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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 computationThu, 03 Dec 2009 06:33:46 -0700
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/Dec/03/t12598472619khg0oezoew9snf.htm/, Retrieved Fri, 19 Apr 2024 15:56:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62740, Retrieved Fri, 19 Apr 2024 15:56:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJSSHWWS9P10
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD    [Exponential Smoothing] [Exponential Smoot...] [2009-12-03 13:33:46] [c8fd62404619100d8e91184019148412] [Current]
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Dataseries X:
11.1
10.9
10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3
8.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62740&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62740&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0.428593928188172

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.428593928188172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62740&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.428593928188172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62740&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
alpha1
beta0
gamma0.428593928188172







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310.310.3771634615385-0.077163461538472
1410.210.2079399766900-0.00793997668997548
159.69.60377331002331-0.00377331002331083
169.29.187106643356640.0128933566433567
179.39.282939976689980.0170600233100231
189.49.399606643356640.000393356643355602
199.49.40793997668998-0.00793997668997726
209.29.34960664335664-0.149606643356645
2198.832939976689980.167060023310022
2298.803773310023310.196226689976690
2399.08293997668998-0.0829399766899783
249.810.0871066433566-0.287106643356640
25109.999606643356650.000393356643353826
269.89.90793997668997-0.107939976689973
279.39.203773310023310.0962266899766906
2898.887106643356640.112893356643356
2999.08293997668998-0.0829399766899783
309.19.099606643356640.000393356643357379
319.19.10793997668998-0.00793997668997548
329.19.049606643356640.0503933566433563
339.28.732939976689980.467060023310021
348.89.00377331002331-0.203773310023308
358.38.88293997668998-0.582939976689978
368.49.38710664335664-0.987106643356642
378.18.59960664335665-0.499606643356646
387.78.00793997668997-0.307939976689974
397.97.103773310023310.796226689976692
407.97.487106643356640.412893356643358
4187.982939976689980.0170600233100213
427.98.09960664335664-0.199606643356642
437.67.90793997668997-0.307939976689975
447.17.54960664335664-0.449606643356643
456.86.732939976689980.067060023310022
466.56.60377331002331-0.103773310023309
476.96.582939976689980.317060023310023
488.27.987106643356640.212893356643360
498.78.399606643356640.300393356643355
508.38.60793997668997-0.307939976689973
517.97.703773310023310.196226689976691
527.57.487106643356640.0128933566433576
537.87.582939976689980.217060023310022
548.37.899606643356640.400393356643360
558.48.307939976689980.0920600233100242
568.28.34960664335664-0.149606643356645
577.77.83293997668998-0.132939976689978
587.27.50377331002331-0.303773310023311
597.37.282939976689980.0170600233100222
608.18.38710664335664-0.287106643356639

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 10.3 & 10.3771634615385 & -0.077163461538472 \tabularnewline
14 & 10.2 & 10.2079399766900 & -0.00793997668997548 \tabularnewline
15 & 9.6 & 9.60377331002331 & -0.00377331002331083 \tabularnewline
16 & 9.2 & 9.18710664335664 & 0.0128933566433567 \tabularnewline
17 & 9.3 & 9.28293997668998 & 0.0170600233100231 \tabularnewline
18 & 9.4 & 9.39960664335664 & 0.000393356643355602 \tabularnewline
19 & 9.4 & 9.40793997668998 & -0.00793997668997726 \tabularnewline
20 & 9.2 & 9.34960664335664 & -0.149606643356645 \tabularnewline
21 & 9 & 8.83293997668998 & 0.167060023310022 \tabularnewline
22 & 9 & 8.80377331002331 & 0.196226689976690 \tabularnewline
23 & 9 & 9.08293997668998 & -0.0829399766899783 \tabularnewline
24 & 9.8 & 10.0871066433566 & -0.287106643356640 \tabularnewline
25 & 10 & 9.99960664335665 & 0.000393356643353826 \tabularnewline
26 & 9.8 & 9.90793997668997 & -0.107939976689973 \tabularnewline
27 & 9.3 & 9.20377331002331 & 0.0962266899766906 \tabularnewline
28 & 9 & 8.88710664335664 & 0.112893356643356 \tabularnewline
29 & 9 & 9.08293997668998 & -0.0829399766899783 \tabularnewline
30 & 9.1 & 9.09960664335664 & 0.000393356643357379 \tabularnewline
31 & 9.1 & 9.10793997668998 & -0.00793997668997548 \tabularnewline
32 & 9.1 & 9.04960664335664 & 0.0503933566433563 \tabularnewline
33 & 9.2 & 8.73293997668998 & 0.467060023310021 \tabularnewline
34 & 8.8 & 9.00377331002331 & -0.203773310023308 \tabularnewline
35 & 8.3 & 8.88293997668998 & -0.582939976689978 \tabularnewline
36 & 8.4 & 9.38710664335664 & -0.987106643356642 \tabularnewline
37 & 8.1 & 8.59960664335665 & -0.499606643356646 \tabularnewline
38 & 7.7 & 8.00793997668997 & -0.307939976689974 \tabularnewline
39 & 7.9 & 7.10377331002331 & 0.796226689976692 \tabularnewline
40 & 7.9 & 7.48710664335664 & 0.412893356643358 \tabularnewline
41 & 8 & 7.98293997668998 & 0.0170600233100213 \tabularnewline
42 & 7.9 & 8.09960664335664 & -0.199606643356642 \tabularnewline
43 & 7.6 & 7.90793997668997 & -0.307939976689975 \tabularnewline
44 & 7.1 & 7.54960664335664 & -0.449606643356643 \tabularnewline
45 & 6.8 & 6.73293997668998 & 0.067060023310022 \tabularnewline
46 & 6.5 & 6.60377331002331 & -0.103773310023309 \tabularnewline
47 & 6.9 & 6.58293997668998 & 0.317060023310023 \tabularnewline
48 & 8.2 & 7.98710664335664 & 0.212893356643360 \tabularnewline
49 & 8.7 & 8.39960664335664 & 0.300393356643355 \tabularnewline
50 & 8.3 & 8.60793997668997 & -0.307939976689973 \tabularnewline
51 & 7.9 & 7.70377331002331 & 0.196226689976691 \tabularnewline
52 & 7.5 & 7.48710664335664 & 0.0128933566433576 \tabularnewline
53 & 7.8 & 7.58293997668998 & 0.217060023310022 \tabularnewline
54 & 8.3 & 7.89960664335664 & 0.400393356643360 \tabularnewline
55 & 8.4 & 8.30793997668998 & 0.0920600233100242 \tabularnewline
56 & 8.2 & 8.34960664335664 & -0.149606643356645 \tabularnewline
57 & 7.7 & 7.83293997668998 & -0.132939976689978 \tabularnewline
58 & 7.2 & 7.50377331002331 & -0.303773310023311 \tabularnewline
59 & 7.3 & 7.28293997668998 & 0.0170600233100222 \tabularnewline
60 & 8.1 & 8.38710664335664 & -0.287106643356639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62740&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]10.3[/C][C]10.3771634615385[/C][C]-0.077163461538472[/C][/ROW]
[ROW][C]14[/C][C]10.2[/C][C]10.2079399766900[/C][C]-0.00793997668997548[/C][/ROW]
[ROW][C]15[/C][C]9.6[/C][C]9.60377331002331[/C][C]-0.00377331002331083[/C][/ROW]
[ROW][C]16[/C][C]9.2[/C][C]9.18710664335664[/C][C]0.0128933566433567[/C][/ROW]
[ROW][C]17[/C][C]9.3[/C][C]9.28293997668998[/C][C]0.0170600233100231[/C][/ROW]
[ROW][C]18[/C][C]9.4[/C][C]9.39960664335664[/C][C]0.000393356643355602[/C][/ROW]
[ROW][C]19[/C][C]9.4[/C][C]9.40793997668998[/C][C]-0.00793997668997726[/C][/ROW]
[ROW][C]20[/C][C]9.2[/C][C]9.34960664335664[/C][C]-0.149606643356645[/C][/ROW]
[ROW][C]21[/C][C]9[/C][C]8.83293997668998[/C][C]0.167060023310022[/C][/ROW]
[ROW][C]22[/C][C]9[/C][C]8.80377331002331[/C][C]0.196226689976690[/C][/ROW]
[ROW][C]23[/C][C]9[/C][C]9.08293997668998[/C][C]-0.0829399766899783[/C][/ROW]
[ROW][C]24[/C][C]9.8[/C][C]10.0871066433566[/C][C]-0.287106643356640[/C][/ROW]
[ROW][C]25[/C][C]10[/C][C]9.99960664335665[/C][C]0.000393356643353826[/C][/ROW]
[ROW][C]26[/C][C]9.8[/C][C]9.90793997668997[/C][C]-0.107939976689973[/C][/ROW]
[ROW][C]27[/C][C]9.3[/C][C]9.20377331002331[/C][C]0.0962266899766906[/C][/ROW]
[ROW][C]28[/C][C]9[/C][C]8.88710664335664[/C][C]0.112893356643356[/C][/ROW]
[ROW][C]29[/C][C]9[/C][C]9.08293997668998[/C][C]-0.0829399766899783[/C][/ROW]
[ROW][C]30[/C][C]9.1[/C][C]9.09960664335664[/C][C]0.000393356643357379[/C][/ROW]
[ROW][C]31[/C][C]9.1[/C][C]9.10793997668998[/C][C]-0.00793997668997548[/C][/ROW]
[ROW][C]32[/C][C]9.1[/C][C]9.04960664335664[/C][C]0.0503933566433563[/C][/ROW]
[ROW][C]33[/C][C]9.2[/C][C]8.73293997668998[/C][C]0.467060023310021[/C][/ROW]
[ROW][C]34[/C][C]8.8[/C][C]9.00377331002331[/C][C]-0.203773310023308[/C][/ROW]
[ROW][C]35[/C][C]8.3[/C][C]8.88293997668998[/C][C]-0.582939976689978[/C][/ROW]
[ROW][C]36[/C][C]8.4[/C][C]9.38710664335664[/C][C]-0.987106643356642[/C][/ROW]
[ROW][C]37[/C][C]8.1[/C][C]8.59960664335665[/C][C]-0.499606643356646[/C][/ROW]
[ROW][C]38[/C][C]7.7[/C][C]8.00793997668997[/C][C]-0.307939976689974[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.10377331002331[/C][C]0.796226689976692[/C][/ROW]
[ROW][C]40[/C][C]7.9[/C][C]7.48710664335664[/C][C]0.412893356643358[/C][/ROW]
[ROW][C]41[/C][C]8[/C][C]7.98293997668998[/C][C]0.0170600233100213[/C][/ROW]
[ROW][C]42[/C][C]7.9[/C][C]8.09960664335664[/C][C]-0.199606643356642[/C][/ROW]
[ROW][C]43[/C][C]7.6[/C][C]7.90793997668997[/C][C]-0.307939976689975[/C][/ROW]
[ROW][C]44[/C][C]7.1[/C][C]7.54960664335664[/C][C]-0.449606643356643[/C][/ROW]
[ROW][C]45[/C][C]6.8[/C][C]6.73293997668998[/C][C]0.067060023310022[/C][/ROW]
[ROW][C]46[/C][C]6.5[/C][C]6.60377331002331[/C][C]-0.103773310023309[/C][/ROW]
[ROW][C]47[/C][C]6.9[/C][C]6.58293997668998[/C][C]0.317060023310023[/C][/ROW]
[ROW][C]48[/C][C]8.2[/C][C]7.98710664335664[/C][C]0.212893356643360[/C][/ROW]
[ROW][C]49[/C][C]8.7[/C][C]8.39960664335664[/C][C]0.300393356643355[/C][/ROW]
[ROW][C]50[/C][C]8.3[/C][C]8.60793997668997[/C][C]-0.307939976689973[/C][/ROW]
[ROW][C]51[/C][C]7.9[/C][C]7.70377331002331[/C][C]0.196226689976691[/C][/ROW]
[ROW][C]52[/C][C]7.5[/C][C]7.48710664335664[/C][C]0.0128933566433576[/C][/ROW]
[ROW][C]53[/C][C]7.8[/C][C]7.58293997668998[/C][C]0.217060023310022[/C][/ROW]
[ROW][C]54[/C][C]8.3[/C][C]7.89960664335664[/C][C]0.400393356643360[/C][/ROW]
[ROW][C]55[/C][C]8.4[/C][C]8.30793997668998[/C][C]0.0920600233100242[/C][/ROW]
[ROW][C]56[/C][C]8.2[/C][C]8.34960664335664[/C][C]-0.149606643356645[/C][/ROW]
[ROW][C]57[/C][C]7.7[/C][C]7.83293997668998[/C][C]-0.132939976689978[/C][/ROW]
[ROW][C]58[/C][C]7.2[/C][C]7.50377331002331[/C][C]-0.303773310023311[/C][/ROW]
[ROW][C]59[/C][C]7.3[/C][C]7.28293997668998[/C][C]0.0170600233100222[/C][/ROW]
[ROW][C]60[/C][C]8.1[/C][C]8.38710664335664[/C][C]-0.287106643356639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62740&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
1310.310.3771634615385-0.077163461538472
1410.210.2079399766900-0.00793997668997548
159.69.60377331002331-0.00377331002331083
169.29.187106643356640.0128933566433567
179.39.282939976689980.0170600233100231
189.49.399606643356640.000393356643355602
199.49.40793997668998-0.00793997668997726
209.29.34960664335664-0.149606643356645
2198.832939976689980.167060023310022
2298.803773310023310.196226689976690
2399.08293997668998-0.0829399766899783
249.810.0871066433566-0.287106643356640
25109.999606643356650.000393356643353826
269.89.90793997668997-0.107939976689973
279.39.203773310023310.0962266899766906
2898.887106643356640.112893356643356
2999.08293997668998-0.0829399766899783
309.19.099606643356640.000393356643357379
319.19.10793997668998-0.00793997668997548
329.19.049606643356640.0503933566433563
339.28.732939976689980.467060023310021
348.89.00377331002331-0.203773310023308
358.38.88293997668998-0.582939976689978
368.49.38710664335664-0.987106643356642
378.18.59960664335665-0.499606643356646
387.78.00793997668997-0.307939976689974
397.97.103773310023310.796226689976692
407.97.487106643356640.412893356643358
4187.982939976689980.0170600233100213
427.98.09960664335664-0.199606643356642
437.67.90793997668997-0.307939976689975
447.17.54960664335664-0.449606643356643
456.86.732939976689980.067060023310022
466.56.60377331002331-0.103773310023309
476.96.582939976689980.317060023310023
488.27.987106643356640.212893356643360
498.78.399606643356640.300393356643355
508.38.60793997668997-0.307939976689973
517.97.703773310023310.196226689976691
527.57.487106643356640.0128933566433576
537.87.582939976689980.217060023310022
548.37.899606643356640.400393356643360
558.48.307939976689980.0920600233100242
568.28.34960664335664-0.149606643356645
577.77.83293997668998-0.132939976689978
587.27.50377331002331-0.303773310023311
597.37.282939976689980.0170600233100222
608.18.38710664335664-0.287106643356639







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
618.299606643356657.723614767536168.87559851917713
628.207546620046627.392971097444579.02212214264867
637.611319930069936.613672736401948.60896712373791
647.198426573426576.04644282178568.35041032506754
657.281366550116555.993409561294328.56932353893877
667.380973193473195.970087001724478.79185938522191
677.388913170163165.864981909548568.91284443077777
687.338519813519815.70936876831578.96767085872391
696.971459790209795.243484162748328.69943541767125
706.77523310023314.953786858887498.5966793415787
716.858173076923074.947824142533548.76852201131261
727.945279720279715.949985332943749.94057410761569

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 8.29960664335665 & 7.72361476753616 & 8.87559851917713 \tabularnewline
62 & 8.20754662004662 & 7.39297109744457 & 9.02212214264867 \tabularnewline
63 & 7.61131993006993 & 6.61367273640194 & 8.60896712373791 \tabularnewline
64 & 7.19842657342657 & 6.0464428217856 & 8.35041032506754 \tabularnewline
65 & 7.28136655011655 & 5.99340956129432 & 8.56932353893877 \tabularnewline
66 & 7.38097319347319 & 5.97008700172447 & 8.79185938522191 \tabularnewline
67 & 7.38891317016316 & 5.86498190954856 & 8.91284443077777 \tabularnewline
68 & 7.33851981351981 & 5.7093687683157 & 8.96767085872391 \tabularnewline
69 & 6.97145979020979 & 5.24348416274832 & 8.69943541767125 \tabularnewline
70 & 6.7752331002331 & 4.95378685888749 & 8.5966793415787 \tabularnewline
71 & 6.85817307692307 & 4.94782414253354 & 8.76852201131261 \tabularnewline
72 & 7.94527972027971 & 5.94998533294374 & 9.94057410761569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62740&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]8.29960664335665[/C][C]7.72361476753616[/C][C]8.87559851917713[/C][/ROW]
[ROW][C]62[/C][C]8.20754662004662[/C][C]7.39297109744457[/C][C]9.02212214264867[/C][/ROW]
[ROW][C]63[/C][C]7.61131993006993[/C][C]6.61367273640194[/C][C]8.60896712373791[/C][/ROW]
[ROW][C]64[/C][C]7.19842657342657[/C][C]6.0464428217856[/C][C]8.35041032506754[/C][/ROW]
[ROW][C]65[/C][C]7.28136655011655[/C][C]5.99340956129432[/C][C]8.56932353893877[/C][/ROW]
[ROW][C]66[/C][C]7.38097319347319[/C][C]5.97008700172447[/C][C]8.79185938522191[/C][/ROW]
[ROW][C]67[/C][C]7.38891317016316[/C][C]5.86498190954856[/C][C]8.91284443077777[/C][/ROW]
[ROW][C]68[/C][C]7.33851981351981[/C][C]5.7093687683157[/C][C]8.96767085872391[/C][/ROW]
[ROW][C]69[/C][C]6.97145979020979[/C][C]5.24348416274832[/C][C]8.69943541767125[/C][/ROW]
[ROW][C]70[/C][C]6.7752331002331[/C][C]4.95378685888749[/C][C]8.5966793415787[/C][/ROW]
[ROW][C]71[/C][C]6.85817307692307[/C][C]4.94782414253354[/C][C]8.76852201131261[/C][/ROW]
[ROW][C]72[/C][C]7.94527972027971[/C][C]5.94998533294374[/C][C]9.94057410761569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62740&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62740&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
618.299606643356657.723614767536168.87559851917713
628.207546620046627.392971097444579.02212214264867
637.611319930069936.613672736401948.60896712373791
647.198426573426576.04644282178568.35041032506754
657.281366550116555.993409561294328.56932353893877
667.380973193473195.970087001724478.79185938522191
677.388913170163165.864981909548568.91284443077777
687.338519813519815.70936876831578.96767085872391
696.971459790209795.243484162748328.69943541767125
706.77523310023314.953786858887498.5966793415787
716.858173076923074.947824142533548.76852201131261
727.945279720279715.949985332943749.94057410761569



Parameters (Session):
par1 = 12 ; par2 = Single ; 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')