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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 24 May 2016 19:29:19 +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/May/24/t1464114651qhm9pj11c68mfdj.htm/, Retrieved Tue, 21 May 2024 21:26:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295580, Retrieved Tue, 21 May 2024 21:26:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-05-24 18:29:19] [be6cd4bb5de010eb7c002bb036e110fa] [Current]
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Dataseries X:
81432
81935
82229
82963
82975
82892
82692
82648
83479
84176
84589
84857
84586
84635
84927
85563
86962
87780
88515
88800
89218
89626
89939
90663
91302
91560
92290
93281
94535
94855
95536
96008
96627
96738
96212
94198
93123
93022
93993
94876
95251
96216
96632
97023
97799
98001
98069
98172
98448
98157
98009
98020
97802
98006
98262
98629
99043
99289
99682
99979




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295580&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295580&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295580&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295580&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[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295580&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295580&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







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138458682738.17922008551847.82077991453
148463584523.9876165501111.012383449895
158492784819.4876165501107.512383449895
168556385484.737616550178.2623834498663
178696286899.945949883462.0540501165669
188778087703.112616550176.8873834498663
198851587235.52928321681279.47071678324
208880088615.0292832168184.970716783209
218921889794.0292832168-576.029283216791
228962690082.1959498834-456.195949883419
238993990152.4876165501-213.487616550119
249066390225.1542832168437.845716783195
259130290333.6542832168968.345716783224
269156091239.9876165501320.012383449895
279229091744.4876165501545.512383449895
289328192847.7376165501433.262383449866
299453594617.9459498834-82.9459498834331
309485595276.1126165501-421.112616550134
319553694310.52928321681225.47071678324
329600895636.0292832168371.970716783209
339662797002.0292832168-375.029283216791
349673897491.1959498834-753.195949883419
359621297264.4876165501-1052.48761655012
369419896498.1542832168-2300.15428321681
379312393868.6542832168-745.654283216776
389302293060.9876165501-38.9876165501046
399399393206.4876165501786.512383449895
409487694550.7376165501325.262383449866
419525196212.9459498834-961.945949883433
429621695992.1126165501223.887383449866
439663295671.5292832168960.470716783238
449702396732.0292832168290.970716783209
459779998017.0292832168-218.029283216791
469800198663.1959498834-662.195949883419
479806998527.4876165501-458.487616550119
489817298355.1542832168-183.154283216805
499844897842.6542832168605.345716783224
509815798385.9876165501-228.987616550105
519800998341.4876165501-332.487616550105
529802098566.7376165501-546.737616550134
539780299356.9459498834-1554.94594988343
549800698543.1126165501-537.112616550134
559826297461.5292832168800.470716783238
569862998362.0292832168266.970716783209
579904399623.0292832168-580.029283216791
589928999907.1959498834-618.195949883419
599968299815.4876165501-133.487616550119
609997999968.154283216810.8457167831948

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 84586 & 82738.1792200855 & 1847.82077991453 \tabularnewline
14 & 84635 & 84523.9876165501 & 111.012383449895 \tabularnewline
15 & 84927 & 84819.4876165501 & 107.512383449895 \tabularnewline
16 & 85563 & 85484.7376165501 & 78.2623834498663 \tabularnewline
17 & 86962 & 86899.9459498834 & 62.0540501165669 \tabularnewline
18 & 87780 & 87703.1126165501 & 76.8873834498663 \tabularnewline
19 & 88515 & 87235.5292832168 & 1279.47071678324 \tabularnewline
20 & 88800 & 88615.0292832168 & 184.970716783209 \tabularnewline
21 & 89218 & 89794.0292832168 & -576.029283216791 \tabularnewline
22 & 89626 & 90082.1959498834 & -456.195949883419 \tabularnewline
23 & 89939 & 90152.4876165501 & -213.487616550119 \tabularnewline
24 & 90663 & 90225.1542832168 & 437.845716783195 \tabularnewline
25 & 91302 & 90333.6542832168 & 968.345716783224 \tabularnewline
26 & 91560 & 91239.9876165501 & 320.012383449895 \tabularnewline
27 & 92290 & 91744.4876165501 & 545.512383449895 \tabularnewline
28 & 93281 & 92847.7376165501 & 433.262383449866 \tabularnewline
29 & 94535 & 94617.9459498834 & -82.9459498834331 \tabularnewline
30 & 94855 & 95276.1126165501 & -421.112616550134 \tabularnewline
31 & 95536 & 94310.5292832168 & 1225.47071678324 \tabularnewline
32 & 96008 & 95636.0292832168 & 371.970716783209 \tabularnewline
33 & 96627 & 97002.0292832168 & -375.029283216791 \tabularnewline
34 & 96738 & 97491.1959498834 & -753.195949883419 \tabularnewline
35 & 96212 & 97264.4876165501 & -1052.48761655012 \tabularnewline
36 & 94198 & 96498.1542832168 & -2300.15428321681 \tabularnewline
37 & 93123 & 93868.6542832168 & -745.654283216776 \tabularnewline
38 & 93022 & 93060.9876165501 & -38.9876165501046 \tabularnewline
39 & 93993 & 93206.4876165501 & 786.512383449895 \tabularnewline
40 & 94876 & 94550.7376165501 & 325.262383449866 \tabularnewline
41 & 95251 & 96212.9459498834 & -961.945949883433 \tabularnewline
42 & 96216 & 95992.1126165501 & 223.887383449866 \tabularnewline
43 & 96632 & 95671.5292832168 & 960.470716783238 \tabularnewline
44 & 97023 & 96732.0292832168 & 290.970716783209 \tabularnewline
45 & 97799 & 98017.0292832168 & -218.029283216791 \tabularnewline
46 & 98001 & 98663.1959498834 & -662.195949883419 \tabularnewline
47 & 98069 & 98527.4876165501 & -458.487616550119 \tabularnewline
48 & 98172 & 98355.1542832168 & -183.154283216805 \tabularnewline
49 & 98448 & 97842.6542832168 & 605.345716783224 \tabularnewline
50 & 98157 & 98385.9876165501 & -228.987616550105 \tabularnewline
51 & 98009 & 98341.4876165501 & -332.487616550105 \tabularnewline
52 & 98020 & 98566.7376165501 & -546.737616550134 \tabularnewline
53 & 97802 & 99356.9459498834 & -1554.94594988343 \tabularnewline
54 & 98006 & 98543.1126165501 & -537.112616550134 \tabularnewline
55 & 98262 & 97461.5292832168 & 800.470716783238 \tabularnewline
56 & 98629 & 98362.0292832168 & 266.970716783209 \tabularnewline
57 & 99043 & 99623.0292832168 & -580.029283216791 \tabularnewline
58 & 99289 & 99907.1959498834 & -618.195949883419 \tabularnewline
59 & 99682 & 99815.4876165501 & -133.487616550119 \tabularnewline
60 & 99979 & 99968.1542832168 & 10.8457167831948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295580&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]84586[/C][C]82738.1792200855[/C][C]1847.82077991453[/C][/ROW]
[ROW][C]14[/C][C]84635[/C][C]84523.9876165501[/C][C]111.012383449895[/C][/ROW]
[ROW][C]15[/C][C]84927[/C][C]84819.4876165501[/C][C]107.512383449895[/C][/ROW]
[ROW][C]16[/C][C]85563[/C][C]85484.7376165501[/C][C]78.2623834498663[/C][/ROW]
[ROW][C]17[/C][C]86962[/C][C]86899.9459498834[/C][C]62.0540501165669[/C][/ROW]
[ROW][C]18[/C][C]87780[/C][C]87703.1126165501[/C][C]76.8873834498663[/C][/ROW]
[ROW][C]19[/C][C]88515[/C][C]87235.5292832168[/C][C]1279.47071678324[/C][/ROW]
[ROW][C]20[/C][C]88800[/C][C]88615.0292832168[/C][C]184.970716783209[/C][/ROW]
[ROW][C]21[/C][C]89218[/C][C]89794.0292832168[/C][C]-576.029283216791[/C][/ROW]
[ROW][C]22[/C][C]89626[/C][C]90082.1959498834[/C][C]-456.195949883419[/C][/ROW]
[ROW][C]23[/C][C]89939[/C][C]90152.4876165501[/C][C]-213.487616550119[/C][/ROW]
[ROW][C]24[/C][C]90663[/C][C]90225.1542832168[/C][C]437.845716783195[/C][/ROW]
[ROW][C]25[/C][C]91302[/C][C]90333.6542832168[/C][C]968.345716783224[/C][/ROW]
[ROW][C]26[/C][C]91560[/C][C]91239.9876165501[/C][C]320.012383449895[/C][/ROW]
[ROW][C]27[/C][C]92290[/C][C]91744.4876165501[/C][C]545.512383449895[/C][/ROW]
[ROW][C]28[/C][C]93281[/C][C]92847.7376165501[/C][C]433.262383449866[/C][/ROW]
[ROW][C]29[/C][C]94535[/C][C]94617.9459498834[/C][C]-82.9459498834331[/C][/ROW]
[ROW][C]30[/C][C]94855[/C][C]95276.1126165501[/C][C]-421.112616550134[/C][/ROW]
[ROW][C]31[/C][C]95536[/C][C]94310.5292832168[/C][C]1225.47071678324[/C][/ROW]
[ROW][C]32[/C][C]96008[/C][C]95636.0292832168[/C][C]371.970716783209[/C][/ROW]
[ROW][C]33[/C][C]96627[/C][C]97002.0292832168[/C][C]-375.029283216791[/C][/ROW]
[ROW][C]34[/C][C]96738[/C][C]97491.1959498834[/C][C]-753.195949883419[/C][/ROW]
[ROW][C]35[/C][C]96212[/C][C]97264.4876165501[/C][C]-1052.48761655012[/C][/ROW]
[ROW][C]36[/C][C]94198[/C][C]96498.1542832168[/C][C]-2300.15428321681[/C][/ROW]
[ROW][C]37[/C][C]93123[/C][C]93868.6542832168[/C][C]-745.654283216776[/C][/ROW]
[ROW][C]38[/C][C]93022[/C][C]93060.9876165501[/C][C]-38.9876165501046[/C][/ROW]
[ROW][C]39[/C][C]93993[/C][C]93206.4876165501[/C][C]786.512383449895[/C][/ROW]
[ROW][C]40[/C][C]94876[/C][C]94550.7376165501[/C][C]325.262383449866[/C][/ROW]
[ROW][C]41[/C][C]95251[/C][C]96212.9459498834[/C][C]-961.945949883433[/C][/ROW]
[ROW][C]42[/C][C]96216[/C][C]95992.1126165501[/C][C]223.887383449866[/C][/ROW]
[ROW][C]43[/C][C]96632[/C][C]95671.5292832168[/C][C]960.470716783238[/C][/ROW]
[ROW][C]44[/C][C]97023[/C][C]96732.0292832168[/C][C]290.970716783209[/C][/ROW]
[ROW][C]45[/C][C]97799[/C][C]98017.0292832168[/C][C]-218.029283216791[/C][/ROW]
[ROW][C]46[/C][C]98001[/C][C]98663.1959498834[/C][C]-662.195949883419[/C][/ROW]
[ROW][C]47[/C][C]98069[/C][C]98527.4876165501[/C][C]-458.487616550119[/C][/ROW]
[ROW][C]48[/C][C]98172[/C][C]98355.1542832168[/C][C]-183.154283216805[/C][/ROW]
[ROW][C]49[/C][C]98448[/C][C]97842.6542832168[/C][C]605.345716783224[/C][/ROW]
[ROW][C]50[/C][C]98157[/C][C]98385.9876165501[/C][C]-228.987616550105[/C][/ROW]
[ROW][C]51[/C][C]98009[/C][C]98341.4876165501[/C][C]-332.487616550105[/C][/ROW]
[ROW][C]52[/C][C]98020[/C][C]98566.7376165501[/C][C]-546.737616550134[/C][/ROW]
[ROW][C]53[/C][C]97802[/C][C]99356.9459498834[/C][C]-1554.94594988343[/C][/ROW]
[ROW][C]54[/C][C]98006[/C][C]98543.1126165501[/C][C]-537.112616550134[/C][/ROW]
[ROW][C]55[/C][C]98262[/C][C]97461.5292832168[/C][C]800.470716783238[/C][/ROW]
[ROW][C]56[/C][C]98629[/C][C]98362.0292832168[/C][C]266.970716783209[/C][/ROW]
[ROW][C]57[/C][C]99043[/C][C]99623.0292832168[/C][C]-580.029283216791[/C][/ROW]
[ROW][C]58[/C][C]99289[/C][C]99907.1959498834[/C][C]-618.195949883419[/C][/ROW]
[ROW][C]59[/C][C]99682[/C][C]99815.4876165501[/C][C]-133.487616550119[/C][/ROW]
[ROW][C]60[/C][C]99979[/C][C]99968.1542832168[/C][C]10.8457167831948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295580&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295580&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
138458682738.17922008551847.82077991453
148463584523.9876165501111.012383449895
158492784819.4876165501107.512383449895
168556385484.737616550178.2623834498663
178696286899.945949883462.0540501165669
188778087703.112616550176.8873834498663
198851587235.52928321681279.47071678324
208880088615.0292832168184.970716783209
218921889794.0292832168-576.029283216791
228962690082.1959498834-456.195949883419
238993990152.4876165501-213.487616550119
249066390225.1542832168437.845716783195
259130290333.6542832168968.345716783224
269156091239.9876165501320.012383449895
279229091744.4876165501545.512383449895
289328192847.7376165501433.262383449866
299453594617.9459498834-82.9459498834331
309485595276.1126165501-421.112616550134
319553694310.52928321681225.47071678324
329600895636.0292832168371.970716783209
339662797002.0292832168-375.029283216791
349673897491.1959498834-753.195949883419
359621297264.4876165501-1052.48761655012
369419896498.1542832168-2300.15428321681
379312393868.6542832168-745.654283216776
389302293060.9876165501-38.9876165501046
399399393206.4876165501786.512383449895
409487694550.7376165501325.262383449866
419525196212.9459498834-961.945949883433
429621695992.1126165501223.887383449866
439663295671.5292832168960.470716783238
449702396732.0292832168290.970716783209
459779998017.0292832168-218.029283216791
469800198663.1959498834-662.195949883419
479806998527.4876165501-458.487616550119
489817298355.1542832168-183.154283216805
499844897842.6542832168605.345716783224
509815798385.9876165501-228.987616550105
519800998341.4876165501-332.487616550105
529802098566.7376165501-546.737616550134
539780299356.9459498834-1554.94594988343
549800698543.1126165501-537.112616550134
559826297461.5292832168800.470716783238
569862998362.0292832168266.970716783209
579904399623.0292832168-580.029283216791
589928999907.1959498834-618.195949883419
599968299815.4876165501-133.487616550119
609997999968.154283216810.8457167831948







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6199649.654283216898212.3482677897101086.960298644
6299587.641899766997554.9842394695101620.299560064
6399772.12951631797282.642471573102261.616561061
64100329.86713286797455.2551020131103204.479163721
65101666.81308275198452.8991277864104880.727037715
66102407.92569930198887.2593572716105928.59204133
67101863.45498251798060.7007078004105666.209257235
68101963.48426573497898.1689451396106028.799586329
69102957.51354895198645.59550267107269.431595232
70103821.70949883499276.5487954239108366.870202245
71104348.19711538599581.1923532924109115.201877477
72104634.35139860199655.3773091134109613.325488089

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 99649.6542832168 & 98212.3482677897 & 101086.960298644 \tabularnewline
62 & 99587.6418997669 & 97554.9842394695 & 101620.299560064 \tabularnewline
63 & 99772.129516317 & 97282.642471573 & 102261.616561061 \tabularnewline
64 & 100329.867132867 & 97455.2551020131 & 103204.479163721 \tabularnewline
65 & 101666.813082751 & 98452.8991277864 & 104880.727037715 \tabularnewline
66 & 102407.925699301 & 98887.2593572716 & 105928.59204133 \tabularnewline
67 & 101863.454982517 & 98060.7007078004 & 105666.209257235 \tabularnewline
68 & 101963.484265734 & 97898.1689451396 & 106028.799586329 \tabularnewline
69 & 102957.513548951 & 98645.59550267 & 107269.431595232 \tabularnewline
70 & 103821.709498834 & 99276.5487954239 & 108366.870202245 \tabularnewline
71 & 104348.197115385 & 99581.1923532924 & 109115.201877477 \tabularnewline
72 & 104634.351398601 & 99655.3773091134 & 109613.325488089 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295580&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]99649.6542832168[/C][C]98212.3482677897[/C][C]101086.960298644[/C][/ROW]
[ROW][C]62[/C][C]99587.6418997669[/C][C]97554.9842394695[/C][C]101620.299560064[/C][/ROW]
[ROW][C]63[/C][C]99772.129516317[/C][C]97282.642471573[/C][C]102261.616561061[/C][/ROW]
[ROW][C]64[/C][C]100329.867132867[/C][C]97455.2551020131[/C][C]103204.479163721[/C][/ROW]
[ROW][C]65[/C][C]101666.813082751[/C][C]98452.8991277864[/C][C]104880.727037715[/C][/ROW]
[ROW][C]66[/C][C]102407.925699301[/C][C]98887.2593572716[/C][C]105928.59204133[/C][/ROW]
[ROW][C]67[/C][C]101863.454982517[/C][C]98060.7007078004[/C][C]105666.209257235[/C][/ROW]
[ROW][C]68[/C][C]101963.484265734[/C][C]97898.1689451396[/C][C]106028.799586329[/C][/ROW]
[ROW][C]69[/C][C]102957.513548951[/C][C]98645.59550267[/C][C]107269.431595232[/C][/ROW]
[ROW][C]70[/C][C]103821.709498834[/C][C]99276.5487954239[/C][C]108366.870202245[/C][/ROW]
[ROW][C]71[/C][C]104348.197115385[/C][C]99581.1923532924[/C][C]109115.201877477[/C][/ROW]
[ROW][C]72[/C][C]104634.351398601[/C][C]99655.3773091134[/C][C]109613.325488089[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295580&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295580&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
6199649.654283216898212.3482677897101086.960298644
6299587.641899766997554.9842394695101620.299560064
6399772.12951631797282.642471573102261.616561061
64100329.86713286797455.2551020131103204.479163721
65101666.81308275198452.8991277864104880.727037715
66102407.92569930198887.2593572716105928.59204133
67101863.45498251798060.7007078004105666.209257235
68101963.48426573497898.1689451396106028.799586329
69102957.51354895198645.59550267107269.431595232
70103821.70949883499276.5487954239108366.870202245
71104348.19711538599581.1923532924109115.201877477
72104634.35139860199655.3773091134109613.325488089



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=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')