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Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 15:56:11 +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/07/t14811226957wo7j6yb3foirpj.htm/, Retrieved Tue, 07 May 2024 10:56:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298177, Retrieved Tue, 07 May 2024 10:56:55 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact46
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N1291 F1 competitie] [2016-12-07 14:56:11] [fe6e63930acb843607fc81833855c27b] [Current]
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Dataseries X:
5010.31
4985.1
5034.83
4927.21
4887.11
4866.77
4814.47
4894.77
4825.44
4689.02
4667.94
4736.54
4752.72
4738.47
4731.49
4709.92
4646.62
4512.63
4439.56
4424.31
4311.83
4259.99
4289.13
4229.25
4155.83
4214.14
4210.33
4212.37
4361.1
4376.61
4411.53
4449.33
4603
4743.48
4784.04
4836.4
4893.96
4888.67
4933.85
4991.99
4933.19
4983.9
5058.6
5024.31
5046.82
5077.08
5100.87
5141.18
4955.94
4884.8
4855.36
4622.92
4624.77
4592.49
4474.46




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298177&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298177&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298177&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.950530420604445
beta0.200250520811498
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.950530420604445 \tabularnewline
beta & 0.200250520811498 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298177&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]0.950530420604445[/C][/ROW]
[ROW][C]beta[/C][C]0.200250520811498[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298177&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298177&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
alpha0.950530420604445
beta0.200250520811498
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134752.724893.18196848291-140.461968482906
144738.474724.0776947290314.3923052709752
154731.494717.9557776078913.5342223921125
164709.924697.2781375001812.6418624998187
174646.624630.8119208549315.8080791450711
184512.634502.935099147069.69490085293637
194439.564444.07288376702-4.51288376701723
204424.314496.24506892619-71.9350689261873
214311.834322.91424207433-11.084242074332
224259.994137.00165594336122.988344056643
234289.134214.6605109057474.4694890942637
244229.254355.75763778962-126.507637789617
254155.834227.97213395775-72.1421339577455
264214.144127.1566946845386.9833053154753
274210.334199.497736697610.8322633023963
284212.374185.198809667127.1711903328978
294361.14144.45651803357216.643481966427
304376.614257.16202183879119.447978161208
314411.534372.7960370117638.7339629882372
324449.334541.84755036842-92.5175503684168
3346034427.15218928112175.847810718878
344743.484536.32763030127207.152369698731
354784.044818.37778967051-34.3377896705124
364836.44952.18824351981-115.788243519811
374893.964945.4018726426-51.4418726426047
384888.674984.19528894197-95.525288941968
394933.854956.61050448301-22.7605044830052
404991.994982.116025113099.8739748869084
414933.195001.94000924562-68.7500092456239
424983.94851.87378865393132.026211346065
435058.64991.1767941407467.423205859257
445024.315202.17206516639-177.86206516639
455046.825024.551950407622.2680495924033
465077.084964.9826436162112.0973563838
475100.875102.3293967644-1.45939676439593
485141.185227.21634751804-86.0363475180402
494955.945221.41025191732-265.47025191732
504884.84983.36033678382-98.5603367838239
514855.364884.6905285191-29.3305285191009
524622.924832.51512757444-209.595127574436
534624.774525.0125568601399.7574431398734
544592.494462.2995280978130.190471902201
554474.464513.56171856542-39.1017185654173

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4752.72 & 4893.18196848291 & -140.461968482906 \tabularnewline
14 & 4738.47 & 4724.07769472903 & 14.3923052709752 \tabularnewline
15 & 4731.49 & 4717.95577760789 & 13.5342223921125 \tabularnewline
16 & 4709.92 & 4697.27813750018 & 12.6418624998187 \tabularnewline
17 & 4646.62 & 4630.81192085493 & 15.8080791450711 \tabularnewline
18 & 4512.63 & 4502.93509914706 & 9.69490085293637 \tabularnewline
19 & 4439.56 & 4444.07288376702 & -4.51288376701723 \tabularnewline
20 & 4424.31 & 4496.24506892619 & -71.9350689261873 \tabularnewline
21 & 4311.83 & 4322.91424207433 & -11.084242074332 \tabularnewline
22 & 4259.99 & 4137.00165594336 & 122.988344056643 \tabularnewline
23 & 4289.13 & 4214.66051090574 & 74.4694890942637 \tabularnewline
24 & 4229.25 & 4355.75763778962 & -126.507637789617 \tabularnewline
25 & 4155.83 & 4227.97213395775 & -72.1421339577455 \tabularnewline
26 & 4214.14 & 4127.15669468453 & 86.9833053154753 \tabularnewline
27 & 4210.33 & 4199.4977366976 & 10.8322633023963 \tabularnewline
28 & 4212.37 & 4185.1988096671 & 27.1711903328978 \tabularnewline
29 & 4361.1 & 4144.45651803357 & 216.643481966427 \tabularnewline
30 & 4376.61 & 4257.16202183879 & 119.447978161208 \tabularnewline
31 & 4411.53 & 4372.79603701176 & 38.7339629882372 \tabularnewline
32 & 4449.33 & 4541.84755036842 & -92.5175503684168 \tabularnewline
33 & 4603 & 4427.15218928112 & 175.847810718878 \tabularnewline
34 & 4743.48 & 4536.32763030127 & 207.152369698731 \tabularnewline
35 & 4784.04 & 4818.37778967051 & -34.3377896705124 \tabularnewline
36 & 4836.4 & 4952.18824351981 & -115.788243519811 \tabularnewline
37 & 4893.96 & 4945.4018726426 & -51.4418726426047 \tabularnewline
38 & 4888.67 & 4984.19528894197 & -95.525288941968 \tabularnewline
39 & 4933.85 & 4956.61050448301 & -22.7605044830052 \tabularnewline
40 & 4991.99 & 4982.11602511309 & 9.8739748869084 \tabularnewline
41 & 4933.19 & 5001.94000924562 & -68.7500092456239 \tabularnewline
42 & 4983.9 & 4851.87378865393 & 132.026211346065 \tabularnewline
43 & 5058.6 & 4991.17679414074 & 67.423205859257 \tabularnewline
44 & 5024.31 & 5202.17206516639 & -177.86206516639 \tabularnewline
45 & 5046.82 & 5024.5519504076 & 22.2680495924033 \tabularnewline
46 & 5077.08 & 4964.9826436162 & 112.0973563838 \tabularnewline
47 & 5100.87 & 5102.3293967644 & -1.45939676439593 \tabularnewline
48 & 5141.18 & 5227.21634751804 & -86.0363475180402 \tabularnewline
49 & 4955.94 & 5221.41025191732 & -265.47025191732 \tabularnewline
50 & 4884.8 & 4983.36033678382 & -98.5603367838239 \tabularnewline
51 & 4855.36 & 4884.6905285191 & -29.3305285191009 \tabularnewline
52 & 4622.92 & 4832.51512757444 & -209.595127574436 \tabularnewline
53 & 4624.77 & 4525.01255686013 & 99.7574431398734 \tabularnewline
54 & 4592.49 & 4462.2995280978 & 130.190471902201 \tabularnewline
55 & 4474.46 & 4513.56171856542 & -39.1017185654173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298177&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]4752.72[/C][C]4893.18196848291[/C][C]-140.461968482906[/C][/ROW]
[ROW][C]14[/C][C]4738.47[/C][C]4724.07769472903[/C][C]14.3923052709752[/C][/ROW]
[ROW][C]15[/C][C]4731.49[/C][C]4717.95577760789[/C][C]13.5342223921125[/C][/ROW]
[ROW][C]16[/C][C]4709.92[/C][C]4697.27813750018[/C][C]12.6418624998187[/C][/ROW]
[ROW][C]17[/C][C]4646.62[/C][C]4630.81192085493[/C][C]15.8080791450711[/C][/ROW]
[ROW][C]18[/C][C]4512.63[/C][C]4502.93509914706[/C][C]9.69490085293637[/C][/ROW]
[ROW][C]19[/C][C]4439.56[/C][C]4444.07288376702[/C][C]-4.51288376701723[/C][/ROW]
[ROW][C]20[/C][C]4424.31[/C][C]4496.24506892619[/C][C]-71.9350689261873[/C][/ROW]
[ROW][C]21[/C][C]4311.83[/C][C]4322.91424207433[/C][C]-11.084242074332[/C][/ROW]
[ROW][C]22[/C][C]4259.99[/C][C]4137.00165594336[/C][C]122.988344056643[/C][/ROW]
[ROW][C]23[/C][C]4289.13[/C][C]4214.66051090574[/C][C]74.4694890942637[/C][/ROW]
[ROW][C]24[/C][C]4229.25[/C][C]4355.75763778962[/C][C]-126.507637789617[/C][/ROW]
[ROW][C]25[/C][C]4155.83[/C][C]4227.97213395775[/C][C]-72.1421339577455[/C][/ROW]
[ROW][C]26[/C][C]4214.14[/C][C]4127.15669468453[/C][C]86.9833053154753[/C][/ROW]
[ROW][C]27[/C][C]4210.33[/C][C]4199.4977366976[/C][C]10.8322633023963[/C][/ROW]
[ROW][C]28[/C][C]4212.37[/C][C]4185.1988096671[/C][C]27.1711903328978[/C][/ROW]
[ROW][C]29[/C][C]4361.1[/C][C]4144.45651803357[/C][C]216.643481966427[/C][/ROW]
[ROW][C]30[/C][C]4376.61[/C][C]4257.16202183879[/C][C]119.447978161208[/C][/ROW]
[ROW][C]31[/C][C]4411.53[/C][C]4372.79603701176[/C][C]38.7339629882372[/C][/ROW]
[ROW][C]32[/C][C]4449.33[/C][C]4541.84755036842[/C][C]-92.5175503684168[/C][/ROW]
[ROW][C]33[/C][C]4603[/C][C]4427.15218928112[/C][C]175.847810718878[/C][/ROW]
[ROW][C]34[/C][C]4743.48[/C][C]4536.32763030127[/C][C]207.152369698731[/C][/ROW]
[ROW][C]35[/C][C]4784.04[/C][C]4818.37778967051[/C][C]-34.3377896705124[/C][/ROW]
[ROW][C]36[/C][C]4836.4[/C][C]4952.18824351981[/C][C]-115.788243519811[/C][/ROW]
[ROW][C]37[/C][C]4893.96[/C][C]4945.4018726426[/C][C]-51.4418726426047[/C][/ROW]
[ROW][C]38[/C][C]4888.67[/C][C]4984.19528894197[/C][C]-95.525288941968[/C][/ROW]
[ROW][C]39[/C][C]4933.85[/C][C]4956.61050448301[/C][C]-22.7605044830052[/C][/ROW]
[ROW][C]40[/C][C]4991.99[/C][C]4982.11602511309[/C][C]9.8739748869084[/C][/ROW]
[ROW][C]41[/C][C]4933.19[/C][C]5001.94000924562[/C][C]-68.7500092456239[/C][/ROW]
[ROW][C]42[/C][C]4983.9[/C][C]4851.87378865393[/C][C]132.026211346065[/C][/ROW]
[ROW][C]43[/C][C]5058.6[/C][C]4991.17679414074[/C][C]67.423205859257[/C][/ROW]
[ROW][C]44[/C][C]5024.31[/C][C]5202.17206516639[/C][C]-177.86206516639[/C][/ROW]
[ROW][C]45[/C][C]5046.82[/C][C]5024.5519504076[/C][C]22.2680495924033[/C][/ROW]
[ROW][C]46[/C][C]5077.08[/C][C]4964.9826436162[/C][C]112.0973563838[/C][/ROW]
[ROW][C]47[/C][C]5100.87[/C][C]5102.3293967644[/C][C]-1.45939676439593[/C][/ROW]
[ROW][C]48[/C][C]5141.18[/C][C]5227.21634751804[/C][C]-86.0363475180402[/C][/ROW]
[ROW][C]49[/C][C]4955.94[/C][C]5221.41025191732[/C][C]-265.47025191732[/C][/ROW]
[ROW][C]50[/C][C]4884.8[/C][C]4983.36033678382[/C][C]-98.5603367838239[/C][/ROW]
[ROW][C]51[/C][C]4855.36[/C][C]4884.6905285191[/C][C]-29.3305285191009[/C][/ROW]
[ROW][C]52[/C][C]4622.92[/C][C]4832.51512757444[/C][C]-209.595127574436[/C][/ROW]
[ROW][C]53[/C][C]4624.77[/C][C]4525.01255686013[/C][C]99.7574431398734[/C][/ROW]
[ROW][C]54[/C][C]4592.49[/C][C]4462.2995280978[/C][C]130.190471902201[/C][/ROW]
[ROW][C]55[/C][C]4474.46[/C][C]4513.56171856542[/C][C]-39.1017185654173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298177&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298177&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
134752.724893.18196848291-140.461968482906
144738.474724.0776947290314.3923052709752
154731.494717.9557776078913.5342223921125
164709.924697.2781375001812.6418624998187
174646.624630.8119208549315.8080791450711
184512.634502.935099147069.69490085293637
194439.564444.07288376702-4.51288376701723
204424.314496.24506892619-71.9350689261873
214311.834322.91424207433-11.084242074332
224259.994137.00165594336122.988344056643
234289.134214.6605109057474.4694890942637
244229.254355.75763778962-126.507637789617
254155.834227.97213395775-72.1421339577455
264214.144127.1566946845386.9833053154753
274210.334199.497736697610.8322633023963
284212.374185.198809667127.1711903328978
294361.14144.45651803357216.643481966427
304376.614257.16202183879119.447978161208
314411.534372.7960370117638.7339629882372
324449.334541.84755036842-92.5175503684168
3346034427.15218928112175.847810718878
344743.484536.32763030127207.152369698731
354784.044818.37778967051-34.3377896705124
364836.44952.18824351981-115.788243519811
374893.964945.4018726426-51.4418726426047
384888.674984.19528894197-95.525288941968
394933.854956.61050448301-22.7605044830052
404991.994982.116025113099.8739748869084
414933.195001.94000924562-68.7500092456239
424983.94851.87378865393132.026211346065
435058.64991.1767941407467.423205859257
445024.315202.17206516639-177.86206516639
455046.825024.551950407622.2680495924033
465077.084964.9826436162112.0973563838
475100.875102.3293967644-1.45939676439593
485141.185227.21634751804-86.0363475180402
494955.945221.41025191732-265.47025191732
504884.84983.36033678382-98.5603367838239
514855.364884.6905285191-29.3305285191009
524622.924832.51512757444-209.595127574436
534624.774525.0125568601399.7574431398734
544592.494462.2995280978130.190471902201
554474.464513.56171856542-39.1017185654173







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
564507.791241085074298.193369599224717.38911257092
574439.613389040224121.632284352214757.59449372823
584289.561453880953866.519495710234712.60341205168
594219.641584111383689.856576362084749.42659186068
604246.912466641893607.054442132394886.77049115139
614235.567254543913481.65330053174989.48120855612
624230.199816461483357.984607689655102.41502523332
634219.487729228043224.640508290835214.33495016524
644182.705523486613060.896957715845304.51408925738
654126.059507938712873.00599491345379.11302096401
663987.367720878112598.854026954575375.88141480166
673899.062308073142370.952588922485427.1720272238

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
56 & 4507.79124108507 & 4298.19336959922 & 4717.38911257092 \tabularnewline
57 & 4439.61338904022 & 4121.63228435221 & 4757.59449372823 \tabularnewline
58 & 4289.56145388095 & 3866.51949571023 & 4712.60341205168 \tabularnewline
59 & 4219.64158411138 & 3689.85657636208 & 4749.42659186068 \tabularnewline
60 & 4246.91246664189 & 3607.05444213239 & 4886.77049115139 \tabularnewline
61 & 4235.56725454391 & 3481.6533005317 & 4989.48120855612 \tabularnewline
62 & 4230.19981646148 & 3357.98460768965 & 5102.41502523332 \tabularnewline
63 & 4219.48772922804 & 3224.64050829083 & 5214.33495016524 \tabularnewline
64 & 4182.70552348661 & 3060.89695771584 & 5304.51408925738 \tabularnewline
65 & 4126.05950793871 & 2873.0059949134 & 5379.11302096401 \tabularnewline
66 & 3987.36772087811 & 2598.85402695457 & 5375.88141480166 \tabularnewline
67 & 3899.06230807314 & 2370.95258892248 & 5427.1720272238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298177&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]56[/C][C]4507.79124108507[/C][C]4298.19336959922[/C][C]4717.38911257092[/C][/ROW]
[ROW][C]57[/C][C]4439.61338904022[/C][C]4121.63228435221[/C][C]4757.59449372823[/C][/ROW]
[ROW][C]58[/C][C]4289.56145388095[/C][C]3866.51949571023[/C][C]4712.60341205168[/C][/ROW]
[ROW][C]59[/C][C]4219.64158411138[/C][C]3689.85657636208[/C][C]4749.42659186068[/C][/ROW]
[ROW][C]60[/C][C]4246.91246664189[/C][C]3607.05444213239[/C][C]4886.77049115139[/C][/ROW]
[ROW][C]61[/C][C]4235.56725454391[/C][C]3481.6533005317[/C][C]4989.48120855612[/C][/ROW]
[ROW][C]62[/C][C]4230.19981646148[/C][C]3357.98460768965[/C][C]5102.41502523332[/C][/ROW]
[ROW][C]63[/C][C]4219.48772922804[/C][C]3224.64050829083[/C][C]5214.33495016524[/C][/ROW]
[ROW][C]64[/C][C]4182.70552348661[/C][C]3060.89695771584[/C][C]5304.51408925738[/C][/ROW]
[ROW][C]65[/C][C]4126.05950793871[/C][C]2873.0059949134[/C][C]5379.11302096401[/C][/ROW]
[ROW][C]66[/C][C]3987.36772087811[/C][C]2598.85402695457[/C][C]5375.88141480166[/C][/ROW]
[ROW][C]67[/C][C]3899.06230807314[/C][C]2370.95258892248[/C][C]5427.1720272238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298177&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298177&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
564507.791241085074298.193369599224717.38911257092
574439.613389040224121.632284352214757.59449372823
584289.561453880953866.519495710234712.60341205168
594219.641584111383689.856576362084749.42659186068
604246.912466641893607.054442132394886.77049115139
614235.567254543913481.65330053174989.48120855612
624230.199816461483357.984607689655102.41502523332
634219.487729228043224.640508290835214.33495016524
644182.705523486613060.896957715845304.51408925738
654126.059507938712873.00599491345379.11302096401
663987.367720878112598.854026954575375.88141480166
673899.062308073142370.952588922485427.1720272238



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Triple'
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')