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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 03 Dec 2009 10:28:15 -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/2009/Dec/03/t12598613961qnyew3brlmwc18.htm/, Retrieved Thu, 25 Apr 2024 07:57:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62952, Retrieved Thu, 25 Apr 2024 07:57:20 +0000
QR Codes:

Original text written by user:Uitleg in Word document
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [Exponential Smoot...] [2009-12-03 17:28:15] [8eb8270f5a1cfdf0409dcfcbf10be18b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
96.96
93.11
95.62
98.30
96.38
100.82
99.06
94.03
102.07
99.31
98.64
101.82
99.14
97.63
100.06
101.32
101.49
105.43
105.09
99.48
108.53
104.34
106.10
107.35
103.00
104.50
105.17
104.84
106.18
108.86
107.77
102.74
112.63
106.26
108.86
111.38
106.85
107.86
107.94
111.38
111.29
113.72
111.88
109.87
113.72
111.71
114.81
112.05
111.54
110.87
110.87
115.48
111.63
116.24
113.56
106.01
110.45
107.77
108.61
108.19

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' @ 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62952&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62952&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62952&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' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.176261864801442
beta1
gamma0.600923944155917

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.176261864801442 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.600923944155917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62952&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]0.176261864801442[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.600923944155917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62952&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62952&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
alpha0.176261864801442
beta1
gamma0.600923944155917






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1399.1496.97010780860232.16989219139769
1497.6396.20305911867731.42694088132269
15100.0699.4313789044460.628621095554024
16101.32101.501848185809-0.181848185808690
17101.49102.267284361111-0.777284361111484
18105.43106.577629786737-1.14762978673657
19105.09105.527295103797-0.437295103797226
2099.48100.520382405752-1.04038240575231
21108.53109.072585741727-0.542585741727265
22104.34106.155697584904-1.81569758490407
23106.1104.9001623906931.19983760930700
24107.35108.418033329171-1.0680333291713
25103106.238976848037-3.23897684803737
26104.5102.789440142731.71055985726996
27105.17104.6058624707630.564137529236874
28104.84105.107030858014-0.267030858013840
29106.18104.3563477700341.82365222996579
30108.86108.2860052110300.573994788969728
31107.77107.4185817164260.351418283574333
32102.74101.8405465867260.899453413274145
33112.63111.2261873320721.40381266792828
34106.26108.310144341984-2.05014434198399
35108.86108.864245321722-0.00424532172155523
36111.38111.2372556961410.142744303859160
37106.85108.419593267117-1.56959326711744
38107.86108.334309597288-0.474309597288027
39107.94109.479637970686-1.53963797068599
40111.38109.0653734536842.31462654631638
41111.29110.1415180754641.14848192453621
42113.72113.6621201313140.0578798686858164
43111.88112.640248565069-0.760248565068508
44109.87106.7983330893543.0716669106464
45113.72117.568547610295-3.8485476102947
46111.71111.2071562954110.502843704588955
47114.81113.1618864921911.64811350780889
48112.05116.154619004939-4.10461900493868
49111.54111.0307747282330.509225271766581
50110.87111.681541542628-0.81154154262758
51110.87112.005327353228-1.13532735322833
52115.48113.4396404604572.04035953954320
53111.63113.646580715151-2.01658071515121
54116.24115.3060571994030.93394280059708
55113.56113.3563290301390.203670969861363
56106.01109.066993650808-3.05699365080753
57110.45113.672010559872-3.22201055987207
58107.77108.156438072855-0.38643807285456
59108.61108.787487038676-0.177487038676162
60108.19106.659773981561.53022601844008

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 99.14 & 96.9701078086023 & 2.16989219139769 \tabularnewline
14 & 97.63 & 96.2030591186773 & 1.42694088132269 \tabularnewline
15 & 100.06 & 99.431378904446 & 0.628621095554024 \tabularnewline
16 & 101.32 & 101.501848185809 & -0.181848185808690 \tabularnewline
17 & 101.49 & 102.267284361111 & -0.777284361111484 \tabularnewline
18 & 105.43 & 106.577629786737 & -1.14762978673657 \tabularnewline
19 & 105.09 & 105.527295103797 & -0.437295103797226 \tabularnewline
20 & 99.48 & 100.520382405752 & -1.04038240575231 \tabularnewline
21 & 108.53 & 109.072585741727 & -0.542585741727265 \tabularnewline
22 & 104.34 & 106.155697584904 & -1.81569758490407 \tabularnewline
23 & 106.1 & 104.900162390693 & 1.19983760930700 \tabularnewline
24 & 107.35 & 108.418033329171 & -1.0680333291713 \tabularnewline
25 & 103 & 106.238976848037 & -3.23897684803737 \tabularnewline
26 & 104.5 & 102.78944014273 & 1.71055985726996 \tabularnewline
27 & 105.17 & 104.605862470763 & 0.564137529236874 \tabularnewline
28 & 104.84 & 105.107030858014 & -0.267030858013840 \tabularnewline
29 & 106.18 & 104.356347770034 & 1.82365222996579 \tabularnewline
30 & 108.86 & 108.286005211030 & 0.573994788969728 \tabularnewline
31 & 107.77 & 107.418581716426 & 0.351418283574333 \tabularnewline
32 & 102.74 & 101.840546586726 & 0.899453413274145 \tabularnewline
33 & 112.63 & 111.226187332072 & 1.40381266792828 \tabularnewline
34 & 106.26 & 108.310144341984 & -2.05014434198399 \tabularnewline
35 & 108.86 & 108.864245321722 & -0.00424532172155523 \tabularnewline
36 & 111.38 & 111.237255696141 & 0.142744303859160 \tabularnewline
37 & 106.85 & 108.419593267117 & -1.56959326711744 \tabularnewline
38 & 107.86 & 108.334309597288 & -0.474309597288027 \tabularnewline
39 & 107.94 & 109.479637970686 & -1.53963797068599 \tabularnewline
40 & 111.38 & 109.065373453684 & 2.31462654631638 \tabularnewline
41 & 111.29 & 110.141518075464 & 1.14848192453621 \tabularnewline
42 & 113.72 & 113.662120131314 & 0.0578798686858164 \tabularnewline
43 & 111.88 & 112.640248565069 & -0.760248565068508 \tabularnewline
44 & 109.87 & 106.798333089354 & 3.0716669106464 \tabularnewline
45 & 113.72 & 117.568547610295 & -3.8485476102947 \tabularnewline
46 & 111.71 & 111.207156295411 & 0.502843704588955 \tabularnewline
47 & 114.81 & 113.161886492191 & 1.64811350780889 \tabularnewline
48 & 112.05 & 116.154619004939 & -4.10461900493868 \tabularnewline
49 & 111.54 & 111.030774728233 & 0.509225271766581 \tabularnewline
50 & 110.87 & 111.681541542628 & -0.81154154262758 \tabularnewline
51 & 110.87 & 112.005327353228 & -1.13532735322833 \tabularnewline
52 & 115.48 & 113.439640460457 & 2.04035953954320 \tabularnewline
53 & 111.63 & 113.646580715151 & -2.01658071515121 \tabularnewline
54 & 116.24 & 115.306057199403 & 0.93394280059708 \tabularnewline
55 & 113.56 & 113.356329030139 & 0.203670969861363 \tabularnewline
56 & 106.01 & 109.066993650808 & -3.05699365080753 \tabularnewline
57 & 110.45 & 113.672010559872 & -3.22201055987207 \tabularnewline
58 & 107.77 & 108.156438072855 & -0.38643807285456 \tabularnewline
59 & 108.61 & 108.787487038676 & -0.177487038676162 \tabularnewline
60 & 108.19 & 106.65977398156 & 1.53022601844008 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62952&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]99.14[/C][C]96.9701078086023[/C][C]2.16989219139769[/C][/ROW]
[ROW][C]14[/C][C]97.63[/C][C]96.2030591186773[/C][C]1.42694088132269[/C][/ROW]
[ROW][C]15[/C][C]100.06[/C][C]99.431378904446[/C][C]0.628621095554024[/C][/ROW]
[ROW][C]16[/C][C]101.32[/C][C]101.501848185809[/C][C]-0.181848185808690[/C][/ROW]
[ROW][C]17[/C][C]101.49[/C][C]102.267284361111[/C][C]-0.777284361111484[/C][/ROW]
[ROW][C]18[/C][C]105.43[/C][C]106.577629786737[/C][C]-1.14762978673657[/C][/ROW]
[ROW][C]19[/C][C]105.09[/C][C]105.527295103797[/C][C]-0.437295103797226[/C][/ROW]
[ROW][C]20[/C][C]99.48[/C][C]100.520382405752[/C][C]-1.04038240575231[/C][/ROW]
[ROW][C]21[/C][C]108.53[/C][C]109.072585741727[/C][C]-0.542585741727265[/C][/ROW]
[ROW][C]22[/C][C]104.34[/C][C]106.155697584904[/C][C]-1.81569758490407[/C][/ROW]
[ROW][C]23[/C][C]106.1[/C][C]104.900162390693[/C][C]1.19983760930700[/C][/ROW]
[ROW][C]24[/C][C]107.35[/C][C]108.418033329171[/C][C]-1.0680333291713[/C][/ROW]
[ROW][C]25[/C][C]103[/C][C]106.238976848037[/C][C]-3.23897684803737[/C][/ROW]
[ROW][C]26[/C][C]104.5[/C][C]102.78944014273[/C][C]1.71055985726996[/C][/ROW]
[ROW][C]27[/C][C]105.17[/C][C]104.605862470763[/C][C]0.564137529236874[/C][/ROW]
[ROW][C]28[/C][C]104.84[/C][C]105.107030858014[/C][C]-0.267030858013840[/C][/ROW]
[ROW][C]29[/C][C]106.18[/C][C]104.356347770034[/C][C]1.82365222996579[/C][/ROW]
[ROW][C]30[/C][C]108.86[/C][C]108.286005211030[/C][C]0.573994788969728[/C][/ROW]
[ROW][C]31[/C][C]107.77[/C][C]107.418581716426[/C][C]0.351418283574333[/C][/ROW]
[ROW][C]32[/C][C]102.74[/C][C]101.840546586726[/C][C]0.899453413274145[/C][/ROW]
[ROW][C]33[/C][C]112.63[/C][C]111.226187332072[/C][C]1.40381266792828[/C][/ROW]
[ROW][C]34[/C][C]106.26[/C][C]108.310144341984[/C][C]-2.05014434198399[/C][/ROW]
[ROW][C]35[/C][C]108.86[/C][C]108.864245321722[/C][C]-0.00424532172155523[/C][/ROW]
[ROW][C]36[/C][C]111.38[/C][C]111.237255696141[/C][C]0.142744303859160[/C][/ROW]
[ROW][C]37[/C][C]106.85[/C][C]108.419593267117[/C][C]-1.56959326711744[/C][/ROW]
[ROW][C]38[/C][C]107.86[/C][C]108.334309597288[/C][C]-0.474309597288027[/C][/ROW]
[ROW][C]39[/C][C]107.94[/C][C]109.479637970686[/C][C]-1.53963797068599[/C][/ROW]
[ROW][C]40[/C][C]111.38[/C][C]109.065373453684[/C][C]2.31462654631638[/C][/ROW]
[ROW][C]41[/C][C]111.29[/C][C]110.141518075464[/C][C]1.14848192453621[/C][/ROW]
[ROW][C]42[/C][C]113.72[/C][C]113.662120131314[/C][C]0.0578798686858164[/C][/ROW]
[ROW][C]43[/C][C]111.88[/C][C]112.640248565069[/C][C]-0.760248565068508[/C][/ROW]
[ROW][C]44[/C][C]109.87[/C][C]106.798333089354[/C][C]3.0716669106464[/C][/ROW]
[ROW][C]45[/C][C]113.72[/C][C]117.568547610295[/C][C]-3.8485476102947[/C][/ROW]
[ROW][C]46[/C][C]111.71[/C][C]111.207156295411[/C][C]0.502843704588955[/C][/ROW]
[ROW][C]47[/C][C]114.81[/C][C]113.161886492191[/C][C]1.64811350780889[/C][/ROW]
[ROW][C]48[/C][C]112.05[/C][C]116.154619004939[/C][C]-4.10461900493868[/C][/ROW]
[ROW][C]49[/C][C]111.54[/C][C]111.030774728233[/C][C]0.509225271766581[/C][/ROW]
[ROW][C]50[/C][C]110.87[/C][C]111.681541542628[/C][C]-0.81154154262758[/C][/ROW]
[ROW][C]51[/C][C]110.87[/C][C]112.005327353228[/C][C]-1.13532735322833[/C][/ROW]
[ROW][C]52[/C][C]115.48[/C][C]113.439640460457[/C][C]2.04035953954320[/C][/ROW]
[ROW][C]53[/C][C]111.63[/C][C]113.646580715151[/C][C]-2.01658071515121[/C][/ROW]
[ROW][C]54[/C][C]116.24[/C][C]115.306057199403[/C][C]0.93394280059708[/C][/ROW]
[ROW][C]55[/C][C]113.56[/C][C]113.356329030139[/C][C]0.203670969861363[/C][/ROW]
[ROW][C]56[/C][C]106.01[/C][C]109.066993650808[/C][C]-3.05699365080753[/C][/ROW]
[ROW][C]57[/C][C]110.45[/C][C]113.672010559872[/C][C]-3.22201055987207[/C][/ROW]
[ROW][C]58[/C][C]107.77[/C][C]108.156438072855[/C][C]-0.38643807285456[/C][/ROW]
[ROW][C]59[/C][C]108.61[/C][C]108.787487038676[/C][C]-0.177487038676162[/C][/ROW]
[ROW][C]60[/C][C]108.19[/C][C]106.65977398156[/C][C]1.53022601844008[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62952&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62952&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
1399.1496.97010780860232.16989219139769
1497.6396.20305911867731.42694088132269
15100.0699.4313789044460.628621095554024
16101.32101.501848185809-0.181848185808690
17101.49102.267284361111-0.777284361111484
18105.43106.577629786737-1.14762978673657
19105.09105.527295103797-0.437295103797226
2099.48100.520382405752-1.04038240575231
21108.53109.072585741727-0.542585741727265
22104.34106.155697584904-1.81569758490407
23106.1104.9001623906931.19983760930700
24107.35108.418033329171-1.0680333291713
25103106.238976848037-3.23897684803737
26104.5102.789440142731.71055985726996
27105.17104.6058624707630.564137529236874
28104.84105.107030858014-0.267030858013840
29106.18104.3563477700341.82365222996579
30108.86108.2860052110300.573994788969728
31107.77107.4185817164260.351418283574333
32102.74101.8405465867260.899453413274145
33112.63111.2261873320721.40381266792828
34106.26108.310144341984-2.05014434198399
35108.86108.864245321722-0.00424532172155523
36111.38111.2372556961410.142744303859160
37106.85108.419593267117-1.56959326711744
38107.86108.334309597288-0.474309597288027
39107.94109.479637970686-1.53963797068599
40111.38109.0653734536842.31462654631638
41111.29110.1415180754641.14848192453621
42113.72113.6621201313140.0578798686858164
43111.88112.640248565069-0.760248565068508
44109.87106.7983330893543.0716669106464
45113.72117.568547610295-3.8485476102947
46111.71111.2071562954110.502843704588955
47114.81113.1618864921911.64811350780889
48112.05116.154619004939-4.10461900493868
49111.54111.0307747282330.509225271766581
50110.87111.681541542628-0.81154154262758
51110.87112.005327353228-1.13532735322833
52115.48113.4396404604572.04035953954320
53111.63113.646580715151-2.01658071515121
54116.24115.3060571994030.93394280059708
55113.56113.3563290301390.203670969861363
56106.01109.066993650808-3.05699365080753
57110.45113.672010559872-3.22201055987207
58107.77108.156438072855-0.38643807285456
59108.61108.787487038676-0.177487038676162
60108.19106.659773981561.53022601844008






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61103.951517191193101.767746706038106.135287676349
62102.799120961628100.333140101633105.265101821623
63102.14507735327599.1337009786908105.156453727859
64104.307857934344100.438799593681108.176916275008
65101.25197951209196.4615776124803106.042381411702
66103.58724081572197.5004115900556109.674070041386
67100.44591095407093.2043623606451107.687459547494
6894.27008029067786.0728884430293102.467272138325
6998.253408616442388.1760156747464108.330801558138
7095.154642160947283.7527780355253106.556506286369
7195.94906364897982.6914742122405109.206653085718
7294.958394657164379.9845144089064109.932274905422

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 103.951517191193 & 101.767746706038 & 106.135287676349 \tabularnewline
62 & 102.799120961628 & 100.333140101633 & 105.265101821623 \tabularnewline
63 & 102.145077353275 & 99.1337009786908 & 105.156453727859 \tabularnewline
64 & 104.307857934344 & 100.438799593681 & 108.176916275008 \tabularnewline
65 & 101.251979512091 & 96.4615776124803 & 106.042381411702 \tabularnewline
66 & 103.587240815721 & 97.5004115900556 & 109.674070041386 \tabularnewline
67 & 100.445910954070 & 93.2043623606451 & 107.687459547494 \tabularnewline
68 & 94.270080290677 & 86.0728884430293 & 102.467272138325 \tabularnewline
69 & 98.2534086164423 & 88.1760156747464 & 108.330801558138 \tabularnewline
70 & 95.1546421609472 & 83.7527780355253 & 106.556506286369 \tabularnewline
71 & 95.949063648979 & 82.6914742122405 & 109.206653085718 \tabularnewline
72 & 94.9583946571643 & 79.9845144089064 & 109.932274905422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62952&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]103.951517191193[/C][C]101.767746706038[/C][C]106.135287676349[/C][/ROW]
[ROW][C]62[/C][C]102.799120961628[/C][C]100.333140101633[/C][C]105.265101821623[/C][/ROW]
[ROW][C]63[/C][C]102.145077353275[/C][C]99.1337009786908[/C][C]105.156453727859[/C][/ROW]
[ROW][C]64[/C][C]104.307857934344[/C][C]100.438799593681[/C][C]108.176916275008[/C][/ROW]
[ROW][C]65[/C][C]101.251979512091[/C][C]96.4615776124803[/C][C]106.042381411702[/C][/ROW]
[ROW][C]66[/C][C]103.587240815721[/C][C]97.5004115900556[/C][C]109.674070041386[/C][/ROW]
[ROW][C]67[/C][C]100.445910954070[/C][C]93.2043623606451[/C][C]107.687459547494[/C][/ROW]
[ROW][C]68[/C][C]94.270080290677[/C][C]86.0728884430293[/C][C]102.467272138325[/C][/ROW]
[ROW][C]69[/C][C]98.2534086164423[/C][C]88.1760156747464[/C][C]108.330801558138[/C][/ROW]
[ROW][C]70[/C][C]95.1546421609472[/C][C]83.7527780355253[/C][C]106.556506286369[/C][/ROW]
[ROW][C]71[/C][C]95.949063648979[/C][C]82.6914742122405[/C][C]109.206653085718[/C][/ROW]
[ROW][C]72[/C][C]94.9583946571643[/C][C]79.9845144089064[/C][C]109.932274905422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62952&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62952&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
61103.951517191193101.767746706038106.135287676349
62102.799120961628100.333140101633105.265101821623
63102.14507735327599.1337009786908105.156453727859
64104.307857934344100.438799593681108.176916275008
65101.25197951209196.4615776124803106.042381411702
66103.58724081572197.5004115900556109.674070041386
67100.44591095407093.2043623606451107.687459547494
6894.27008029067786.0728884430293102.467272138325
6998.253408616442388.1760156747464108.330801558138
7095.154642160947283.7527780355253106.556506286369
7195.94906364897982.6914742122405109.206653085718
7294.958394657164379.9845144089064109.932274905422


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')