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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 09:39:07 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t1243957174kxe9zsnjodthlfs.htm/, Retrieved Fri, 10 May 2024 21:18:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41284, Retrieved Fri, 10 May 2024 21:18:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [] [2009-06-01 15:27:11] [5c738c8b19699587b9bfe8605ebf60ee]
- RMPD    [Exponential Smoothing] [] [2009-06-02 15:39:07] [738a25b0d97c8f3fa6714f905e8e3fd3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98.8
100.5
110.4
96.4
101.9
106.2
81.0
94.7
101.0
109.4
102.3
90.7
96.2
96.1
106.0
103.1
102.0
104.7
86.0
92.1
106.9
112.6
101.7
92.0
97.4
97.0
105.4
102.7
98.1
104.5
87.4
89.9
109.8
111.7
98.6
96.9
95.1
97.0
112.7
102.9
97.4
111.4
87.4
96.8
114.1
110.3
103.9
101.6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41284&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41284&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41284&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.096080656622426
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.096080656622426 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41284&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]0.096080656622426[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41284&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41284&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
alpha0.096080656622426
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1396.296.17096688034190.0290331196581519
1496.196.06097959501560.0390204049844129
15106105.9144518946210.0855481053786491
16103.1102.7307279395650.369272060434525
17102101.6450977017440.354902298255823
18104.7104.4372534744040.262746525596071
198681.41222152658164.58777847341835
2092.195.9319081548858-3.83190815488577
21106.9102.3176257633874.58237423661264
22112.6111.1492931490711.45070685092934
23101.7103.992567876014-2.29256787601446
249292.317852975942-0.317852975942031
2597.497.7549469119016-0.354946911901592
269797.6170942734074-0.617094273407403
27105.4107.449583932283-2.0495839322829
28102.7104.317178660228-1.61717866022752
2998.1103.027699826824-4.92769982682388
30104.5105.228998333120-0.72899833311989
3187.486.01815892643281.38184107356720
3289.992.6190993757672-2.71909937576724
33109.8106.7175689967783.08243100322152
34111.7112.574346124757-0.874346124757366
3598.6101.810609801854-3.21060980185437
3696.991.83267182657175.06732817342831
3795.197.7536475771576-2.65364757715763
389797.1579741984867-0.157974198486713
39112.7105.7397213037836.96027869621678
40102.9103.863849038741-0.963849038741245
4197.499.6446984252135-2.24469842521354
42111.4105.8990689651235.50093103487747
4387.489.1948338332921-1.79483383329207
4496.891.78363787350665.01636212649342
45114.1111.8694512456932.23054875430692
46110.3114.067771584417-3.76777158441718
47103.9100.9142391145042.98576088549640
48101.699.01424076267542.58575923732464

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 96.2 & 96.1709668803419 & 0.0290331196581519 \tabularnewline
14 & 96.1 & 96.0609795950156 & 0.0390204049844129 \tabularnewline
15 & 106 & 105.914451894621 & 0.0855481053786491 \tabularnewline
16 & 103.1 & 102.730727939565 & 0.369272060434525 \tabularnewline
17 & 102 & 101.645097701744 & 0.354902298255823 \tabularnewline
18 & 104.7 & 104.437253474404 & 0.262746525596071 \tabularnewline
19 & 86 & 81.4122215265816 & 4.58777847341835 \tabularnewline
20 & 92.1 & 95.9319081548858 & -3.83190815488577 \tabularnewline
21 & 106.9 & 102.317625763387 & 4.58237423661264 \tabularnewline
22 & 112.6 & 111.149293149071 & 1.45070685092934 \tabularnewline
23 & 101.7 & 103.992567876014 & -2.29256787601446 \tabularnewline
24 & 92 & 92.317852975942 & -0.317852975942031 \tabularnewline
25 & 97.4 & 97.7549469119016 & -0.354946911901592 \tabularnewline
26 & 97 & 97.6170942734074 & -0.617094273407403 \tabularnewline
27 & 105.4 & 107.449583932283 & -2.0495839322829 \tabularnewline
28 & 102.7 & 104.317178660228 & -1.61717866022752 \tabularnewline
29 & 98.1 & 103.027699826824 & -4.92769982682388 \tabularnewline
30 & 104.5 & 105.228998333120 & -0.72899833311989 \tabularnewline
31 & 87.4 & 86.0181589264328 & 1.38184107356720 \tabularnewline
32 & 89.9 & 92.6190993757672 & -2.71909937576724 \tabularnewline
33 & 109.8 & 106.717568996778 & 3.08243100322152 \tabularnewline
34 & 111.7 & 112.574346124757 & -0.874346124757366 \tabularnewline
35 & 98.6 & 101.810609801854 & -3.21060980185437 \tabularnewline
36 & 96.9 & 91.8326718265717 & 5.06732817342831 \tabularnewline
37 & 95.1 & 97.7536475771576 & -2.65364757715763 \tabularnewline
38 & 97 & 97.1579741984867 & -0.157974198486713 \tabularnewline
39 & 112.7 & 105.739721303783 & 6.96027869621678 \tabularnewline
40 & 102.9 & 103.863849038741 & -0.963849038741245 \tabularnewline
41 & 97.4 & 99.6446984252135 & -2.24469842521354 \tabularnewline
42 & 111.4 & 105.899068965123 & 5.50093103487747 \tabularnewline
43 & 87.4 & 89.1948338332921 & -1.79483383329207 \tabularnewline
44 & 96.8 & 91.7836378735066 & 5.01636212649342 \tabularnewline
45 & 114.1 & 111.869451245693 & 2.23054875430692 \tabularnewline
46 & 110.3 & 114.067771584417 & -3.76777158441718 \tabularnewline
47 & 103.9 & 100.914239114504 & 2.98576088549640 \tabularnewline
48 & 101.6 & 99.0142407626754 & 2.58575923732464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41284&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]96.2[/C][C]96.1709668803419[/C][C]0.0290331196581519[/C][/ROW]
[ROW][C]14[/C][C]96.1[/C][C]96.0609795950156[/C][C]0.0390204049844129[/C][/ROW]
[ROW][C]15[/C][C]106[/C][C]105.914451894621[/C][C]0.0855481053786491[/C][/ROW]
[ROW][C]16[/C][C]103.1[/C][C]102.730727939565[/C][C]0.369272060434525[/C][/ROW]
[ROW][C]17[/C][C]102[/C][C]101.645097701744[/C][C]0.354902298255823[/C][/ROW]
[ROW][C]18[/C][C]104.7[/C][C]104.437253474404[/C][C]0.262746525596071[/C][/ROW]
[ROW][C]19[/C][C]86[/C][C]81.4122215265816[/C][C]4.58777847341835[/C][/ROW]
[ROW][C]20[/C][C]92.1[/C][C]95.9319081548858[/C][C]-3.83190815488577[/C][/ROW]
[ROW][C]21[/C][C]106.9[/C][C]102.317625763387[/C][C]4.58237423661264[/C][/ROW]
[ROW][C]22[/C][C]112.6[/C][C]111.149293149071[/C][C]1.45070685092934[/C][/ROW]
[ROW][C]23[/C][C]101.7[/C][C]103.992567876014[/C][C]-2.29256787601446[/C][/ROW]
[ROW][C]24[/C][C]92[/C][C]92.317852975942[/C][C]-0.317852975942031[/C][/ROW]
[ROW][C]25[/C][C]97.4[/C][C]97.7549469119016[/C][C]-0.354946911901592[/C][/ROW]
[ROW][C]26[/C][C]97[/C][C]97.6170942734074[/C][C]-0.617094273407403[/C][/ROW]
[ROW][C]27[/C][C]105.4[/C][C]107.449583932283[/C][C]-2.0495839322829[/C][/ROW]
[ROW][C]28[/C][C]102.7[/C][C]104.317178660228[/C][C]-1.61717866022752[/C][/ROW]
[ROW][C]29[/C][C]98.1[/C][C]103.027699826824[/C][C]-4.92769982682388[/C][/ROW]
[ROW][C]30[/C][C]104.5[/C][C]105.228998333120[/C][C]-0.72899833311989[/C][/ROW]
[ROW][C]31[/C][C]87.4[/C][C]86.0181589264328[/C][C]1.38184107356720[/C][/ROW]
[ROW][C]32[/C][C]89.9[/C][C]92.6190993757672[/C][C]-2.71909937576724[/C][/ROW]
[ROW][C]33[/C][C]109.8[/C][C]106.717568996778[/C][C]3.08243100322152[/C][/ROW]
[ROW][C]34[/C][C]111.7[/C][C]112.574346124757[/C][C]-0.874346124757366[/C][/ROW]
[ROW][C]35[/C][C]98.6[/C][C]101.810609801854[/C][C]-3.21060980185437[/C][/ROW]
[ROW][C]36[/C][C]96.9[/C][C]91.8326718265717[/C][C]5.06732817342831[/C][/ROW]
[ROW][C]37[/C][C]95.1[/C][C]97.7536475771576[/C][C]-2.65364757715763[/C][/ROW]
[ROW][C]38[/C][C]97[/C][C]97.1579741984867[/C][C]-0.157974198486713[/C][/ROW]
[ROW][C]39[/C][C]112.7[/C][C]105.739721303783[/C][C]6.96027869621678[/C][/ROW]
[ROW][C]40[/C][C]102.9[/C][C]103.863849038741[/C][C]-0.963849038741245[/C][/ROW]
[ROW][C]41[/C][C]97.4[/C][C]99.6446984252135[/C][C]-2.24469842521354[/C][/ROW]
[ROW][C]42[/C][C]111.4[/C][C]105.899068965123[/C][C]5.50093103487747[/C][/ROW]
[ROW][C]43[/C][C]87.4[/C][C]89.1948338332921[/C][C]-1.79483383329207[/C][/ROW]
[ROW][C]44[/C][C]96.8[/C][C]91.7836378735066[/C][C]5.01636212649342[/C][/ROW]
[ROW][C]45[/C][C]114.1[/C][C]111.869451245693[/C][C]2.23054875430692[/C][/ROW]
[ROW][C]46[/C][C]110.3[/C][C]114.067771584417[/C][C]-3.76777158441718[/C][/ROW]
[ROW][C]47[/C][C]103.9[/C][C]100.914239114504[/C][C]2.98576088549640[/C][/ROW]
[ROW][C]48[/C][C]101.6[/C][C]99.0142407626754[/C][C]2.58575923732464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41284&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41284&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
1396.296.17096688034190.0290331196581519
1496.196.06097959501560.0390204049844129
15106105.9144518946210.0855481053786491
16103.1102.7307279395650.369272060434525
17102101.6450977017440.354902298255823
18104.7104.4372534744040.262746525596071
198681.41222152658164.58777847341835
2092.195.9319081548858-3.83190815488577
21106.9102.3176257633874.58237423661264
22112.6111.1492931490711.45070685092934
23101.7103.992567876014-2.29256787601446
249292.317852975942-0.317852975942031
2597.497.7549469119016-0.354946911901592
269797.6170942734074-0.617094273407403
27105.4107.449583932283-2.0495839322829
28102.7104.317178660228-1.61717866022752
2998.1103.027699826824-4.92769982682388
30104.5105.228998333120-0.72899833311989
3187.486.01815892643281.38184107356720
3289.992.6190993757672-2.71909937576724
33109.8106.7175689967783.08243100322152
34111.7112.574346124757-0.874346124757366
3598.6101.810609801854-3.21060980185437
3696.991.83267182657175.06732817342831
3795.197.7536475771576-2.65364757715763
389797.1579741984867-0.157974198486713
39112.7105.7397213037836.96027869621678
40102.9103.863849038741-0.963849038741245
4197.499.6446984252135-2.24469842521354
42111.4105.8990689651235.50093103487747
4387.489.1948338332921-1.79483383329207
4496.891.78363787350665.01636212649342
45114.1111.8694512456932.23054875430692
46110.3114.067771584417-3.76777158441718
47103.9100.9142391145042.98576088549640
48101.699.01424076267542.58575923732464






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
4997.717646409722891.9462690226163103.489023796829
5099.632824674442893.8348692713593105.430780077526
51114.664076527035108.839664387781120.488488666289
52104.95668377556299.105934534685110.807433016440
5399.672355874176293.7953875578274105.549324190525
54113.143822808311107.240751869968119.046893746654
5589.316271621541483.387212976625695.2453302664572
5698.23429625457292.27936331401104.189229195134
57115.319983665630109.339288368398121.300678962862
58111.881993633464105.875646478156117.888340788772
59105.19511976706899.163229842524111.227009691612
60102.64667832167896.5893533367072108.704003306649

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
49 & 97.7176464097228 & 91.9462690226163 & 103.489023796829 \tabularnewline
50 & 99.6328246744428 & 93.8348692713593 & 105.430780077526 \tabularnewline
51 & 114.664076527035 & 108.839664387781 & 120.488488666289 \tabularnewline
52 & 104.956683775562 & 99.105934534685 & 110.807433016440 \tabularnewline
53 & 99.6723558741762 & 93.7953875578274 & 105.549324190525 \tabularnewline
54 & 113.143822808311 & 107.240751869968 & 119.046893746654 \tabularnewline
55 & 89.3162716215414 & 83.3872129766256 & 95.2453302664572 \tabularnewline
56 & 98.234296254572 & 92.27936331401 & 104.189229195134 \tabularnewline
57 & 115.319983665630 & 109.339288368398 & 121.300678962862 \tabularnewline
58 & 111.881993633464 & 105.875646478156 & 117.888340788772 \tabularnewline
59 & 105.195119767068 & 99.163229842524 & 111.227009691612 \tabularnewline
60 & 102.646678321678 & 96.5893533367072 & 108.704003306649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41284&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]97.7176464097228[/C][C]91.9462690226163[/C][C]103.489023796829[/C][/ROW]
[ROW][C]50[/C][C]99.6328246744428[/C][C]93.8348692713593[/C][C]105.430780077526[/C][/ROW]
[ROW][C]51[/C][C]114.664076527035[/C][C]108.839664387781[/C][C]120.488488666289[/C][/ROW]
[ROW][C]52[/C][C]104.956683775562[/C][C]99.105934534685[/C][C]110.807433016440[/C][/ROW]
[ROW][C]53[/C][C]99.6723558741762[/C][C]93.7953875578274[/C][C]105.549324190525[/C][/ROW]
[ROW][C]54[/C][C]113.143822808311[/C][C]107.240751869968[/C][C]119.046893746654[/C][/ROW]
[ROW][C]55[/C][C]89.3162716215414[/C][C]83.3872129766256[/C][C]95.2453302664572[/C][/ROW]
[ROW][C]56[/C][C]98.234296254572[/C][C]92.27936331401[/C][C]104.189229195134[/C][/ROW]
[ROW][C]57[/C][C]115.319983665630[/C][C]109.339288368398[/C][C]121.300678962862[/C][/ROW]
[ROW][C]58[/C][C]111.881993633464[/C][C]105.875646478156[/C][C]117.888340788772[/C][/ROW]
[ROW][C]59[/C][C]105.195119767068[/C][C]99.163229842524[/C][C]111.227009691612[/C][/ROW]
[ROW][C]60[/C][C]102.646678321678[/C][C]96.5893533367072[/C][C]108.704003306649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41284&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41284&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
4997.717646409722891.9462690226163103.489023796829
5099.632824674442893.8348692713593105.430780077526
51114.664076527035108.839664387781120.488488666289
52104.95668377556299.105934534685110.807433016440
5399.672355874176293.7953875578274105.549324190525
54113.143822808311107.240751869968119.046893746654
5589.316271621541483.387212976625695.2453302664572
5698.23429625457292.27936331401104.189229195134
57115.319983665630109.339288368398121.300678962862
58111.881993633464105.875646478156117.888340788772
59105.19511976706899.163229842524111.227009691612
60102.64667832167896.5893533367072108.704003306649


Figures (Output of Computation)

Input Parameters & R Code

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):
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')