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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 19:29:34 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/26/t1461695407nbdy4c3zov18mq8.htm/, Retrieved Fri, 03 May 2024 22:01:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294956, Retrieved Fri, 03 May 2024 22:01:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [CPI Wijnen - Trip...] [2016-04-26 18:29:34] [25a5f245cb671e152cfd8b6d35402e87] [Current]
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Dataseries X:
110.27
110.91
110.27
109.41
111.47
110.77
110.83
110.52
110.44
109.99
110.55
109.99
111.2
111.81
110.36
111.24
112.6
111.75
112.49
111.94
113.22
112.85
114.37
113.68
118
118.27
119.2
117.98
117.59
117.41
118.31
118.4
117.92
118.94
118.81
117.44
120.21
119.74
118.79
118.19
119.16
118.88
119.59
119.44
119.84
119.31
118.15
118.23
119.89
118.83
118.95
119.86
119.07
119.52
119.92
119.68
119.81
120.09
119.98
118.96




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294956&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294956&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294956&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.698951252681756
beta0
gamma0.958229011597004

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.698951252681756 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.958229011597004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294956&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]0.698951252681756[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.958229011597004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294956&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294956&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
alpha0.698951252681756
beta0
gamma0.958229011597004







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13111.2110.6491693376070.550830662393125
14111.81111.6565842496380.153415750361816
15110.36110.2795588444040.0804411555958779
16111.24111.1215277547440.118472245255518
17112.6112.426745209510.173254790490034
18111.75111.5256696595590.224330340441099
19112.49112.551543429227-0.0615434292274983
20111.94112.263022036144-0.323022036144067
21113.22112.0567398432071.16326015679317
22112.85112.4805464508620.369453549138356
23114.37113.3161876023761.05381239762426
24113.68113.545578894990.134421105010432
25118115.0391772867722.96082271322803
26118.27117.6164154339990.653584566001356
27119.2116.5679324017672.63206759823312
28117.98119.204334777568-1.22433477756806
29117.59119.58679890205-1.9967989020498
30117.41117.1836955553040.226304444696126
31118.31118.1284820796730.181517920327323
32118.4117.9344190348820.465580965117709
33117.92118.708085137138-0.788085137138069
34118.94117.5390042227731.40099577722725
35118.81119.293062597346-0.483062597346276
36117.44118.183033030949-0.743033030949306
37120.21119.878676125390.331323874610334
38119.74119.95244537049-0.21244537048986
39118.79118.869389838367-0.0793898383672058
40118.19118.498145197785-0.308145197785052
41119.16119.298145636222-0.138145636221921
42118.88118.835457040430.0445429595701512
43119.59119.640281415212-0.0502814152123392
44119.44119.3661466360140.0738533639856627
45119.84119.5043646123920.335635387608235
46119.31119.752201713932-0.442201713932022
47118.15119.674453709079-1.52445370907931
48118.23117.7615479023990.46845209760103
49119.89120.613883696103-0.723883696102689
50118.83119.79325119241-0.963251192410084
51118.95118.2238020046860.726197995313868
52119.86118.349634097581.51036590242038
53119.07120.469725540453-1.39972554045278
54119.52119.177954935110.342045064889973
55119.92120.163364446187-0.243364446187073
56119.68119.790083652669-0.110083652668564
57119.81119.875255835021-0.0652558350205226
58120.09119.6185040115180.471495988481834
59119.98119.8671849840230.112815015977503
60118.96119.673551003073-0.713551003072638

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 111.2 & 110.649169337607 & 0.550830662393125 \tabularnewline
14 & 111.81 & 111.656584249638 & 0.153415750361816 \tabularnewline
15 & 110.36 & 110.279558844404 & 0.0804411555958779 \tabularnewline
16 & 111.24 & 111.121527754744 & 0.118472245255518 \tabularnewline
17 & 112.6 & 112.42674520951 & 0.173254790490034 \tabularnewline
18 & 111.75 & 111.525669659559 & 0.224330340441099 \tabularnewline
19 & 112.49 & 112.551543429227 & -0.0615434292274983 \tabularnewline
20 & 111.94 & 112.263022036144 & -0.323022036144067 \tabularnewline
21 & 113.22 & 112.056739843207 & 1.16326015679317 \tabularnewline
22 & 112.85 & 112.480546450862 & 0.369453549138356 \tabularnewline
23 & 114.37 & 113.316187602376 & 1.05381239762426 \tabularnewline
24 & 113.68 & 113.54557889499 & 0.134421105010432 \tabularnewline
25 & 118 & 115.039177286772 & 2.96082271322803 \tabularnewline
26 & 118.27 & 117.616415433999 & 0.653584566001356 \tabularnewline
27 & 119.2 & 116.567932401767 & 2.63206759823312 \tabularnewline
28 & 117.98 & 119.204334777568 & -1.22433477756806 \tabularnewline
29 & 117.59 & 119.58679890205 & -1.9967989020498 \tabularnewline
30 & 117.41 & 117.183695555304 & 0.226304444696126 \tabularnewline
31 & 118.31 & 118.128482079673 & 0.181517920327323 \tabularnewline
32 & 118.4 & 117.934419034882 & 0.465580965117709 \tabularnewline
33 & 117.92 & 118.708085137138 & -0.788085137138069 \tabularnewline
34 & 118.94 & 117.539004222773 & 1.40099577722725 \tabularnewline
35 & 118.81 & 119.293062597346 & -0.483062597346276 \tabularnewline
36 & 117.44 & 118.183033030949 & -0.743033030949306 \tabularnewline
37 & 120.21 & 119.87867612539 & 0.331323874610334 \tabularnewline
38 & 119.74 & 119.95244537049 & -0.21244537048986 \tabularnewline
39 & 118.79 & 118.869389838367 & -0.0793898383672058 \tabularnewline
40 & 118.19 & 118.498145197785 & -0.308145197785052 \tabularnewline
41 & 119.16 & 119.298145636222 & -0.138145636221921 \tabularnewline
42 & 118.88 & 118.83545704043 & 0.0445429595701512 \tabularnewline
43 & 119.59 & 119.640281415212 & -0.0502814152123392 \tabularnewline
44 & 119.44 & 119.366146636014 & 0.0738533639856627 \tabularnewline
45 & 119.84 & 119.504364612392 & 0.335635387608235 \tabularnewline
46 & 119.31 & 119.752201713932 & -0.442201713932022 \tabularnewline
47 & 118.15 & 119.674453709079 & -1.52445370907931 \tabularnewline
48 & 118.23 & 117.761547902399 & 0.46845209760103 \tabularnewline
49 & 119.89 & 120.613883696103 & -0.723883696102689 \tabularnewline
50 & 118.83 & 119.79325119241 & -0.963251192410084 \tabularnewline
51 & 118.95 & 118.223802004686 & 0.726197995313868 \tabularnewline
52 & 119.86 & 118.34963409758 & 1.51036590242038 \tabularnewline
53 & 119.07 & 120.469725540453 & -1.39972554045278 \tabularnewline
54 & 119.52 & 119.17795493511 & 0.342045064889973 \tabularnewline
55 & 119.92 & 120.163364446187 & -0.243364446187073 \tabularnewline
56 & 119.68 & 119.790083652669 & -0.110083652668564 \tabularnewline
57 & 119.81 & 119.875255835021 & -0.0652558350205226 \tabularnewline
58 & 120.09 & 119.618504011518 & 0.471495988481834 \tabularnewline
59 & 119.98 & 119.867184984023 & 0.112815015977503 \tabularnewline
60 & 118.96 & 119.673551003073 & -0.713551003072638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294956&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]111.2[/C][C]110.649169337607[/C][C]0.550830662393125[/C][/ROW]
[ROW][C]14[/C][C]111.81[/C][C]111.656584249638[/C][C]0.153415750361816[/C][/ROW]
[ROW][C]15[/C][C]110.36[/C][C]110.279558844404[/C][C]0.0804411555958779[/C][/ROW]
[ROW][C]16[/C][C]111.24[/C][C]111.121527754744[/C][C]0.118472245255518[/C][/ROW]
[ROW][C]17[/C][C]112.6[/C][C]112.42674520951[/C][C]0.173254790490034[/C][/ROW]
[ROW][C]18[/C][C]111.75[/C][C]111.525669659559[/C][C]0.224330340441099[/C][/ROW]
[ROW][C]19[/C][C]112.49[/C][C]112.551543429227[/C][C]-0.0615434292274983[/C][/ROW]
[ROW][C]20[/C][C]111.94[/C][C]112.263022036144[/C][C]-0.323022036144067[/C][/ROW]
[ROW][C]21[/C][C]113.22[/C][C]112.056739843207[/C][C]1.16326015679317[/C][/ROW]
[ROW][C]22[/C][C]112.85[/C][C]112.480546450862[/C][C]0.369453549138356[/C][/ROW]
[ROW][C]23[/C][C]114.37[/C][C]113.316187602376[/C][C]1.05381239762426[/C][/ROW]
[ROW][C]24[/C][C]113.68[/C][C]113.54557889499[/C][C]0.134421105010432[/C][/ROW]
[ROW][C]25[/C][C]118[/C][C]115.039177286772[/C][C]2.96082271322803[/C][/ROW]
[ROW][C]26[/C][C]118.27[/C][C]117.616415433999[/C][C]0.653584566001356[/C][/ROW]
[ROW][C]27[/C][C]119.2[/C][C]116.567932401767[/C][C]2.63206759823312[/C][/ROW]
[ROW][C]28[/C][C]117.98[/C][C]119.204334777568[/C][C]-1.22433477756806[/C][/ROW]
[ROW][C]29[/C][C]117.59[/C][C]119.58679890205[/C][C]-1.9967989020498[/C][/ROW]
[ROW][C]30[/C][C]117.41[/C][C]117.183695555304[/C][C]0.226304444696126[/C][/ROW]
[ROW][C]31[/C][C]118.31[/C][C]118.128482079673[/C][C]0.181517920327323[/C][/ROW]
[ROW][C]32[/C][C]118.4[/C][C]117.934419034882[/C][C]0.465580965117709[/C][/ROW]
[ROW][C]33[/C][C]117.92[/C][C]118.708085137138[/C][C]-0.788085137138069[/C][/ROW]
[ROW][C]34[/C][C]118.94[/C][C]117.539004222773[/C][C]1.40099577722725[/C][/ROW]
[ROW][C]35[/C][C]118.81[/C][C]119.293062597346[/C][C]-0.483062597346276[/C][/ROW]
[ROW][C]36[/C][C]117.44[/C][C]118.183033030949[/C][C]-0.743033030949306[/C][/ROW]
[ROW][C]37[/C][C]120.21[/C][C]119.87867612539[/C][C]0.331323874610334[/C][/ROW]
[ROW][C]38[/C][C]119.74[/C][C]119.95244537049[/C][C]-0.21244537048986[/C][/ROW]
[ROW][C]39[/C][C]118.79[/C][C]118.869389838367[/C][C]-0.0793898383672058[/C][/ROW]
[ROW][C]40[/C][C]118.19[/C][C]118.498145197785[/C][C]-0.308145197785052[/C][/ROW]
[ROW][C]41[/C][C]119.16[/C][C]119.298145636222[/C][C]-0.138145636221921[/C][/ROW]
[ROW][C]42[/C][C]118.88[/C][C]118.83545704043[/C][C]0.0445429595701512[/C][/ROW]
[ROW][C]43[/C][C]119.59[/C][C]119.640281415212[/C][C]-0.0502814152123392[/C][/ROW]
[ROW][C]44[/C][C]119.44[/C][C]119.366146636014[/C][C]0.0738533639856627[/C][/ROW]
[ROW][C]45[/C][C]119.84[/C][C]119.504364612392[/C][C]0.335635387608235[/C][/ROW]
[ROW][C]46[/C][C]119.31[/C][C]119.752201713932[/C][C]-0.442201713932022[/C][/ROW]
[ROW][C]47[/C][C]118.15[/C][C]119.674453709079[/C][C]-1.52445370907931[/C][/ROW]
[ROW][C]48[/C][C]118.23[/C][C]117.761547902399[/C][C]0.46845209760103[/C][/ROW]
[ROW][C]49[/C][C]119.89[/C][C]120.613883696103[/C][C]-0.723883696102689[/C][/ROW]
[ROW][C]50[/C][C]118.83[/C][C]119.79325119241[/C][C]-0.963251192410084[/C][/ROW]
[ROW][C]51[/C][C]118.95[/C][C]118.223802004686[/C][C]0.726197995313868[/C][/ROW]
[ROW][C]52[/C][C]119.86[/C][C]118.34963409758[/C][C]1.51036590242038[/C][/ROW]
[ROW][C]53[/C][C]119.07[/C][C]120.469725540453[/C][C]-1.39972554045278[/C][/ROW]
[ROW][C]54[/C][C]119.52[/C][C]119.17795493511[/C][C]0.342045064889973[/C][/ROW]
[ROW][C]55[/C][C]119.92[/C][C]120.163364446187[/C][C]-0.243364446187073[/C][/ROW]
[ROW][C]56[/C][C]119.68[/C][C]119.790083652669[/C][C]-0.110083652668564[/C][/ROW]
[ROW][C]57[/C][C]119.81[/C][C]119.875255835021[/C][C]-0.0652558350205226[/C][/ROW]
[ROW][C]58[/C][C]120.09[/C][C]119.618504011518[/C][C]0.471495988481834[/C][/ROW]
[ROW][C]59[/C][C]119.98[/C][C]119.867184984023[/C][C]0.112815015977503[/C][/ROW]
[ROW][C]60[/C][C]118.96[/C][C]119.673551003073[/C][C]-0.713551003072638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294956&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294956&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
13111.2110.6491693376070.550830662393125
14111.81111.6565842496380.153415750361816
15110.36110.2795588444040.0804411555958779
16111.24111.1215277547440.118472245255518
17112.6112.426745209510.173254790490034
18111.75111.5256696595590.224330340441099
19112.49112.551543429227-0.0615434292274983
20111.94112.263022036144-0.323022036144067
21113.22112.0567398432071.16326015679317
22112.85112.4805464508620.369453549138356
23114.37113.3161876023761.05381239762426
24113.68113.545578894990.134421105010432
25118115.0391772867722.96082271322803
26118.27117.6164154339990.653584566001356
27119.2116.5679324017672.63206759823312
28117.98119.204334777568-1.22433477756806
29117.59119.58679890205-1.9967989020498
30117.41117.1836955553040.226304444696126
31118.31118.1284820796730.181517920327323
32118.4117.9344190348820.465580965117709
33117.92118.708085137138-0.788085137138069
34118.94117.5390042227731.40099577722725
35118.81119.293062597346-0.483062597346276
36117.44118.183033030949-0.743033030949306
37120.21119.878676125390.331323874610334
38119.74119.95244537049-0.21244537048986
39118.79118.869389838367-0.0793898383672058
40118.19118.498145197785-0.308145197785052
41119.16119.298145636222-0.138145636221921
42118.88118.835457040430.0445429595701512
43119.59119.640281415212-0.0502814152123392
44119.44119.3661466360140.0738533639856627
45119.84119.5043646123920.335635387608235
46119.31119.752201713932-0.442201713932022
47118.15119.674453709079-1.52445370907931
48118.23117.7615479023990.46845209760103
49119.89120.613883696103-0.723883696102689
50118.83119.79325119241-0.963251192410084
51118.95118.2238020046860.726197995313868
52119.86118.349634097581.51036590242038
53119.07120.469725540453-1.39972554045278
54119.52119.177954935110.342045064889973
55119.92120.163364446187-0.243364446187073
56119.68119.790083652669-0.110083652668564
57119.81119.875255835021-0.0652558350205226
58120.09119.6185040115180.471495988481834
59119.98119.8671849840230.112815015977503
60118.96119.673551003073-0.713551003072638







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61121.3557667981119.585824324251123.125709271949
62120.972042496779118.812616310638123.131468682919
63120.563220499472118.074536802004123.051904196939
64120.407687367191117.628483949179123.186890785204
65120.632621988868117.590517991411123.674725986325
66120.821646216248117.537620969087124.10567146341
67121.399107686097117.889799076606124.908416295588
68121.234374773225117.513397480994124.955352065457
69121.409421706401117.488185026225125.330658386576
70121.353119284758117.241365134203125.464873435312
71121.168777538455116.874950889968125.462604186942
72120.657906544316116.189419957125125.126393131507

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 121.3557667981 & 119.585824324251 & 123.125709271949 \tabularnewline
62 & 120.972042496779 & 118.812616310638 & 123.131468682919 \tabularnewline
63 & 120.563220499472 & 118.074536802004 & 123.051904196939 \tabularnewline
64 & 120.407687367191 & 117.628483949179 & 123.186890785204 \tabularnewline
65 & 120.632621988868 & 117.590517991411 & 123.674725986325 \tabularnewline
66 & 120.821646216248 & 117.537620969087 & 124.10567146341 \tabularnewline
67 & 121.399107686097 & 117.889799076606 & 124.908416295588 \tabularnewline
68 & 121.234374773225 & 117.513397480994 & 124.955352065457 \tabularnewline
69 & 121.409421706401 & 117.488185026225 & 125.330658386576 \tabularnewline
70 & 121.353119284758 & 117.241365134203 & 125.464873435312 \tabularnewline
71 & 121.168777538455 & 116.874950889968 & 125.462604186942 \tabularnewline
72 & 120.657906544316 & 116.189419957125 & 125.126393131507 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294956&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]121.3557667981[/C][C]119.585824324251[/C][C]123.125709271949[/C][/ROW]
[ROW][C]62[/C][C]120.972042496779[/C][C]118.812616310638[/C][C]123.131468682919[/C][/ROW]
[ROW][C]63[/C][C]120.563220499472[/C][C]118.074536802004[/C][C]123.051904196939[/C][/ROW]
[ROW][C]64[/C][C]120.407687367191[/C][C]117.628483949179[/C][C]123.186890785204[/C][/ROW]
[ROW][C]65[/C][C]120.632621988868[/C][C]117.590517991411[/C][C]123.674725986325[/C][/ROW]
[ROW][C]66[/C][C]120.821646216248[/C][C]117.537620969087[/C][C]124.10567146341[/C][/ROW]
[ROW][C]67[/C][C]121.399107686097[/C][C]117.889799076606[/C][C]124.908416295588[/C][/ROW]
[ROW][C]68[/C][C]121.234374773225[/C][C]117.513397480994[/C][C]124.955352065457[/C][/ROW]
[ROW][C]69[/C][C]121.409421706401[/C][C]117.488185026225[/C][C]125.330658386576[/C][/ROW]
[ROW][C]70[/C][C]121.353119284758[/C][C]117.241365134203[/C][C]125.464873435312[/C][/ROW]
[ROW][C]71[/C][C]121.168777538455[/C][C]116.874950889968[/C][C]125.462604186942[/C][/ROW]
[ROW][C]72[/C][C]120.657906544316[/C][C]116.189419957125[/C][C]125.126393131507[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294956&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294956&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
61121.3557667981119.585824324251123.125709271949
62120.972042496779118.812616310638123.131468682919
63120.563220499472118.074536802004123.051904196939
64120.407687367191117.628483949179123.186890785204
65120.632621988868117.590517991411123.674725986325
66120.821646216248117.537620969087124.10567146341
67121.399107686097117.889799076606124.908416295588
68121.234374773225117.513397480994124.955352065457
69121.409421706401117.488185026225125.330658386576
70121.353119284758117.241365134203125.464873435312
71121.168777538455116.874950889968125.462604186942
72120.657906544316116.189419957125125.126393131507



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')