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Author's title

Author*The author of this computation has been verified*
R Software Module--
Title produced by softwareExponential Smoothing
Date of computationTue, 29 Nov 2011 17:31:59 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t1322605934powa5v7511nfpzc.htm/, Retrieved Thu, 31 Oct 2024 23:31:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148759, Retrieved Thu, 31 Oct 2024 23:31:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197
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]
- RM        [Exponential Smoothing] [] [2011-11-29 22:31:59] [4be1b05f688f7fa8db5b9e9e4d3a7e33] [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 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=148759&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=148759&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148759&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
alpha0.800425855635785
beta0.0331010367864571
gamma0.15549908037103

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.800425855635785 \tabularnewline
beta & 0.0331010367864571 \tabularnewline
gamma & 0.15549908037103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148759&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]0.800425855635785[/C][/ROW]
[ROW][C]beta[/C][C]0.0331010367864571[/C][/ROW]
[ROW][C]gamma[/C][C]0.15549908037103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148759&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148759&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
alpha0.800425855635785
beta0.0331010367864571
gamma0.15549908037103







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13104.73103.3681490384621.36185096153845
14104.86104.6080754077880.251924592212262
15105.03104.9804294032710.0495705967293389
16105.62105.6108773980550.00912260194529324
17105.63105.6258581413320.00414185866766559
18105.63105.6048785738150.02512142618545
19105.94106.117190518231-0.177190518231455
20106.61106.1162054351530.493794564847491
21107.69107.6687105449520.0212894550478779
22107.78107.852324410478-0.0723244104776057
23107.93107.954507754376-0.0245077543758043
24108.48108.106398788350.37360121164977
25108.14108.929524867536-0.789524867535889
26108.48108.4173615513360.0626384486637335
27108.48108.63128328867-0.151283288669632
28108.89109.093742822269-0.203742822268879
29108.93108.9265815808820.00341841911752283
30109.21108.894050432610.315949567390405
31109.47109.628952151197-0.158952151197155
32109.8109.6599537103050.140046289695292
33111.73110.9018385890920.82816141090828
34111.85111.7369590353650.113040964634919
35112.12112.002479362830.117520637169548
36112.15112.297653199898-0.147653199897903
37112.17112.670892042561-0.500892042561063
38112.67112.4272851560980.242714843901879
39112.8112.794558607960.00544139203962857
40113.44113.4008417015620.0391582984381671
41113.53113.4609744842640.0690255157358877
42114.53113.5188349014111.01116509858875
43114.51114.842065865822-0.332065865822315
44115.05114.7857937610140.264206238986347
45116.67116.1937158011340.476284198866352
46117.07116.7609705504060.309029449594419
47116.92117.224675529818-0.304675529817999
48117117.203668665731-0.203668665731101
49117.02117.549610208876-0.529610208875951
50117.35117.3338336686740.0161663313261471
51117.36117.534146312554-0.174146312553987
52117.82118.01470888547-0.19470888547032
53117.88117.899358685458-0.0193586854579308
54118.24117.9241538199240.315846180076178
55118.5118.639167572072-0.139167572071685
56118.8118.75093085760.0490691423998584
57119.76119.982663244383-0.222663244382872
58120.09119.956183411040.133816588960045

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.73 & 103.368149038462 & 1.36185096153845 \tabularnewline
14 & 104.86 & 104.608075407788 & 0.251924592212262 \tabularnewline
15 & 105.03 & 104.980429403271 & 0.0495705967293389 \tabularnewline
16 & 105.62 & 105.610877398055 & 0.00912260194529324 \tabularnewline
17 & 105.63 & 105.625858141332 & 0.00414185866766559 \tabularnewline
18 & 105.63 & 105.604878573815 & 0.02512142618545 \tabularnewline
19 & 105.94 & 106.117190518231 & -0.177190518231455 \tabularnewline
20 & 106.61 & 106.116205435153 & 0.493794564847491 \tabularnewline
21 & 107.69 & 107.668710544952 & 0.0212894550478779 \tabularnewline
22 & 107.78 & 107.852324410478 & -0.0723244104776057 \tabularnewline
23 & 107.93 & 107.954507754376 & -0.0245077543758043 \tabularnewline
24 & 108.48 & 108.10639878835 & 0.37360121164977 \tabularnewline
25 & 108.14 & 108.929524867536 & -0.789524867535889 \tabularnewline
26 & 108.48 & 108.417361551336 & 0.0626384486637335 \tabularnewline
27 & 108.48 & 108.63128328867 & -0.151283288669632 \tabularnewline
28 & 108.89 & 109.093742822269 & -0.203742822268879 \tabularnewline
29 & 108.93 & 108.926581580882 & 0.00341841911752283 \tabularnewline
30 & 109.21 & 108.89405043261 & 0.315949567390405 \tabularnewline
31 & 109.47 & 109.628952151197 & -0.158952151197155 \tabularnewline
32 & 109.8 & 109.659953710305 & 0.140046289695292 \tabularnewline
33 & 111.73 & 110.901838589092 & 0.82816141090828 \tabularnewline
34 & 111.85 & 111.736959035365 & 0.113040964634919 \tabularnewline
35 & 112.12 & 112.00247936283 & 0.117520637169548 \tabularnewline
36 & 112.15 & 112.297653199898 & -0.147653199897903 \tabularnewline
37 & 112.17 & 112.670892042561 & -0.500892042561063 \tabularnewline
38 & 112.67 & 112.427285156098 & 0.242714843901879 \tabularnewline
39 & 112.8 & 112.79455860796 & 0.00544139203962857 \tabularnewline
40 & 113.44 & 113.400841701562 & 0.0391582984381671 \tabularnewline
41 & 113.53 & 113.460974484264 & 0.0690255157358877 \tabularnewline
42 & 114.53 & 113.518834901411 & 1.01116509858875 \tabularnewline
43 & 114.51 & 114.842065865822 & -0.332065865822315 \tabularnewline
44 & 115.05 & 114.785793761014 & 0.264206238986347 \tabularnewline
45 & 116.67 & 116.193715801134 & 0.476284198866352 \tabularnewline
46 & 117.07 & 116.760970550406 & 0.309029449594419 \tabularnewline
47 & 116.92 & 117.224675529818 & -0.304675529817999 \tabularnewline
48 & 117 & 117.203668665731 & -0.203668665731101 \tabularnewline
49 & 117.02 & 117.549610208876 & -0.529610208875951 \tabularnewline
50 & 117.35 & 117.333833668674 & 0.0161663313261471 \tabularnewline
51 & 117.36 & 117.534146312554 & -0.174146312553987 \tabularnewline
52 & 117.82 & 118.01470888547 & -0.19470888547032 \tabularnewline
53 & 117.88 & 117.899358685458 & -0.0193586854579308 \tabularnewline
54 & 118.24 & 117.924153819924 & 0.315846180076178 \tabularnewline
55 & 118.5 & 118.639167572072 & -0.139167572071685 \tabularnewline
56 & 118.8 & 118.7509308576 & 0.0490691423998584 \tabularnewline
57 & 119.76 & 119.982663244383 & -0.222663244382872 \tabularnewline
58 & 120.09 & 119.95618341104 & 0.133816588960045 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148759&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]1.36185096153845[/C][/ROW]
[ROW][C]14[/C][C]104.86[/C][C]104.608075407788[/C][C]0.251924592212262[/C][/ROW]
[ROW][C]15[/C][C]105.03[/C][C]104.980429403271[/C][C]0.0495705967293389[/C][/ROW]
[ROW][C]16[/C][C]105.62[/C][C]105.610877398055[/C][C]0.00912260194529324[/C][/ROW]
[ROW][C]17[/C][C]105.63[/C][C]105.625858141332[/C][C]0.00414185866766559[/C][/ROW]
[ROW][C]18[/C][C]105.63[/C][C]105.604878573815[/C][C]0.02512142618545[/C][/ROW]
[ROW][C]19[/C][C]105.94[/C][C]106.117190518231[/C][C]-0.177190518231455[/C][/ROW]
[ROW][C]20[/C][C]106.61[/C][C]106.116205435153[/C][C]0.493794564847491[/C][/ROW]
[ROW][C]21[/C][C]107.69[/C][C]107.668710544952[/C][C]0.0212894550478779[/C][/ROW]
[ROW][C]22[/C][C]107.78[/C][C]107.852324410478[/C][C]-0.0723244104776057[/C][/ROW]
[ROW][C]23[/C][C]107.93[/C][C]107.954507754376[/C][C]-0.0245077543758043[/C][/ROW]
[ROW][C]24[/C][C]108.48[/C][C]108.10639878835[/C][C]0.37360121164977[/C][/ROW]
[ROW][C]25[/C][C]108.14[/C][C]108.929524867536[/C][C]-0.789524867535889[/C][/ROW]
[ROW][C]26[/C][C]108.48[/C][C]108.417361551336[/C][C]0.0626384486637335[/C][/ROW]
[ROW][C]27[/C][C]108.48[/C][C]108.63128328867[/C][C]-0.151283288669632[/C][/ROW]
[ROW][C]28[/C][C]108.89[/C][C]109.093742822269[/C][C]-0.203742822268879[/C][/ROW]
[ROW][C]29[/C][C]108.93[/C][C]108.926581580882[/C][C]0.00341841911752283[/C][/ROW]
[ROW][C]30[/C][C]109.21[/C][C]108.89405043261[/C][C]0.315949567390405[/C][/ROW]
[ROW][C]31[/C][C]109.47[/C][C]109.628952151197[/C][C]-0.158952151197155[/C][/ROW]
[ROW][C]32[/C][C]109.8[/C][C]109.659953710305[/C][C]0.140046289695292[/C][/ROW]
[ROW][C]33[/C][C]111.73[/C][C]110.901838589092[/C][C]0.82816141090828[/C][/ROW]
[ROW][C]34[/C][C]111.85[/C][C]111.736959035365[/C][C]0.113040964634919[/C][/ROW]
[ROW][C]35[/C][C]112.12[/C][C]112.00247936283[/C][C]0.117520637169548[/C][/ROW]
[ROW][C]36[/C][C]112.15[/C][C]112.297653199898[/C][C]-0.147653199897903[/C][/ROW]
[ROW][C]37[/C][C]112.17[/C][C]112.670892042561[/C][C]-0.500892042561063[/C][/ROW]
[ROW][C]38[/C][C]112.67[/C][C]112.427285156098[/C][C]0.242714843901879[/C][/ROW]
[ROW][C]39[/C][C]112.8[/C][C]112.79455860796[/C][C]0.00544139203962857[/C][/ROW]
[ROW][C]40[/C][C]113.44[/C][C]113.400841701562[/C][C]0.0391582984381671[/C][/ROW]
[ROW][C]41[/C][C]113.53[/C][C]113.460974484264[/C][C]0.0690255157358877[/C][/ROW]
[ROW][C]42[/C][C]114.53[/C][C]113.518834901411[/C][C]1.01116509858875[/C][/ROW]
[ROW][C]43[/C][C]114.51[/C][C]114.842065865822[/C][C]-0.332065865822315[/C][/ROW]
[ROW][C]44[/C][C]115.05[/C][C]114.785793761014[/C][C]0.264206238986347[/C][/ROW]
[ROW][C]45[/C][C]116.67[/C][C]116.193715801134[/C][C]0.476284198866352[/C][/ROW]
[ROW][C]46[/C][C]117.07[/C][C]116.760970550406[/C][C]0.309029449594419[/C][/ROW]
[ROW][C]47[/C][C]116.92[/C][C]117.224675529818[/C][C]-0.304675529817999[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]117.203668665731[/C][C]-0.203668665731101[/C][/ROW]
[ROW][C]49[/C][C]117.02[/C][C]117.549610208876[/C][C]-0.529610208875951[/C][/ROW]
[ROW][C]50[/C][C]117.35[/C][C]117.333833668674[/C][C]0.0161663313261471[/C][/ROW]
[ROW][C]51[/C][C]117.36[/C][C]117.534146312554[/C][C]-0.174146312553987[/C][/ROW]
[ROW][C]52[/C][C]117.82[/C][C]118.01470888547[/C][C]-0.19470888547032[/C][/ROW]
[ROW][C]53[/C][C]117.88[/C][C]117.899358685458[/C][C]-0.0193586854579308[/C][/ROW]
[ROW][C]54[/C][C]118.24[/C][C]117.924153819924[/C][C]0.315846180076178[/C][/ROW]
[ROW][C]55[/C][C]118.5[/C][C]118.639167572072[/C][C]-0.139167572071685[/C][/ROW]
[ROW][C]56[/C][C]118.8[/C][C]118.7509308576[/C][C]0.0490691423998584[/C][/ROW]
[ROW][C]57[/C][C]119.76[/C][C]119.982663244383[/C][C]-0.222663244382872[/C][/ROW]
[ROW][C]58[/C][C]120.09[/C][C]119.95618341104[/C][C]0.133816588960045[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148759&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148759&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
13104.73103.3681490384621.36185096153845
14104.86104.6080754077880.251924592212262
15105.03104.9804294032710.0495705967293389
16105.62105.6108773980550.00912260194529324
17105.63105.6258581413320.00414185866766559
18105.63105.6048785738150.02512142618545
19105.94106.117190518231-0.177190518231455
20106.61106.1162054351530.493794564847491
21107.69107.6687105449520.0212894550478779
22107.78107.852324410478-0.0723244104776057
23107.93107.954507754376-0.0245077543758043
24108.48108.106398788350.37360121164977
25108.14108.929524867536-0.789524867535889
26108.48108.4173615513360.0626384486637335
27108.48108.63128328867-0.151283288669632
28108.89109.093742822269-0.203742822268879
29108.93108.9265815808820.00341841911752283
30109.21108.894050432610.315949567390405
31109.47109.628952151197-0.158952151197155
32109.8109.6599537103050.140046289695292
33111.73110.9018385890920.82816141090828
34111.85111.7369590353650.113040964634919
35112.12112.002479362830.117520637169548
36112.15112.297653199898-0.147653199897903
37112.17112.670892042561-0.500892042561063
38112.67112.4272851560980.242714843901879
39112.8112.794558607960.00544139203962857
40113.44113.4008417015620.0391582984381671
41113.53113.4609744842640.0690255157358877
42114.53113.5188349014111.01116509858875
43114.51114.842065865822-0.332065865822315
44115.05114.7857937610140.264206238986347
45116.67116.1937158011340.476284198866352
46117.07116.7609705504060.309029449594419
47116.92117.224675529818-0.304675529817999
48117117.203668665731-0.203668665731101
49117.02117.549610208876-0.529610208875951
50117.35117.3338336686740.0161663313261471
51117.36117.534146312554-0.174146312553987
52117.82118.01470888547-0.19470888547032
53117.88117.899358685458-0.0193586854579308
54118.24117.9241538199240.315846180076178
55118.5118.639167572072-0.139167572071685
56118.8118.75093085760.0490691423998584
57119.76119.982663244383-0.222663244382872
58120.09119.956183411040.133816588960045







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
59120.226867301492119.495761998803120.957972604181
60120.427206858052119.478515540883121.37589817522
61120.905792758049119.770313880317122.041271635781
62121.124637143139119.81958672192122.429687564358
63121.29944523809119.83578591485122.76310456133
64121.916716371613120.301944326303123.531488416924
65121.96577222251120.205238930538123.726305514482
66122.020092346032120.11772140566123.922463286405
67122.463432799591120.422145861161124.504719738021
68122.691377167953120.513364444936124.86938989097
69123.873046525823121.559947564813126.186145486833
70124.039400422065121.592429856407126.486370987722

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
59 & 120.226867301492 & 119.495761998803 & 120.957972604181 \tabularnewline
60 & 120.427206858052 & 119.478515540883 & 121.37589817522 \tabularnewline
61 & 120.905792758049 & 119.770313880317 & 122.041271635781 \tabularnewline
62 & 121.124637143139 & 119.81958672192 & 122.429687564358 \tabularnewline
63 & 121.29944523809 & 119.83578591485 & 122.76310456133 \tabularnewline
64 & 121.916716371613 & 120.301944326303 & 123.531488416924 \tabularnewline
65 & 121.96577222251 & 120.205238930538 & 123.726305514482 \tabularnewline
66 & 122.020092346032 & 120.11772140566 & 123.922463286405 \tabularnewline
67 & 122.463432799591 & 120.422145861161 & 124.504719738021 \tabularnewline
68 & 122.691377167953 & 120.513364444936 & 124.86938989097 \tabularnewline
69 & 123.873046525823 & 121.559947564813 & 126.186145486833 \tabularnewline
70 & 124.039400422065 & 121.592429856407 & 126.486370987722 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148759&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]120.226867301492[/C][C]119.495761998803[/C][C]120.957972604181[/C][/ROW]
[ROW][C]60[/C][C]120.427206858052[/C][C]119.478515540883[/C][C]121.37589817522[/C][/ROW]
[ROW][C]61[/C][C]120.905792758049[/C][C]119.770313880317[/C][C]122.041271635781[/C][/ROW]
[ROW][C]62[/C][C]121.124637143139[/C][C]119.81958672192[/C][C]122.429687564358[/C][/ROW]
[ROW][C]63[/C][C]121.29944523809[/C][C]119.83578591485[/C][C]122.76310456133[/C][/ROW]
[ROW][C]64[/C][C]121.916716371613[/C][C]120.301944326303[/C][C]123.531488416924[/C][/ROW]
[ROW][C]65[/C][C]121.96577222251[/C][C]120.205238930538[/C][C]123.726305514482[/C][/ROW]
[ROW][C]66[/C][C]122.020092346032[/C][C]120.11772140566[/C][C]123.922463286405[/C][/ROW]
[ROW][C]67[/C][C]122.463432799591[/C][C]120.422145861161[/C][C]124.504719738021[/C][/ROW]
[ROW][C]68[/C][C]122.691377167953[/C][C]120.513364444936[/C][C]124.86938989097[/C][/ROW]
[ROW][C]69[/C][C]123.873046525823[/C][C]121.559947564813[/C][C]126.186145486833[/C][/ROW]
[ROW][C]70[/C][C]124.039400422065[/C][C]121.592429856407[/C][C]126.486370987722[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148759&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148759&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
59120.226867301492119.495761998803120.957972604181
60120.427206858052119.478515540883121.37589817522
61120.905792758049119.770313880317122.041271635781
62121.124637143139119.81958672192122.429687564358
63121.29944523809119.83578591485122.76310456133
64121.916716371613120.301944326303123.531488416924
65121.96577222251120.205238930538123.726305514482
66122.020092346032120.11772140566123.922463286405
67122.463432799591120.422145861161124.504719738021
68122.691377167953120.513364444936124.86938989097
69123.873046525823121.559947564813126.186145486833
70124.039400422065121.592429856407126.486370987722



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')