Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 24 Nov 2016 18:14:34 +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/2016/Nov/24/t1480011296t9id0e291g9bknj.htm/, Retrieved Tue, 07 May 2024 12:52:32 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 07 May 2024 12:52:32 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
28886
28549
33348
29017
30924
30435
29431
30290
31286
30622
31742
30391
30740
32086
33947
31312
33239
32362
32170
32665
31412
34891
33919
30706
32846
31368
33130
31665
33139
32201
32230
30287
31918
33853
32232
31484
31902
30260
32823
32018
32100
31952
33274
29491
32751
33643
31226
30976
28880
29325
34923
32642
31487
33832
32724
29545
32338
32743
32231
32536




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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.343513938777603
beta0.0547729055626988
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.343513938777603 \tabularnewline
beta & 0.0547729055626988 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.343513938777603[/C][/ROW]
[ROW][C]beta[/C][C]0.0547729055626988[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.343513938777603
beta0.0547729055626988
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133074029698.54807692311041.45192307693
143208631386.2817122964699.718287703647
153394733593.6654596503353.334540349664
163131231113.7929749725198.207025027536
173323933060.9030091818178.096990818245
183236232365.2059069-3.20590689998789
193217031610.6267454838559.373254516155
203266532671.5761189587-6.57611895865557
213141233727.2819293039-2315.28192930391
223489132338.10248982392552.89751017607
233391934381.7439658199-462.743965819856
243070632925.0972473649-2219.0972473649
253284633189.397815578-343.397815577991
263136834161.8574597025-2793.85745970248
273313034860.8051811524-1730.80518115238
283166531443.0010182341221.998981765915
293313933265.3680338107-126.368033810679
303220132220.6176086911-19.6176086911037
313223031703.974868579526.025131420989
323028732255.5520602285-1968.55206022851
333191830958.3647609431959.635239056865
343385333788.38152701364.6184729869856
353223232849.0448314604-617.044831460415
363148430034.97591253591449.0240874641
373190232708.3182098522-806.31820985223
383026031821.9760695241-1561.97606952408
393282333574.059810489-751.059810489009
403201831725.3233004298292.676699570216
413210033295.1235750392-1195.12357503922
423195231885.064548530166.9354514699189
433327431689.73302039581584.26697960416
442949130920.4591504531-1429.4591504531
453275131694.19836591131056.80163408874
463364333935.2817615288-292.281761528771
473122632384.3818833418-1158.38188334177
483097630689.0556733099286.94432669006
492888031409.0958495424-2529.0958495424
502932529328.9514775937-3.95147759369502
513492332071.98298904962851.01701095044
523264232136.9719309042505.028069095832
533148732798.1565489508-1311.15654895081
543383232169.73837796911662.2616220309
553272433541.5227360185-817.522736018538
562954529946.5332456222-401.533245622199
573233832702.717398227-364.717398227043
583274333540.2310132954-797.231013295415
593223131208.18688739081022.81311260923
603253631212.90333208481323.09666791516

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 30740 & 29698.5480769231 & 1041.45192307693 \tabularnewline
14 & 32086 & 31386.2817122964 & 699.718287703647 \tabularnewline
15 & 33947 & 33593.6654596503 & 353.334540349664 \tabularnewline
16 & 31312 & 31113.7929749725 & 198.207025027536 \tabularnewline
17 & 33239 & 33060.9030091818 & 178.096990818245 \tabularnewline
18 & 32362 & 32365.2059069 & -3.20590689998789 \tabularnewline
19 & 32170 & 31610.6267454838 & 559.373254516155 \tabularnewline
20 & 32665 & 32671.5761189587 & -6.57611895865557 \tabularnewline
21 & 31412 & 33727.2819293039 & -2315.28192930391 \tabularnewline
22 & 34891 & 32338.1024898239 & 2552.89751017607 \tabularnewline
23 & 33919 & 34381.7439658199 & -462.743965819856 \tabularnewline
24 & 30706 & 32925.0972473649 & -2219.0972473649 \tabularnewline
25 & 32846 & 33189.397815578 & -343.397815577991 \tabularnewline
26 & 31368 & 34161.8574597025 & -2793.85745970248 \tabularnewline
27 & 33130 & 34860.8051811524 & -1730.80518115238 \tabularnewline
28 & 31665 & 31443.0010182341 & 221.998981765915 \tabularnewline
29 & 33139 & 33265.3680338107 & -126.368033810679 \tabularnewline
30 & 32201 & 32220.6176086911 & -19.6176086911037 \tabularnewline
31 & 32230 & 31703.974868579 & 526.025131420989 \tabularnewline
32 & 30287 & 32255.5520602285 & -1968.55206022851 \tabularnewline
33 & 31918 & 30958.3647609431 & 959.635239056865 \tabularnewline
34 & 33853 & 33788.381527013 & 64.6184729869856 \tabularnewline
35 & 32232 & 32849.0448314604 & -617.044831460415 \tabularnewline
36 & 31484 & 30034.9759125359 & 1449.0240874641 \tabularnewline
37 & 31902 & 32708.3182098522 & -806.31820985223 \tabularnewline
38 & 30260 & 31821.9760695241 & -1561.97606952408 \tabularnewline
39 & 32823 & 33574.059810489 & -751.059810489009 \tabularnewline
40 & 32018 & 31725.3233004298 & 292.676699570216 \tabularnewline
41 & 32100 & 33295.1235750392 & -1195.12357503922 \tabularnewline
42 & 31952 & 31885.0645485301 & 66.9354514699189 \tabularnewline
43 & 33274 & 31689.7330203958 & 1584.26697960416 \tabularnewline
44 & 29491 & 30920.4591504531 & -1429.4591504531 \tabularnewline
45 & 32751 & 31694.1983659113 & 1056.80163408874 \tabularnewline
46 & 33643 & 33935.2817615288 & -292.281761528771 \tabularnewline
47 & 31226 & 32384.3818833418 & -1158.38188334177 \tabularnewline
48 & 30976 & 30689.0556733099 & 286.94432669006 \tabularnewline
49 & 28880 & 31409.0958495424 & -2529.0958495424 \tabularnewline
50 & 29325 & 29328.9514775937 & -3.95147759369502 \tabularnewline
51 & 34923 & 32071.9829890496 & 2851.01701095044 \tabularnewline
52 & 32642 & 32136.9719309042 & 505.028069095832 \tabularnewline
53 & 31487 & 32798.1565489508 & -1311.15654895081 \tabularnewline
54 & 33832 & 32169.7383779691 & 1662.2616220309 \tabularnewline
55 & 32724 & 33541.5227360185 & -817.522736018538 \tabularnewline
56 & 29545 & 29946.5332456222 & -401.533245622199 \tabularnewline
57 & 32338 & 32702.717398227 & -364.717398227043 \tabularnewline
58 & 32743 & 33540.2310132954 & -797.231013295415 \tabularnewline
59 & 32231 & 31208.1868873908 & 1022.81311260923 \tabularnewline
60 & 32536 & 31212.9033320848 & 1323.09666791516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]30740[/C][C]29698.5480769231[/C][C]1041.45192307693[/C][/ROW]
[ROW][C]14[/C][C]32086[/C][C]31386.2817122964[/C][C]699.718287703647[/C][/ROW]
[ROW][C]15[/C][C]33947[/C][C]33593.6654596503[/C][C]353.334540349664[/C][/ROW]
[ROW][C]16[/C][C]31312[/C][C]31113.7929749725[/C][C]198.207025027536[/C][/ROW]
[ROW][C]17[/C][C]33239[/C][C]33060.9030091818[/C][C]178.096990818245[/C][/ROW]
[ROW][C]18[/C][C]32362[/C][C]32365.2059069[/C][C]-3.20590689998789[/C][/ROW]
[ROW][C]19[/C][C]32170[/C][C]31610.6267454838[/C][C]559.373254516155[/C][/ROW]
[ROW][C]20[/C][C]32665[/C][C]32671.5761189587[/C][C]-6.57611895865557[/C][/ROW]
[ROW][C]21[/C][C]31412[/C][C]33727.2819293039[/C][C]-2315.28192930391[/C][/ROW]
[ROW][C]22[/C][C]34891[/C][C]32338.1024898239[/C][C]2552.89751017607[/C][/ROW]
[ROW][C]23[/C][C]33919[/C][C]34381.7439658199[/C][C]-462.743965819856[/C][/ROW]
[ROW][C]24[/C][C]30706[/C][C]32925.0972473649[/C][C]-2219.0972473649[/C][/ROW]
[ROW][C]25[/C][C]32846[/C][C]33189.397815578[/C][C]-343.397815577991[/C][/ROW]
[ROW][C]26[/C][C]31368[/C][C]34161.8574597025[/C][C]-2793.85745970248[/C][/ROW]
[ROW][C]27[/C][C]33130[/C][C]34860.8051811524[/C][C]-1730.80518115238[/C][/ROW]
[ROW][C]28[/C][C]31665[/C][C]31443.0010182341[/C][C]221.998981765915[/C][/ROW]
[ROW][C]29[/C][C]33139[/C][C]33265.3680338107[/C][C]-126.368033810679[/C][/ROW]
[ROW][C]30[/C][C]32201[/C][C]32220.6176086911[/C][C]-19.6176086911037[/C][/ROW]
[ROW][C]31[/C][C]32230[/C][C]31703.974868579[/C][C]526.025131420989[/C][/ROW]
[ROW][C]32[/C][C]30287[/C][C]32255.5520602285[/C][C]-1968.55206022851[/C][/ROW]
[ROW][C]33[/C][C]31918[/C][C]30958.3647609431[/C][C]959.635239056865[/C][/ROW]
[ROW][C]34[/C][C]33853[/C][C]33788.381527013[/C][C]64.6184729869856[/C][/ROW]
[ROW][C]35[/C][C]32232[/C][C]32849.0448314604[/C][C]-617.044831460415[/C][/ROW]
[ROW][C]36[/C][C]31484[/C][C]30034.9759125359[/C][C]1449.0240874641[/C][/ROW]
[ROW][C]37[/C][C]31902[/C][C]32708.3182098522[/C][C]-806.31820985223[/C][/ROW]
[ROW][C]38[/C][C]30260[/C][C]31821.9760695241[/C][C]-1561.97606952408[/C][/ROW]
[ROW][C]39[/C][C]32823[/C][C]33574.059810489[/C][C]-751.059810489009[/C][/ROW]
[ROW][C]40[/C][C]32018[/C][C]31725.3233004298[/C][C]292.676699570216[/C][/ROW]
[ROW][C]41[/C][C]32100[/C][C]33295.1235750392[/C][C]-1195.12357503922[/C][/ROW]
[ROW][C]42[/C][C]31952[/C][C]31885.0645485301[/C][C]66.9354514699189[/C][/ROW]
[ROW][C]43[/C][C]33274[/C][C]31689.7330203958[/C][C]1584.26697960416[/C][/ROW]
[ROW][C]44[/C][C]29491[/C][C]30920.4591504531[/C][C]-1429.4591504531[/C][/ROW]
[ROW][C]45[/C][C]32751[/C][C]31694.1983659113[/C][C]1056.80163408874[/C][/ROW]
[ROW][C]46[/C][C]33643[/C][C]33935.2817615288[/C][C]-292.281761528771[/C][/ROW]
[ROW][C]47[/C][C]31226[/C][C]32384.3818833418[/C][C]-1158.38188334177[/C][/ROW]
[ROW][C]48[/C][C]30976[/C][C]30689.0556733099[/C][C]286.94432669006[/C][/ROW]
[ROW][C]49[/C][C]28880[/C][C]31409.0958495424[/C][C]-2529.0958495424[/C][/ROW]
[ROW][C]50[/C][C]29325[/C][C]29328.9514775937[/C][C]-3.95147759369502[/C][/ROW]
[ROW][C]51[/C][C]34923[/C][C]32071.9829890496[/C][C]2851.01701095044[/C][/ROW]
[ROW][C]52[/C][C]32642[/C][C]32136.9719309042[/C][C]505.028069095832[/C][/ROW]
[ROW][C]53[/C][C]31487[/C][C]32798.1565489508[/C][C]-1311.15654895081[/C][/ROW]
[ROW][C]54[/C][C]33832[/C][C]32169.7383779691[/C][C]1662.2616220309[/C][/ROW]
[ROW][C]55[/C][C]32724[/C][C]33541.5227360185[/C][C]-817.522736018538[/C][/ROW]
[ROW][C]56[/C][C]29545[/C][C]29946.5332456222[/C][C]-401.533245622199[/C][/ROW]
[ROW][C]57[/C][C]32338[/C][C]32702.717398227[/C][C]-364.717398227043[/C][/ROW]
[ROW][C]58[/C][C]32743[/C][C]33540.2310132954[/C][C]-797.231013295415[/C][/ROW]
[ROW][C]59[/C][C]32231[/C][C]31208.1868873908[/C][C]1022.81311260923[/C][/ROW]
[ROW][C]60[/C][C]32536[/C][C]31212.9033320848[/C][C]1323.09666791516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
133074029698.54807692311041.45192307693
143208631386.2817122964699.718287703647
153394733593.6654596503353.334540349664
163131231113.7929749725198.207025027536
173323933060.9030091818178.096990818245
183236232365.2059069-3.20590689998789
193217031610.6267454838559.373254516155
203266532671.5761189587-6.57611895865557
213141233727.2819293039-2315.28192930391
223489132338.10248982392552.89751017607
233391934381.7439658199-462.743965819856
243070632925.0972473649-2219.0972473649
253284633189.397815578-343.397815577991
263136834161.8574597025-2793.85745970248
273313034860.8051811524-1730.80518115238
283166531443.0010182341221.998981765915
293313933265.3680338107-126.368033810679
303220132220.6176086911-19.6176086911037
313223031703.974868579526.025131420989
323028732255.5520602285-1968.55206022851
333191830958.3647609431959.635239056865
343385333788.38152701364.6184729869856
353223232849.0448314604-617.044831460415
363148430034.97591253591449.0240874641
373190232708.3182098522-806.31820985223
383026031821.9760695241-1561.97606952408
393282333574.059810489-751.059810489009
403201831725.3233004298292.676699570216
413210033295.1235750392-1195.12357503922
423195231885.064548530166.9354514699189
433327431689.73302039581584.26697960416
442949130920.4591504531-1429.4591504531
453275131694.19836591131056.80163408874
463364333935.2817615288-292.281761528771
473122632384.3818833418-1158.38188334177
483097630689.0556733099286.94432669006
492888031409.0958495424-2529.0958495424
502932529328.9514775937-3.95147759369502
513492332071.98298904962851.01701095044
523264232136.9719309042505.028069095832
533148732798.1565489508-1311.15654895081
543383232169.73837796911662.2616220309
553272433541.5227360185-817.522736018538
562954529946.5332456222-401.533245622199
573233832702.717398227-364.717398227043
583274333540.2310132954-797.231013295415
593223131208.18688739081022.81311260923
603253631212.90333208481323.09666791516







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6130461.615888408128023.133172208632900.0986046077
6230976.989594955628383.376407129933570.6027827813
6335664.716178981932909.60455774538419.8278002188
6433225.680048326330303.037397806736148.3226988458
6532527.026416689229431.119523265835622.9333101126
6634331.631944322331056.994802743837606.2690859009
6733503.802085272830045.207445160736962.3967253848
6830477.455937882826829.890312323134125.0215634425
6933418.017984765729576.659786593837259.3761829376
7034126.016738543530086.217189122338165.8162879648
7133306.805071910229064.071537443337549.5386063771
7233182.197327349528732.178763925637632.2158907734

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 30461.6158884081 & 28023.1331722086 & 32900.0986046077 \tabularnewline
62 & 30976.9895949556 & 28383.3764071299 & 33570.6027827813 \tabularnewline
63 & 35664.7161789819 & 32909.604557745 & 38419.8278002188 \tabularnewline
64 & 33225.6800483263 & 30303.0373978067 & 36148.3226988458 \tabularnewline
65 & 32527.0264166892 & 29431.1195232658 & 35622.9333101126 \tabularnewline
66 & 34331.6319443223 & 31056.9948027438 & 37606.2690859009 \tabularnewline
67 & 33503.8020852728 & 30045.2074451607 & 36962.3967253848 \tabularnewline
68 & 30477.4559378828 & 26829.8903123231 & 34125.0215634425 \tabularnewline
69 & 33418.0179847657 & 29576.6597865938 & 37259.3761829376 \tabularnewline
70 & 34126.0167385435 & 30086.2171891223 & 38165.8162879648 \tabularnewline
71 & 33306.8050719102 & 29064.0715374433 & 37549.5386063771 \tabularnewline
72 & 33182.1973273495 & 28732.1787639256 & 37632.2158907734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]30461.6158884081[/C][C]28023.1331722086[/C][C]32900.0986046077[/C][/ROW]
[ROW][C]62[/C][C]30976.9895949556[/C][C]28383.3764071299[/C][C]33570.6027827813[/C][/ROW]
[ROW][C]63[/C][C]35664.7161789819[/C][C]32909.604557745[/C][C]38419.8278002188[/C][/ROW]
[ROW][C]64[/C][C]33225.6800483263[/C][C]30303.0373978067[/C][C]36148.3226988458[/C][/ROW]
[ROW][C]65[/C][C]32527.0264166892[/C][C]29431.1195232658[/C][C]35622.9333101126[/C][/ROW]
[ROW][C]66[/C][C]34331.6319443223[/C][C]31056.9948027438[/C][C]37606.2690859009[/C][/ROW]
[ROW][C]67[/C][C]33503.8020852728[/C][C]30045.2074451607[/C][C]36962.3967253848[/C][/ROW]
[ROW][C]68[/C][C]30477.4559378828[/C][C]26829.8903123231[/C][C]34125.0215634425[/C][/ROW]
[ROW][C]69[/C][C]33418.0179847657[/C][C]29576.6597865938[/C][C]37259.3761829376[/C][/ROW]
[ROW][C]70[/C][C]34126.0167385435[/C][C]30086.2171891223[/C][C]38165.8162879648[/C][/ROW]
[ROW][C]71[/C][C]33306.8050719102[/C][C]29064.0715374433[/C][C]37549.5386063771[/C][/ROW]
[ROW][C]72[/C][C]33182.1973273495[/C][C]28732.1787639256[/C][C]37632.2158907734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
6130461.615888408128023.133172208632900.0986046077
6230976.989594955628383.376407129933570.6027827813
6335664.716178981932909.60455774538419.8278002188
6433225.680048326330303.037397806736148.3226988458
6532527.026416689229431.119523265835622.9333101126
6634331.631944322331056.994802743837606.2690859009
6733503.802085272830045.207445160736962.3967253848
6830477.455937882826829.890312323134125.0215634425
6933418.017984765729576.659786593837259.3761829376
7034126.016738543530086.217189122338165.8162879648
7133306.805071910229064.071537443337549.5386063771
7233182.197327349528732.178763925637632.2158907734



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')