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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 computationTue, 07 Dec 2010 08:23:30 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/07/t1291710106m0ykuor1tp9b3k5.htm/, Retrieved Fri, 03 May 2024 20:36:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106003, Retrieved Fri, 03 May 2024 20:36:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact179
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]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [ES-Model - Uitvoer] [2010-12-07 08:23:30] [85c2b01fe80f9fc86b9396d4d142e465] [Current]
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Dataseries X:
16198,9
16554,2
19554,2
15903,8
18003,8
18329,6
16260,7
14851,9
18174,1
18406,6
18466,5
16016,5
17428,5
17167,2
19630
17183,6
18344,7
19301,4
18147,5
16192,9
18374,4
20515,2
18957,2
16471,5
18746,8
19009,5
19211,2
20547,7
19325,8
20605,5
20056,9
16141,4
20359,8
19711,6
15638,6
14384,5
13855,6
14308,3
15290,6
14423,8
13779,7
15686,3
14733,8
12522,5
16189,4
16059,1
16007,1
15806,8
15160
15692,1
18908,9
16969,9
16997,5
19858,9
17681,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106003&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106003&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106003&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.622309773779561
beta0
gamma0.742362409692478

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.622309773779561 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.742362409692478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106003&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]0.622309773779561[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.742362409692478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106003&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106003&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
alpha0.622309773779561
beta0
gamma0.742362409692478







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1317428.516963.6914457071464.808554292926
1417167.216857.1546853132310.045314686755
151963019448.6780816240181.321918375961
1617183.617018.9123169632164.687683036809
1718344.718174.1949050714170.505094928558
1819301.419197.5977254580103.802274541973
1918147.517067.41156211271080.08843788728
2016192.916253.9861535563-61.086153556269
2118374.419509.4716431556-1135.0716431556
2220515.218979.12213234651536.07786765349
2318957.219927.4092360071-970.209236007075
2416471.516818.9427124953-347.44271249534
2518746.818025.9418125222720.858187477828
2619009.518035.3542559273974.145744072674
2719211.221004.0619847831-1792.86198478308
2820547.717341.07832470093206.62167529907
2919325.820391.0172709386-1065.21727093861
3020605.520626.7156467150-21.2156467150235
3120056.918692.46367823811364.4363217619
3216141.417736.0247513087-1594.62475130867
3320359.819736.0468811166623.753118883385
3419711.621049.1761940425-1337.57619404248
3515638.619506.4399253606-3867.83992536057
3614384.514769.3626656972-384.862665697196
3713855.616252.6084026105-2397.00840261047
3814308.314392.7595253442-84.4595253442058
3915290.615926.8648472283-636.264847228269
4014423.814385.413249494638.3867505053895
4113779.714265.9775041320-486.277504131951
4215686.315154.6760902448531.623909755175
4314733.813952.9748736252780.825126374813
4412522.511803.6784965886718.821503411446
4516189.415865.3763428862324.023657113756
4616059.116442.0576336315-382.957633631491
4716007.114783.94682261021223.15317738981
4815806.814191.61203416861615.18796583136
491516016355.3373157533-1195.33731575325
5015692.115891.6995537380-199.599553737955
5118908.917199.43526443591709.46473556411
5216969.917306.9149694926-337.014969492571
5316997.516806.7561130939190.743886906082
5419858.918402.17400696541456.72599303462
5517681.217846.0446498263-164.844649826282

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 17428.5 & 16963.6914457071 & 464.808554292926 \tabularnewline
14 & 17167.2 & 16857.1546853132 & 310.045314686755 \tabularnewline
15 & 19630 & 19448.6780816240 & 181.321918375961 \tabularnewline
16 & 17183.6 & 17018.9123169632 & 164.687683036809 \tabularnewline
17 & 18344.7 & 18174.1949050714 & 170.505094928558 \tabularnewline
18 & 19301.4 & 19197.5977254580 & 103.802274541973 \tabularnewline
19 & 18147.5 & 17067.4115621127 & 1080.08843788728 \tabularnewline
20 & 16192.9 & 16253.9861535563 & -61.086153556269 \tabularnewline
21 & 18374.4 & 19509.4716431556 & -1135.0716431556 \tabularnewline
22 & 20515.2 & 18979.1221323465 & 1536.07786765349 \tabularnewline
23 & 18957.2 & 19927.4092360071 & -970.209236007075 \tabularnewline
24 & 16471.5 & 16818.9427124953 & -347.44271249534 \tabularnewline
25 & 18746.8 & 18025.9418125222 & 720.858187477828 \tabularnewline
26 & 19009.5 & 18035.3542559273 & 974.145744072674 \tabularnewline
27 & 19211.2 & 21004.0619847831 & -1792.86198478308 \tabularnewline
28 & 20547.7 & 17341.0783247009 & 3206.62167529907 \tabularnewline
29 & 19325.8 & 20391.0172709386 & -1065.21727093861 \tabularnewline
30 & 20605.5 & 20626.7156467150 & -21.2156467150235 \tabularnewline
31 & 20056.9 & 18692.4636782381 & 1364.4363217619 \tabularnewline
32 & 16141.4 & 17736.0247513087 & -1594.62475130867 \tabularnewline
33 & 20359.8 & 19736.0468811166 & 623.753118883385 \tabularnewline
34 & 19711.6 & 21049.1761940425 & -1337.57619404248 \tabularnewline
35 & 15638.6 & 19506.4399253606 & -3867.83992536057 \tabularnewline
36 & 14384.5 & 14769.3626656972 & -384.862665697196 \tabularnewline
37 & 13855.6 & 16252.6084026105 & -2397.00840261047 \tabularnewline
38 & 14308.3 & 14392.7595253442 & -84.4595253442058 \tabularnewline
39 & 15290.6 & 15926.8648472283 & -636.264847228269 \tabularnewline
40 & 14423.8 & 14385.4132494946 & 38.3867505053895 \tabularnewline
41 & 13779.7 & 14265.9775041320 & -486.277504131951 \tabularnewline
42 & 15686.3 & 15154.6760902448 & 531.623909755175 \tabularnewline
43 & 14733.8 & 13952.9748736252 & 780.825126374813 \tabularnewline
44 & 12522.5 & 11803.6784965886 & 718.821503411446 \tabularnewline
45 & 16189.4 & 15865.3763428862 & 324.023657113756 \tabularnewline
46 & 16059.1 & 16442.0576336315 & -382.957633631491 \tabularnewline
47 & 16007.1 & 14783.9468226102 & 1223.15317738981 \tabularnewline
48 & 15806.8 & 14191.6120341686 & 1615.18796583136 \tabularnewline
49 & 15160 & 16355.3373157533 & -1195.33731575325 \tabularnewline
50 & 15692.1 & 15891.6995537380 & -199.599553737955 \tabularnewline
51 & 18908.9 & 17199.4352644359 & 1709.46473556411 \tabularnewline
52 & 16969.9 & 17306.9149694926 & -337.014969492571 \tabularnewline
53 & 16997.5 & 16806.7561130939 & 190.743886906082 \tabularnewline
54 & 19858.9 & 18402.1740069654 & 1456.72599303462 \tabularnewline
55 & 17681.2 & 17846.0446498263 & -164.844649826282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106003&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]17428.5[/C][C]16963.6914457071[/C][C]464.808554292926[/C][/ROW]
[ROW][C]14[/C][C]17167.2[/C][C]16857.1546853132[/C][C]310.045314686755[/C][/ROW]
[ROW][C]15[/C][C]19630[/C][C]19448.6780816240[/C][C]181.321918375961[/C][/ROW]
[ROW][C]16[/C][C]17183.6[/C][C]17018.9123169632[/C][C]164.687683036809[/C][/ROW]
[ROW][C]17[/C][C]18344.7[/C][C]18174.1949050714[/C][C]170.505094928558[/C][/ROW]
[ROW][C]18[/C][C]19301.4[/C][C]19197.5977254580[/C][C]103.802274541973[/C][/ROW]
[ROW][C]19[/C][C]18147.5[/C][C]17067.4115621127[/C][C]1080.08843788728[/C][/ROW]
[ROW][C]20[/C][C]16192.9[/C][C]16253.9861535563[/C][C]-61.086153556269[/C][/ROW]
[ROW][C]21[/C][C]18374.4[/C][C]19509.4716431556[/C][C]-1135.0716431556[/C][/ROW]
[ROW][C]22[/C][C]20515.2[/C][C]18979.1221323465[/C][C]1536.07786765349[/C][/ROW]
[ROW][C]23[/C][C]18957.2[/C][C]19927.4092360071[/C][C]-970.209236007075[/C][/ROW]
[ROW][C]24[/C][C]16471.5[/C][C]16818.9427124953[/C][C]-347.44271249534[/C][/ROW]
[ROW][C]25[/C][C]18746.8[/C][C]18025.9418125222[/C][C]720.858187477828[/C][/ROW]
[ROW][C]26[/C][C]19009.5[/C][C]18035.3542559273[/C][C]974.145744072674[/C][/ROW]
[ROW][C]27[/C][C]19211.2[/C][C]21004.0619847831[/C][C]-1792.86198478308[/C][/ROW]
[ROW][C]28[/C][C]20547.7[/C][C]17341.0783247009[/C][C]3206.62167529907[/C][/ROW]
[ROW][C]29[/C][C]19325.8[/C][C]20391.0172709386[/C][C]-1065.21727093861[/C][/ROW]
[ROW][C]30[/C][C]20605.5[/C][C]20626.7156467150[/C][C]-21.2156467150235[/C][/ROW]
[ROW][C]31[/C][C]20056.9[/C][C]18692.4636782381[/C][C]1364.4363217619[/C][/ROW]
[ROW][C]32[/C][C]16141.4[/C][C]17736.0247513087[/C][C]-1594.62475130867[/C][/ROW]
[ROW][C]33[/C][C]20359.8[/C][C]19736.0468811166[/C][C]623.753118883385[/C][/ROW]
[ROW][C]34[/C][C]19711.6[/C][C]21049.1761940425[/C][C]-1337.57619404248[/C][/ROW]
[ROW][C]35[/C][C]15638.6[/C][C]19506.4399253606[/C][C]-3867.83992536057[/C][/ROW]
[ROW][C]36[/C][C]14384.5[/C][C]14769.3626656972[/C][C]-384.862665697196[/C][/ROW]
[ROW][C]37[/C][C]13855.6[/C][C]16252.6084026105[/C][C]-2397.00840261047[/C][/ROW]
[ROW][C]38[/C][C]14308.3[/C][C]14392.7595253442[/C][C]-84.4595253442058[/C][/ROW]
[ROW][C]39[/C][C]15290.6[/C][C]15926.8648472283[/C][C]-636.264847228269[/C][/ROW]
[ROW][C]40[/C][C]14423.8[/C][C]14385.4132494946[/C][C]38.3867505053895[/C][/ROW]
[ROW][C]41[/C][C]13779.7[/C][C]14265.9775041320[/C][C]-486.277504131951[/C][/ROW]
[ROW][C]42[/C][C]15686.3[/C][C]15154.6760902448[/C][C]531.623909755175[/C][/ROW]
[ROW][C]43[/C][C]14733.8[/C][C]13952.9748736252[/C][C]780.825126374813[/C][/ROW]
[ROW][C]44[/C][C]12522.5[/C][C]11803.6784965886[/C][C]718.821503411446[/C][/ROW]
[ROW][C]45[/C][C]16189.4[/C][C]15865.3763428862[/C][C]324.023657113756[/C][/ROW]
[ROW][C]46[/C][C]16059.1[/C][C]16442.0576336315[/C][C]-382.957633631491[/C][/ROW]
[ROW][C]47[/C][C]16007.1[/C][C]14783.9468226102[/C][C]1223.15317738981[/C][/ROW]
[ROW][C]48[/C][C]15806.8[/C][C]14191.6120341686[/C][C]1615.18796583136[/C][/ROW]
[ROW][C]49[/C][C]15160[/C][C]16355.3373157533[/C][C]-1195.33731575325[/C][/ROW]
[ROW][C]50[/C][C]15692.1[/C][C]15891.6995537380[/C][C]-199.599553737955[/C][/ROW]
[ROW][C]51[/C][C]18908.9[/C][C]17199.4352644359[/C][C]1709.46473556411[/C][/ROW]
[ROW][C]52[/C][C]16969.9[/C][C]17306.9149694926[/C][C]-337.014969492571[/C][/ROW]
[ROW][C]53[/C][C]16997.5[/C][C]16806.7561130939[/C][C]190.743886906082[/C][/ROW]
[ROW][C]54[/C][C]19858.9[/C][C]18402.1740069654[/C][C]1456.72599303462[/C][/ROW]
[ROW][C]55[/C][C]17681.2[/C][C]17846.0446498263[/C][C]-164.844649826282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106003&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106003&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
1317428.516963.6914457071464.808554292926
1417167.216857.1546853132310.045314686755
151963019448.6780816240181.321918375961
1617183.617018.9123169632164.687683036809
1718344.718174.1949050714170.505094928558
1819301.419197.5977254580103.802274541973
1918147.517067.41156211271080.08843788728
2016192.916253.9861535563-61.086153556269
2118374.419509.4716431556-1135.0716431556
2220515.218979.12213234651536.07786765349
2318957.219927.4092360071-970.209236007075
2416471.516818.9427124953-347.44271249534
2518746.818025.9418125222720.858187477828
2619009.518035.3542559273974.145744072674
2719211.221004.0619847831-1792.86198478308
2820547.717341.07832470093206.62167529907
2919325.820391.0172709386-1065.21727093861
3020605.520626.7156467150-21.2156467150235
3120056.918692.46367823811364.4363217619
3216141.417736.0247513087-1594.62475130867
3320359.819736.0468811166623.753118883385
3419711.621049.1761940425-1337.57619404248
3515638.619506.4399253606-3867.83992536057
3614384.514769.3626656972-384.862665697196
3713855.616252.6084026105-2397.00840261047
3814308.314392.7595253442-84.4595253442058
3915290.615926.8648472283-636.264847228269
4014423.814385.413249494638.3867505053895
4113779.714265.9775041320-486.277504131951
4215686.315154.6760902448531.623909755175
4314733.813952.9748736252780.825126374813
4412522.511803.6784965886718.821503411446
4516189.415865.3763428862324.023657113756
4616059.116442.0576336315-382.957633631491
4716007.114783.94682261021223.15317738981
4815806.814191.61203416861615.18796583136
491516016355.3373157533-1195.33731575325
5015692.115891.6995537380-199.599553737955
5118908.917199.43526443591709.46473556411
5216969.917306.9149694926-337.014969492571
5316997.516806.7561130939190.743886906082
5419858.918402.17400696541456.72599303462
5517681.217846.0446498263-164.844649826282







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
5615090.863964834212692.114042469017489.6138871993
5718594.537548973415769.232239392221419.8428585546
5818771.350197015315575.931758899721966.7686351308
5917801.883874361514274.980431261621328.7873174613
6016558.288809259312728.485054593720388.0925639249
6116928.843248838912818.399756762721039.2867409151
6217488.263548649013115.153144845721861.3739524523
6319455.481235610414834.610808282524076.3516629383
6417925.346154513013069.340346397222781.3519626288
6517782.889632934712702.619826048922863.1594398205
6619614.565636049114319.521706764324909.6095653339
6717697.240571271012195.800840131823198.6803024102

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
56 & 15090.8639648342 & 12692.1140424690 & 17489.6138871993 \tabularnewline
57 & 18594.5375489734 & 15769.2322393922 & 21419.8428585546 \tabularnewline
58 & 18771.3501970153 & 15575.9317588997 & 21966.7686351308 \tabularnewline
59 & 17801.8838743615 & 14274.9804312616 & 21328.7873174613 \tabularnewline
60 & 16558.2888092593 & 12728.4850545937 & 20388.0925639249 \tabularnewline
61 & 16928.8432488389 & 12818.3997567627 & 21039.2867409151 \tabularnewline
62 & 17488.2635486490 & 13115.1531448457 & 21861.3739524523 \tabularnewline
63 & 19455.4812356104 & 14834.6108082825 & 24076.3516629383 \tabularnewline
64 & 17925.3461545130 & 13069.3403463972 & 22781.3519626288 \tabularnewline
65 & 17782.8896329347 & 12702.6198260489 & 22863.1594398205 \tabularnewline
66 & 19614.5656360491 & 14319.5217067643 & 24909.6095653339 \tabularnewline
67 & 17697.2405712710 & 12195.8008401318 & 23198.6803024102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106003&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]15090.8639648342[/C][C]12692.1140424690[/C][C]17489.6138871993[/C][/ROW]
[ROW][C]57[/C][C]18594.5375489734[/C][C]15769.2322393922[/C][C]21419.8428585546[/C][/ROW]
[ROW][C]58[/C][C]18771.3501970153[/C][C]15575.9317588997[/C][C]21966.7686351308[/C][/ROW]
[ROW][C]59[/C][C]17801.8838743615[/C][C]14274.9804312616[/C][C]21328.7873174613[/C][/ROW]
[ROW][C]60[/C][C]16558.2888092593[/C][C]12728.4850545937[/C][C]20388.0925639249[/C][/ROW]
[ROW][C]61[/C][C]16928.8432488389[/C][C]12818.3997567627[/C][C]21039.2867409151[/C][/ROW]
[ROW][C]62[/C][C]17488.2635486490[/C][C]13115.1531448457[/C][C]21861.3739524523[/C][/ROW]
[ROW][C]63[/C][C]19455.4812356104[/C][C]14834.6108082825[/C][C]24076.3516629383[/C][/ROW]
[ROW][C]64[/C][C]17925.3461545130[/C][C]13069.3403463972[/C][C]22781.3519626288[/C][/ROW]
[ROW][C]65[/C][C]17782.8896329347[/C][C]12702.6198260489[/C][C]22863.1594398205[/C][/ROW]
[ROW][C]66[/C][C]19614.5656360491[/C][C]14319.5217067643[/C][C]24909.6095653339[/C][/ROW]
[ROW][C]67[/C][C]17697.2405712710[/C][C]12195.8008401318[/C][C]23198.6803024102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106003&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106003&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
5615090.863964834212692.114042469017489.6138871993
5718594.537548973415769.232239392221419.8428585546
5818771.350197015315575.931758899721966.7686351308
5917801.883874361514274.980431261621328.7873174613
6016558.288809259312728.485054593720388.0925639249
6116928.843248838912818.399756762721039.2867409151
6217488.263548649013115.153144845721861.3739524523
6319455.481235610414834.610808282524076.3516629383
6417925.346154513013069.340346397222781.3519626288
6517782.889632934712702.619826048922863.1594398205
6619614.565636049114319.521706764324909.6095653339
6717697.240571271012195.800840131823198.6803024102



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')