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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 computationFri, 04 Dec 2009 07:57:32 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t12599386844ywpxzftsroyeqa.htm/, Retrieved Sun, 28 Apr 2024 05:35:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63688, Retrieved Sun, 28 Apr 2024 05:35:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
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] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [] [2009-12-04 14:57:32] [6974478841a4d28b8cb590971bfdefb0] [Current]
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Dataseries X:
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63688&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63688&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63688&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.69080418869719
beta0.352314670027524
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.69080418869719 \tabularnewline
beta & 0.352314670027524 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63688&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]0.69080418869719[/C][/ROW]
[ROW][C]beta[/C][C]0.352314670027524[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63688&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63688&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
alpha0.69080418869719
beta0.352314670027524
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13612612.089400000477-0.0894000004768714
14595594.7900953393270.209904660672578
15597596.6237350215420.376264978457925
16593592.9560583999740.0439416000259598
17590590.356680910183-0.356680910182945
18580580.67094089129-0.670940891289547
19574573.5997406189450.400259381055207
20573567.8385000651085.16149993489239
21573574.610761589671-1.61076158967148
22620626.737257475476-6.73725747547621
23626629.320333110901-3.32033311090072
24620624.710194311144-4.71019431114405
25588603.191287814961-15.1912878149610
26566569.986732423449-3.98673242344898
27557561.747652815059-4.7476528150587
28561546.37394261819114.6260573818089
29549549.142751099696-0.14275109969617
30532535.543173268248-3.54317326824810
31526522.0466314100143.95336858998564
32511516.222920374891-5.22292037489058
33499506.843186145951-7.84318614595105
34555537.57235741332517.4276425866749
35565553.5496902678211.4503097321800
36542559.096056446606-17.0960564466064
37527525.25787168311.74212831690045
38510509.9756185840740.0243814159264275
39514506.4983643523497.5016356476512
40517510.6908679081846.30913209181563
41508507.0135816624150.986418337584666
42493497.367925723622-4.36792572362214
43490489.1048223597320.895177640268116
44469481.279505899806-12.2795058998058
45478467.01405853100910.9859414689914
46528521.7757699139376.22423008606313
47534530.9425694390093.05743056099061
48518523.385386140949-5.38538614094898
49506507.70786057647-1.70786057647018
50502492.8756501659559.12434983404512
51516503.03317576021312.9668242397867
52528517.08431169351410.9156883064862
53533522.28585666057810.7141433394219
54536526.8502072677799.14979273222082
55537542.295806022562-5.29580602256215
56524536.096310404435-12.0963104044349
57536541.154767022147-5.15476702214653
58587597.340633201987-10.3406332019869
59597598.710239866005-1.71023986600528
60581586.630095682546-5.63009568254608

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 612 & 612.089400000477 & -0.0894000004768714 \tabularnewline
14 & 595 & 594.790095339327 & 0.209904660672578 \tabularnewline
15 & 597 & 596.623735021542 & 0.376264978457925 \tabularnewline
16 & 593 & 592.956058399974 & 0.0439416000259598 \tabularnewline
17 & 590 & 590.356680910183 & -0.356680910182945 \tabularnewline
18 & 580 & 580.67094089129 & -0.670940891289547 \tabularnewline
19 & 574 & 573.599740618945 & 0.400259381055207 \tabularnewline
20 & 573 & 567.838500065108 & 5.16149993489239 \tabularnewline
21 & 573 & 574.610761589671 & -1.61076158967148 \tabularnewline
22 & 620 & 626.737257475476 & -6.73725747547621 \tabularnewline
23 & 626 & 629.320333110901 & -3.32033311090072 \tabularnewline
24 & 620 & 624.710194311144 & -4.71019431114405 \tabularnewline
25 & 588 & 603.191287814961 & -15.1912878149610 \tabularnewline
26 & 566 & 569.986732423449 & -3.98673242344898 \tabularnewline
27 & 557 & 561.747652815059 & -4.7476528150587 \tabularnewline
28 & 561 & 546.373942618191 & 14.6260573818089 \tabularnewline
29 & 549 & 549.142751099696 & -0.14275109969617 \tabularnewline
30 & 532 & 535.543173268248 & -3.54317326824810 \tabularnewline
31 & 526 & 522.046631410014 & 3.95336858998564 \tabularnewline
32 & 511 & 516.222920374891 & -5.22292037489058 \tabularnewline
33 & 499 & 506.843186145951 & -7.84318614595105 \tabularnewline
34 & 555 & 537.572357413325 & 17.4276425866749 \tabularnewline
35 & 565 & 553.54969026782 & 11.4503097321800 \tabularnewline
36 & 542 & 559.096056446606 & -17.0960564466064 \tabularnewline
37 & 527 & 525.2578716831 & 1.74212831690045 \tabularnewline
38 & 510 & 509.975618584074 & 0.0243814159264275 \tabularnewline
39 & 514 & 506.498364352349 & 7.5016356476512 \tabularnewline
40 & 517 & 510.690867908184 & 6.30913209181563 \tabularnewline
41 & 508 & 507.013581662415 & 0.986418337584666 \tabularnewline
42 & 493 & 497.367925723622 & -4.36792572362214 \tabularnewline
43 & 490 & 489.104822359732 & 0.895177640268116 \tabularnewline
44 & 469 & 481.279505899806 & -12.2795058998058 \tabularnewline
45 & 478 & 467.014058531009 & 10.9859414689914 \tabularnewline
46 & 528 & 521.775769913937 & 6.22423008606313 \tabularnewline
47 & 534 & 530.942569439009 & 3.05743056099061 \tabularnewline
48 & 518 & 523.385386140949 & -5.38538614094898 \tabularnewline
49 & 506 & 507.70786057647 & -1.70786057647018 \tabularnewline
50 & 502 & 492.875650165955 & 9.12434983404512 \tabularnewline
51 & 516 & 503.033175760213 & 12.9668242397867 \tabularnewline
52 & 528 & 517.084311693514 & 10.9156883064862 \tabularnewline
53 & 533 & 522.285856660578 & 10.7141433394219 \tabularnewline
54 & 536 & 526.850207267779 & 9.14979273222082 \tabularnewline
55 & 537 & 542.295806022562 & -5.29580602256215 \tabularnewline
56 & 524 & 536.096310404435 & -12.0963104044349 \tabularnewline
57 & 536 & 541.154767022147 & -5.15476702214653 \tabularnewline
58 & 587 & 597.340633201987 & -10.3406332019869 \tabularnewline
59 & 597 & 598.710239866005 & -1.71023986600528 \tabularnewline
60 & 581 & 586.630095682546 & -5.63009568254608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63688&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]612[/C][C]612.089400000477[/C][C]-0.0894000004768714[/C][/ROW]
[ROW][C]14[/C][C]595[/C][C]594.790095339327[/C][C]0.209904660672578[/C][/ROW]
[ROW][C]15[/C][C]597[/C][C]596.623735021542[/C][C]0.376264978457925[/C][/ROW]
[ROW][C]16[/C][C]593[/C][C]592.956058399974[/C][C]0.0439416000259598[/C][/ROW]
[ROW][C]17[/C][C]590[/C][C]590.356680910183[/C][C]-0.356680910182945[/C][/ROW]
[ROW][C]18[/C][C]580[/C][C]580.67094089129[/C][C]-0.670940891289547[/C][/ROW]
[ROW][C]19[/C][C]574[/C][C]573.599740618945[/C][C]0.400259381055207[/C][/ROW]
[ROW][C]20[/C][C]573[/C][C]567.838500065108[/C][C]5.16149993489239[/C][/ROW]
[ROW][C]21[/C][C]573[/C][C]574.610761589671[/C][C]-1.61076158967148[/C][/ROW]
[ROW][C]22[/C][C]620[/C][C]626.737257475476[/C][C]-6.73725747547621[/C][/ROW]
[ROW][C]23[/C][C]626[/C][C]629.320333110901[/C][C]-3.32033311090072[/C][/ROW]
[ROW][C]24[/C][C]620[/C][C]624.710194311144[/C][C]-4.71019431114405[/C][/ROW]
[ROW][C]25[/C][C]588[/C][C]603.191287814961[/C][C]-15.1912878149610[/C][/ROW]
[ROW][C]26[/C][C]566[/C][C]569.986732423449[/C][C]-3.98673242344898[/C][/ROW]
[ROW][C]27[/C][C]557[/C][C]561.747652815059[/C][C]-4.7476528150587[/C][/ROW]
[ROW][C]28[/C][C]561[/C][C]546.373942618191[/C][C]14.6260573818089[/C][/ROW]
[ROW][C]29[/C][C]549[/C][C]549.142751099696[/C][C]-0.14275109969617[/C][/ROW]
[ROW][C]30[/C][C]532[/C][C]535.543173268248[/C][C]-3.54317326824810[/C][/ROW]
[ROW][C]31[/C][C]526[/C][C]522.046631410014[/C][C]3.95336858998564[/C][/ROW]
[ROW][C]32[/C][C]511[/C][C]516.222920374891[/C][C]-5.22292037489058[/C][/ROW]
[ROW][C]33[/C][C]499[/C][C]506.843186145951[/C][C]-7.84318614595105[/C][/ROW]
[ROW][C]34[/C][C]555[/C][C]537.572357413325[/C][C]17.4276425866749[/C][/ROW]
[ROW][C]35[/C][C]565[/C][C]553.54969026782[/C][C]11.4503097321800[/C][/ROW]
[ROW][C]36[/C][C]542[/C][C]559.096056446606[/C][C]-17.0960564466064[/C][/ROW]
[ROW][C]37[/C][C]527[/C][C]525.2578716831[/C][C]1.74212831690045[/C][/ROW]
[ROW][C]38[/C][C]510[/C][C]509.975618584074[/C][C]0.0243814159264275[/C][/ROW]
[ROW][C]39[/C][C]514[/C][C]506.498364352349[/C][C]7.5016356476512[/C][/ROW]
[ROW][C]40[/C][C]517[/C][C]510.690867908184[/C][C]6.30913209181563[/C][/ROW]
[ROW][C]41[/C][C]508[/C][C]507.013581662415[/C][C]0.986418337584666[/C][/ROW]
[ROW][C]42[/C][C]493[/C][C]497.367925723622[/C][C]-4.36792572362214[/C][/ROW]
[ROW][C]43[/C][C]490[/C][C]489.104822359732[/C][C]0.895177640268116[/C][/ROW]
[ROW][C]44[/C][C]469[/C][C]481.279505899806[/C][C]-12.2795058998058[/C][/ROW]
[ROW][C]45[/C][C]478[/C][C]467.014058531009[/C][C]10.9859414689914[/C][/ROW]
[ROW][C]46[/C][C]528[/C][C]521.775769913937[/C][C]6.22423008606313[/C][/ROW]
[ROW][C]47[/C][C]534[/C][C]530.942569439009[/C][C]3.05743056099061[/C][/ROW]
[ROW][C]48[/C][C]518[/C][C]523.385386140949[/C][C]-5.38538614094898[/C][/ROW]
[ROW][C]49[/C][C]506[/C][C]507.70786057647[/C][C]-1.70786057647018[/C][/ROW]
[ROW][C]50[/C][C]502[/C][C]492.875650165955[/C][C]9.12434983404512[/C][/ROW]
[ROW][C]51[/C][C]516[/C][C]503.033175760213[/C][C]12.9668242397867[/C][/ROW]
[ROW][C]52[/C][C]528[/C][C]517.084311693514[/C][C]10.9156883064862[/C][/ROW]
[ROW][C]53[/C][C]533[/C][C]522.285856660578[/C][C]10.7141433394219[/C][/ROW]
[ROW][C]54[/C][C]536[/C][C]526.850207267779[/C][C]9.14979273222082[/C][/ROW]
[ROW][C]55[/C][C]537[/C][C]542.295806022562[/C][C]-5.29580602256215[/C][/ROW]
[ROW][C]56[/C][C]524[/C][C]536.096310404435[/C][C]-12.0963104044349[/C][/ROW]
[ROW][C]57[/C][C]536[/C][C]541.154767022147[/C][C]-5.15476702214653[/C][/ROW]
[ROW][C]58[/C][C]587[/C][C]597.340633201987[/C][C]-10.3406332019869[/C][/ROW]
[ROW][C]59[/C][C]597[/C][C]598.710239866005[/C][C]-1.71023986600528[/C][/ROW]
[ROW][C]60[/C][C]581[/C][C]586.630095682546[/C][C]-5.63009568254608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63688&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63688&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
13612612.089400000477-0.0894000004768714
14595594.7900953393270.209904660672578
15597596.6237350215420.376264978457925
16593592.9560583999740.0439416000259598
17590590.356680910183-0.356680910182945
18580580.67094089129-0.670940891289547
19574573.5997406189450.400259381055207
20573567.8385000651085.16149993489239
21573574.610761589671-1.61076158967148
22620626.737257475476-6.73725747547621
23626629.320333110901-3.32033311090072
24620624.710194311144-4.71019431114405
25588603.191287814961-15.1912878149610
26566569.986732423449-3.98673242344898
27557561.747652815059-4.7476528150587
28561546.37394261819114.6260573818089
29549549.142751099696-0.14275109969617
30532535.543173268248-3.54317326824810
31526522.0466314100143.95336858998564
32511516.222920374891-5.22292037489058
33499506.843186145951-7.84318614595105
34555537.57235741332517.4276425866749
35565553.5496902678211.4503097321800
36542559.096056446606-17.0960564466064
37527525.25787168311.74212831690045
38510509.9756185840740.0243814159264275
39514506.4983643523497.5016356476512
40517510.6908679081846.30913209181563
41508507.0135816624150.986418337584666
42493497.367925723622-4.36792572362214
43490489.1048223597320.895177640268116
44469481.279505899806-12.2795058998058
45478467.01405853100910.9859414689914
46528521.7757699139376.22423008606313
47534530.9425694390093.05743056099061
48518523.385386140949-5.38538614094898
49506507.70786057647-1.70786057647018
50502492.8756501659559.12434983404512
51516503.03317576021312.9668242397867
52528517.08431169351410.9156883064862
53533522.28585666057810.7141433394219
54536526.8502072677799.14979273222082
55537542.295806022562-5.29580602256215
56524536.096310404435-12.0963104044349
57536541.154767022147-5.15476702214653
58587597.340633201987-10.3406332019869
59597598.710239866005-1.71023986600528
60581586.630095682546-5.63009568254608







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61573.468638679858558.290906496002588.646370863714
62565.078142844615544.470844444672585.685441244558
63571.481702111999544.107572778173598.855831445825
64573.654937785177538.766432850576608.543442719777
65565.546262902462523.077712615336608.014813189589
66554.093135344403503.931279072496604.25499161631
67549.038307628732490.32242553036607.754189727104
68536.024972635493469.333113677823602.716831593163
69546.621595847538468.66320942911624.579982265965
70601.46993997143504.447779178355698.492100764505
71611.030188362045500.509429594391721.5509471297
72597.19299396077477.409265719101716.976722202439

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 573.468638679858 & 558.290906496002 & 588.646370863714 \tabularnewline
62 & 565.078142844615 & 544.470844444672 & 585.685441244558 \tabularnewline
63 & 571.481702111999 & 544.107572778173 & 598.855831445825 \tabularnewline
64 & 573.654937785177 & 538.766432850576 & 608.543442719777 \tabularnewline
65 & 565.546262902462 & 523.077712615336 & 608.014813189589 \tabularnewline
66 & 554.093135344403 & 503.931279072496 & 604.25499161631 \tabularnewline
67 & 549.038307628732 & 490.32242553036 & 607.754189727104 \tabularnewline
68 & 536.024972635493 & 469.333113677823 & 602.716831593163 \tabularnewline
69 & 546.621595847538 & 468.66320942911 & 624.579982265965 \tabularnewline
70 & 601.46993997143 & 504.447779178355 & 698.492100764505 \tabularnewline
71 & 611.030188362045 & 500.509429594391 & 721.5509471297 \tabularnewline
72 & 597.19299396077 & 477.409265719101 & 716.976722202439 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63688&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]573.468638679858[/C][C]558.290906496002[/C][C]588.646370863714[/C][/ROW]
[ROW][C]62[/C][C]565.078142844615[/C][C]544.470844444672[/C][C]585.685441244558[/C][/ROW]
[ROW][C]63[/C][C]571.481702111999[/C][C]544.107572778173[/C][C]598.855831445825[/C][/ROW]
[ROW][C]64[/C][C]573.654937785177[/C][C]538.766432850576[/C][C]608.543442719777[/C][/ROW]
[ROW][C]65[/C][C]565.546262902462[/C][C]523.077712615336[/C][C]608.014813189589[/C][/ROW]
[ROW][C]66[/C][C]554.093135344403[/C][C]503.931279072496[/C][C]604.25499161631[/C][/ROW]
[ROW][C]67[/C][C]549.038307628732[/C][C]490.32242553036[/C][C]607.754189727104[/C][/ROW]
[ROW][C]68[/C][C]536.024972635493[/C][C]469.333113677823[/C][C]602.716831593163[/C][/ROW]
[ROW][C]69[/C][C]546.621595847538[/C][C]468.66320942911[/C][C]624.579982265965[/C][/ROW]
[ROW][C]70[/C][C]601.46993997143[/C][C]504.447779178355[/C][C]698.492100764505[/C][/ROW]
[ROW][C]71[/C][C]611.030188362045[/C][C]500.509429594391[/C][C]721.5509471297[/C][/ROW]
[ROW][C]72[/C][C]597.19299396077[/C][C]477.409265719101[/C][C]716.976722202439[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63688&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63688&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
61573.468638679858558.290906496002588.646370863714
62565.078142844615544.470844444672585.685441244558
63571.481702111999544.107572778173598.855831445825
64573.654937785177538.766432850576608.543442719777
65565.546262902462523.077712615336608.014813189589
66554.093135344403503.931279072496604.25499161631
67549.038307628732490.32242553036607.754189727104
68536.024972635493469.333113677823602.716831593163
69546.621595847538468.66320942911624.579982265965
70601.46993997143504.447779178355698.492100764505
71611.030188362045500.509429594391721.5509471297
72597.19299396077477.409265719101716.976722202439



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')