FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Apr 2017 10:44:14 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Apr/30/t1493545536kehhl8d1jtui3jv.htm/, Retrieved Sun, 12 May 2024 19:05:43 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 12 May 2024 19:05:43 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93.09
93.02
93.23
92.7
92.68
93.11
93.02
93.29
93.2
92.86
93.04
92.8
93.11
93.42
94.01
94.47
94.07
94.33
94.43
95.37
95.83
95.46
96
95.35
96.85
97.84
98.38
98.9
99.51
99.95
99.93
101.4
101.7
101.65
102.33
101.56
101.91
102.29
102.44
102.84
103.2
103.23
103.16
103.31
103.04
102.57
102.88
101.91
102.59
103.27
103.59
104.35
104.6
105.08
104.93
105.15
104.67
104.55
109.82
109.25

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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.886216716375698
beta0.0367812897408182
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.886216716375698 \tabularnewline
beta & 0.0367812897408182 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.886216716375698[/C][/ROW]
[ROW][C]beta[/C][C]0.0367812897408182[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.886216716375698
beta0.0367812897408182
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1393.1192.50925926606350.600740733936547
1493.4293.36724456634630.0527554336537008
1594.0193.97057521486620.0394247851338037
1694.4794.41155356073910.0584464392609192
1794.0793.99798413291850.0720158670815323
1894.3394.26079826925630.0692017307436856
1994.4394.7268468330713-0.296846833071342
2095.3794.88163258902830.488367410971733
2195.8395.34931829306630.480681706933723
2295.4695.5089858623782-0.0489858623782311
239695.70604488257390.293955117426052
2495.3595.8067999260268-0.45679992602679
2596.8595.86362502790520.986374972094779
2697.8497.06151082616640.778489173833648
2798.3898.4051496651788-0.0251496651788301
2898.998.88097701576590.0190229842341125
2999.5198.4813002996421.02869970035802
3099.9599.70136552696710.248634473032936
3199.93100.410182166521-0.480182166520606
32101.4100.620412582770.779587417229507
33101.7101.4539444898640.246055510136102
34101.65101.4233708233580.226629176641552
35102.33102.0280176067670.301982393233416
36101.56102.139458844283-0.579458844282883
37101.91102.394609853487-0.484609853486859
38102.29102.335895582663-0.0458955826632632
39102.44102.912213932533-0.472213932532995
40102.84103.033419191266-0.19341919126596
41103.2102.556093144970.643906855029968
42103.23103.350347772715-0.120347772715121
43103.16103.647023096443-0.487023096443238
44103.31104.004410213523-0.694410213522914
45103.04103.412531620386-0.372531620386141
46102.57102.750044672747-0.180044672747329
47102.88102.916440787311-0.0364407873113493
48101.91102.526460306018-0.616460306018283
49102.59102.661907510687-0.0719075106873959
50103.27102.9336465936390.336353406360729
51103.59103.728741001294-0.138741001294136
52104.35104.1174049422950.232595057705467
53104.6104.0565857313320.543414268668073
54105.08104.6206201875480.459379812452482
55104.93105.357118414531-0.427118414531407
56105.15105.720718805436-0.570718805436428
57104.67105.244034104366-0.574034104366447
58104.55104.3820182072140.167981792785582
59109.82104.8528251510494.96717484895123
60109.25108.9304566866180.319543313381914

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 93.11 & 92.5092592660635 & 0.600740733936547 \tabularnewline
14 & 93.42 & 93.3672445663463 & 0.0527554336537008 \tabularnewline
15 & 94.01 & 93.9705752148662 & 0.0394247851338037 \tabularnewline
16 & 94.47 & 94.4115535607391 & 0.0584464392609192 \tabularnewline
17 & 94.07 & 93.9979841329185 & 0.0720158670815323 \tabularnewline
18 & 94.33 & 94.2607982692563 & 0.0692017307436856 \tabularnewline
19 & 94.43 & 94.7268468330713 & -0.296846833071342 \tabularnewline
20 & 95.37 & 94.8816325890283 & 0.488367410971733 \tabularnewline
21 & 95.83 & 95.3493182930663 & 0.480681706933723 \tabularnewline
22 & 95.46 & 95.5089858623782 & -0.0489858623782311 \tabularnewline
23 & 96 & 95.7060448825739 & 0.293955117426052 \tabularnewline
24 & 95.35 & 95.8067999260268 & -0.45679992602679 \tabularnewline
25 & 96.85 & 95.8636250279052 & 0.986374972094779 \tabularnewline
26 & 97.84 & 97.0615108261664 & 0.778489173833648 \tabularnewline
27 & 98.38 & 98.4051496651788 & -0.0251496651788301 \tabularnewline
28 & 98.9 & 98.8809770157659 & 0.0190229842341125 \tabularnewline
29 & 99.51 & 98.481300299642 & 1.02869970035802 \tabularnewline
30 & 99.95 & 99.7013655269671 & 0.248634473032936 \tabularnewline
31 & 99.93 & 100.410182166521 & -0.480182166520606 \tabularnewline
32 & 101.4 & 100.62041258277 & 0.779587417229507 \tabularnewline
33 & 101.7 & 101.453944489864 & 0.246055510136102 \tabularnewline
34 & 101.65 & 101.423370823358 & 0.226629176641552 \tabularnewline
35 & 102.33 & 102.028017606767 & 0.301982393233416 \tabularnewline
36 & 101.56 & 102.139458844283 & -0.579458844282883 \tabularnewline
37 & 101.91 & 102.394609853487 & -0.484609853486859 \tabularnewline
38 & 102.29 & 102.335895582663 & -0.0458955826632632 \tabularnewline
39 & 102.44 & 102.912213932533 & -0.472213932532995 \tabularnewline
40 & 102.84 & 103.033419191266 & -0.19341919126596 \tabularnewline
41 & 103.2 & 102.55609314497 & 0.643906855029968 \tabularnewline
42 & 103.23 & 103.350347772715 & -0.120347772715121 \tabularnewline
43 & 103.16 & 103.647023096443 & -0.487023096443238 \tabularnewline
44 & 103.31 & 104.004410213523 & -0.694410213522914 \tabularnewline
45 & 103.04 & 103.412531620386 & -0.372531620386141 \tabularnewline
46 & 102.57 & 102.750044672747 & -0.180044672747329 \tabularnewline
47 & 102.88 & 102.916440787311 & -0.0364407873113493 \tabularnewline
48 & 101.91 & 102.526460306018 & -0.616460306018283 \tabularnewline
49 & 102.59 & 102.661907510687 & -0.0719075106873959 \tabularnewline
50 & 103.27 & 102.933646593639 & 0.336353406360729 \tabularnewline
51 & 103.59 & 103.728741001294 & -0.138741001294136 \tabularnewline
52 & 104.35 & 104.117404942295 & 0.232595057705467 \tabularnewline
53 & 104.6 & 104.056585731332 & 0.543414268668073 \tabularnewline
54 & 105.08 & 104.620620187548 & 0.459379812452482 \tabularnewline
55 & 104.93 & 105.357118414531 & -0.427118414531407 \tabularnewline
56 & 105.15 & 105.720718805436 & -0.570718805436428 \tabularnewline
57 & 104.67 & 105.244034104366 & -0.574034104366447 \tabularnewline
58 & 104.55 & 104.382018207214 & 0.167981792785582 \tabularnewline
59 & 109.82 & 104.852825151049 & 4.96717484895123 \tabularnewline
60 & 109.25 & 108.930456686618 & 0.319543313381914 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]93.11[/C][C]92.5092592660635[/C][C]0.600740733936547[/C][/ROW]
[ROW][C]14[/C][C]93.42[/C][C]93.3672445663463[/C][C]0.0527554336537008[/C][/ROW]
[ROW][C]15[/C][C]94.01[/C][C]93.9705752148662[/C][C]0.0394247851338037[/C][/ROW]
[ROW][C]16[/C][C]94.47[/C][C]94.4115535607391[/C][C]0.0584464392609192[/C][/ROW]
[ROW][C]17[/C][C]94.07[/C][C]93.9979841329185[/C][C]0.0720158670815323[/C][/ROW]
[ROW][C]18[/C][C]94.33[/C][C]94.2607982692563[/C][C]0.0692017307436856[/C][/ROW]
[ROW][C]19[/C][C]94.43[/C][C]94.7268468330713[/C][C]-0.296846833071342[/C][/ROW]
[ROW][C]20[/C][C]95.37[/C][C]94.8816325890283[/C][C]0.488367410971733[/C][/ROW]
[ROW][C]21[/C][C]95.83[/C][C]95.3493182930663[/C][C]0.480681706933723[/C][/ROW]
[ROW][C]22[/C][C]95.46[/C][C]95.5089858623782[/C][C]-0.0489858623782311[/C][/ROW]
[ROW][C]23[/C][C]96[/C][C]95.7060448825739[/C][C]0.293955117426052[/C][/ROW]
[ROW][C]24[/C][C]95.35[/C][C]95.8067999260268[/C][C]-0.45679992602679[/C][/ROW]
[ROW][C]25[/C][C]96.85[/C][C]95.8636250279052[/C][C]0.986374972094779[/C][/ROW]
[ROW][C]26[/C][C]97.84[/C][C]97.0615108261664[/C][C]0.778489173833648[/C][/ROW]
[ROW][C]27[/C][C]98.38[/C][C]98.4051496651788[/C][C]-0.0251496651788301[/C][/ROW]
[ROW][C]28[/C][C]98.9[/C][C]98.8809770157659[/C][C]0.0190229842341125[/C][/ROW]
[ROW][C]29[/C][C]99.51[/C][C]98.481300299642[/C][C]1.02869970035802[/C][/ROW]
[ROW][C]30[/C][C]99.95[/C][C]99.7013655269671[/C][C]0.248634473032936[/C][/ROW]
[ROW][C]31[/C][C]99.93[/C][C]100.410182166521[/C][C]-0.480182166520606[/C][/ROW]
[ROW][C]32[/C][C]101.4[/C][C]100.62041258277[/C][C]0.779587417229507[/C][/ROW]
[ROW][C]33[/C][C]101.7[/C][C]101.453944489864[/C][C]0.246055510136102[/C][/ROW]
[ROW][C]34[/C][C]101.65[/C][C]101.423370823358[/C][C]0.226629176641552[/C][/ROW]
[ROW][C]35[/C][C]102.33[/C][C]102.028017606767[/C][C]0.301982393233416[/C][/ROW]
[ROW][C]36[/C][C]101.56[/C][C]102.139458844283[/C][C]-0.579458844282883[/C][/ROW]
[ROW][C]37[/C][C]101.91[/C][C]102.394609853487[/C][C]-0.484609853486859[/C][/ROW]
[ROW][C]38[/C][C]102.29[/C][C]102.335895582663[/C][C]-0.0458955826632632[/C][/ROW]
[ROW][C]39[/C][C]102.44[/C][C]102.912213932533[/C][C]-0.472213932532995[/C][/ROW]
[ROW][C]40[/C][C]102.84[/C][C]103.033419191266[/C][C]-0.19341919126596[/C][/ROW]
[ROW][C]41[/C][C]103.2[/C][C]102.55609314497[/C][C]0.643906855029968[/C][/ROW]
[ROW][C]42[/C][C]103.23[/C][C]103.350347772715[/C][C]-0.120347772715121[/C][/ROW]
[ROW][C]43[/C][C]103.16[/C][C]103.647023096443[/C][C]-0.487023096443238[/C][/ROW]
[ROW][C]44[/C][C]103.31[/C][C]104.004410213523[/C][C]-0.694410213522914[/C][/ROW]
[ROW][C]45[/C][C]103.04[/C][C]103.412531620386[/C][C]-0.372531620386141[/C][/ROW]
[ROW][C]46[/C][C]102.57[/C][C]102.750044672747[/C][C]-0.180044672747329[/C][/ROW]
[ROW][C]47[/C][C]102.88[/C][C]102.916440787311[/C][C]-0.0364407873113493[/C][/ROW]
[ROW][C]48[/C][C]101.91[/C][C]102.526460306018[/C][C]-0.616460306018283[/C][/ROW]
[ROW][C]49[/C][C]102.59[/C][C]102.661907510687[/C][C]-0.0719075106873959[/C][/ROW]
[ROW][C]50[/C][C]103.27[/C][C]102.933646593639[/C][C]0.336353406360729[/C][/ROW]
[ROW][C]51[/C][C]103.59[/C][C]103.728741001294[/C][C]-0.138741001294136[/C][/ROW]
[ROW][C]52[/C][C]104.35[/C][C]104.117404942295[/C][C]0.232595057705467[/C][/ROW]
[ROW][C]53[/C][C]104.6[/C][C]104.056585731332[/C][C]0.543414268668073[/C][/ROW]
[ROW][C]54[/C][C]105.08[/C][C]104.620620187548[/C][C]0.459379812452482[/C][/ROW]
[ROW][C]55[/C][C]104.93[/C][C]105.357118414531[/C][C]-0.427118414531407[/C][/ROW]
[ROW][C]56[/C][C]105.15[/C][C]105.720718805436[/C][C]-0.570718805436428[/C][/ROW]
[ROW][C]57[/C][C]104.67[/C][C]105.244034104366[/C][C]-0.574034104366447[/C][/ROW]
[ROW][C]58[/C][C]104.55[/C][C]104.382018207214[/C][C]0.167981792785582[/C][/ROW]
[ROW][C]59[/C][C]109.82[/C][C]104.852825151049[/C][C]4.96717484895123[/C][/ROW]
[ROW][C]60[/C][C]109.25[/C][C]108.930456686618[/C][C]0.319543313381914[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1393.1192.50925926606350.600740733936547
1493.4293.36724456634630.0527554336537008
1594.0193.97057521486620.0394247851338037
1694.4794.41155356073910.0584464392609192
1794.0793.99798413291850.0720158670815323
1894.3394.26079826925630.0692017307436856
1994.4394.7268468330713-0.296846833071342
2095.3794.88163258902830.488367410971733
2195.8395.34931829306630.480681706933723
2295.4695.5089858623782-0.0489858623782311
239695.70604488257390.293955117426052
2495.3595.8067999260268-0.45679992602679
2596.8595.86362502790520.986374972094779
2697.8497.06151082616640.778489173833648
2798.3898.4051496651788-0.0251496651788301
2898.998.88097701576590.0190229842341125
2999.5198.4813002996421.02869970035802
3099.9599.70136552696710.248634473032936
3199.93100.410182166521-0.480182166520606
32101.4100.620412582770.779587417229507
33101.7101.4539444898640.246055510136102
34101.65101.4233708233580.226629176641552
35102.33102.0280176067670.301982393233416
36101.56102.139458844283-0.579458844282883
37101.91102.394609853487-0.484609853486859
38102.29102.335895582663-0.0458955826632632
39102.44102.912213932533-0.472213932532995
40102.84103.033419191266-0.19341919126596
41103.2102.556093144970.643906855029968
42103.23103.350347772715-0.120347772715121
43103.16103.647023096443-0.487023096443238
44103.31104.004410213523-0.694410213522914
45103.04103.412531620386-0.372531620386141
46102.57102.750044672747-0.180044672747329
47102.88102.916440787311-0.0364407873113493
48101.91102.526460306018-0.616460306018283
49102.59102.661907510687-0.0719075106873959
50103.27102.9336465936390.336353406360729
51103.59103.728741001294-0.138741001294136
52104.35104.1174049422950.232595057705467
53104.6104.0565857313320.543414268668073
54105.08104.6206201875480.459379812452482
55104.93105.357118414531-0.427118414531407
56105.15105.720718805436-0.570718805436428
57104.67105.244034104366-0.574034104366447
58104.55104.3820182072140.167981792785582
59109.82104.8528251510494.96717484895123
60109.25108.9304566866180.319543313381914






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61110.167272625116108.529758524654111.804786725577
62110.736251854124108.510654379662112.961849328586
63111.359064674379108.638346306971114.079783041787
64112.107076923054108.936900175441115.277253670667
65112.00200432773108.432605436081115.571403219378
66112.205459200435108.24904829889116.161870101979
67112.559576145386108.225593318974116.893558971797
68113.462393190357108.740807519828118.183978860886
69113.635976717386108.561691476648118.710261958124
70113.505162871941108.097135581997118.913190161885
71114.578923387086108.786410914846120.371435859326
72113.683529342015106.377641265759120.989417418271

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 110.167272625116 & 108.529758524654 & 111.804786725577 \tabularnewline
62 & 110.736251854124 & 108.510654379662 & 112.961849328586 \tabularnewline
63 & 111.359064674379 & 108.638346306971 & 114.079783041787 \tabularnewline
64 & 112.107076923054 & 108.936900175441 & 115.277253670667 \tabularnewline
65 & 112.00200432773 & 108.432605436081 & 115.571403219378 \tabularnewline
66 & 112.205459200435 & 108.24904829889 & 116.161870101979 \tabularnewline
67 & 112.559576145386 & 108.225593318974 & 116.893558971797 \tabularnewline
68 & 113.462393190357 & 108.740807519828 & 118.183978860886 \tabularnewline
69 & 113.635976717386 & 108.561691476648 & 118.710261958124 \tabularnewline
70 & 113.505162871941 & 108.097135581997 & 118.913190161885 \tabularnewline
71 & 114.578923387086 & 108.786410914846 & 120.371435859326 \tabularnewline
72 & 113.683529342015 & 106.377641265759 & 120.989417418271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]61[/C][C]110.167272625116[/C][C]108.529758524654[/C][C]111.804786725577[/C][/ROW]
[ROW][C]62[/C][C]110.736251854124[/C][C]108.510654379662[/C][C]112.961849328586[/C][/ROW]
[ROW][C]63[/C][C]111.359064674379[/C][C]108.638346306971[/C][C]114.079783041787[/C][/ROW]
[ROW][C]64[/C][C]112.107076923054[/C][C]108.936900175441[/C][C]115.277253670667[/C][/ROW]
[ROW][C]65[/C][C]112.00200432773[/C][C]108.432605436081[/C][C]115.571403219378[/C][/ROW]
[ROW][C]66[/C][C]112.205459200435[/C][C]108.24904829889[/C][C]116.161870101979[/C][/ROW]
[ROW][C]67[/C][C]112.559576145386[/C][C]108.225593318974[/C][C]116.893558971797[/C][/ROW]
[ROW][C]68[/C][C]113.462393190357[/C][C]108.740807519828[/C][C]118.183978860886[/C][/ROW]
[ROW][C]69[/C][C]113.635976717386[/C][C]108.561691476648[/C][C]118.710261958124[/C][/ROW]
[ROW][C]70[/C][C]113.505162871941[/C][C]108.097135581997[/C][C]118.913190161885[/C][/ROW]
[ROW][C]71[/C][C]114.578923387086[/C][C]108.786410914846[/C][C]120.371435859326[/C][/ROW]
[ROW][C]72[/C][C]113.683529342015[/C][C]106.377641265759[/C][C]120.989417418271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61110.167272625116108.529758524654111.804786725577
62110.736251854124108.510654379662112.961849328586
63111.359064674379108.638346306971114.079783041787
64112.107076923054108.936900175441115.277253670667
65112.00200432773108.432605436081115.571403219378
66112.205459200435108.24904829889116.161870101979
67112.559576145386108.225593318974116.893558971797
68113.462393190357108.740807519828118.183978860886
69113.635976717386108.561691476648118.710261958124
70113.505162871941108.097135581997118.913190161885
71114.578923387086108.786410914846120.371435859326
72113.683529342015106.377641265759120.989417418271


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')