & 124.643778086254 & 0.916221913745801 \tabularnewline
82 & 125.64 & 124.036851064629 & 1.60314893537115 \tabularnewline
83 & 128.26 & 129.472335531010 & -1.21233553100973 \tabularnewline
84 & 125.47 & 130.250391586619 & -4.78039158661872 \tabularnewline
85 & 134.4 & 125.421815418854 & 8.97818458114577 \tabularnewline
86 & 134.5 & 132.393040314408 & 2.10695968559151 \tabularnewline
87 & 131.22 & 127.947892413523 & 3.27210758647696 \tabularnewline
88 & 121.62 & 129.183984927775 & -7.56398492777458 \tabularnewline
89 & 124.16 & 125.507505568038 & -1.34750556803806 \tabularnewline
90 & 127.5 & 125.585318150925 & 1.91468184907498 \tabularnewline
91 & 132.86 & 129.375072072604 & 3.48492792739628 \tabularnewline
92 & 127.87 & 127.945864632671 & -0.0758646326710419 \tabularnewline
93 & 124.07 & 126.65203302007 & -2.58203302007001 \tabularnewline
94 & 124.25 & 125.619617850366 & -1.36961785036640 \tabularnewline
95 & 131.16 & 129.869667656014 & 1.29033234398639 \tabularnewline
96 & 129.24 & 130.408260719601 & -1.16826071960111 \tabularnewline
97 & 129.24 & 129.541197716841 & -0.301197716840733 \tabularnewline
98 & 135.51 & 133.122845507648 & 2.38715449235212 \tabularnewline
99 & 128.97 & 128.943238492594 & 0.0267615074057801 \tabularnewline
100 & 126.89 & 126.986168482726 & -0.0961684827264833 \tabularnewline
101 & 127.52 & 126.198938274467 & 1.32106172553317 \tabularnewline
102 & 130.31 & 127.643051773363 & 2.66694822663679 \tabularnewline
103 & 132.39 & 132.068035005663 & 0.321964994336554 \tabularnewline
104 & 132.69 & 129.288267995644 & 3.40173200435555 \tabularnewline
105 & 128.73 & 128.244684696683 & 0.485315303317236 \tabularnewline
106 & 129.66 & 128.295608866186 & 1.36439113381445 \tabularnewline
107 & 127.72 & 133.957687935371 & -6.23768793537073 \tabularnewline
108 & 132.63 & 132.596580060621 & 0.0334199393790016 \tabularnewline
109 & 129.74 & 132.287854035257 & -2.54785403525716 \tabularnewline
110 & 138.46 & 136.118786968167 & 2.34121303183309 \tabularnewline
111 & 134.31 & 131.474868873174 & 2.83513112682562 \tabularnewline
112 & 128.8 & 130.175277777956 & -1.37527777795646 \tabularnewline
113 & 129.95 & 129.573957903431 & 0.376042096568767 \tabularnewline
114 & 134.15 & 131.229026554189 & 2.92097344581143 \tabularnewline
115 & 136.01 & 135.271483872538 & 0.738516127462276 \tabularnewline
116 & 135.1 & 133.371348136016 & 1.72865186398420 \tabularnewline
117 & 132.27 & 131.414893879386 & 0.855106120613897 \tabularnewline
118 & 132.49 & 131.809260558351 & 0.680739441649138 \tabularnewline
119 & 130.06 & 135.686855801320 & -5.62685580131964 \tabularnewline
120 & 136.11 & 135.927081330937 & 0.182918669063412 \tabularnewline
121 & 131.47 & 135.142651879377 & -3.67265187937747 \tabularnewline
122 & 140.61 & 139.905933508318 & 0.704066491682426 \tabularnewline
123 & 141.65 & 135.066580776184 & 6.58341922381572 \tabularnewline
124 & 126.75 & 133.641587229086 & -6.89158722908567 \tabularnewline
125 & 133.9 & 132.337729219414 & 1.56227078058606 \tabularnewline
126 & 138.75 & 134.788002209638 & 3.96199779036246 \tabularnewline
127 & 141.86 & 138.55954672637 & 3.30045327363004 \tabularnewline
128 & 141.13 & 137.458015129690 & 3.67198487030984 \tabularnewline
129 & 138.76 & 135.809463574725 & 2.95053642527520 \tabularnewline
130 & 138.65 & 136.749784368819 & 1.90021563118111 \tabularnewline
131 & 138.59 & 139.654616096987 & -1.06461609698732 \tabularnewline
132 & 147.09 & 142.404068362978 & 4.68593163702161 \tabularnewline
133 & 140.17 & 142.053191249567 & -1.88319124956735 \tabularnewline
134 & 152.38 & 148.624069705725 & 3.75593029427472 \tabularnewline
135 & 144.02 & 146.248340050457 & -2.22834005045721 \tabularnewline
136 & 139.55 & 140.432192999611 & -0.88219299961051 \tabularnewline
137 & 141.1 & 142.67168680762 & -1.57168680762013 \tabularnewline
138 & 145.85 & 145.466265966126 & 0.383734033874106 \tabularnewline
139 & 147.88 & 148.719908643336 & -0.839908643336287 \tabularnewline
140 & 145.17 & 147.123081524382 & -1.95308152438204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72413&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]106.47[/C][C]105.551482371795[/C][C]0.918517628205095[/C][/ROW]
[ROW][C]14[/C][C]112.33[/C][C]111.861993372184[/C][C]0.46800662781601[/C][/ROW]
[ROW][C]15[/C][C]106.81[/C][C]106.593952474425[/C][C]0.216047525574922[/C][/ROW]
[ROW][C]16[/C][C]103.49[/C][C]103.314388412293[/C][C]0.175611587706996[/C][/ROW]
[ROW][C]17[/C][C]104.13[/C][C]103.974686964947[/C][C]0.155313035052657[/C][/ROW]
[ROW][C]18[/C][C]103.2[/C][C]102.878642237662[/C][C]0.321357762338479[/C][/ROW]
[ROW][C]19[/C][C]105.55[/C][C]107.995780266074[/C][C]-2.44578026607390[/C][/ROW]
[ROW][C]20[/C][C]102.8[/C][C]106.136521342062[/C][C]-3.33652134206226[/C][/ROW]
[ROW][C]21[/C][C]106.68[/C][C]104.669728536730[/C][C]2.01027146326953[/C][/ROW]
[ROW][C]22[/C][C]105.43[/C][C]104.076813415260[/C][C]1.35318658474043[/C][/ROW]
[ROW][C]23[/C][C]109.01[/C][C]107.014405259950[/C][C]1.99559474005021[/C][/ROW]
[ROW][C]24[/C][C]112.24[/C][C]106.965892097590[/C][C]5.27410790240981[/C][/ROW]
[ROW][C]25[/C][C]112.87[/C][C]108.444161152929[/C][C]4.42583884707123[/C][/ROW]
[ROW][C]26[/C][C]110.98[/C][C]115.588951832551[/C][C]-4.60895183255118[/C][/ROW]
[ROW][C]27[/C][C]112.85[/C][C]109.422985495042[/C][C]3.42701450495809[/C][/ROW]
[ROW][C]28[/C][C]112.08[/C][C]106.967116475584[/C][C]5.11288352441589[/C][/ROW]
[ROW][C]29[/C][C]110.72[/C][C]108.909135177863[/C][C]1.81086482213715[/C][/ROW]
[ROW][C]30[/C][C]109.69[/C][C]108.545756784914[/C][C]1.14424321508602[/C][/ROW]
[ROW][C]31[/C][C]112.53[/C][C]113.595493962886[/C][C]-1.06549396288563[/C][/ROW]
[ROW][C]32[/C][C]112.99[/C][C]112.232225922287[/C][C]0.757774077712995[/C][/ROW]
[ROW][C]33[/C][C]111.74[/C][C]113.287859006119[/C][C]-1.54785900611947[/C][/ROW]
[ROW][C]34[/C][C]111.15[/C][C]112.306175986157[/C][C]-1.15617598615718[/C][/ROW]
[ROW][C]35[/C][C]114.82[/C][C]115.287646212105[/C][C]-0.46764621210518[/C][/ROW]
[ROW][C]36[/C][C]117.38[/C][C]115.824567396278[/C][C]1.55543260372221[/C][/ROW]
[ROW][C]37[/C][C]117.81[/C][C]116.626741390459[/C][C]1.18325860954052[/C][/ROW]
[ROW][C]38[/C][C]122.85[/C][C]121.265365868894[/C][C]1.58463413110579[/C][/ROW]
[ROW][C]39[/C][C]116.96[/C][C]118.402664935398[/C][C]-1.44266493539767[/C][/ROW]
[ROW][C]40[/C][C]119.16[/C][C]115.572272724875[/C][C]3.58772727512513[/C][/ROW]
[ROW][C]41[/C][C]117.74[/C][C]116.623694282382[/C][C]1.11630571761812[/C][/ROW]
[ROW][C]42[/C][C]118.84[/C][C]116.105532527152[/C][C]2.73446747284784[/C][/ROW]
[ROW][C]43[/C][C]123.81[/C][C]121.132063254033[/C][C]2.67793674596714[/C][/ROW]
[ROW][C]44[/C][C]120.33[/C][C]121.159419551819[/C][C]-0.829419551819441[/C][/ROW]
[ROW][C]45[/C][C]119.2[/C][C]121.611653517556[/C][C]-2.41165351755623[/C][/ROW]
[ROW][C]46[/C][C]117.32[/C][C]120.751529924536[/C][C]-3.43152992453589[/C][/ROW]
[ROW][C]47[/C][C]128.58[/C][C]123.593801149405[/C][C]4.98619885059472[/C][/ROW]
[ROW][C]48[/C][C]129.2[/C][C]125.913374731223[/C][C]3.28662526877739[/C][/ROW]
[ROW][C]49[/C][C]126.19[/C][C]127.285241492775[/C][C]-1.09524149277451[/C][/ROW]
[ROW][C]50[/C][C]132.1[/C][C]131.839923872836[/C][C]0.260076127164268[/C][/ROW]
[ROW][C]51[/C][C]128.12[/C][C]128.272861505131[/C][C]-0.152861505130772[/C][/ROW]
[ROW][C]52[/C][C]122.28[/C][C]127.086063298654[/C][C]-4.806063298654[/C][/ROW]
[ROW][C]53[/C][C]122.36[/C][C]126.023151597029[/C][C]-3.66315159702911[/C][/ROW]
[ROW][C]54[/C][C]123.13[/C][C]124.889169112345[/C][C]-1.75916911234523[/C][/ROW]
[ROW][C]55[/C][C]125.97[/C][C]128.867723195293[/C][C]-2.89772319529294[/C][/ROW]
[ROW][C]56[/C][C]126.14[/C][C]126.725453167908[/C][C]-0.58545316790817[/C][/ROW]
[ROW][C]57[/C][C]122.7[/C][C]126.567338579470[/C][C]-3.86733857947016[/C][/ROW]
[ROW][C]58[/C][C]122.67[/C][C]124.860528905382[/C][C]-2.19052890538217[/C][/ROW]
[ROW][C]59[/C][C]129.19[/C][C]129.529216933957[/C][C]-0.339216933957431[/C][/ROW]
[ROW][C]60[/C][C]133.01[/C][C]130.004063651710[/C][C]3.00593634828965[/C][/ROW]
[ROW][C]61[/C][C]123.96[/C][C]129.891718014941[/C][C]-5.9317180149407[/C][/ROW]
[ROW][C]62[/C][C]128.96[/C][C]133.257526732992[/C][C]-4.29752673299203[/C][/ROW]
[ROW][C]63[/C][C]127.32[/C][C]128.045474056270[/C][C]-0.725474056269633[/C][/ROW]
[ROW][C]64[/C][C]131.38[/C][C]125.012497821632[/C][C]6.36750217836797[/C][/ROW]
[ROW][C]65[/C][C]125.25[/C][C]125.942770027757[/C][C]-0.692770027757291[/C][/ROW]
[ROW][C]66[/C][C]127.91[/C][C]125.467287337001[/C][C]2.44271266299889[/C][/ROW]
[ROW][C]67[/C][C]130.42[/C][C]129.759927869398[/C][C]0.660072130601662[/C][/ROW]
[ROW][C]68[/C][C]128.44[/C][C]128.671621144527[/C][C]-0.231621144526656[/C][/ROW]
[ROW][C]69[/C][C]125.86[/C][C]127.700722994668[/C][C]-1.84072299466835[/C][/ROW]
[ROW][C]70[/C][C]125.71[/C][C]126.668631848210[/C][C]-0.958631848209578[/C][/ROW]
[ROW][C]71[/C][C]130.63[/C][C]131.928592321967[/C][C]-1.29859232196711[/C][/ROW]
[ROW][C]72[/C][C]131.78[/C][C]132.885535267363[/C][C]-1.10553526736291[/C][/ROW]
[ROW][C]73[/C][C]125.61[/C][C]129.783835781963[/C][C]-4.17383578196264[/C][/ROW]
[ROW][C]74[/C][C]131.84[/C][C]133.711950959510[/C][C]-1.87195095950980[/C][/ROW]
[ROW][C]75[/C][C]122.14[/C][C]129.686321260562[/C][C]-7.54632126056227[/C][/ROW]
[ROW][C]76[/C][C]127.13[/C][C]126.684881808903[/C][C]0.44511819109718[/C][/ROW]
[ROW][C]77[/C][C]124.49[/C][C]124.489512308610[/C][C]0.000487691390347322[/C][/ROW]
[ROW][C]78[/C][C]125.48[/C][C]124.472919743057[/C][C]1.00708025694263[/C][/ROW]
[ROW][C]79[/C][C]129.86[/C][C]127.672801620409[/C][C]2.18719837959097[/C][/ROW]
[ROW][C]80[/C][C]126.32[/C][C]126.299953632264[/C][C]0.0200463677359011[/C][/ROW]
[ROW][C]81[/C][C]125.56[/C][C]124.643778086254[/C][C]0.916221913745801[/C][/ROW]
[ROW][C]82[/C][C]125.64[/C][C]124.036851064629[/C][C]1.60314893537115[/C][/ROW]
[ROW][C]83[/C][C]128.26[/C][C]129.472335531010[/C][C]-1.21233553100973[/C][/ROW]
[ROW][C]84[/C][C]125.47[/C][C]130.250391586619[/C][C]-4.78039158661872[/C][/ROW]
[ROW][C]85[/C][C]134.4[/C][C]125.421815418854[/C][C]8.97818458114577[/C][/ROW]
[ROW][C]86[/C][C]134.5[/C][C]132.393040314408[/C][C]2.10695968559151[/C][/ROW]
[ROW][C]87[/C][C]131.22[/C][C]127.947892413523[/C][C]3.27210758647696[/C][/ROW]
[ROW][C]88[/C][C]121.62[/C][C]129.183984927775[/C][C]-7.56398492777458[/C][/ROW]
[ROW][C]89[/C][C]124.16[/C][C]125.507505568038[/C][C]-1.34750556803806[/C][/ROW]
[ROW][C]90[/C][C]127.5[/C][C]125.585318150925[/C][C]1.91468184907498[/C][/ROW]
[ROW][C]91[/C][C]132.86[/C][C]129.375072072604[/C][C]3.48492792739628[/C][/ROW]
[ROW][C]92[/C][C]127.87[/C][C]127.945864632671[/C][C]-0.0758646326710419[/C][/ROW]
[ROW][C]93[/C][C]124.07[/C][C]126.65203302007[/C][C]-2.58203302007001[/C][/ROW]
[ROW][C]94[/C][C]124.25[/C][C]125.619617850366[/C][C]-1.36961785036640[/C][/ROW]
[ROW][C]95[/C][C]131.16[/C][C]129.869667656014[/C][C]1.29033234398639[/C][/ROW]
[ROW][C]96[/C][C]129.24[/C][C]130.408260719601[/C][C]-1.16826071960111[/C][/ROW]
[ROW][C]97[/C][C]129.24[/C][C]129.541197716841[/C][C]-0.301197716840733[/C][/ROW]
[ROW][C]98[/C][C]135.51[/C][C]133.122845507648[/C][C]2.38715449235212[/C][/ROW]
[ROW][C]99[/C][C]128.97[/C][C]128.943238492594[/C][C]0.0267615074057801[/C][/ROW]
[ROW][C]100[/C][C]126.89[/C][C]126.986168482726[/C][C]-0.0961684827264833[/C][/ROW]
[ROW][C]101[/C][C]127.52[/C][C]126.198938274467[/C][C]1.32106172553317[/C][/ROW]
[ROW][C]102[/C][C]130.31[/C][C]127.643051773363[/C][C]2.66694822663679[/C][/ROW]
[ROW][C]103[/C][C]132.39[/C][C]132.068035005663[/C][C]0.321964994336554[/C][/ROW]
[ROW][C]104[/C][C]132.69[/C][C]129.288267995644[/C][C]3.40173200435555[/C][/ROW]
[ROW][C]105[/C][C]128.73[/C][C]128.244684696683[/C][C]0.485315303317236[/C][/ROW]
[ROW][C]106[/C][C]129.66[/C][C]128.295608866186[/C][C]1.36439113381445[/C][/ROW]
[ROW][C]107[/C][C]127.72[/C][C]133.957687935371[/C][C]-6.23768793537073[/C][/ROW]
[ROW][C]108[/C][C]132.63[/C][C]132.596580060621[/C][C]0.0334199393790016[/C][/ROW]
[ROW][C]109[/C][C]129.74[/C][C]132.287854035257[/C][C]-2.54785403525716[/C][/ROW]
[ROW][C]110[/C][C]138.46[/C][C]136.118786968167[/C][C]2.34121303183309[/C][/ROW]
[ROW][C]111[/C][C]134.31[/C][C]131.474868873174[/C][C]2.83513112682562[/C][/ROW]
[ROW][C]112[/C][C]128.8[/C][C]130.175277777956[/C][C]-1.37527777795646[/C][/ROW]
[ROW][C]113[/C][C]129.95[/C][C]129.573957903431[/C][C]0.376042096568767[/C][/ROW]
[ROW][C]114[/C][C]134.15[/C][C]131.229026554189[/C][C]2.92097344581143[/C][/ROW]
[ROW][C]115[/C][C]136.01[/C][C]135.271483872538[/C][C]0.738516127462276[/C][/ROW]
[ROW][C]116[/C][C]135.1[/C][C]133.371348136016[/C][C]1.72865186398420[/C][/ROW]
[ROW][C]117[/C][C]132.27[/C][C]131.414893879386[/C][C]0.855106120613897[/C][/ROW]
[ROW][C]118[/C][C]132.49[/C][C]131.809260558351[/C][C]0.680739441649138[/C][/ROW]
[ROW][C]119[/C][C]130.06[/C][C]135.686855801320[/C][C]-5.62685580131964[/C][/ROW]
[ROW][C]120[/C][C]136.11[/C][C]135.927081330937[/C][C]0.182918669063412[/C][/ROW]
[ROW][C]121[/C][C]131.47[/C][C]135.142651879377[/C][C]-3.67265187937747[/C][/ROW]
[ROW][C]122[/C][C]140.61[/C][C]139.905933508318[/C][C]0.704066491682426[/C][/ROW]
[ROW][C]123[/C][C]141.65[/C][C]135.066580776184[/C][C]6.58341922381572[/C][/ROW]
[ROW][C]124[/C][C]126.75[/C][C]133.641587229086[/C][C]-6.89158722908567[/C][/ROW]
[ROW][C]125[/C][C]133.9[/C][C]132.337729219414[/C][C]1.56227078058606[/C][/ROW]
[ROW][C]126[/C][C]138.75[/C][C]134.788002209638[/C][C]3.96199779036246[/C][/ROW]
[ROW][C]127[/C][C]141.86[/C][C]138.55954672637[/C][C]3.30045327363004[/C][/ROW]
[ROW][C]128[/C][C]141.13[/C][C]137.458015129690[/C][C]3.67198487030984[/C][/ROW]
[ROW][C]129[/C][C]138.76[/C][C]135.809463574725[/C][C]2.95053642527520[/C][/ROW]
[ROW][C]130[/C][C]138.65[/C][C]136.749784368819[/C][C]1.90021563118111[/C][/ROW]
[ROW][C]131[/C][C]138.59[/C][C]139.654616096987[/C][C]-1.06461609698732[/C][/ROW]
[ROW][C]132[/C][C]147.09[/C][C]142.404068362978[/C][C]4.68593163702161[/C][/ROW]
[ROW][C]133[/C][C]140.17[/C][C]142.053191249567[/C][C]-1.88319124956735[/C][/ROW]
[ROW][C]134[/C][C]152.38[/C][C]148.624069705725[/C][C]3.75593029427472[/C][/ROW]
[ROW][C]135[/C][C]144.02[/C][C]146.248340050457[/C][C]-2.22834005045721[/C][/ROW]
[ROW][C]136[/C][C]139.55[/C][C]140.432192999611[/C][C]-0.88219299961051[/C][/ROW]
[ROW][C]137[/C][C]141.1[/C][C]142.67168680762[/C][C]-1.57168680762013[/C][/ROW]
[ROW][C]138[/C][C]145.85[/C][C]145.466265966126[/C][C]0.383734033874106[/C][/ROW]
[ROW][C]139[/C][C]147.88[/C][C]148.719908643336[/C][C]-0.839908643336287[/C][/ROW]
[ROW][C]140[/C][C]145.17[/C][C]147.123081524382[/C][C]-1.95308152438204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72413&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72413&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
13106.47105.5514823717950.918517628205095
14112.33111.8619933721840.46800662781601
15106.81106.5939524744250.216047525574922
16103.49103.3143884122930.175611587706996
17104.13103.9746869649470.155313035052657
18103.2102.8786422376620.321357762338479
19105.55107.995780266074-2.44578026607390
20102.8106.136521342062-3.33652134206226
21106.68104.6697285367302.01027146326953
22105.43104.0768134152601.35318658474043
23109.01107.0144052599501.99559474005021
24112.24106.9658920975905.27410790240981
25112.87108.4441611529294.42583884707123
26110.98115.588951832551-4.60895183255118
27112.85109.4229854950423.42701450495809
28112.08106.9671164755845.11288352441589
29110.72108.9091351778631.81086482213715
30109.69108.5457567849141.14424321508602
31112.53113.595493962886-1.06549396288563
32112.99112.2322259222870.757774077712995
33111.74113.287859006119-1.54785900611947
34111.15112.306175986157-1.15617598615718
35114.82115.287646212105-0.46764621210518
36117.38115.8245673962781.55543260372221
37117.81116.6267413904591.18325860954052
38122.85121.2653658688941.58463413110579
39116.96118.402664935398-1.44266493539767
40119.16115.5722727248753.58772727512513
41117.74116.6236942823821.11630571761812
42118.84116.1055325271522.73446747284784
43123.81121.1320632540332.67793674596714
44120.33121.159419551819-0.829419551819441
45119.2121.611653517556-2.41165351755623
46117.32120.751529924536-3.43152992453589
47128.58123.5938011494054.98619885059472
48129.2125.9133747312233.28662526877739
49126.19127.285241492775-1.09524149277451
50132.1131.8399238728360.260076127164268
51128.12128.272861505131-0.152861505130772
52122.28127.086063298654-4.806063298654
53122.36126.023151597029-3.66315159702911
54123.13124.889169112345-1.75916911234523
55125.97128.867723195293-2.89772319529294
56126.14126.725453167908-0.58545316790817
57122.7126.567338579470-3.86733857947016
58122.67124.860528905382-2.19052890538217
59129.19129.529216933957-0.339216933957431
60133.01130.0040636517103.00593634828965
61123.96129.891718014941-5.9317180149407
62128.96133.257526732992-4.29752673299203
63127.32128.045474056270-0.725474056269633
64131.38125.0124978216326.36750217836797
65125.25125.942770027757-0.692770027757291
66127.91125.4672873370012.44271266299889
67130.42129.7599278693980.660072130601662
68128.44128.671621144527-0.231621144526656
69125.86127.700722994668-1.84072299466835
70125.71126.668631848210-0.958631848209578
71130.63131.928592321967-1.29859232196711
72131.78132.885535267363-1.10553526736291
73125.61129.783835781963-4.17383578196264
74131.84133.711950959510-1.87195095950980
75122.14129.686321260562-7.54632126056227
76127.13126.6848818089030.44511819109718
77124.49124.4895123086100.000487691390347322
78125.48124.4729197430571.00708025694263
79129.86127.6728016204092.18719837959097
80126.32126.2999536322640.0200463677359011
81125.56124.6437780862540.916221913745801
82125.64124.0368510646291.60314893537115
83128.26129.472335531010-1.21233553100973
84125.47130.250391586619-4.78039158661872
85134.4125.4218154188548.97818458114577
86134.5132.3930403144082.10695968559151
87131.22127.9478924135233.27210758647696
88121.62129.183984927775-7.56398492777458
89124.16125.507505568038-1.34750556803806
90127.5125.5853181509251.91468184907498
91132.86129.3750720726043.48492792739628
92127.87127.945864632671-0.0758646326710419
93124.07126.65203302007-2.58203302007001
94124.25125.619617850366-1.36961785036640
95131.16129.8696676560141.29033234398639
96129.24130.408260719601-1.16826071960111
97129.24129.541197716841-0.301197716840733
98135.51133.1228455076482.38715449235212
99128.97128.9432384925940.0267615074057801
100126.89126.986168482726-0.0961684827264833
101127.52126.1989382744671.32106172553317
102130.31127.6430517733632.66694822663679
103132.39132.0680350056630.321964994336554
104132.69129.2882679956443.40173200435555
105128.73128.2446846966830.485315303317236
106129.66128.2956088661861.36439113381445
107127.72133.957687935371-6.23768793537073
108132.63132.5965800606210.0334199393790016
109129.74132.287854035257-2.54785403525716
110138.46136.1187869681672.34121303183309
111134.31131.4748688731742.83513112682562
112128.8130.175277777956-1.37527777795646
113129.95129.5739579034310.376042096568767
114134.15131.2290265541892.92097344581143
115136.01135.2714838725380.738516127462276
116135.1133.3713481360161.72865186398420
117132.27131.4148938793860.855106120613897
118132.49131.8092605583510.680739441649138
119130.06135.686855801320-5.62685580131964
120136.11135.9270813309370.182918669063412
121131.47135.142651879377-3.67265187937747
122140.61139.9059335083180.704066491682426
123141.65135.0665807761846.58341922381572
124126.75133.641587229086-6.89158722908567
125133.9132.3377292194141.56227078058606
126138.75134.7880022096383.96199779036246
127141.86138.559546726373.30045327363004
128141.13137.4580151296903.67198487030984
129138.76135.8094635747252.95053642527520
130138.65136.7497843688191.90021563118111
131138.59139.654616096987-1.06461609698732
132147.09142.4040683629784.68593163702161
133140.17142.053191249567-1.88319124956735
134152.38148.6240697057253.75593029427472
135144.02146.248340050457-2.22834005045721
136139.55140.432192999611-0.88219299961051
137141.1142.67168680762-1.57168680762013
138145.85145.4662659661260.383734033874106
139147.88148.719908643336-0.839908643336287
140145.17147.123081524382-1.95308152438204






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
141144.309416864195138.640816787854149.978016940536
142144.452943639876138.652384600902150.253502678850
143146.285686063592140.325670711995152.245701415188
144150.520919778240144.372939051838156.668900504642
145147.661848428151141.296875220489154.026821635813
146155.782168282825149.171103280559162.393233285091
147151.162858917366144.276909214617158.048808620116
148145.959093788209138.770074440977153.148113135442
149148.115488622158140.596046171468155.634931072847
150151.593411892844143.717175685198159.469648100490
151154.429279909891146.170951267248162.687608552534
152152.695673980046144.031065103138161.360282856954

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
141 & 144.309416864195 & 138.640816787854 & 149.978016940536 \tabularnewline
142 & 144.452943639876 & 138.652384600902 & 150.253502678850 \tabularnewline
143 & 146.285686063592 & 140.325670711995 & 152.245701415188 \tabularnewline
144 & 150.520919778240 & 144.372939051838 & 156.668900504642 \tabularnewline
145 & 147.661848428151 & 141.296875220489 & 154.026821635813 \tabularnewline
146 & 155.782168282825 & 149.171103280559 & 162.393233285091 \tabularnewline
147 & 151.162858917366 & 144.276909214617 & 158.048808620116 \tabularnewline
148 & 145.959093788209 & 138.770074440977 & 153.148113135442 \tabularnewline
149 & 148.115488622158 & 140.596046171468 & 155.634931072847 \tabularnewline
150 & 151.593411892844 & 143.717175685198 & 159.469648100490 \tabularnewline
151 & 154.429279909891 & 146.170951267248 & 162.687608552534 \tabularnewline
152 & 152.695673980046 & 144.031065103138 & 161.360282856954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72413&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]141[/C][C]144.309416864195[/C][C]138.640816787854[/C][C]149.978016940536[/C][/ROW]
[ROW][C]142[/C][C]144.452943639876[/C][C]138.652384600902[/C][C]150.253502678850[/C][/ROW]
[ROW][C]143[/C][C]146.285686063592[/C][C]140.325670711995[/C][C]152.245701415188[/C][/ROW]
[ROW][C]144[/C][C]150.520919778240[/C][C]144.372939051838[/C][C]156.668900504642[/C][/ROW]
[ROW][C]145[/C][C]147.661848428151[/C][C]141.296875220489[/C][C]154.026821635813[/C][/ROW]
[ROW][C]146[/C][C]155.782168282825[/C][C]149.171103280559[/C][C]162.393233285091[/C][/ROW]
[ROW][C]147[/C][C]151.162858917366[/C][C]144.276909214617[/C][C]158.048808620116[/C][/ROW]
[ROW][C]148[/C][C]145.959093788209[/C][C]138.770074440977[/C][C]153.148113135442[/C][/ROW]
[ROW][C]149[/C][C]148.115488622158[/C][C]140.596046171468[/C][C]155.634931072847[/C][/ROW]
[ROW][C]150[/C][C]151.593411892844[/C][C]143.717175685198[/C][C]159.469648100490[/C][/ROW]
[ROW][C]151[/C][C]154.429279909891[/C][C]146.170951267248[/C][C]162.687608552534[/C][/ROW]
[ROW][C]152[/C][C]152.695673980046[/C][C]144.031065103138[/C][C]161.360282856954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72413&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72413&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
141144.309416864195138.640816787854149.978016940536
142144.452943639876138.652384600902150.253502678850
143146.285686063592140.325670711995152.245701415188
144150.520919778240144.372939051838156.668900504642
145147.661848428151141.296875220489154.026821635813
146155.782168282825149.171103280559162.393233285091
147151.162858917366144.276909214617158.048808620116
148145.959093788209138.770074440977153.148113135442
149148.115488622158140.596046171468155.634931072847
150151.593411892844143.717175685198159.469648100490
151154.429279909891146.170951267248162.687608552534
152152.695673980046144.031065103138161.360282856954


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')