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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 computationFri, 16 Dec 2016 21:02:42 +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/Dec/16/t1481918578u10858kbtp6o950.htm/, Retrieved Thu, 02 May 2024 23:59:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300521, Retrieved Thu, 02 May 2024 23:59:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-16 20:02:42] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataseries X:
4210
4220
3850
4000
4060
3940
4210
3910
3960
4030
3870
3730
3880
3900
3780
3900
3870
3980
4200
4340
4280
4330
4410
4260
4120
4330
4540
4520
4070
4290
4380
4520
4450
4180
4080
3820
3700
3820
3670
3610
3700




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300521&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300521&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300521&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.842770100942162
beta0.000418629062036998
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.842770100942162 \tabularnewline
beta & 0.000418629062036998 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300521&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]0.842770100942162[/C][/ROW]
[ROW][C]beta[/C][C]0.000418629062036998[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300521&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300521&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
alpha0.842770100942162
beta0.000418629062036998
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
338504230-380
440003919.6132945803780.3867054196321
540603997.2551004370162.7448995629943
639404060.05105669714-120.051056697136
742103968.74969146806241.250308531941
839104182.0274293362-272.027429336204
939603962.63406278109-2.63406278108869
1040303970.2764416322159.7235583677943
1138704030.49303010606-160.493030106056
1237303905.06103884857-175.061038848568
1338803767.28980244768112.710197552322
1439003872.083325062427.9166749375959
1537803905.42525129172-125.425251291716
1639003809.4909358348990.5090641651063
1738703895.57153753955-25.5715375395521
1839803883.8138569836896.1861430163226
1942003974.70384440658225.296155593423
2043404174.4833764606165.516623539403
2142804323.94090184951-43.940901849508
2243304296.8583847191133.1416152808888
2344104334.7504009604675.2495990395355
2442604408.15631558938-148.15631558938
2541204293.23013425359-173.230134253592
2643304157.1113712441172.888628755896
2745404312.75214957526227.247850424736
2845204514.285429511955.71457048805314
2940704529.11910090085-459.119100900853
3042904152.04287121415137.957128785846
3143804278.21330827722101.786691722783
3245204373.93629361044146.063706389557
3344504507.02615551623-57.0261555162333
3441804468.93783471623-288.937834716234
3540804235.29934503116-155.299345031161
3638204114.23258792758-294.232587927581
3737003875.97324005635-175.973240056348
3838203737.3172499510282.6827500489762
3936703816.67796587644-146.67796587644
4036103702.6885789211-92.6885789210996
4137003634.1671317824965.8328682175061

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3850 & 4230 & -380 \tabularnewline
4 & 4000 & 3919.61329458037 & 80.3867054196321 \tabularnewline
5 & 4060 & 3997.25510043701 & 62.7448995629943 \tabularnewline
6 & 3940 & 4060.05105669714 & -120.051056697136 \tabularnewline
7 & 4210 & 3968.74969146806 & 241.250308531941 \tabularnewline
8 & 3910 & 4182.0274293362 & -272.027429336204 \tabularnewline
9 & 3960 & 3962.63406278109 & -2.63406278108869 \tabularnewline
10 & 4030 & 3970.27644163221 & 59.7235583677943 \tabularnewline
11 & 3870 & 4030.49303010606 & -160.493030106056 \tabularnewline
12 & 3730 & 3905.06103884857 & -175.061038848568 \tabularnewline
13 & 3880 & 3767.28980244768 & 112.710197552322 \tabularnewline
14 & 3900 & 3872.0833250624 & 27.9166749375959 \tabularnewline
15 & 3780 & 3905.42525129172 & -125.425251291716 \tabularnewline
16 & 3900 & 3809.49093583489 & 90.5090641651063 \tabularnewline
17 & 3870 & 3895.57153753955 & -25.5715375395521 \tabularnewline
18 & 3980 & 3883.81385698368 & 96.1861430163226 \tabularnewline
19 & 4200 & 3974.70384440658 & 225.296155593423 \tabularnewline
20 & 4340 & 4174.4833764606 & 165.516623539403 \tabularnewline
21 & 4280 & 4323.94090184951 & -43.940901849508 \tabularnewline
22 & 4330 & 4296.85838471911 & 33.1416152808888 \tabularnewline
23 & 4410 & 4334.75040096046 & 75.2495990395355 \tabularnewline
24 & 4260 & 4408.15631558938 & -148.15631558938 \tabularnewline
25 & 4120 & 4293.23013425359 & -173.230134253592 \tabularnewline
26 & 4330 & 4157.1113712441 & 172.888628755896 \tabularnewline
27 & 4540 & 4312.75214957526 & 227.247850424736 \tabularnewline
28 & 4520 & 4514.28542951195 & 5.71457048805314 \tabularnewline
29 & 4070 & 4529.11910090085 & -459.119100900853 \tabularnewline
30 & 4290 & 4152.04287121415 & 137.957128785846 \tabularnewline
31 & 4380 & 4278.21330827722 & 101.786691722783 \tabularnewline
32 & 4520 & 4373.93629361044 & 146.063706389557 \tabularnewline
33 & 4450 & 4507.02615551623 & -57.0261555162333 \tabularnewline
34 & 4180 & 4468.93783471623 & -288.937834716234 \tabularnewline
35 & 4080 & 4235.29934503116 & -155.299345031161 \tabularnewline
36 & 3820 & 4114.23258792758 & -294.232587927581 \tabularnewline
37 & 3700 & 3875.97324005635 & -175.973240056348 \tabularnewline
38 & 3820 & 3737.31724995102 & 82.6827500489762 \tabularnewline
39 & 3670 & 3816.67796587644 & -146.67796587644 \tabularnewline
40 & 3610 & 3702.6885789211 & -92.6885789210996 \tabularnewline
41 & 3700 & 3634.16713178249 & 65.8328682175061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300521&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]3[/C][C]3850[/C][C]4230[/C][C]-380[/C][/ROW]
[ROW][C]4[/C][C]4000[/C][C]3919.61329458037[/C][C]80.3867054196321[/C][/ROW]
[ROW][C]5[/C][C]4060[/C][C]3997.25510043701[/C][C]62.7448995629943[/C][/ROW]
[ROW][C]6[/C][C]3940[/C][C]4060.05105669714[/C][C]-120.051056697136[/C][/ROW]
[ROW][C]7[/C][C]4210[/C][C]3968.74969146806[/C][C]241.250308531941[/C][/ROW]
[ROW][C]8[/C][C]3910[/C][C]4182.0274293362[/C][C]-272.027429336204[/C][/ROW]
[ROW][C]9[/C][C]3960[/C][C]3962.63406278109[/C][C]-2.63406278108869[/C][/ROW]
[ROW][C]10[/C][C]4030[/C][C]3970.27644163221[/C][C]59.7235583677943[/C][/ROW]
[ROW][C]11[/C][C]3870[/C][C]4030.49303010606[/C][C]-160.493030106056[/C][/ROW]
[ROW][C]12[/C][C]3730[/C][C]3905.06103884857[/C][C]-175.061038848568[/C][/ROW]
[ROW][C]13[/C][C]3880[/C][C]3767.28980244768[/C][C]112.710197552322[/C][/ROW]
[ROW][C]14[/C][C]3900[/C][C]3872.0833250624[/C][C]27.9166749375959[/C][/ROW]
[ROW][C]15[/C][C]3780[/C][C]3905.42525129172[/C][C]-125.425251291716[/C][/ROW]
[ROW][C]16[/C][C]3900[/C][C]3809.49093583489[/C][C]90.5090641651063[/C][/ROW]
[ROW][C]17[/C][C]3870[/C][C]3895.57153753955[/C][C]-25.5715375395521[/C][/ROW]
[ROW][C]18[/C][C]3980[/C][C]3883.81385698368[/C][C]96.1861430163226[/C][/ROW]
[ROW][C]19[/C][C]4200[/C][C]3974.70384440658[/C][C]225.296155593423[/C][/ROW]
[ROW][C]20[/C][C]4340[/C][C]4174.4833764606[/C][C]165.516623539403[/C][/ROW]
[ROW][C]21[/C][C]4280[/C][C]4323.94090184951[/C][C]-43.940901849508[/C][/ROW]
[ROW][C]22[/C][C]4330[/C][C]4296.85838471911[/C][C]33.1416152808888[/C][/ROW]
[ROW][C]23[/C][C]4410[/C][C]4334.75040096046[/C][C]75.2495990395355[/C][/ROW]
[ROW][C]24[/C][C]4260[/C][C]4408.15631558938[/C][C]-148.15631558938[/C][/ROW]
[ROW][C]25[/C][C]4120[/C][C]4293.23013425359[/C][C]-173.230134253592[/C][/ROW]
[ROW][C]26[/C][C]4330[/C][C]4157.1113712441[/C][C]172.888628755896[/C][/ROW]
[ROW][C]27[/C][C]4540[/C][C]4312.75214957526[/C][C]227.247850424736[/C][/ROW]
[ROW][C]28[/C][C]4520[/C][C]4514.28542951195[/C][C]5.71457048805314[/C][/ROW]
[ROW][C]29[/C][C]4070[/C][C]4529.11910090085[/C][C]-459.119100900853[/C][/ROW]
[ROW][C]30[/C][C]4290[/C][C]4152.04287121415[/C][C]137.957128785846[/C][/ROW]
[ROW][C]31[/C][C]4380[/C][C]4278.21330827722[/C][C]101.786691722783[/C][/ROW]
[ROW][C]32[/C][C]4520[/C][C]4373.93629361044[/C][C]146.063706389557[/C][/ROW]
[ROW][C]33[/C][C]4450[/C][C]4507.02615551623[/C][C]-57.0261555162333[/C][/ROW]
[ROW][C]34[/C][C]4180[/C][C]4468.93783471623[/C][C]-288.937834716234[/C][/ROW]
[ROW][C]35[/C][C]4080[/C][C]4235.29934503116[/C][C]-155.299345031161[/C][/ROW]
[ROW][C]36[/C][C]3820[/C][C]4114.23258792758[/C][C]-294.232587927581[/C][/ROW]
[ROW][C]37[/C][C]3700[/C][C]3875.97324005635[/C][C]-175.973240056348[/C][/ROW]
[ROW][C]38[/C][C]3820[/C][C]3737.31724995102[/C][C]82.6827500489762[/C][/ROW]
[ROW][C]39[/C][C]3670[/C][C]3816.67796587644[/C][C]-146.67796587644[/C][/ROW]
[ROW][C]40[/C][C]3610[/C][C]3702.6885789211[/C][C]-92.6885789210996[/C][/ROW]
[ROW][C]41[/C][C]3700[/C][C]3634.16713178249[/C][C]65.8328682175061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300521&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300521&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
338504230-380
440003919.6132945803780.3867054196321
540603997.2551004370162.7448995629943
639404060.05105669714-120.051056697136
742103968.74969146806241.250308531941
839104182.0274293362-272.027429336204
939603962.63406278109-2.63406278108869
1040303970.2764416322159.7235583677943
1138704030.49303010606-160.493030106056
1237303905.06103884857-175.061038848568
1338803767.28980244768112.710197552322
1439003872.083325062427.9166749375959
1537803905.42525129172-125.425251291716
1639003809.4909358348990.5090641651063
1738703895.57153753955-25.5715375395521
1839803883.8138569836896.1861430163226
1942003974.70384440658225.296155593423
2043404174.4833764606165.516623539403
2142804323.94090184951-43.940901849508
2243304296.8583847191133.1416152808888
2344104334.7504009604675.2495990395355
2442604408.15631558938-148.15631558938
2541204293.23013425359-173.230134253592
2643304157.1113712441172.888628755896
2745404312.75214957526227.247850424736
2845204514.285429511955.71457048805314
2940704529.11910090085-459.119100900853
3042904152.04287121415137.957128785846
3143804278.21330827722101.786691722783
3245204373.93629361044146.063706389557
3344504507.02615551623-57.0261555162333
3441804468.93783471623-288.937834716234
3540804235.29934503116-155.299345031161
3638204114.23258792758-294.232587927581
3737003875.97324005635-175.973240056348
3838203737.3172499510282.6827500489762
3936703816.67796587644-146.67796587644
4036103702.6885789211-92.6885789210996
4137003634.1671317824965.8328682175061







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
423699.26604701673361.277587415094037.25450661831
433708.882989257933266.795086737374150.97089177849
443718.499931499163192.462666629244244.53719636908
453728.116873740393129.738482842944326.49526463784
463737.733815981623074.811327316924400.65630464632
473747.350758222853025.586382319114469.11513412658
483756.967700464082980.765734368454533.1696665597
493766.58464270532939.479275803854593.69000960676
503776.201584946532901.110029666814651.29314022626
513785.818527187762865.201697500424706.43535687511
523795.435469428992831.405559446414759.46537941158
533805.052411670222799.448006711194810.65681662925

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
42 & 3699.2660470167 & 3361.27758741509 & 4037.25450661831 \tabularnewline
43 & 3708.88298925793 & 3266.79508673737 & 4150.97089177849 \tabularnewline
44 & 3718.49993149916 & 3192.46266662924 & 4244.53719636908 \tabularnewline
45 & 3728.11687374039 & 3129.73848284294 & 4326.49526463784 \tabularnewline
46 & 3737.73381598162 & 3074.81132731692 & 4400.65630464632 \tabularnewline
47 & 3747.35075822285 & 3025.58638231911 & 4469.11513412658 \tabularnewline
48 & 3756.96770046408 & 2980.76573436845 & 4533.1696665597 \tabularnewline
49 & 3766.5846427053 & 2939.47927580385 & 4593.69000960676 \tabularnewline
50 & 3776.20158494653 & 2901.11002966681 & 4651.29314022626 \tabularnewline
51 & 3785.81852718776 & 2865.20169750042 & 4706.43535687511 \tabularnewline
52 & 3795.43546942899 & 2831.40555944641 & 4759.46537941158 \tabularnewline
53 & 3805.05241167022 & 2799.44800671119 & 4810.65681662925 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300521&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]42[/C][C]3699.2660470167[/C][C]3361.27758741509[/C][C]4037.25450661831[/C][/ROW]
[ROW][C]43[/C][C]3708.88298925793[/C][C]3266.79508673737[/C][C]4150.97089177849[/C][/ROW]
[ROW][C]44[/C][C]3718.49993149916[/C][C]3192.46266662924[/C][C]4244.53719636908[/C][/ROW]
[ROW][C]45[/C][C]3728.11687374039[/C][C]3129.73848284294[/C][C]4326.49526463784[/C][/ROW]
[ROW][C]46[/C][C]3737.73381598162[/C][C]3074.81132731692[/C][C]4400.65630464632[/C][/ROW]
[ROW][C]47[/C][C]3747.35075822285[/C][C]3025.58638231911[/C][C]4469.11513412658[/C][/ROW]
[ROW][C]48[/C][C]3756.96770046408[/C][C]2980.76573436845[/C][C]4533.1696665597[/C][/ROW]
[ROW][C]49[/C][C]3766.5846427053[/C][C]2939.47927580385[/C][C]4593.69000960676[/C][/ROW]
[ROW][C]50[/C][C]3776.20158494653[/C][C]2901.11002966681[/C][C]4651.29314022626[/C][/ROW]
[ROW][C]51[/C][C]3785.81852718776[/C][C]2865.20169750042[/C][C]4706.43535687511[/C][/ROW]
[ROW][C]52[/C][C]3795.43546942899[/C][C]2831.40555944641[/C][C]4759.46537941158[/C][/ROW]
[ROW][C]53[/C][C]3805.05241167022[/C][C]2799.44800671119[/C][C]4810.65681662925[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300521&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300521&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
423699.26604701673361.277587415094037.25450661831
433708.882989257933266.795086737374150.97089177849
443718.499931499163192.462666629244244.53719636908
453728.116873740393129.738482842944326.49526463784
463737.733815981623074.811327316924400.65630464632
473747.350758222853025.586382319114469.11513412658
483756.967700464082980.765734368454533.1696665597
493766.58464270532939.479275803854593.69000960676
503776.201584946532901.110029666814651.29314022626
513785.818527187762865.201697500424706.43535687511
523795.435469428992831.405559446414759.46537941158
533805.052411670222799.448006711194810.65681662925



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')