Free Statistics

of Irreproducible Research!

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, 28 Dec 2010 23:11:20 +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/29/t1293577801kr98xey9m3hxr6a.htm/, Retrieved Fri, 03 May 2024 05:59:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116586, Retrieved Fri, 03 May 2024 05:59:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Paper Exponential...] [2010-12-28 23:11:20] [a2e464febd5f86100a78930292e787b9] [Current]
Feedback Forum

Post a new message
Dataseries X:
1203
1319
1328
1260
1286
1274
1389
1255
1244
1336
1214
1239
1174
1061
1116
1123
1086
1074
965
1035
1016
941
1003
998
891
828
833
887
842
793
778
699
686
727
641
619
627
593
535
536
504
487
477
435
433
393
389
377
339
370
350
341
367
396
408
405
391
396
368
356




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116586&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116586&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116586&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.51204887375077
beta0
gamma0.581472577695563

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.51204887375077 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.581472577695563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116586&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]0.51204887375077[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.581472577695563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116586&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116586&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
alpha0.51204887375077
beta0
gamma0.581472577695563







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311741274.22783119658-100.227831196582
1410611116.34086936098-55.3408693609758
1511161141.27155911272-25.2715591127196
1611231140.89087197821-17.8908719782114
1710861099.5811240451-13.5811240451021
1810741079.06151102062-5.06151102062427
199651152.73768958346-187.737689583456
201035914.166403318762120.833596681238
211016964.2236966577351.776303342269
229411076.87861405154-135.878614051538
231003878.945042340052124.054957659948
24998963.73516327344734.2648367265526
25891893.444024734543-2.44402473454306
26828798.36293749062229.6370625093784
27833875.33805293588-42.33805293588
28887868.3126106910318.6873893089695
29842846.955525893215-4.95552589321539
30793833.26991218812-40.2699121881208
31778837.086920059398-59.0869200593984
32699751.942107946567-52.9421079465669
33686693.424107852443-7.42410785244329
34727722.5221542811174.47784571888337
35641670.208953791284-29.2089537912836
36619651.044292583544-32.044292583544
37627536.38422648836590.615773511635
38593498.05667740116894.9433225988323
39535588.050275933568-53.0502759335682
40536592.854412849929-56.8544128499291
41504526.108024296281-22.1080242962807
42487493.619735244879-6.61973524487928
43477509.328324930364-32.3283249303644
44435439.628690081141-4.62869008114097
45433418.76435242456614.2356475754337
46393462.330195883101-69.330195883101
47389362.66570848281626.3342915171839
48377371.1374322394995.86256776050124
49339310.68989627425628.3101037257437
50370241.686655509333128.313344490667
51350306.77708298106343.2229170189369
52341359.798451396197-18.7984513961973
53367322.39717478918644.6028252108143
54396328.462596432267.5374035678003
55408374.84896225546533.1510377445351
56405346.53718423053758.4628157694629
57391363.33116336850727.6688366314934
58396390.0653027458135.93469725418726
59368356.08302317298811.9169768270118
60356351.3639309212294.63606907877067

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1174 & 1274.22783119658 & -100.227831196582 \tabularnewline
14 & 1061 & 1116.34086936098 & -55.3408693609758 \tabularnewline
15 & 1116 & 1141.27155911272 & -25.2715591127196 \tabularnewline
16 & 1123 & 1140.89087197821 & -17.8908719782114 \tabularnewline
17 & 1086 & 1099.5811240451 & -13.5811240451021 \tabularnewline
18 & 1074 & 1079.06151102062 & -5.06151102062427 \tabularnewline
19 & 965 & 1152.73768958346 & -187.737689583456 \tabularnewline
20 & 1035 & 914.166403318762 & 120.833596681238 \tabularnewline
21 & 1016 & 964.22369665773 & 51.776303342269 \tabularnewline
22 & 941 & 1076.87861405154 & -135.878614051538 \tabularnewline
23 & 1003 & 878.945042340052 & 124.054957659948 \tabularnewline
24 & 998 & 963.735163273447 & 34.2648367265526 \tabularnewline
25 & 891 & 893.444024734543 & -2.44402473454306 \tabularnewline
26 & 828 & 798.362937490622 & 29.6370625093784 \tabularnewline
27 & 833 & 875.33805293588 & -42.33805293588 \tabularnewline
28 & 887 & 868.31261069103 & 18.6873893089695 \tabularnewline
29 & 842 & 846.955525893215 & -4.95552589321539 \tabularnewline
30 & 793 & 833.26991218812 & -40.2699121881208 \tabularnewline
31 & 778 & 837.086920059398 & -59.0869200593984 \tabularnewline
32 & 699 & 751.942107946567 & -52.9421079465669 \tabularnewline
33 & 686 & 693.424107852443 & -7.42410785244329 \tabularnewline
34 & 727 & 722.522154281117 & 4.47784571888337 \tabularnewline
35 & 641 & 670.208953791284 & -29.2089537912836 \tabularnewline
36 & 619 & 651.044292583544 & -32.044292583544 \tabularnewline
37 & 627 & 536.384226488365 & 90.615773511635 \tabularnewline
38 & 593 & 498.056677401168 & 94.9433225988323 \tabularnewline
39 & 535 & 588.050275933568 & -53.0502759335682 \tabularnewline
40 & 536 & 592.854412849929 & -56.8544128499291 \tabularnewline
41 & 504 & 526.108024296281 & -22.1080242962807 \tabularnewline
42 & 487 & 493.619735244879 & -6.61973524487928 \tabularnewline
43 & 477 & 509.328324930364 & -32.3283249303644 \tabularnewline
44 & 435 & 439.628690081141 & -4.62869008114097 \tabularnewline
45 & 433 & 418.764352424566 & 14.2356475754337 \tabularnewline
46 & 393 & 462.330195883101 & -69.330195883101 \tabularnewline
47 & 389 & 362.665708482816 & 26.3342915171839 \tabularnewline
48 & 377 & 371.137432239499 & 5.86256776050124 \tabularnewline
49 & 339 & 310.689896274256 & 28.3101037257437 \tabularnewline
50 & 370 & 241.686655509333 & 128.313344490667 \tabularnewline
51 & 350 & 306.777082981063 & 43.2229170189369 \tabularnewline
52 & 341 & 359.798451396197 & -18.7984513961973 \tabularnewline
53 & 367 & 322.397174789186 & 44.6028252108143 \tabularnewline
54 & 396 & 328.4625964322 & 67.5374035678003 \tabularnewline
55 & 408 & 374.848962255465 & 33.1510377445351 \tabularnewline
56 & 405 & 346.537184230537 & 58.4628157694629 \tabularnewline
57 & 391 & 363.331163368507 & 27.6688366314934 \tabularnewline
58 & 396 & 390.065302745813 & 5.93469725418726 \tabularnewline
59 & 368 & 356.083023172988 & 11.9169768270118 \tabularnewline
60 & 356 & 351.363930921229 & 4.63606907877067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116586&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]1174[/C][C]1274.22783119658[/C][C]-100.227831196582[/C][/ROW]
[ROW][C]14[/C][C]1061[/C][C]1116.34086936098[/C][C]-55.3408693609758[/C][/ROW]
[ROW][C]15[/C][C]1116[/C][C]1141.27155911272[/C][C]-25.2715591127196[/C][/ROW]
[ROW][C]16[/C][C]1123[/C][C]1140.89087197821[/C][C]-17.8908719782114[/C][/ROW]
[ROW][C]17[/C][C]1086[/C][C]1099.5811240451[/C][C]-13.5811240451021[/C][/ROW]
[ROW][C]18[/C][C]1074[/C][C]1079.06151102062[/C][C]-5.06151102062427[/C][/ROW]
[ROW][C]19[/C][C]965[/C][C]1152.73768958346[/C][C]-187.737689583456[/C][/ROW]
[ROW][C]20[/C][C]1035[/C][C]914.166403318762[/C][C]120.833596681238[/C][/ROW]
[ROW][C]21[/C][C]1016[/C][C]964.22369665773[/C][C]51.776303342269[/C][/ROW]
[ROW][C]22[/C][C]941[/C][C]1076.87861405154[/C][C]-135.878614051538[/C][/ROW]
[ROW][C]23[/C][C]1003[/C][C]878.945042340052[/C][C]124.054957659948[/C][/ROW]
[ROW][C]24[/C][C]998[/C][C]963.735163273447[/C][C]34.2648367265526[/C][/ROW]
[ROW][C]25[/C][C]891[/C][C]893.444024734543[/C][C]-2.44402473454306[/C][/ROW]
[ROW][C]26[/C][C]828[/C][C]798.362937490622[/C][C]29.6370625093784[/C][/ROW]
[ROW][C]27[/C][C]833[/C][C]875.33805293588[/C][C]-42.33805293588[/C][/ROW]
[ROW][C]28[/C][C]887[/C][C]868.31261069103[/C][C]18.6873893089695[/C][/ROW]
[ROW][C]29[/C][C]842[/C][C]846.955525893215[/C][C]-4.95552589321539[/C][/ROW]
[ROW][C]30[/C][C]793[/C][C]833.26991218812[/C][C]-40.2699121881208[/C][/ROW]
[ROW][C]31[/C][C]778[/C][C]837.086920059398[/C][C]-59.0869200593984[/C][/ROW]
[ROW][C]32[/C][C]699[/C][C]751.942107946567[/C][C]-52.9421079465669[/C][/ROW]
[ROW][C]33[/C][C]686[/C][C]693.424107852443[/C][C]-7.42410785244329[/C][/ROW]
[ROW][C]34[/C][C]727[/C][C]722.522154281117[/C][C]4.47784571888337[/C][/ROW]
[ROW][C]35[/C][C]641[/C][C]670.208953791284[/C][C]-29.2089537912836[/C][/ROW]
[ROW][C]36[/C][C]619[/C][C]651.044292583544[/C][C]-32.044292583544[/C][/ROW]
[ROW][C]37[/C][C]627[/C][C]536.384226488365[/C][C]90.615773511635[/C][/ROW]
[ROW][C]38[/C][C]593[/C][C]498.056677401168[/C][C]94.9433225988323[/C][/ROW]
[ROW][C]39[/C][C]535[/C][C]588.050275933568[/C][C]-53.0502759335682[/C][/ROW]
[ROW][C]40[/C][C]536[/C][C]592.854412849929[/C][C]-56.8544128499291[/C][/ROW]
[ROW][C]41[/C][C]504[/C][C]526.108024296281[/C][C]-22.1080242962807[/C][/ROW]
[ROW][C]42[/C][C]487[/C][C]493.619735244879[/C][C]-6.61973524487928[/C][/ROW]
[ROW][C]43[/C][C]477[/C][C]509.328324930364[/C][C]-32.3283249303644[/C][/ROW]
[ROW][C]44[/C][C]435[/C][C]439.628690081141[/C][C]-4.62869008114097[/C][/ROW]
[ROW][C]45[/C][C]433[/C][C]418.764352424566[/C][C]14.2356475754337[/C][/ROW]
[ROW][C]46[/C][C]393[/C][C]462.330195883101[/C][C]-69.330195883101[/C][/ROW]
[ROW][C]47[/C][C]389[/C][C]362.665708482816[/C][C]26.3342915171839[/C][/ROW]
[ROW][C]48[/C][C]377[/C][C]371.137432239499[/C][C]5.86256776050124[/C][/ROW]
[ROW][C]49[/C][C]339[/C][C]310.689896274256[/C][C]28.3101037257437[/C][/ROW]
[ROW][C]50[/C][C]370[/C][C]241.686655509333[/C][C]128.313344490667[/C][/ROW]
[ROW][C]51[/C][C]350[/C][C]306.777082981063[/C][C]43.2229170189369[/C][/ROW]
[ROW][C]52[/C][C]341[/C][C]359.798451396197[/C][C]-18.7984513961973[/C][/ROW]
[ROW][C]53[/C][C]367[/C][C]322.397174789186[/C][C]44.6028252108143[/C][/ROW]
[ROW][C]54[/C][C]396[/C][C]328.4625964322[/C][C]67.5374035678003[/C][/ROW]
[ROW][C]55[/C][C]408[/C][C]374.848962255465[/C][C]33.1510377445351[/C][/ROW]
[ROW][C]56[/C][C]405[/C][C]346.537184230537[/C][C]58.4628157694629[/C][/ROW]
[ROW][C]57[/C][C]391[/C][C]363.331163368507[/C][C]27.6688366314934[/C][/ROW]
[ROW][C]58[/C][C]396[/C][C]390.065302745813[/C][C]5.93469725418726[/C][/ROW]
[ROW][C]59[/C][C]368[/C][C]356.083023172988[/C][C]11.9169768270118[/C][/ROW]
[ROW][C]60[/C][C]356[/C][C]351.363930921229[/C][C]4.63606907877067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116586&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116586&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
1311741274.22783119658-100.227831196582
1410611116.34086936098-55.3408693609758
1511161141.27155911272-25.2715591127196
1611231140.89087197821-17.8908719782114
1710861099.5811240451-13.5811240451021
1810741079.06151102062-5.06151102062427
199651152.73768958346-187.737689583456
201035914.166403318762120.833596681238
211016964.2236966577351.776303342269
229411076.87861405154-135.878614051538
231003878.945042340052124.054957659948
24998963.73516327344734.2648367265526
25891893.444024734543-2.44402473454306
26828798.36293749062229.6370625093784
27833875.33805293588-42.33805293588
28887868.3126106910318.6873893089695
29842846.955525893215-4.95552589321539
30793833.26991218812-40.2699121881208
31778837.086920059398-59.0869200593984
32699751.942107946567-52.9421079465669
33686693.424107852443-7.42410785244329
34727722.5221542811174.47784571888337
35641670.208953791284-29.2089537912836
36619651.044292583544-32.044292583544
37627536.38422648836590.615773511635
38593498.05667740116894.9433225988323
39535588.050275933568-53.0502759335682
40536592.854412849929-56.8544128499291
41504526.108024296281-22.1080242962807
42487493.619735244879-6.61973524487928
43477509.328324930364-32.3283249303644
44435439.628690081141-4.62869008114097
45433418.76435242456614.2356475754337
46393462.330195883101-69.330195883101
47389362.66570848281626.3342915171839
48377371.1374322394995.86256776050124
49339310.68989627425628.3101037257437
50370241.686655509333128.313344490667
51350306.77708298106343.2229170189369
52341359.798451396197-18.7984513961973
53367322.39717478918644.6028252108143
54396328.462596432267.5374035678003
55408374.84896225546533.1510377445351
56405346.53718423053758.4628157694629
57391363.33116336850727.6688366314934
58396390.0653027458135.93469725418726
59368356.08302317298811.9169768270118
60356351.3639309212294.63606907877067







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61296.657411537635176.420513171112416.894309904157
62241.531953464013106.448912512924376.614994415102
63216.77695346812368.3251290388298365.228777897416
64230.06874069029169.356387710883390.781093669699
65220.28204678827448.1804005905409392.383692986008
66210.01587450108727.2332362452558392.798512756918
67212.06333846765519.1902997308891404.936377204421
68173.958324722318-28.5028451235221376.419494568158
69152.079303055195-59.53601188949363.69461799988
70158.479014103048-61.9105449575624378.868573163659
71123.155232859851-105.672374667568351.98284038727
72110.268252639763-126.69712498008347.233630259605

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 296.657411537635 & 176.420513171112 & 416.894309904157 \tabularnewline
62 & 241.531953464013 & 106.448912512924 & 376.614994415102 \tabularnewline
63 & 216.776953468123 & 68.3251290388298 & 365.228777897416 \tabularnewline
64 & 230.068740690291 & 69.356387710883 & 390.781093669699 \tabularnewline
65 & 220.282046788274 & 48.1804005905409 & 392.383692986008 \tabularnewline
66 & 210.015874501087 & 27.2332362452558 & 392.798512756918 \tabularnewline
67 & 212.063338467655 & 19.1902997308891 & 404.936377204421 \tabularnewline
68 & 173.958324722318 & -28.5028451235221 & 376.419494568158 \tabularnewline
69 & 152.079303055195 & -59.53601188949 & 363.69461799988 \tabularnewline
70 & 158.479014103048 & -61.9105449575624 & 378.868573163659 \tabularnewline
71 & 123.155232859851 & -105.672374667568 & 351.98284038727 \tabularnewline
72 & 110.268252639763 & -126.69712498008 & 347.233630259605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116586&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]296.657411537635[/C][C]176.420513171112[/C][C]416.894309904157[/C][/ROW]
[ROW][C]62[/C][C]241.531953464013[/C][C]106.448912512924[/C][C]376.614994415102[/C][/ROW]
[ROW][C]63[/C][C]216.776953468123[/C][C]68.3251290388298[/C][C]365.228777897416[/C][/ROW]
[ROW][C]64[/C][C]230.068740690291[/C][C]69.356387710883[/C][C]390.781093669699[/C][/ROW]
[ROW][C]65[/C][C]220.282046788274[/C][C]48.1804005905409[/C][C]392.383692986008[/C][/ROW]
[ROW][C]66[/C][C]210.015874501087[/C][C]27.2332362452558[/C][C]392.798512756918[/C][/ROW]
[ROW][C]67[/C][C]212.063338467655[/C][C]19.1902997308891[/C][C]404.936377204421[/C][/ROW]
[ROW][C]68[/C][C]173.958324722318[/C][C]-28.5028451235221[/C][C]376.419494568158[/C][/ROW]
[ROW][C]69[/C][C]152.079303055195[/C][C]-59.53601188949[/C][C]363.69461799988[/C][/ROW]
[ROW][C]70[/C][C]158.479014103048[/C][C]-61.9105449575624[/C][C]378.868573163659[/C][/ROW]
[ROW][C]71[/C][C]123.155232859851[/C][C]-105.672374667568[/C][C]351.98284038727[/C][/ROW]
[ROW][C]72[/C][C]110.268252639763[/C][C]-126.69712498008[/C][C]347.233630259605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116586&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116586&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
61296.657411537635176.420513171112416.894309904157
62241.531953464013106.448912512924376.614994415102
63216.77695346812368.3251290388298365.228777897416
64230.06874069029169.356387710883390.781093669699
65220.28204678827448.1804005905409392.383692986008
66210.01587450108727.2332362452558392.798512756918
67212.06333846765519.1902997308891404.936377204421
68173.958324722318-28.5028451235221376.419494568158
69152.079303055195-59.53601188949363.69461799988
70158.479014103048-61.9105449575624378.868573163659
71123.155232859851-105.672374667568351.98284038727
72110.268252639763-126.69712498008347.233630259605



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')