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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 19:06:40 +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/t1292439889oez96yvva3y48b0.htm/, Retrieved Fri, 03 May 2024 11:30:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110664, Retrieved Fri, 03 May 2024 11:30:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163

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] [additive methode] [2010-12-15 19:06:40] [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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110664&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110664&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110664&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.907995640815674
beta0.174326898805076
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.907995640815674 \tabularnewline
beta & 0.174326898805076 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110664&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]0.907995640815674[/C][/ROW]
[ROW][C]beta[/C][C]0.174326898805076[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110664&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110664&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
alpha0.907995640815674
beta0.174326898805076
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13557582.066773504274-25.0667735042737
14561560.2947750858440.705224914155792
15549545.4936009062723.50639909372796
16532529.3325684624142.66743153758591
17526523.8319797092422.16802029075768
18511508.3044327892622.69556721073764
19499514.307572288637-15.3075722886368
20555541.04093361653613.9590663834637
21565555.5994955424629.40050445753764
22542556.173557430937-14.1735574309371
23527507.39063558656819.6093644134315
24510502.9697211772737.0302788227275
25514500.01694201200313.9830579879970
26517523.392995833222-6.39299583322224
27508508.600664042223-0.600664042222547
28493494.179424078068-1.17942407806777
29490490.077224430754-0.0772244307538017
30469477.141411514237-8.14141151423672
31478474.5147596815583.48524031844158
32528526.8457546229351.15424537706497
33534533.172520346480.827479653519504
34518526.250722148035-8.25072214803527
35506489.34872465008816.6512753499119
36502484.01115701811517.9888429818855
37516496.30961169872619.6903883012735
38528528.557832425678-0.557832425678157
39533526.0849817019226.91501829807805
40536526.1126012581569.88739874184398
41537541.590082786025-4.59008278602460
42524532.529989302095-8.52998930209537
43536539.274021469171-3.27402146917098
44587592.837072298615-5.83707229861511
45597599.262943859248-2.26294385924803
46581594.687898969429-13.6878989694292
47564560.2674992735853.73250072641531
48558546.4053531568211.5946468431795

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 557 & 582.066773504274 & -25.0667735042737 \tabularnewline
14 & 561 & 560.294775085844 & 0.705224914155792 \tabularnewline
15 & 549 & 545.493600906272 & 3.50639909372796 \tabularnewline
16 & 532 & 529.332568462414 & 2.66743153758591 \tabularnewline
17 & 526 & 523.831979709242 & 2.16802029075768 \tabularnewline
18 & 511 & 508.304432789262 & 2.69556721073764 \tabularnewline
19 & 499 & 514.307572288637 & -15.3075722886368 \tabularnewline
20 & 555 & 541.040933616536 & 13.9590663834637 \tabularnewline
21 & 565 & 555.599495542462 & 9.40050445753764 \tabularnewline
22 & 542 & 556.173557430937 & -14.1735574309371 \tabularnewline
23 & 527 & 507.390635586568 & 19.6093644134315 \tabularnewline
24 & 510 & 502.969721177273 & 7.0302788227275 \tabularnewline
25 & 514 & 500.016942012003 & 13.9830579879970 \tabularnewline
26 & 517 & 523.392995833222 & -6.39299583322224 \tabularnewline
27 & 508 & 508.600664042223 & -0.600664042222547 \tabularnewline
28 & 493 & 494.179424078068 & -1.17942407806777 \tabularnewline
29 & 490 & 490.077224430754 & -0.0772244307538017 \tabularnewline
30 & 469 & 477.141411514237 & -8.14141151423672 \tabularnewline
31 & 478 & 474.514759681558 & 3.48524031844158 \tabularnewline
32 & 528 & 526.845754622935 & 1.15424537706497 \tabularnewline
33 & 534 & 533.17252034648 & 0.827479653519504 \tabularnewline
34 & 518 & 526.250722148035 & -8.25072214803527 \tabularnewline
35 & 506 & 489.348724650088 & 16.6512753499119 \tabularnewline
36 & 502 & 484.011157018115 & 17.9888429818855 \tabularnewline
37 & 516 & 496.309611698726 & 19.6903883012735 \tabularnewline
38 & 528 & 528.557832425678 & -0.557832425678157 \tabularnewline
39 & 533 & 526.084981701922 & 6.91501829807805 \tabularnewline
40 & 536 & 526.112601258156 & 9.88739874184398 \tabularnewline
41 & 537 & 541.590082786025 & -4.59008278602460 \tabularnewline
42 & 524 & 532.529989302095 & -8.52998930209537 \tabularnewline
43 & 536 & 539.274021469171 & -3.27402146917098 \tabularnewline
44 & 587 & 592.837072298615 & -5.83707229861511 \tabularnewline
45 & 597 & 599.262943859248 & -2.26294385924803 \tabularnewline
46 & 581 & 594.687898969429 & -13.6878989694292 \tabularnewline
47 & 564 & 560.267499273585 & 3.73250072641531 \tabularnewline
48 & 558 & 546.40535315682 & 11.5946468431795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110664&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]582.066773504274[/C][C]-25.0667735042737[/C][/ROW]
[ROW][C]14[/C][C]561[/C][C]560.294775085844[/C][C]0.705224914155792[/C][/ROW]
[ROW][C]15[/C][C]549[/C][C]545.493600906272[/C][C]3.50639909372796[/C][/ROW]
[ROW][C]16[/C][C]532[/C][C]529.332568462414[/C][C]2.66743153758591[/C][/ROW]
[ROW][C]17[/C][C]526[/C][C]523.831979709242[/C][C]2.16802029075768[/C][/ROW]
[ROW][C]18[/C][C]511[/C][C]508.304432789262[/C][C]2.69556721073764[/C][/ROW]
[ROW][C]19[/C][C]499[/C][C]514.307572288637[/C][C]-15.3075722886368[/C][/ROW]
[ROW][C]20[/C][C]555[/C][C]541.040933616536[/C][C]13.9590663834637[/C][/ROW]
[ROW][C]21[/C][C]565[/C][C]555.599495542462[/C][C]9.40050445753764[/C][/ROW]
[ROW][C]22[/C][C]542[/C][C]556.173557430937[/C][C]-14.1735574309371[/C][/ROW]
[ROW][C]23[/C][C]527[/C][C]507.390635586568[/C][C]19.6093644134315[/C][/ROW]
[ROW][C]24[/C][C]510[/C][C]502.969721177273[/C][C]7.0302788227275[/C][/ROW]
[ROW][C]25[/C][C]514[/C][C]500.016942012003[/C][C]13.9830579879970[/C][/ROW]
[ROW][C]26[/C][C]517[/C][C]523.392995833222[/C][C]-6.39299583322224[/C][/ROW]
[ROW][C]27[/C][C]508[/C][C]508.600664042223[/C][C]-0.600664042222547[/C][/ROW]
[ROW][C]28[/C][C]493[/C][C]494.179424078068[/C][C]-1.17942407806777[/C][/ROW]
[ROW][C]29[/C][C]490[/C][C]490.077224430754[/C][C]-0.0772244307538017[/C][/ROW]
[ROW][C]30[/C][C]469[/C][C]477.141411514237[/C][C]-8.14141151423672[/C][/ROW]
[ROW][C]31[/C][C]478[/C][C]474.514759681558[/C][C]3.48524031844158[/C][/ROW]
[ROW][C]32[/C][C]528[/C][C]526.845754622935[/C][C]1.15424537706497[/C][/ROW]
[ROW][C]33[/C][C]534[/C][C]533.17252034648[/C][C]0.827479653519504[/C][/ROW]
[ROW][C]34[/C][C]518[/C][C]526.250722148035[/C][C]-8.25072214803527[/C][/ROW]
[ROW][C]35[/C][C]506[/C][C]489.348724650088[/C][C]16.6512753499119[/C][/ROW]
[ROW][C]36[/C][C]502[/C][C]484.011157018115[/C][C]17.9888429818855[/C][/ROW]
[ROW][C]37[/C][C]516[/C][C]496.309611698726[/C][C]19.6903883012735[/C][/ROW]
[ROW][C]38[/C][C]528[/C][C]528.557832425678[/C][C]-0.557832425678157[/C][/ROW]
[ROW][C]39[/C][C]533[/C][C]526.084981701922[/C][C]6.91501829807805[/C][/ROW]
[ROW][C]40[/C][C]536[/C][C]526.112601258156[/C][C]9.88739874184398[/C][/ROW]
[ROW][C]41[/C][C]537[/C][C]541.590082786025[/C][C]-4.59008278602460[/C][/ROW]
[ROW][C]42[/C][C]524[/C][C]532.529989302095[/C][C]-8.52998930209537[/C][/ROW]
[ROW][C]43[/C][C]536[/C][C]539.274021469171[/C][C]-3.27402146917098[/C][/ROW]
[ROW][C]44[/C][C]587[/C][C]592.837072298615[/C][C]-5.83707229861511[/C][/ROW]
[ROW][C]45[/C][C]597[/C][C]599.262943859248[/C][C]-2.26294385924803[/C][/ROW]
[ROW][C]46[/C][C]581[/C][C]594.687898969429[/C][C]-13.6878989694292[/C][/ROW]
[ROW][C]47[/C][C]564[/C][C]560.267499273585[/C][C]3.73250072641531[/C][/ROW]
[ROW][C]48[/C][C]558[/C][C]546.40535315682[/C][C]11.5946468431795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110664&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110664&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
13557582.066773504274-25.0667735042737
14561560.2947750858440.705224914155792
15549545.4936009062723.50639909372796
16532529.3325684624142.66743153758591
17526523.8319797092422.16802029075768
18511508.3044327892622.69556721073764
19499514.307572288637-15.3075722886368
20555541.04093361653613.9590663834637
21565555.5994955424629.40050445753764
22542556.173557430937-14.1735574309371
23527507.39063558656819.6093644134315
24510502.9697211772737.0302788227275
25514500.01694201200313.9830579879970
26517523.392995833222-6.39299583322224
27508508.600664042223-0.600664042222547
28493494.179424078068-1.17942407806777
29490490.077224430754-0.0772244307538017
30469477.141411514237-8.14141151423672
31478474.5147596815583.48524031844158
32528526.8457546229351.15424537706497
33534533.172520346480.827479653519504
34518526.250722148035-8.25072214803527
35506489.34872465008816.6512753499119
36502484.01115701811517.9888429818855
37516496.30961169872619.6903883012735
38528528.557832425678-0.557832425678157
39533526.0849817019226.91501829807805
40536526.1126012581569.88739874184398
41537541.590082786025-4.59008278602460
42524532.529989302095-8.52998930209537
43536539.274021469171-3.27402146917098
44587592.837072298615-5.83707229861511
45597599.262943859248-2.26294385924803
46581594.687898969429-13.6878989694292
47564560.2674992735853.73250072641531
48558546.4053531568211.5946468431795






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
49555.12488078002534.852106432984575.397655127056
50566.585062319765536.949615584372596.220509055158
51564.348226192678525.688641063513603.007811321843
52556.31791671955508.563425768233604.072407670868
53557.868040156977500.801080162402614.935000151552
54549.722136854898483.061821507585616.38245220221
55563.154033166462486.590561899827639.717504433098
56618.431406978829531.642381391265705.220432566393
57630.38742662323533.046265231125727.728588015336
58627.075452707047518.855953921443735.294951492652
59609.112462836496489.691341672756728.533584000236
60594.419868249887463.478167261278725.361569238497

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
49 & 555.12488078002 & 534.852106432984 & 575.397655127056 \tabularnewline
50 & 566.585062319765 & 536.949615584372 & 596.220509055158 \tabularnewline
51 & 564.348226192678 & 525.688641063513 & 603.007811321843 \tabularnewline
52 & 556.31791671955 & 508.563425768233 & 604.072407670868 \tabularnewline
53 & 557.868040156977 & 500.801080162402 & 614.935000151552 \tabularnewline
54 & 549.722136854898 & 483.061821507585 & 616.38245220221 \tabularnewline
55 & 563.154033166462 & 486.590561899827 & 639.717504433098 \tabularnewline
56 & 618.431406978829 & 531.642381391265 & 705.220432566393 \tabularnewline
57 & 630.38742662323 & 533.046265231125 & 727.728588015336 \tabularnewline
58 & 627.075452707047 & 518.855953921443 & 735.294951492652 \tabularnewline
59 & 609.112462836496 & 489.691341672756 & 728.533584000236 \tabularnewline
60 & 594.419868249887 & 463.478167261278 & 725.361569238497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110664&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]555.12488078002[/C][C]534.852106432984[/C][C]575.397655127056[/C][/ROW]
[ROW][C]50[/C][C]566.585062319765[/C][C]536.949615584372[/C][C]596.220509055158[/C][/ROW]
[ROW][C]51[/C][C]564.348226192678[/C][C]525.688641063513[/C][C]603.007811321843[/C][/ROW]
[ROW][C]52[/C][C]556.31791671955[/C][C]508.563425768233[/C][C]604.072407670868[/C][/ROW]
[ROW][C]53[/C][C]557.868040156977[/C][C]500.801080162402[/C][C]614.935000151552[/C][/ROW]
[ROW][C]54[/C][C]549.722136854898[/C][C]483.061821507585[/C][C]616.38245220221[/C][/ROW]
[ROW][C]55[/C][C]563.154033166462[/C][C]486.590561899827[/C][C]639.717504433098[/C][/ROW]
[ROW][C]56[/C][C]618.431406978829[/C][C]531.642381391265[/C][C]705.220432566393[/C][/ROW]
[ROW][C]57[/C][C]630.38742662323[/C][C]533.046265231125[/C][C]727.728588015336[/C][/ROW]
[ROW][C]58[/C][C]627.075452707047[/C][C]518.855953921443[/C][C]735.294951492652[/C][/ROW]
[ROW][C]59[/C][C]609.112462836496[/C][C]489.691341672756[/C][C]728.533584000236[/C][/ROW]
[ROW][C]60[/C][C]594.419868249887[/C][C]463.478167261278[/C][C]725.361569238497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110664&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110664&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
49555.12488078002534.852106432984575.397655127056
50566.585062319765536.949615584372596.220509055158
51564.348226192678525.688641063513603.007811321843
52556.31791671955508.563425768233604.072407670868
53557.868040156977500.801080162402614.935000151552
54549.722136854898483.061821507585616.38245220221
55563.154033166462486.590561899827639.717504433098
56618.431406978829531.642381391265705.220432566393
57630.38742662323533.046265231125727.728588015336
58627.075452707047518.855953921443735.294951492652
59609.112462836496489.691341672756728.533584000236
60594.419868249887463.478167261278725.361569238497


Figures (Output of Computation)

Input Parameters & R Code

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