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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 23 May 2012 07:48:01 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/23/t1337773715ow7fn2ug731evyg.htm/, Retrieved Mon, 29 Apr 2024 06:26:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167169, Retrieved Mon, 29 Apr 2024 06:26:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact183
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-23 11:48:01] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
98,19
98,19
98,19
98,19
98,19
98,19
98,19
100,48
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
104,47
104,47
104,47
104,47
104,47
104,47
104,47
104,47
105,5
105,5
105,5
105,5
106,61
106,61
106,61
106,61
106,61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167169&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167169&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167169&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.759709371745411
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.759709371745411 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167169&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]0.759709371745411[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167169&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167169&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.759709371745411
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13102.78100.497660256412.28233974358974
14102.78102.2171520721990.562847927800675
15102.78102.867829840894-0.0878298408939031
16102.78103.120014944058-0.340014944058154
17102.78103.180612660934-0.40061266093393
18102.78103.195173724393-0.415173724392815
19102.78100.7778392781462.00216072185398
20101.67104.432809798689-2.7628097986893
21101.67104.477787558685-2.80778755868523
22101.67102.188595292892-0.518595292892158
23101.67101.6385238451490.0314761548508073
24101.67101.5063468313860.163653168613877
25101.67102.023010784586-0.353010784585763
26101.67101.3272243375910.342775662408897
27101.67101.6543593739750.01564062602462
28101.67101.924554243681-0.25455424368073
29101.67102.03551619209-0.365516192090283
30101.67102.073241484758-0.403241484758269
31101.67100.2458348855781.42416511442215
32105.79102.3167189663323.47328103366846
33105.79107.088505640518-1.29850564051839
34105.79106.496000440306-0.706000440305516
35105.79105.935732559522-0.145732559522358
36105.79105.7006893223730.0893106776270116
37105.79106.03672508254-0.246725082540166
38105.79105.5888758419510.201124158048543
39105.79105.7297894195340.0602105804655366
40105.79105.968919206334-0.178919206334172
41105.79106.110678685153-0.320678685152529
42105.79106.173402417771-0.383402417770554
43105.79104.8001764235010.989823576498978
44104.47107.033470518958-2.56347051895835
45104.47106.072464845879-1.60246484587871
46104.47105.391412435529-0.921412435528566
47104.47104.802121164252-0.332121164252328
48104.47104.481955444425-0.0119554444246575
49104.47104.660312138702-0.190312138702296
50104.47104.3629343156190.107065684380629
51104.47104.3985305771780.0714694228222186
52105.5104.5887531653260.911246834673619
53105.5105.524658528031-0.0246585280306419
54105.5105.797199623122-0.297199623122452
55105.5104.8194360367160.680563963283703
56106.61105.9639594351410.646040564859149
57106.61107.672170068099-1.06217006809868
58106.61107.56523517549-0.955235175490472
59106.61107.091849621487-0.481849621486987
60106.61106.734866611444-0.124866611444133

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 102.78 & 100.49766025641 & 2.28233974358974 \tabularnewline
14 & 102.78 & 102.217152072199 & 0.562847927800675 \tabularnewline
15 & 102.78 & 102.867829840894 & -0.0878298408939031 \tabularnewline
16 & 102.78 & 103.120014944058 & -0.340014944058154 \tabularnewline
17 & 102.78 & 103.180612660934 & -0.40061266093393 \tabularnewline
18 & 102.78 & 103.195173724393 & -0.415173724392815 \tabularnewline
19 & 102.78 & 100.777839278146 & 2.00216072185398 \tabularnewline
20 & 101.67 & 104.432809798689 & -2.7628097986893 \tabularnewline
21 & 101.67 & 104.477787558685 & -2.80778755868523 \tabularnewline
22 & 101.67 & 102.188595292892 & -0.518595292892158 \tabularnewline
23 & 101.67 & 101.638523845149 & 0.0314761548508073 \tabularnewline
24 & 101.67 & 101.506346831386 & 0.163653168613877 \tabularnewline
25 & 101.67 & 102.023010784586 & -0.353010784585763 \tabularnewline
26 & 101.67 & 101.327224337591 & 0.342775662408897 \tabularnewline
27 & 101.67 & 101.654359373975 & 0.01564062602462 \tabularnewline
28 & 101.67 & 101.924554243681 & -0.25455424368073 \tabularnewline
29 & 101.67 & 102.03551619209 & -0.365516192090283 \tabularnewline
30 & 101.67 & 102.073241484758 & -0.403241484758269 \tabularnewline
31 & 101.67 & 100.245834885578 & 1.42416511442215 \tabularnewline
32 & 105.79 & 102.316718966332 & 3.47328103366846 \tabularnewline
33 & 105.79 & 107.088505640518 & -1.29850564051839 \tabularnewline
34 & 105.79 & 106.496000440306 & -0.706000440305516 \tabularnewline
35 & 105.79 & 105.935732559522 & -0.145732559522358 \tabularnewline
36 & 105.79 & 105.700689322373 & 0.0893106776270116 \tabularnewline
37 & 105.79 & 106.03672508254 & -0.246725082540166 \tabularnewline
38 & 105.79 & 105.588875841951 & 0.201124158048543 \tabularnewline
39 & 105.79 & 105.729789419534 & 0.0602105804655366 \tabularnewline
40 & 105.79 & 105.968919206334 & -0.178919206334172 \tabularnewline
41 & 105.79 & 106.110678685153 & -0.320678685152529 \tabularnewline
42 & 105.79 & 106.173402417771 & -0.383402417770554 \tabularnewline
43 & 105.79 & 104.800176423501 & 0.989823576498978 \tabularnewline
44 & 104.47 & 107.033470518958 & -2.56347051895835 \tabularnewline
45 & 104.47 & 106.072464845879 & -1.60246484587871 \tabularnewline
46 & 104.47 & 105.391412435529 & -0.921412435528566 \tabularnewline
47 & 104.47 & 104.802121164252 & -0.332121164252328 \tabularnewline
48 & 104.47 & 104.481955444425 & -0.0119554444246575 \tabularnewline
49 & 104.47 & 104.660312138702 & -0.190312138702296 \tabularnewline
50 & 104.47 & 104.362934315619 & 0.107065684380629 \tabularnewline
51 & 104.47 & 104.398530577178 & 0.0714694228222186 \tabularnewline
52 & 105.5 & 104.588753165326 & 0.911246834673619 \tabularnewline
53 & 105.5 & 105.524658528031 & -0.0246585280306419 \tabularnewline
54 & 105.5 & 105.797199623122 & -0.297199623122452 \tabularnewline
55 & 105.5 & 104.819436036716 & 0.680563963283703 \tabularnewline
56 & 106.61 & 105.963959435141 & 0.646040564859149 \tabularnewline
57 & 106.61 & 107.672170068099 & -1.06217006809868 \tabularnewline
58 & 106.61 & 107.56523517549 & -0.955235175490472 \tabularnewline
59 & 106.61 & 107.091849621487 & -0.481849621486987 \tabularnewline
60 & 106.61 & 106.734866611444 & -0.124866611444133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167169&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]102.78[/C][C]100.49766025641[/C][C]2.28233974358974[/C][/ROW]
[ROW][C]14[/C][C]102.78[/C][C]102.217152072199[/C][C]0.562847927800675[/C][/ROW]
[ROW][C]15[/C][C]102.78[/C][C]102.867829840894[/C][C]-0.0878298408939031[/C][/ROW]
[ROW][C]16[/C][C]102.78[/C][C]103.120014944058[/C][C]-0.340014944058154[/C][/ROW]
[ROW][C]17[/C][C]102.78[/C][C]103.180612660934[/C][C]-0.40061266093393[/C][/ROW]
[ROW][C]18[/C][C]102.78[/C][C]103.195173724393[/C][C]-0.415173724392815[/C][/ROW]
[ROW][C]19[/C][C]102.78[/C][C]100.777839278146[/C][C]2.00216072185398[/C][/ROW]
[ROW][C]20[/C][C]101.67[/C][C]104.432809798689[/C][C]-2.7628097986893[/C][/ROW]
[ROW][C]21[/C][C]101.67[/C][C]104.477787558685[/C][C]-2.80778755868523[/C][/ROW]
[ROW][C]22[/C][C]101.67[/C][C]102.188595292892[/C][C]-0.518595292892158[/C][/ROW]
[ROW][C]23[/C][C]101.67[/C][C]101.638523845149[/C][C]0.0314761548508073[/C][/ROW]
[ROW][C]24[/C][C]101.67[/C][C]101.506346831386[/C][C]0.163653168613877[/C][/ROW]
[ROW][C]25[/C][C]101.67[/C][C]102.023010784586[/C][C]-0.353010784585763[/C][/ROW]
[ROW][C]26[/C][C]101.67[/C][C]101.327224337591[/C][C]0.342775662408897[/C][/ROW]
[ROW][C]27[/C][C]101.67[/C][C]101.654359373975[/C][C]0.01564062602462[/C][/ROW]
[ROW][C]28[/C][C]101.67[/C][C]101.924554243681[/C][C]-0.25455424368073[/C][/ROW]
[ROW][C]29[/C][C]101.67[/C][C]102.03551619209[/C][C]-0.365516192090283[/C][/ROW]
[ROW][C]30[/C][C]101.67[/C][C]102.073241484758[/C][C]-0.403241484758269[/C][/ROW]
[ROW][C]31[/C][C]101.67[/C][C]100.245834885578[/C][C]1.42416511442215[/C][/ROW]
[ROW][C]32[/C][C]105.79[/C][C]102.316718966332[/C][C]3.47328103366846[/C][/ROW]
[ROW][C]33[/C][C]105.79[/C][C]107.088505640518[/C][C]-1.29850564051839[/C][/ROW]
[ROW][C]34[/C][C]105.79[/C][C]106.496000440306[/C][C]-0.706000440305516[/C][/ROW]
[ROW][C]35[/C][C]105.79[/C][C]105.935732559522[/C][C]-0.145732559522358[/C][/ROW]
[ROW][C]36[/C][C]105.79[/C][C]105.700689322373[/C][C]0.0893106776270116[/C][/ROW]
[ROW][C]37[/C][C]105.79[/C][C]106.03672508254[/C][C]-0.246725082540166[/C][/ROW]
[ROW][C]38[/C][C]105.79[/C][C]105.588875841951[/C][C]0.201124158048543[/C][/ROW]
[ROW][C]39[/C][C]105.79[/C][C]105.729789419534[/C][C]0.0602105804655366[/C][/ROW]
[ROW][C]40[/C][C]105.79[/C][C]105.968919206334[/C][C]-0.178919206334172[/C][/ROW]
[ROW][C]41[/C][C]105.79[/C][C]106.110678685153[/C][C]-0.320678685152529[/C][/ROW]
[ROW][C]42[/C][C]105.79[/C][C]106.173402417771[/C][C]-0.383402417770554[/C][/ROW]
[ROW][C]43[/C][C]105.79[/C][C]104.800176423501[/C][C]0.989823576498978[/C][/ROW]
[ROW][C]44[/C][C]104.47[/C][C]107.033470518958[/C][C]-2.56347051895835[/C][/ROW]
[ROW][C]45[/C][C]104.47[/C][C]106.072464845879[/C][C]-1.60246484587871[/C][/ROW]
[ROW][C]46[/C][C]104.47[/C][C]105.391412435529[/C][C]-0.921412435528566[/C][/ROW]
[ROW][C]47[/C][C]104.47[/C][C]104.802121164252[/C][C]-0.332121164252328[/C][/ROW]
[ROW][C]48[/C][C]104.47[/C][C]104.481955444425[/C][C]-0.0119554444246575[/C][/ROW]
[ROW][C]49[/C][C]104.47[/C][C]104.660312138702[/C][C]-0.190312138702296[/C][/ROW]
[ROW][C]50[/C][C]104.47[/C][C]104.362934315619[/C][C]0.107065684380629[/C][/ROW]
[ROW][C]51[/C][C]104.47[/C][C]104.398530577178[/C][C]0.0714694228222186[/C][/ROW]
[ROW][C]52[/C][C]105.5[/C][C]104.588753165326[/C][C]0.911246834673619[/C][/ROW]
[ROW][C]53[/C][C]105.5[/C][C]105.524658528031[/C][C]-0.0246585280306419[/C][/ROW]
[ROW][C]54[/C][C]105.5[/C][C]105.797199623122[/C][C]-0.297199623122452[/C][/ROW]
[ROW][C]55[/C][C]105.5[/C][C]104.819436036716[/C][C]0.680563963283703[/C][/ROW]
[ROW][C]56[/C][C]106.61[/C][C]105.963959435141[/C][C]0.646040564859149[/C][/ROW]
[ROW][C]57[/C][C]106.61[/C][C]107.672170068099[/C][C]-1.06217006809868[/C][/ROW]
[ROW][C]58[/C][C]106.61[/C][C]107.56523517549[/C][C]-0.955235175490472[/C][/ROW]
[ROW][C]59[/C][C]106.61[/C][C]107.091849621487[/C][C]-0.481849621486987[/C][/ROW]
[ROW][C]60[/C][C]106.61[/C][C]106.734866611444[/C][C]-0.124866611444133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167169&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167169&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13102.78100.497660256412.28233974358974
14102.78102.2171520721990.562847927800675
15102.78102.867829840894-0.0878298408939031
16102.78103.120014944058-0.340014944058154
17102.78103.180612660934-0.40061266093393
18102.78103.195173724393-0.415173724392815
19102.78100.7778392781462.00216072185398
20101.67104.432809798689-2.7628097986893
21101.67104.477787558685-2.80778755868523
22101.67102.188595292892-0.518595292892158
23101.67101.6385238451490.0314761548508073
24101.67101.5063468313860.163653168613877
25101.67102.023010784586-0.353010784585763
26101.67101.3272243375910.342775662408897
27101.67101.6543593739750.01564062602462
28101.67101.924554243681-0.25455424368073
29101.67102.03551619209-0.365516192090283
30101.67102.073241484758-0.403241484758269
31101.67100.2458348855781.42416511442215
32105.79102.3167189663323.47328103366846
33105.79107.088505640518-1.29850564051839
34105.79106.496000440306-0.706000440305516
35105.79105.935732559522-0.145732559522358
36105.79105.7006893223730.0893106776270116
37105.79106.03672508254-0.246725082540166
38105.79105.5888758419510.201124158048543
39105.79105.7297894195340.0602105804655366
40105.79105.968919206334-0.178919206334172
41105.79106.110678685153-0.320678685152529
42105.79106.173402417771-0.383402417770554
43105.79104.8001764235010.989823576498978
44104.47107.033470518958-2.56347051895835
45104.47106.072464845879-1.60246484587871
46104.47105.391412435529-0.921412435528566
47104.47104.802121164252-0.332121164252328
48104.47104.481955444425-0.0119554444246575
49104.47104.660312138702-0.190312138702296
50104.47104.3629343156190.107065684380629
51104.47104.3985305771780.0714694228222186
52105.5104.5887531653260.911246834673619
53105.5105.524658528031-0.0246585280306419
54105.5105.797199623122-0.297199623122452
55105.5104.8194360367160.680563963283703
56106.61105.9639594351410.646040564859149
57106.61107.672170068099-1.06217006809868
58106.61107.56523517549-0.955235175490472
59106.61107.091849621487-0.481849621486987
60106.61106.734866611444-0.124866611444133







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61106.784586191841104.617867882716108.951304500966
62106.703247388025103.982174969841109.424319806208
63106.648951397713103.468730968419109.829171827008
64106.986668637439103.405695466246110.567641808631
65107.005401952277103.064217393454110.9465865111
66107.231187291242102.960063012951111.502311569533
67106.714156470263102.136813411839111.291499528688
68107.333353398612102.469030593904112.197676203321
69108.140293953734103.005003969487113.275583937981
70108.865995068775103.473336160944114.258653976606
71109.232060741991103.593768716021114.87035276796
72109.326923076923103.453261200035115.200584953812

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 106.784586191841 & 104.617867882716 & 108.951304500966 \tabularnewline
62 & 106.703247388025 & 103.982174969841 & 109.424319806208 \tabularnewline
63 & 106.648951397713 & 103.468730968419 & 109.829171827008 \tabularnewline
64 & 106.986668637439 & 103.405695466246 & 110.567641808631 \tabularnewline
65 & 107.005401952277 & 103.064217393454 & 110.9465865111 \tabularnewline
66 & 107.231187291242 & 102.960063012951 & 111.502311569533 \tabularnewline
67 & 106.714156470263 & 102.136813411839 & 111.291499528688 \tabularnewline
68 & 107.333353398612 & 102.469030593904 & 112.197676203321 \tabularnewline
69 & 108.140293953734 & 103.005003969487 & 113.275583937981 \tabularnewline
70 & 108.865995068775 & 103.473336160944 & 114.258653976606 \tabularnewline
71 & 109.232060741991 & 103.593768716021 & 114.87035276796 \tabularnewline
72 & 109.326923076923 & 103.453261200035 & 115.200584953812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167169&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]106.784586191841[/C][C]104.617867882716[/C][C]108.951304500966[/C][/ROW]
[ROW][C]62[/C][C]106.703247388025[/C][C]103.982174969841[/C][C]109.424319806208[/C][/ROW]
[ROW][C]63[/C][C]106.648951397713[/C][C]103.468730968419[/C][C]109.829171827008[/C][/ROW]
[ROW][C]64[/C][C]106.986668637439[/C][C]103.405695466246[/C][C]110.567641808631[/C][/ROW]
[ROW][C]65[/C][C]107.005401952277[/C][C]103.064217393454[/C][C]110.9465865111[/C][/ROW]
[ROW][C]66[/C][C]107.231187291242[/C][C]102.960063012951[/C][C]111.502311569533[/C][/ROW]
[ROW][C]67[/C][C]106.714156470263[/C][C]102.136813411839[/C][C]111.291499528688[/C][/ROW]
[ROW][C]68[/C][C]107.333353398612[/C][C]102.469030593904[/C][C]112.197676203321[/C][/ROW]
[ROW][C]69[/C][C]108.140293953734[/C][C]103.005003969487[/C][C]113.275583937981[/C][/ROW]
[ROW][C]70[/C][C]108.865995068775[/C][C]103.473336160944[/C][C]114.258653976606[/C][/ROW]
[ROW][C]71[/C][C]109.232060741991[/C][C]103.593768716021[/C][C]114.87035276796[/C][/ROW]
[ROW][C]72[/C][C]109.326923076923[/C][C]103.453261200035[/C][C]115.200584953812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167169&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167169&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61106.784586191841104.617867882716108.951304500966
62106.703247388025103.982174969841109.424319806208
63106.648951397713103.468730968419109.829171827008
64106.986668637439103.405695466246110.567641808631
65107.005401952277103.064217393454110.9465865111
66107.231187291242102.960063012951111.502311569533
67106.714156470263102.136813411839111.291499528688
68107.333353398612102.469030593904112.197676203321
69108.140293953734103.005003969487113.275583937981
70108.865995068775103.473336160944114.258653976606
71109.232060741991103.593768716021114.87035276796
72109.326923076923103.453261200035115.200584953812



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')