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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 18 Dec 2010 18:52:24 +0000
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/Dec/18/t1292698265xgj228c861kruwl.htm/, Retrieved Tue, 30 Apr 2024 01:17:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112157, Retrieved Tue, 30 Apr 2024 01:17:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
F  MPD  [Exponential Smoothing] [] [2010-11-26 12:44:04] [8a9a6f7c332640af31ddca253a8ded58]
-    D      [Exponential Smoothing] [holt winter model ] [2010-12-18 18:52:24] [e665313c9926a9f4bdf6ad1ee5aefad6] [Current]
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Dataseries X:
101,76
102,37
102,38
102,86
102,87
102,92
102,95
103,02
104,08
104,16
104,24
104,33
104,73
104,86
105,03
105,62
105,63
105,63
105,94
106,61
107,69
107,78
107,93
108,48
108,14
108,48
108,48
108,89
108,93
109,21
109,47
109,80
111,73
111,85
112,12
112,15
112,17
112,67
112,80
113,44
113,53
114,53
114,51
115,05
116,67
117,07
116,92
117,00
117,02
117,35
117,36
117,82
117,88
118,24
118,50
118,80
119,76
120,09
120,16




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112157&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112157&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112157&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.799216301497526
beta0.0327166432819145
gamma0.178232667757671

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.799216301497526 \tabularnewline
beta & 0.0327166432819145 \tabularnewline
gamma & 0.178232667757671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112157&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]0.799216301497526[/C][/ROW]
[ROW][C]beta[/C][C]0.0327166432819145[/C][/ROW]
[ROW][C]gamma[/C][C]0.178232667757671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112157&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112157&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
alpha0.799216301497526
beta0.0327166432819145
gamma0.178232667757671







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13104.73103.3681490384621.36185096153842
14104.86104.6059552711440.254044728856243
15105.03104.9791940493470.0508059506531282
16105.62105.6100795403810.00992045961884003
17105.63105.6252147441030.00478525589682022
18105.63105.604287599280.0257124007200389
19105.94106.116591422565-0.176591422564854
20106.61106.1159266106970.494073389303139
21107.69107.6675202528800.022479747119732
22107.78107.851546361662-0.0715463616618308
23107.93107.953971167219-0.0239711672189173
24108.48108.1058753867740.374124613226144
25108.14108.934878889200-0.794878889200405
26108.48108.4137651533210.066234846678725
27108.48108.629137151196-0.149137151195887
28108.89109.093040757292-0.203040757291632
29108.93108.9265007131330.00349928686733847
30109.21108.8939716768470.316028323153006
31109.47109.62732908891-0.157329088909989
32109.8109.6628313269130.137168673087061
33111.73110.8997438464880.830256153511883
34111.85111.7345541591890.115445840811191
35112.12112.0015790990230.118420900976702
36112.15112.298705324744-0.148705324744242
37112.17112.671523224133-0.501523224132512
38112.67112.4268535030900.243146496910157
39112.8112.7917080401230.00829195987742537
40113.44113.3994181701210.0405818298789029
41113.53113.4612623374510.0687376625489833
42114.53113.5200487195021.00995128049817
43114.51114.837197086984-0.327197086983503
44115.05114.7891714443570.260828555643485
45116.67116.1946457858730.475354214127421
46117.07116.7558803186700.314119681329529
47116.92117.222637946078-0.302637946078235
48117117.203520780676-0.203520780675873
49117.02117.548303100144-0.528303100144043
50117.35117.3365789872860.0134210127140051
51117.36117.531121441968-0.171121441967898
52117.82118.013598569714-0.193598569714439
53117.88117.900167842967-0.0201678429666146
54118.24117.9301356037580.309864396242048
55118.5118.630159634753-0.130159634753085
56118.8118.7560528105720.0439471894284225
57119.76119.985598209489-0.225598209489263
58120.09119.9522510089160.137748991084365
59120.16120.222768045257-0.0627680452567176

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.73 & 103.368149038462 & 1.36185096153842 \tabularnewline
14 & 104.86 & 104.605955271144 & 0.254044728856243 \tabularnewline
15 & 105.03 & 104.979194049347 & 0.0508059506531282 \tabularnewline
16 & 105.62 & 105.610079540381 & 0.00992045961884003 \tabularnewline
17 & 105.63 & 105.625214744103 & 0.00478525589682022 \tabularnewline
18 & 105.63 & 105.60428759928 & 0.0257124007200389 \tabularnewline
19 & 105.94 & 106.116591422565 & -0.176591422564854 \tabularnewline
20 & 106.61 & 106.115926610697 & 0.494073389303139 \tabularnewline
21 & 107.69 & 107.667520252880 & 0.022479747119732 \tabularnewline
22 & 107.78 & 107.851546361662 & -0.0715463616618308 \tabularnewline
23 & 107.93 & 107.953971167219 & -0.0239711672189173 \tabularnewline
24 & 108.48 & 108.105875386774 & 0.374124613226144 \tabularnewline
25 & 108.14 & 108.934878889200 & -0.794878889200405 \tabularnewline
26 & 108.48 & 108.413765153321 & 0.066234846678725 \tabularnewline
27 & 108.48 & 108.629137151196 & -0.149137151195887 \tabularnewline
28 & 108.89 & 109.093040757292 & -0.203040757291632 \tabularnewline
29 & 108.93 & 108.926500713133 & 0.00349928686733847 \tabularnewline
30 & 109.21 & 108.893971676847 & 0.316028323153006 \tabularnewline
31 & 109.47 & 109.62732908891 & -0.157329088909989 \tabularnewline
32 & 109.8 & 109.662831326913 & 0.137168673087061 \tabularnewline
33 & 111.73 & 110.899743846488 & 0.830256153511883 \tabularnewline
34 & 111.85 & 111.734554159189 & 0.115445840811191 \tabularnewline
35 & 112.12 & 112.001579099023 & 0.118420900976702 \tabularnewline
36 & 112.15 & 112.298705324744 & -0.148705324744242 \tabularnewline
37 & 112.17 & 112.671523224133 & -0.501523224132512 \tabularnewline
38 & 112.67 & 112.426853503090 & 0.243146496910157 \tabularnewline
39 & 112.8 & 112.791708040123 & 0.00829195987742537 \tabularnewline
40 & 113.44 & 113.399418170121 & 0.0405818298789029 \tabularnewline
41 & 113.53 & 113.461262337451 & 0.0687376625489833 \tabularnewline
42 & 114.53 & 113.520048719502 & 1.00995128049817 \tabularnewline
43 & 114.51 & 114.837197086984 & -0.327197086983503 \tabularnewline
44 & 115.05 & 114.789171444357 & 0.260828555643485 \tabularnewline
45 & 116.67 & 116.194645785873 & 0.475354214127421 \tabularnewline
46 & 117.07 & 116.755880318670 & 0.314119681329529 \tabularnewline
47 & 116.92 & 117.222637946078 & -0.302637946078235 \tabularnewline
48 & 117 & 117.203520780676 & -0.203520780675873 \tabularnewline
49 & 117.02 & 117.548303100144 & -0.528303100144043 \tabularnewline
50 & 117.35 & 117.336578987286 & 0.0134210127140051 \tabularnewline
51 & 117.36 & 117.531121441968 & -0.171121441967898 \tabularnewline
52 & 117.82 & 118.013598569714 & -0.193598569714439 \tabularnewline
53 & 117.88 & 117.900167842967 & -0.0201678429666146 \tabularnewline
54 & 118.24 & 117.930135603758 & 0.309864396242048 \tabularnewline
55 & 118.5 & 118.630159634753 & -0.130159634753085 \tabularnewline
56 & 118.8 & 118.756052810572 & 0.0439471894284225 \tabularnewline
57 & 119.76 & 119.985598209489 & -0.225598209489263 \tabularnewline
58 & 120.09 & 119.952251008916 & 0.137748991084365 \tabularnewline
59 & 120.16 & 120.222768045257 & -0.0627680452567176 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112157&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]104.73[/C][C]103.368149038462[/C][C]1.36185096153842[/C][/ROW]
[ROW][C]14[/C][C]104.86[/C][C]104.605955271144[/C][C]0.254044728856243[/C][/ROW]
[ROW][C]15[/C][C]105.03[/C][C]104.979194049347[/C][C]0.0508059506531282[/C][/ROW]
[ROW][C]16[/C][C]105.62[/C][C]105.610079540381[/C][C]0.00992045961884003[/C][/ROW]
[ROW][C]17[/C][C]105.63[/C][C]105.625214744103[/C][C]0.00478525589682022[/C][/ROW]
[ROW][C]18[/C][C]105.63[/C][C]105.60428759928[/C][C]0.0257124007200389[/C][/ROW]
[ROW][C]19[/C][C]105.94[/C][C]106.116591422565[/C][C]-0.176591422564854[/C][/ROW]
[ROW][C]20[/C][C]106.61[/C][C]106.115926610697[/C][C]0.494073389303139[/C][/ROW]
[ROW][C]21[/C][C]107.69[/C][C]107.667520252880[/C][C]0.022479747119732[/C][/ROW]
[ROW][C]22[/C][C]107.78[/C][C]107.851546361662[/C][C]-0.0715463616618308[/C][/ROW]
[ROW][C]23[/C][C]107.93[/C][C]107.953971167219[/C][C]-0.0239711672189173[/C][/ROW]
[ROW][C]24[/C][C]108.48[/C][C]108.105875386774[/C][C]0.374124613226144[/C][/ROW]
[ROW][C]25[/C][C]108.14[/C][C]108.934878889200[/C][C]-0.794878889200405[/C][/ROW]
[ROW][C]26[/C][C]108.48[/C][C]108.413765153321[/C][C]0.066234846678725[/C][/ROW]
[ROW][C]27[/C][C]108.48[/C][C]108.629137151196[/C][C]-0.149137151195887[/C][/ROW]
[ROW][C]28[/C][C]108.89[/C][C]109.093040757292[/C][C]-0.203040757291632[/C][/ROW]
[ROW][C]29[/C][C]108.93[/C][C]108.926500713133[/C][C]0.00349928686733847[/C][/ROW]
[ROW][C]30[/C][C]109.21[/C][C]108.893971676847[/C][C]0.316028323153006[/C][/ROW]
[ROW][C]31[/C][C]109.47[/C][C]109.62732908891[/C][C]-0.157329088909989[/C][/ROW]
[ROW][C]32[/C][C]109.8[/C][C]109.662831326913[/C][C]0.137168673087061[/C][/ROW]
[ROW][C]33[/C][C]111.73[/C][C]110.899743846488[/C][C]0.830256153511883[/C][/ROW]
[ROW][C]34[/C][C]111.85[/C][C]111.734554159189[/C][C]0.115445840811191[/C][/ROW]
[ROW][C]35[/C][C]112.12[/C][C]112.001579099023[/C][C]0.118420900976702[/C][/ROW]
[ROW][C]36[/C][C]112.15[/C][C]112.298705324744[/C][C]-0.148705324744242[/C][/ROW]
[ROW][C]37[/C][C]112.17[/C][C]112.671523224133[/C][C]-0.501523224132512[/C][/ROW]
[ROW][C]38[/C][C]112.67[/C][C]112.426853503090[/C][C]0.243146496910157[/C][/ROW]
[ROW][C]39[/C][C]112.8[/C][C]112.791708040123[/C][C]0.00829195987742537[/C][/ROW]
[ROW][C]40[/C][C]113.44[/C][C]113.399418170121[/C][C]0.0405818298789029[/C][/ROW]
[ROW][C]41[/C][C]113.53[/C][C]113.461262337451[/C][C]0.0687376625489833[/C][/ROW]
[ROW][C]42[/C][C]114.53[/C][C]113.520048719502[/C][C]1.00995128049817[/C][/ROW]
[ROW][C]43[/C][C]114.51[/C][C]114.837197086984[/C][C]-0.327197086983503[/C][/ROW]
[ROW][C]44[/C][C]115.05[/C][C]114.789171444357[/C][C]0.260828555643485[/C][/ROW]
[ROW][C]45[/C][C]116.67[/C][C]116.194645785873[/C][C]0.475354214127421[/C][/ROW]
[ROW][C]46[/C][C]117.07[/C][C]116.755880318670[/C][C]0.314119681329529[/C][/ROW]
[ROW][C]47[/C][C]116.92[/C][C]117.222637946078[/C][C]-0.302637946078235[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]117.203520780676[/C][C]-0.203520780675873[/C][/ROW]
[ROW][C]49[/C][C]117.02[/C][C]117.548303100144[/C][C]-0.528303100144043[/C][/ROW]
[ROW][C]50[/C][C]117.35[/C][C]117.336578987286[/C][C]0.0134210127140051[/C][/ROW]
[ROW][C]51[/C][C]117.36[/C][C]117.531121441968[/C][C]-0.171121441967898[/C][/ROW]
[ROW][C]52[/C][C]117.82[/C][C]118.013598569714[/C][C]-0.193598569714439[/C][/ROW]
[ROW][C]53[/C][C]117.88[/C][C]117.900167842967[/C][C]-0.0201678429666146[/C][/ROW]
[ROW][C]54[/C][C]118.24[/C][C]117.930135603758[/C][C]0.309864396242048[/C][/ROW]
[ROW][C]55[/C][C]118.5[/C][C]118.630159634753[/C][C]-0.130159634753085[/C][/ROW]
[ROW][C]56[/C][C]118.8[/C][C]118.756052810572[/C][C]0.0439471894284225[/C][/ROW]
[ROW][C]57[/C][C]119.76[/C][C]119.985598209489[/C][C]-0.225598209489263[/C][/ROW]
[ROW][C]58[/C][C]120.09[/C][C]119.952251008916[/C][C]0.137748991084365[/C][/ROW]
[ROW][C]59[/C][C]120.16[/C][C]120.222768045257[/C][C]-0.0627680452567176[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112157&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112157&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
13104.73103.3681490384621.36185096153842
14104.86104.6059552711440.254044728856243
15105.03104.9791940493470.0508059506531282
16105.62105.6100795403810.00992045961884003
17105.63105.6252147441030.00478525589682022
18105.63105.604287599280.0257124007200389
19105.94106.116591422565-0.176591422564854
20106.61106.1159266106970.494073389303139
21107.69107.6675202528800.022479747119732
22107.78107.851546361662-0.0715463616618308
23107.93107.953971167219-0.0239711672189173
24108.48108.1058753867740.374124613226144
25108.14108.934878889200-0.794878889200405
26108.48108.4137651533210.066234846678725
27108.48108.629137151196-0.149137151195887
28108.89109.093040757292-0.203040757291632
29108.93108.9265007131330.00349928686733847
30109.21108.8939716768470.316028323153006
31109.47109.62732908891-0.157329088909989
32109.8109.6628313269130.137168673087061
33111.73110.8997438464880.830256153511883
34111.85111.7345541591890.115445840811191
35112.12112.0015790990230.118420900976702
36112.15112.298705324744-0.148705324744242
37112.17112.671523224133-0.501523224132512
38112.67112.4268535030900.243146496910157
39112.8112.7917080401230.00829195987742537
40113.44113.3994181701210.0405818298789029
41113.53113.4612623374510.0687376625489833
42114.53113.5200487195021.00995128049817
43114.51114.837197086984-0.327197086983503
44115.05114.7891714443570.260828555643485
45116.67116.1946457858730.475354214127421
46117.07116.7558803186700.314119681329529
47116.92117.222637946078-0.302637946078235
48117117.203520780676-0.203520780675873
49117.02117.548303100144-0.528303100144043
50117.35117.3365789872860.0134210127140051
51117.36117.531121441968-0.171121441967898
52117.82118.013598569714-0.193598569714439
53117.88117.900167842967-0.0201678429666146
54118.24117.9301356037580.309864396242048
55118.5118.630159634753-0.130159634753085
56118.8118.7560528105720.0439471894284225
57119.76119.985598209489-0.225598209489263
58120.09119.9522510089160.137748991084365
59120.16120.222768045257-0.0627680452567176







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
60120.371967043331119.648151913234121.095782173427
61120.846166554290119.907652747071121.784680361508
62121.068253839470119.945453998008122.191053680931
63121.237311691034119.947257936845122.527365445223
64121.852067686060120.405623019414123.298512352706
65121.900952866359120.305557513444123.496348219274
66121.960759387669120.221734500787123.699784274552
67122.391195401520120.512450543337124.269940259704
68122.624555728944120.609009455557124.640102002331
69123.805393517070121.655240600546125.955546433595
70123.967311481243121.684201543424126.250421419063
71124.118920294351121.704082112494126.533758476209

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
60 & 120.371967043331 & 119.648151913234 & 121.095782173427 \tabularnewline
61 & 120.846166554290 & 119.907652747071 & 121.784680361508 \tabularnewline
62 & 121.068253839470 & 119.945453998008 & 122.191053680931 \tabularnewline
63 & 121.237311691034 & 119.947257936845 & 122.527365445223 \tabularnewline
64 & 121.852067686060 & 120.405623019414 & 123.298512352706 \tabularnewline
65 & 121.900952866359 & 120.305557513444 & 123.496348219274 \tabularnewline
66 & 121.960759387669 & 120.221734500787 & 123.699784274552 \tabularnewline
67 & 122.391195401520 & 120.512450543337 & 124.269940259704 \tabularnewline
68 & 122.624555728944 & 120.609009455557 & 124.640102002331 \tabularnewline
69 & 123.805393517070 & 121.655240600546 & 125.955546433595 \tabularnewline
70 & 123.967311481243 & 121.684201543424 & 126.250421419063 \tabularnewline
71 & 124.118920294351 & 121.704082112494 & 126.533758476209 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112157&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]60[/C][C]120.371967043331[/C][C]119.648151913234[/C][C]121.095782173427[/C][/ROW]
[ROW][C]61[/C][C]120.846166554290[/C][C]119.907652747071[/C][C]121.784680361508[/C][/ROW]
[ROW][C]62[/C][C]121.068253839470[/C][C]119.945453998008[/C][C]122.191053680931[/C][/ROW]
[ROW][C]63[/C][C]121.237311691034[/C][C]119.947257936845[/C][C]122.527365445223[/C][/ROW]
[ROW][C]64[/C][C]121.852067686060[/C][C]120.405623019414[/C][C]123.298512352706[/C][/ROW]
[ROW][C]65[/C][C]121.900952866359[/C][C]120.305557513444[/C][C]123.496348219274[/C][/ROW]
[ROW][C]66[/C][C]121.960759387669[/C][C]120.221734500787[/C][C]123.699784274552[/C][/ROW]
[ROW][C]67[/C][C]122.391195401520[/C][C]120.512450543337[/C][C]124.269940259704[/C][/ROW]
[ROW][C]68[/C][C]122.624555728944[/C][C]120.609009455557[/C][C]124.640102002331[/C][/ROW]
[ROW][C]69[/C][C]123.805393517070[/C][C]121.655240600546[/C][C]125.955546433595[/C][/ROW]
[ROW][C]70[/C][C]123.967311481243[/C][C]121.684201543424[/C][C]126.250421419063[/C][/ROW]
[ROW][C]71[/C][C]124.118920294351[/C][C]121.704082112494[/C][C]126.533758476209[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112157&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112157&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
60120.371967043331119.648151913234121.095782173427
61120.846166554290119.907652747071121.784680361508
62121.068253839470119.945453998008122.191053680931
63121.237311691034119.947257936845122.527365445223
64121.852067686060120.405623019414123.298512352706
65121.900952866359120.305557513444123.496348219274
66121.960759387669120.221734500787123.699784274552
67122.391195401520120.512450543337124.269940259704
68122.624555728944120.609009455557124.640102002331
69123.805393517070121.655240600546125.955546433595
70123.967311481243121.684201543424126.250421419063
71124.118920294351121.704082112494126.533758476209



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=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')