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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 computationTue, 21 Dec 2010 00:16:41 +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/21/t12928904901rmaqyx4td16uy3.htm/, Retrieved Fri, 19 Apr 2024 01:53:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113178, Retrieved Fri, 19 Apr 2024 01:53:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [HPC Retail Sales] [2008-03-02 16:19:32] [74be16979710d4c4e7c6647856088456]
-  M D  [Classical Decomposition] [] [2010-11-26 09:51:05] [7789b9488494790f41ddb7f073cada1b]
- RMPD    [Exponential Smoothing] [] [2010-12-17 11:57:35] [7789b9488494790f41ddb7f073cada1b]
-   P         [Exponential Smoothing] [] [2010-12-21 00:16:41] [0bf4568947c4284a0258563e64d5d827] [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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113178&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113178&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113178&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.800425855140645
beta0.0331010367938548
gamma0.155499080750997

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.800425855140645 \tabularnewline
beta & 0.0331010367938548 \tabularnewline
gamma & 0.155499080750997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113178&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]0.800425855140645[/C][/ROW]
[ROW][C]beta[/C][C]0.0331010367938548[/C][/ROW]
[ROW][C]gamma[/C][C]0.155499080750997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113178&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113178&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
alpha0.800425855140645
beta0.0331010367938548
gamma0.155499080750997







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13104.73103.3681490384621.36185096153842
14104.86104.6080754070990.251924592900835
15105.03104.980429403010.049570596990165
16105.62105.6108773979860.00912260201413062
17105.63105.6258581413240.0041418586764479
18105.63105.604878573820.0251214261796378
19105.94106.117190518229-0.177190518229409
20106.61106.1162054352510.493794564749024
21107.69107.6687105447310.0212894552693683
22107.78107.852324410432-0.0723244104318752
23107.93107.954507754413-0.0245077544134489
24108.48108.106398788380.373601211619913
25108.14108.929524867571-0.789524867570535
26108.48108.4173615515990.0626384484012732
27108.48108.631283288652-0.151283288652067
28108.89109.093742822335-0.203742822335499
29108.93108.9265815810020.00341841899826534
30109.21108.8940504326390.315949567361073
31109.47109.628952151016-0.158952151016308
32109.8109.6599537104540.14004628954639
33111.73110.9018385889910.828161411008736
34111.85111.7369590349110.113040965089311
35112.12112.0024793626950.117520637305205
36112.15112.297653199882-0.14765319988237
37112.17112.670892042672-0.500892042671921
38112.67112.4272851563560.242714843643924
39112.8112.7945586078270.00544139217296902
40113.44113.4008417015170.0391582984831871
41113.53113.4609744842710.0690255157290238
42114.53113.5188349014391.01116509856136
43114.51114.842065865226-0.332065865225957
44115.05114.7857937612090.264206238791175
45116.67116.1937158010990.476284198900672
46117.07116.7609705500480.309029449952277
47116.92117.224675529598-0.304675529598185
48117117.203668665873-0.20366866587301
49117.02117.549610208994-0.52961020899393
50117.35117.3338336690630.016166330937466
51117.36117.53414631254-0.174146312539676
52117.82118.014708885544-0.194708885544003
53117.88117.89935868561-0.0193586856101575
54118.24117.9241538201670.31584617983269
55118.5118.639167571678-0.139167571678371
56118.8118.7509308578010.0490691421989595
57119.76119.982663244492-0.222663244491997
58120.09119.9561834110410.133816588958965

\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 & 104.608075407099 & 0.251924592900835 \tabularnewline
15 & 105.03 & 104.98042940301 & 0.049570596990165 \tabularnewline
16 & 105.62 & 105.610877397986 & 0.00912260201413062 \tabularnewline
17 & 105.63 & 105.625858141324 & 0.0041418586764479 \tabularnewline
18 & 105.63 & 105.60487857382 & 0.0251214261796378 \tabularnewline
19 & 105.94 & 106.117190518229 & -0.177190518229409 \tabularnewline
20 & 106.61 & 106.116205435251 & 0.493794564749024 \tabularnewline
21 & 107.69 & 107.668710544731 & 0.0212894552693683 \tabularnewline
22 & 107.78 & 107.852324410432 & -0.0723244104318752 \tabularnewline
23 & 107.93 & 107.954507754413 & -0.0245077544134489 \tabularnewline
24 & 108.48 & 108.10639878838 & 0.373601211619913 \tabularnewline
25 & 108.14 & 108.929524867571 & -0.789524867570535 \tabularnewline
26 & 108.48 & 108.417361551599 & 0.0626384484012732 \tabularnewline
27 & 108.48 & 108.631283288652 & -0.151283288652067 \tabularnewline
28 & 108.89 & 109.093742822335 & -0.203742822335499 \tabularnewline
29 & 108.93 & 108.926581581002 & 0.00341841899826534 \tabularnewline
30 & 109.21 & 108.894050432639 & 0.315949567361073 \tabularnewline
31 & 109.47 & 109.628952151016 & -0.158952151016308 \tabularnewline
32 & 109.8 & 109.659953710454 & 0.14004628954639 \tabularnewline
33 & 111.73 & 110.901838588991 & 0.828161411008736 \tabularnewline
34 & 111.85 & 111.736959034911 & 0.113040965089311 \tabularnewline
35 & 112.12 & 112.002479362695 & 0.117520637305205 \tabularnewline
36 & 112.15 & 112.297653199882 & -0.14765319988237 \tabularnewline
37 & 112.17 & 112.670892042672 & -0.500892042671921 \tabularnewline
38 & 112.67 & 112.427285156356 & 0.242714843643924 \tabularnewline
39 & 112.8 & 112.794558607827 & 0.00544139217296902 \tabularnewline
40 & 113.44 & 113.400841701517 & 0.0391582984831871 \tabularnewline
41 & 113.53 & 113.460974484271 & 0.0690255157290238 \tabularnewline
42 & 114.53 & 113.518834901439 & 1.01116509856136 \tabularnewline
43 & 114.51 & 114.842065865226 & -0.332065865225957 \tabularnewline
44 & 115.05 & 114.785793761209 & 0.264206238791175 \tabularnewline
45 & 116.67 & 116.193715801099 & 0.476284198900672 \tabularnewline
46 & 117.07 & 116.760970550048 & 0.309029449952277 \tabularnewline
47 & 116.92 & 117.224675529598 & -0.304675529598185 \tabularnewline
48 & 117 & 117.203668665873 & -0.20366866587301 \tabularnewline
49 & 117.02 & 117.549610208994 & -0.52961020899393 \tabularnewline
50 & 117.35 & 117.333833669063 & 0.016166330937466 \tabularnewline
51 & 117.36 & 117.53414631254 & -0.174146312539676 \tabularnewline
52 & 117.82 & 118.014708885544 & -0.194708885544003 \tabularnewline
53 & 117.88 & 117.89935868561 & -0.0193586856101575 \tabularnewline
54 & 118.24 & 117.924153820167 & 0.31584617983269 \tabularnewline
55 & 118.5 & 118.639167571678 & -0.139167571678371 \tabularnewline
56 & 118.8 & 118.750930857801 & 0.0490691421989595 \tabularnewline
57 & 119.76 & 119.982663244492 & -0.222663244491997 \tabularnewline
58 & 120.09 & 119.956183411041 & 0.133816588958965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113178&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]104.608075407099[/C][C]0.251924592900835[/C][/ROW]
[ROW][C]15[/C][C]105.03[/C][C]104.98042940301[/C][C]0.049570596990165[/C][/ROW]
[ROW][C]16[/C][C]105.62[/C][C]105.610877397986[/C][C]0.00912260201413062[/C][/ROW]
[ROW][C]17[/C][C]105.63[/C][C]105.625858141324[/C][C]0.0041418586764479[/C][/ROW]
[ROW][C]18[/C][C]105.63[/C][C]105.60487857382[/C][C]0.0251214261796378[/C][/ROW]
[ROW][C]19[/C][C]105.94[/C][C]106.117190518229[/C][C]-0.177190518229409[/C][/ROW]
[ROW][C]20[/C][C]106.61[/C][C]106.116205435251[/C][C]0.493794564749024[/C][/ROW]
[ROW][C]21[/C][C]107.69[/C][C]107.668710544731[/C][C]0.0212894552693683[/C][/ROW]
[ROW][C]22[/C][C]107.78[/C][C]107.852324410432[/C][C]-0.0723244104318752[/C][/ROW]
[ROW][C]23[/C][C]107.93[/C][C]107.954507754413[/C][C]-0.0245077544134489[/C][/ROW]
[ROW][C]24[/C][C]108.48[/C][C]108.10639878838[/C][C]0.373601211619913[/C][/ROW]
[ROW][C]25[/C][C]108.14[/C][C]108.929524867571[/C][C]-0.789524867570535[/C][/ROW]
[ROW][C]26[/C][C]108.48[/C][C]108.417361551599[/C][C]0.0626384484012732[/C][/ROW]
[ROW][C]27[/C][C]108.48[/C][C]108.631283288652[/C][C]-0.151283288652067[/C][/ROW]
[ROW][C]28[/C][C]108.89[/C][C]109.093742822335[/C][C]-0.203742822335499[/C][/ROW]
[ROW][C]29[/C][C]108.93[/C][C]108.926581581002[/C][C]0.00341841899826534[/C][/ROW]
[ROW][C]30[/C][C]109.21[/C][C]108.894050432639[/C][C]0.315949567361073[/C][/ROW]
[ROW][C]31[/C][C]109.47[/C][C]109.628952151016[/C][C]-0.158952151016308[/C][/ROW]
[ROW][C]32[/C][C]109.8[/C][C]109.659953710454[/C][C]0.14004628954639[/C][/ROW]
[ROW][C]33[/C][C]111.73[/C][C]110.901838588991[/C][C]0.828161411008736[/C][/ROW]
[ROW][C]34[/C][C]111.85[/C][C]111.736959034911[/C][C]0.113040965089311[/C][/ROW]
[ROW][C]35[/C][C]112.12[/C][C]112.002479362695[/C][C]0.117520637305205[/C][/ROW]
[ROW][C]36[/C][C]112.15[/C][C]112.297653199882[/C][C]-0.14765319988237[/C][/ROW]
[ROW][C]37[/C][C]112.17[/C][C]112.670892042672[/C][C]-0.500892042671921[/C][/ROW]
[ROW][C]38[/C][C]112.67[/C][C]112.427285156356[/C][C]0.242714843643924[/C][/ROW]
[ROW][C]39[/C][C]112.8[/C][C]112.794558607827[/C][C]0.00544139217296902[/C][/ROW]
[ROW][C]40[/C][C]113.44[/C][C]113.400841701517[/C][C]0.0391582984831871[/C][/ROW]
[ROW][C]41[/C][C]113.53[/C][C]113.460974484271[/C][C]0.0690255157290238[/C][/ROW]
[ROW][C]42[/C][C]114.53[/C][C]113.518834901439[/C][C]1.01116509856136[/C][/ROW]
[ROW][C]43[/C][C]114.51[/C][C]114.842065865226[/C][C]-0.332065865225957[/C][/ROW]
[ROW][C]44[/C][C]115.05[/C][C]114.785793761209[/C][C]0.264206238791175[/C][/ROW]
[ROW][C]45[/C][C]116.67[/C][C]116.193715801099[/C][C]0.476284198900672[/C][/ROW]
[ROW][C]46[/C][C]117.07[/C][C]116.760970550048[/C][C]0.309029449952277[/C][/ROW]
[ROW][C]47[/C][C]116.92[/C][C]117.224675529598[/C][C]-0.304675529598185[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]117.203668665873[/C][C]-0.20366866587301[/C][/ROW]
[ROW][C]49[/C][C]117.02[/C][C]117.549610208994[/C][C]-0.52961020899393[/C][/ROW]
[ROW][C]50[/C][C]117.35[/C][C]117.333833669063[/C][C]0.016166330937466[/C][/ROW]
[ROW][C]51[/C][C]117.36[/C][C]117.53414631254[/C][C]-0.174146312539676[/C][/ROW]
[ROW][C]52[/C][C]117.82[/C][C]118.014708885544[/C][C]-0.194708885544003[/C][/ROW]
[ROW][C]53[/C][C]117.88[/C][C]117.89935868561[/C][C]-0.0193586856101575[/C][/ROW]
[ROW][C]54[/C][C]118.24[/C][C]117.924153820167[/C][C]0.31584617983269[/C][/ROW]
[ROW][C]55[/C][C]118.5[/C][C]118.639167571678[/C][C]-0.139167571678371[/C][/ROW]
[ROW][C]56[/C][C]118.8[/C][C]118.750930857801[/C][C]0.0490691421989595[/C][/ROW]
[ROW][C]57[/C][C]119.76[/C][C]119.982663244492[/C][C]-0.222663244491997[/C][/ROW]
[ROW][C]58[/C][C]120.09[/C][C]119.956183411041[/C][C]0.133816588958965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113178&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113178&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
14104.86104.6080754070990.251924592900835
15105.03104.980429403010.049570596990165
16105.62105.6108773979860.00912260201413062
17105.63105.6258581413240.0041418586764479
18105.63105.604878573820.0251214261796378
19105.94106.117190518229-0.177190518229409
20106.61106.1162054352510.493794564749024
21107.69107.6687105447310.0212894552693683
22107.78107.852324410432-0.0723244104318752
23107.93107.954507754413-0.0245077544134489
24108.48108.106398788380.373601211619913
25108.14108.929524867571-0.789524867570535
26108.48108.4173615515990.0626384484012732
27108.48108.631283288652-0.151283288652067
28108.89109.093742822335-0.203742822335499
29108.93108.9265815810020.00341841899826534
30109.21108.8940504326390.315949567361073
31109.47109.628952151016-0.158952151016308
32109.8109.6599537104540.14004628954639
33111.73110.9018385889910.828161411008736
34111.85111.7369590349110.113040965089311
35112.12112.0024793626950.117520637305205
36112.15112.297653199882-0.14765319988237
37112.17112.670892042672-0.500892042671921
38112.67112.4272851563560.242714843643924
39112.8112.7945586078270.00544139217296902
40113.44113.4008417015170.0391582984831871
41113.53113.4609744842710.0690255157290238
42114.53113.5188349014391.01116509856136
43114.51114.842065865226-0.332065865225957
44115.05114.7857937612090.264206238791175
45116.67116.1937158010990.476284198900672
46117.07116.7609705500480.309029449952277
47116.92117.224675529598-0.304675529598185
48117117.203668665873-0.20366866587301
49117.02117.549610208994-0.52961020899393
50117.35117.3338336690630.016166330937466
51117.36117.53414631254-0.174146312539676
52117.82118.014708885544-0.194708885544003
53117.88117.89935868561-0.0193586856101575
54118.24117.9241538201670.31584617983269
55118.5118.639167571678-0.139167571678371
56118.8118.7509308578010.0490691421989595
57119.76119.982663244492-0.222663244491997
58120.09119.9561834110410.133816588958965







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
59120.226867301325119.495761998643120.957972604006
60120.427206857907119.478515540984121.375898174829
61120.905792757828119.770313880513122.041271635144
62121.124637143078119.819586722415122.429687563741
63121.299445237922119.835785915359122.763104560485
64121.91671637142120.301944326895123.531488415945
65121.965772222373120.205238931287123.726305513459
66122.020092346141120.117721406749123.922463285533
67122.463432799368120.422145862008124.504719736729
68122.691377167944120.513364446082124.869389889805
69123.873046525867121.559947566095126.186145485638
70124.039400422033121.592429857695126.486370986372

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
59 & 120.226867301325 & 119.495761998643 & 120.957972604006 \tabularnewline
60 & 120.427206857907 & 119.478515540984 & 121.375898174829 \tabularnewline
61 & 120.905792757828 & 119.770313880513 & 122.041271635144 \tabularnewline
62 & 121.124637143078 & 119.819586722415 & 122.429687563741 \tabularnewline
63 & 121.299445237922 & 119.835785915359 & 122.763104560485 \tabularnewline
64 & 121.91671637142 & 120.301944326895 & 123.531488415945 \tabularnewline
65 & 121.965772222373 & 120.205238931287 & 123.726305513459 \tabularnewline
66 & 122.020092346141 & 120.117721406749 & 123.922463285533 \tabularnewline
67 & 122.463432799368 & 120.422145862008 & 124.504719736729 \tabularnewline
68 & 122.691377167944 & 120.513364446082 & 124.869389889805 \tabularnewline
69 & 123.873046525867 & 121.559947566095 & 126.186145485638 \tabularnewline
70 & 124.039400422033 & 121.592429857695 & 126.486370986372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113178&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]59[/C][C]120.226867301325[/C][C]119.495761998643[/C][C]120.957972604006[/C][/ROW]
[ROW][C]60[/C][C]120.427206857907[/C][C]119.478515540984[/C][C]121.375898174829[/C][/ROW]
[ROW][C]61[/C][C]120.905792757828[/C][C]119.770313880513[/C][C]122.041271635144[/C][/ROW]
[ROW][C]62[/C][C]121.124637143078[/C][C]119.819586722415[/C][C]122.429687563741[/C][/ROW]
[ROW][C]63[/C][C]121.299445237922[/C][C]119.835785915359[/C][C]122.763104560485[/C][/ROW]
[ROW][C]64[/C][C]121.91671637142[/C][C]120.301944326895[/C][C]123.531488415945[/C][/ROW]
[ROW][C]65[/C][C]121.965772222373[/C][C]120.205238931287[/C][C]123.726305513459[/C][/ROW]
[ROW][C]66[/C][C]122.020092346141[/C][C]120.117721406749[/C][C]123.922463285533[/C][/ROW]
[ROW][C]67[/C][C]122.463432799368[/C][C]120.422145862008[/C][C]124.504719736729[/C][/ROW]
[ROW][C]68[/C][C]122.691377167944[/C][C]120.513364446082[/C][C]124.869389889805[/C][/ROW]
[ROW][C]69[/C][C]123.873046525867[/C][C]121.559947566095[/C][C]126.186145485638[/C][/ROW]
[ROW][C]70[/C][C]124.039400422033[/C][C]121.592429857695[/C][C]126.486370986372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113178&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113178&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
59120.226867301325119.495761998643120.957972604006
60120.427206857907119.478515540984121.375898174829
61120.905792757828119.770313880513122.041271635144
62121.124637143078119.819586722415122.429687563741
63121.299445237922119.835785915359122.763104560485
64121.91671637142120.301944326895123.531488415945
65121.965772222373120.205238931287123.726305513459
66122.020092346141120.117721406749123.922463285533
67122.463432799368120.422145862008124.504719736729
68122.691377167944120.513364446082124.869389889805
69123.873046525867121.559947566095126.186145485638
70124.039400422033121.592429857695126.486370986372



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = no ;
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')