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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 15 Dec 2010 19:00:17 +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/15/t1292439494zdqabf0x1a99azb.htm/, Retrieved Fri, 03 May 2024 09:56:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110661, Retrieved Fri, 03 May 2024 09:56:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
- RMP           [ARIMA Backward Selection] [Births] [2010-11-29 17:47:06] [b98453cac15ba1066b407e146608df68]
- RMPD            [ARIMA Forecasting] [arima forecast paper] [2010-12-12 14:16:56] [7d64bf19f34ddcdf2626356c9d5bd60d]
- RMP               [Exponential Smoothing] [additive hw] [2010-12-15 18:29:19] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   PD                  [Exponential Smoothing] [Exp sm Multi] [2010-12-15 19:00:17] [5842cf9dd57f9603e676e11284d3404a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 9 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110661&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110661&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110661&T=0

As an alternative you can also use a QR Code:  
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 time9 seconds
R Server'George Udny Yule' @ 72.249.76.132






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.844736520425172
beta0.201418589917053
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.844736520425172 \tabularnewline
beta & 0.201418589917053 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110661&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]0.844736520425172[/C][/ROW]
[ROW][C]beta[/C][C]0.201418589917053[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110661&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110661&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.844736520425172
beta0.201418589917053
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13557582.052496527966-25.0524965279658
14561561.593877817214-0.59387781721432
15549545.1319395673283.86806043267177
16532528.7040912951193.29590870488096
17526523.3432175686122.65678243138757
18511508.0657904688322.93420953116845
19499515.704882590008-16.7048825900082
20555535.01001701454719.9899829854526
21565552.93451542989812.0654845701021
22542556.158169828962-14.1581698289621
23527512.4883906494514.5116093505502
24510504.5682073358585.43179266414199
25514498.9440776956815.0559223043196
26517523.126709865252-6.12670986525234
27508510.2048028684-2.20480286839967
28493495.300399761747-2.30039976174669
29490490.085511028767-0.0855110287672005
30469477.622647624964-8.62264762496432
31478474.1347263106833.86527368931695
32528520.8075555313237.19244446867651
33534530.6956097139233.30439028607748
34518525.596810978296-7.59681097829628
35506496.5382622618349.46173773816565
36502486.51895167520315.4810483247966
37516495.44656816086820.5534318391322
38528526.4968228345291.50317716547136
39533527.2962144217625.7037855782379
40536526.500330967079.49966903292977
41537541.542046882319-4.54204688231869
42524531.890508591238-7.89050859123802
43536541.466795338661-5.46679533866097
44587595.153791745806-8.1537917458055
45597598.106445768071-1.10644576807078
46581591.8267065732-10.8267065731999
47564565.016013354905-1.01601335490500
48558547.80422846321210.1957715367879

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 557 & 582.052496527966 & -25.0524965279658 \tabularnewline
14 & 561 & 561.593877817214 & -0.59387781721432 \tabularnewline
15 & 549 & 545.131939567328 & 3.86806043267177 \tabularnewline
16 & 532 & 528.704091295119 & 3.29590870488096 \tabularnewline
17 & 526 & 523.343217568612 & 2.65678243138757 \tabularnewline
18 & 511 & 508.065790468832 & 2.93420953116845 \tabularnewline
19 & 499 & 515.704882590008 & -16.7048825900082 \tabularnewline
20 & 555 & 535.010017014547 & 19.9899829854526 \tabularnewline
21 & 565 & 552.934515429898 & 12.0654845701021 \tabularnewline
22 & 542 & 556.158169828962 & -14.1581698289621 \tabularnewline
23 & 527 & 512.48839064945 & 14.5116093505502 \tabularnewline
24 & 510 & 504.568207335858 & 5.43179266414199 \tabularnewline
25 & 514 & 498.94407769568 & 15.0559223043196 \tabularnewline
26 & 517 & 523.126709865252 & -6.12670986525234 \tabularnewline
27 & 508 & 510.2048028684 & -2.20480286839967 \tabularnewline
28 & 493 & 495.300399761747 & -2.30039976174669 \tabularnewline
29 & 490 & 490.085511028767 & -0.0855110287672005 \tabularnewline
30 & 469 & 477.622647624964 & -8.62264762496432 \tabularnewline
31 & 478 & 474.134726310683 & 3.86527368931695 \tabularnewline
32 & 528 & 520.807555531323 & 7.19244446867651 \tabularnewline
33 & 534 & 530.695609713923 & 3.30439028607748 \tabularnewline
34 & 518 & 525.596810978296 & -7.59681097829628 \tabularnewline
35 & 506 & 496.538262261834 & 9.46173773816565 \tabularnewline
36 & 502 & 486.518951675203 & 15.4810483247966 \tabularnewline
37 & 516 & 495.446568160868 & 20.5534318391322 \tabularnewline
38 & 528 & 526.496822834529 & 1.50317716547136 \tabularnewline
39 & 533 & 527.296214421762 & 5.7037855782379 \tabularnewline
40 & 536 & 526.50033096707 & 9.49966903292977 \tabularnewline
41 & 537 & 541.542046882319 & -4.54204688231869 \tabularnewline
42 & 524 & 531.890508591238 & -7.89050859123802 \tabularnewline
43 & 536 & 541.466795338661 & -5.46679533866097 \tabularnewline
44 & 587 & 595.153791745806 & -8.1537917458055 \tabularnewline
45 & 597 & 598.106445768071 & -1.10644576807078 \tabularnewline
46 & 581 & 591.8267065732 & -10.8267065731999 \tabularnewline
47 & 564 & 565.016013354905 & -1.01601335490500 \tabularnewline
48 & 558 & 547.804228463212 & 10.1957715367879 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110661&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]557[/C][C]582.052496527966[/C][C]-25.0524965279658[/C][/ROW]
[ROW][C]14[/C][C]561[/C][C]561.593877817214[/C][C]-0.59387781721432[/C][/ROW]
[ROW][C]15[/C][C]549[/C][C]545.131939567328[/C][C]3.86806043267177[/C][/ROW]
[ROW][C]16[/C][C]532[/C][C]528.704091295119[/C][C]3.29590870488096[/C][/ROW]
[ROW][C]17[/C][C]526[/C][C]523.343217568612[/C][C]2.65678243138757[/C][/ROW]
[ROW][C]18[/C][C]511[/C][C]508.065790468832[/C][C]2.93420953116845[/C][/ROW]
[ROW][C]19[/C][C]499[/C][C]515.704882590008[/C][C]-16.7048825900082[/C][/ROW]
[ROW][C]20[/C][C]555[/C][C]535.010017014547[/C][C]19.9899829854526[/C][/ROW]
[ROW][C]21[/C][C]565[/C][C]552.934515429898[/C][C]12.0654845701021[/C][/ROW]
[ROW][C]22[/C][C]542[/C][C]556.158169828962[/C][C]-14.1581698289621[/C][/ROW]
[ROW][C]23[/C][C]527[/C][C]512.48839064945[/C][C]14.5116093505502[/C][/ROW]
[ROW][C]24[/C][C]510[/C][C]504.568207335858[/C][C]5.43179266414199[/C][/ROW]
[ROW][C]25[/C][C]514[/C][C]498.94407769568[/C][C]15.0559223043196[/C][/ROW]
[ROW][C]26[/C][C]517[/C][C]523.126709865252[/C][C]-6.12670986525234[/C][/ROW]
[ROW][C]27[/C][C]508[/C][C]510.2048028684[/C][C]-2.20480286839967[/C][/ROW]
[ROW][C]28[/C][C]493[/C][C]495.300399761747[/C][C]-2.30039976174669[/C][/ROW]
[ROW][C]29[/C][C]490[/C][C]490.085511028767[/C][C]-0.0855110287672005[/C][/ROW]
[ROW][C]30[/C][C]469[/C][C]477.622647624964[/C][C]-8.62264762496432[/C][/ROW]
[ROW][C]31[/C][C]478[/C][C]474.134726310683[/C][C]3.86527368931695[/C][/ROW]
[ROW][C]32[/C][C]528[/C][C]520.807555531323[/C][C]7.19244446867651[/C][/ROW]
[ROW][C]33[/C][C]534[/C][C]530.695609713923[/C][C]3.30439028607748[/C][/ROW]
[ROW][C]34[/C][C]518[/C][C]525.596810978296[/C][C]-7.59681097829628[/C][/ROW]
[ROW][C]35[/C][C]506[/C][C]496.538262261834[/C][C]9.46173773816565[/C][/ROW]
[ROW][C]36[/C][C]502[/C][C]486.518951675203[/C][C]15.4810483247966[/C][/ROW]
[ROW][C]37[/C][C]516[/C][C]495.446568160868[/C][C]20.5534318391322[/C][/ROW]
[ROW][C]38[/C][C]528[/C][C]526.496822834529[/C][C]1.50317716547136[/C][/ROW]
[ROW][C]39[/C][C]533[/C][C]527.296214421762[/C][C]5.7037855782379[/C][/ROW]
[ROW][C]40[/C][C]536[/C][C]526.50033096707[/C][C]9.49966903292977[/C][/ROW]
[ROW][C]41[/C][C]537[/C][C]541.542046882319[/C][C]-4.54204688231869[/C][/ROW]
[ROW][C]42[/C][C]524[/C][C]531.890508591238[/C][C]-7.89050859123802[/C][/ROW]
[ROW][C]43[/C][C]536[/C][C]541.466795338661[/C][C]-5.46679533866097[/C][/ROW]
[ROW][C]44[/C][C]587[/C][C]595.153791745806[/C][C]-8.1537917458055[/C][/ROW]
[ROW][C]45[/C][C]597[/C][C]598.106445768071[/C][C]-1.10644576807078[/C][/ROW]
[ROW][C]46[/C][C]581[/C][C]591.8267065732[/C][C]-10.8267065731999[/C][/ROW]
[ROW][C]47[/C][C]564[/C][C]565.016013354905[/C][C]-1.01601335490500[/C][/ROW]
[ROW][C]48[/C][C]558[/C][C]547.804228463212[/C][C]10.1957715367879[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110661&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110661&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13557582.052496527966-25.0524965279658
14561561.593877817214-0.59387781721432
15549545.1319395673283.86806043267177
16532528.7040912951193.29590870488096
17526523.3432175686122.65678243138757
18511508.0657904688322.93420953116845
19499515.704882590008-16.7048825900082
20555535.01001701454719.9899829854526
21565552.93451542989812.0654845701021
22542556.158169828962-14.1581698289621
23527512.4883906494514.5116093505502
24510504.5682073358585.43179266414199
25514498.9440776956815.0559223043196
26517523.126709865252-6.12670986525234
27508510.2048028684-2.20480286839967
28493495.300399761747-2.30039976174669
29490490.085511028767-0.0855110287672005
30469477.622647624964-8.62264762496432
31478474.1347263106833.86527368931695
32528520.8075555313237.19244446867651
33534530.6956097139233.30439028607748
34518525.596810978296-7.59681097829628
35506496.5382622618349.46173773816565
36502486.51895167520315.4810483247966
37516495.44656816086820.5534318391322
38528526.4968228345291.50317716547136
39533527.2962144217625.7037855782379
40536526.500330967079.49966903292977
41537541.542046882319-4.54204688231869
42524531.890508591238-7.89050859123802
43536541.466795338661-5.46679533866097
44587595.153791745806-8.1537917458055
45597598.106445768071-1.10644576807078
46581591.8267065732-10.8267065731999
47564565.016013354905-1.01601335490500
48558547.80422846321210.1957715367879






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
49554.103642111245534.106091829984574.101192392506
50563.383815128361534.71561078866592.052019468062
51561.106066787084524.087928956162598.124204618006
52552.441223075713507.314011723428597.568434427997
53552.54194866692498.474733792012606.609163541827
54542.030427598852479.79223351731604.268621680395
55556.528351509304483.029247911721630.027455106886
56614.705009288946522.995857682173706.414160895719
57625.646056012605521.214163332778730.077948692433
58618.125743458512503.66519861243732.586288304594
59602.5041392458479.616217809035725.392060682565
60588.552268264309458.453463761461718.651072767158

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
49 & 554.103642111245 & 534.106091829984 & 574.101192392506 \tabularnewline
50 & 563.383815128361 & 534.71561078866 & 592.052019468062 \tabularnewline
51 & 561.106066787084 & 524.087928956162 & 598.124204618006 \tabularnewline
52 & 552.441223075713 & 507.314011723428 & 597.568434427997 \tabularnewline
53 & 552.54194866692 & 498.474733792012 & 606.609163541827 \tabularnewline
54 & 542.030427598852 & 479.79223351731 & 604.268621680395 \tabularnewline
55 & 556.528351509304 & 483.029247911721 & 630.027455106886 \tabularnewline
56 & 614.705009288946 & 522.995857682173 & 706.414160895719 \tabularnewline
57 & 625.646056012605 & 521.214163332778 & 730.077948692433 \tabularnewline
58 & 618.125743458512 & 503.66519861243 & 732.586288304594 \tabularnewline
59 & 602.5041392458 & 479.616217809035 & 725.392060682565 \tabularnewline
60 & 588.552268264309 & 458.453463761461 & 718.651072767158 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110661&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]49[/C][C]554.103642111245[/C][C]534.106091829984[/C][C]574.101192392506[/C][/ROW]
[ROW][C]50[/C][C]563.383815128361[/C][C]534.71561078866[/C][C]592.052019468062[/C][/ROW]
[ROW][C]51[/C][C]561.106066787084[/C][C]524.087928956162[/C][C]598.124204618006[/C][/ROW]
[ROW][C]52[/C][C]552.441223075713[/C][C]507.314011723428[/C][C]597.568434427997[/C][/ROW]
[ROW][C]53[/C][C]552.54194866692[/C][C]498.474733792012[/C][C]606.609163541827[/C][/ROW]
[ROW][C]54[/C][C]542.030427598852[/C][C]479.79223351731[/C][C]604.268621680395[/C][/ROW]
[ROW][C]55[/C][C]556.528351509304[/C][C]483.029247911721[/C][C]630.027455106886[/C][/ROW]
[ROW][C]56[/C][C]614.705009288946[/C][C]522.995857682173[/C][C]706.414160895719[/C][/ROW]
[ROW][C]57[/C][C]625.646056012605[/C][C]521.214163332778[/C][C]730.077948692433[/C][/ROW]
[ROW][C]58[/C][C]618.125743458512[/C][C]503.66519861243[/C][C]732.586288304594[/C][/ROW]
[ROW][C]59[/C][C]602.5041392458[/C][C]479.616217809035[/C][C]725.392060682565[/C][/ROW]
[ROW][C]60[/C][C]588.552268264309[/C][C]458.453463761461[/C][C]718.651072767158[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110661&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110661&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
49554.103642111245534.106091829984574.101192392506
50563.383815128361534.71561078866592.052019468062
51561.106066787084524.087928956162598.124204618006
52552.441223075713507.314011723428597.568434427997
53552.54194866692498.474733792012606.609163541827
54542.030427598852479.79223351731604.268621680395
55556.528351509304483.029247911721630.027455106886
56614.705009288946522.995857682173706.414160895719
57625.646056012605521.214163332778730.077948692433
58618.125743458512503.66519861243732.586288304594
59602.5041392458479.616217809035725.392060682565
60588.552268264309458.453463761461718.651072767158


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')