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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 May 2011 12:47:33 +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/2011/May/18/t1305722632wbhg0tcuo6b2idv.htm/, Retrieved Tue, 14 May 2024 06:24:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121826, Retrieved Tue, 14 May 2024 06:24:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gegevens werkloos...] [2011-05-18 12:47:33] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
476
475
470
461
455
456
517
525
523
519
509
512
519
517
510
509
501
507
569
580
578
565
547
555
562
561
555
544
537
543
594
611
613
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121826&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121826&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121826&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 time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121826&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121826&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121826&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
alpha1
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3470474-4
4461469-8
5455460-5
64564542
751745562
85255169
9523524-1
10519522-3
11509518-9
125125084
135195118
14517518-1
15510516-6
165095090
17501508-7
185075007
1956950663
2058056812
21578579-1
22565577-12
23547564-17
245555469
255625548
265615610
27555560-5
28544554-10
29537543-6
305435367
3159454252
3261159318
336136103
34611612-1
35594610-16
365955932
37591594-3
38589590-1
39584588-4
40573583-10
41567572-5
425695663
4362156853
446296209
456286280
46612627-15
47595611-16
485975943
49593596-3
50590592-2
51580589-9
52574579-5
535735730
545735721
5562057248
566266197
57620625-5
58588619-31
59566587-21
60557565-8
615615565
62549560-11
63532548-16
64526531-5
65511525-14
66499510-11
6755549857
6856555411
69542564-22
70527541-14
71510526-16
725145095
735175134
74508516-8
75493507-14
76490492-2
77469489-20
7847846810
7952847751
805345277
81518533-15
82506517-11
83502505-3
8451650115

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 470 & 474 & -4 \tabularnewline
4 & 461 & 469 & -8 \tabularnewline
5 & 455 & 460 & -5 \tabularnewline
6 & 456 & 454 & 2 \tabularnewline
7 & 517 & 455 & 62 \tabularnewline
8 & 525 & 516 & 9 \tabularnewline
9 & 523 & 524 & -1 \tabularnewline
10 & 519 & 522 & -3 \tabularnewline
11 & 509 & 518 & -9 \tabularnewline
12 & 512 & 508 & 4 \tabularnewline
13 & 519 & 511 & 8 \tabularnewline
14 & 517 & 518 & -1 \tabularnewline
15 & 510 & 516 & -6 \tabularnewline
16 & 509 & 509 & 0 \tabularnewline
17 & 501 & 508 & -7 \tabularnewline
18 & 507 & 500 & 7 \tabularnewline
19 & 569 & 506 & 63 \tabularnewline
20 & 580 & 568 & 12 \tabularnewline
21 & 578 & 579 & -1 \tabularnewline
22 & 565 & 577 & -12 \tabularnewline
23 & 547 & 564 & -17 \tabularnewline
24 & 555 & 546 & 9 \tabularnewline
25 & 562 & 554 & 8 \tabularnewline
26 & 561 & 561 & 0 \tabularnewline
27 & 555 & 560 & -5 \tabularnewline
28 & 544 & 554 & -10 \tabularnewline
29 & 537 & 543 & -6 \tabularnewline
30 & 543 & 536 & 7 \tabularnewline
31 & 594 & 542 & 52 \tabularnewline
32 & 611 & 593 & 18 \tabularnewline
33 & 613 & 610 & 3 \tabularnewline
34 & 611 & 612 & -1 \tabularnewline
35 & 594 & 610 & -16 \tabularnewline
36 & 595 & 593 & 2 \tabularnewline
37 & 591 & 594 & -3 \tabularnewline
38 & 589 & 590 & -1 \tabularnewline
39 & 584 & 588 & -4 \tabularnewline
40 & 573 & 583 & -10 \tabularnewline
41 & 567 & 572 & -5 \tabularnewline
42 & 569 & 566 & 3 \tabularnewline
43 & 621 & 568 & 53 \tabularnewline
44 & 629 & 620 & 9 \tabularnewline
45 & 628 & 628 & 0 \tabularnewline
46 & 612 & 627 & -15 \tabularnewline
47 & 595 & 611 & -16 \tabularnewline
48 & 597 & 594 & 3 \tabularnewline
49 & 593 & 596 & -3 \tabularnewline
50 & 590 & 592 & -2 \tabularnewline
51 & 580 & 589 & -9 \tabularnewline
52 & 574 & 579 & -5 \tabularnewline
53 & 573 & 573 & 0 \tabularnewline
54 & 573 & 572 & 1 \tabularnewline
55 & 620 & 572 & 48 \tabularnewline
56 & 626 & 619 & 7 \tabularnewline
57 & 620 & 625 & -5 \tabularnewline
58 & 588 & 619 & -31 \tabularnewline
59 & 566 & 587 & -21 \tabularnewline
60 & 557 & 565 & -8 \tabularnewline
61 & 561 & 556 & 5 \tabularnewline
62 & 549 & 560 & -11 \tabularnewline
63 & 532 & 548 & -16 \tabularnewline
64 & 526 & 531 & -5 \tabularnewline
65 & 511 & 525 & -14 \tabularnewline
66 & 499 & 510 & -11 \tabularnewline
67 & 555 & 498 & 57 \tabularnewline
68 & 565 & 554 & 11 \tabularnewline
69 & 542 & 564 & -22 \tabularnewline
70 & 527 & 541 & -14 \tabularnewline
71 & 510 & 526 & -16 \tabularnewline
72 & 514 & 509 & 5 \tabularnewline
73 & 517 & 513 & 4 \tabularnewline
74 & 508 & 516 & -8 \tabularnewline
75 & 493 & 507 & -14 \tabularnewline
76 & 490 & 492 & -2 \tabularnewline
77 & 469 & 489 & -20 \tabularnewline
78 & 478 & 468 & 10 \tabularnewline
79 & 528 & 477 & 51 \tabularnewline
80 & 534 & 527 & 7 \tabularnewline
81 & 518 & 533 & -15 \tabularnewline
82 & 506 & 517 & -11 \tabularnewline
83 & 502 & 505 & -3 \tabularnewline
84 & 516 & 501 & 15 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121826&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]3[/C][C]470[/C][C]474[/C][C]-4[/C][/ROW]
[ROW][C]4[/C][C]461[/C][C]469[/C][C]-8[/C][/ROW]
[ROW][C]5[/C][C]455[/C][C]460[/C][C]-5[/C][/ROW]
[ROW][C]6[/C][C]456[/C][C]454[/C][C]2[/C][/ROW]
[ROW][C]7[/C][C]517[/C][C]455[/C][C]62[/C][/ROW]
[ROW][C]8[/C][C]525[/C][C]516[/C][C]9[/C][/ROW]
[ROW][C]9[/C][C]523[/C][C]524[/C][C]-1[/C][/ROW]
[ROW][C]10[/C][C]519[/C][C]522[/C][C]-3[/C][/ROW]
[ROW][C]11[/C][C]509[/C][C]518[/C][C]-9[/C][/ROW]
[ROW][C]12[/C][C]512[/C][C]508[/C][C]4[/C][/ROW]
[ROW][C]13[/C][C]519[/C][C]511[/C][C]8[/C][/ROW]
[ROW][C]14[/C][C]517[/C][C]518[/C][C]-1[/C][/ROW]
[ROW][C]15[/C][C]510[/C][C]516[/C][C]-6[/C][/ROW]
[ROW][C]16[/C][C]509[/C][C]509[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]501[/C][C]508[/C][C]-7[/C][/ROW]
[ROW][C]18[/C][C]507[/C][C]500[/C][C]7[/C][/ROW]
[ROW][C]19[/C][C]569[/C][C]506[/C][C]63[/C][/ROW]
[ROW][C]20[/C][C]580[/C][C]568[/C][C]12[/C][/ROW]
[ROW][C]21[/C][C]578[/C][C]579[/C][C]-1[/C][/ROW]
[ROW][C]22[/C][C]565[/C][C]577[/C][C]-12[/C][/ROW]
[ROW][C]23[/C][C]547[/C][C]564[/C][C]-17[/C][/ROW]
[ROW][C]24[/C][C]555[/C][C]546[/C][C]9[/C][/ROW]
[ROW][C]25[/C][C]562[/C][C]554[/C][C]8[/C][/ROW]
[ROW][C]26[/C][C]561[/C][C]561[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]555[/C][C]560[/C][C]-5[/C][/ROW]
[ROW][C]28[/C][C]544[/C][C]554[/C][C]-10[/C][/ROW]
[ROW][C]29[/C][C]537[/C][C]543[/C][C]-6[/C][/ROW]
[ROW][C]30[/C][C]543[/C][C]536[/C][C]7[/C][/ROW]
[ROW][C]31[/C][C]594[/C][C]542[/C][C]52[/C][/ROW]
[ROW][C]32[/C][C]611[/C][C]593[/C][C]18[/C][/ROW]
[ROW][C]33[/C][C]613[/C][C]610[/C][C]3[/C][/ROW]
[ROW][C]34[/C][C]611[/C][C]612[/C][C]-1[/C][/ROW]
[ROW][C]35[/C][C]594[/C][C]610[/C][C]-16[/C][/ROW]
[ROW][C]36[/C][C]595[/C][C]593[/C][C]2[/C][/ROW]
[ROW][C]37[/C][C]591[/C][C]594[/C][C]-3[/C][/ROW]
[ROW][C]38[/C][C]589[/C][C]590[/C][C]-1[/C][/ROW]
[ROW][C]39[/C][C]584[/C][C]588[/C][C]-4[/C][/ROW]
[ROW][C]40[/C][C]573[/C][C]583[/C][C]-10[/C][/ROW]
[ROW][C]41[/C][C]567[/C][C]572[/C][C]-5[/C][/ROW]
[ROW][C]42[/C][C]569[/C][C]566[/C][C]3[/C][/ROW]
[ROW][C]43[/C][C]621[/C][C]568[/C][C]53[/C][/ROW]
[ROW][C]44[/C][C]629[/C][C]620[/C][C]9[/C][/ROW]
[ROW][C]45[/C][C]628[/C][C]628[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]612[/C][C]627[/C][C]-15[/C][/ROW]
[ROW][C]47[/C][C]595[/C][C]611[/C][C]-16[/C][/ROW]
[ROW][C]48[/C][C]597[/C][C]594[/C][C]3[/C][/ROW]
[ROW][C]49[/C][C]593[/C][C]596[/C][C]-3[/C][/ROW]
[ROW][C]50[/C][C]590[/C][C]592[/C][C]-2[/C][/ROW]
[ROW][C]51[/C][C]580[/C][C]589[/C][C]-9[/C][/ROW]
[ROW][C]52[/C][C]574[/C][C]579[/C][C]-5[/C][/ROW]
[ROW][C]53[/C][C]573[/C][C]573[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]573[/C][C]572[/C][C]1[/C][/ROW]
[ROW][C]55[/C][C]620[/C][C]572[/C][C]48[/C][/ROW]
[ROW][C]56[/C][C]626[/C][C]619[/C][C]7[/C][/ROW]
[ROW][C]57[/C][C]620[/C][C]625[/C][C]-5[/C][/ROW]
[ROW][C]58[/C][C]588[/C][C]619[/C][C]-31[/C][/ROW]
[ROW][C]59[/C][C]566[/C][C]587[/C][C]-21[/C][/ROW]
[ROW][C]60[/C][C]557[/C][C]565[/C][C]-8[/C][/ROW]
[ROW][C]61[/C][C]561[/C][C]556[/C][C]5[/C][/ROW]
[ROW][C]62[/C][C]549[/C][C]560[/C][C]-11[/C][/ROW]
[ROW][C]63[/C][C]532[/C][C]548[/C][C]-16[/C][/ROW]
[ROW][C]64[/C][C]526[/C][C]531[/C][C]-5[/C][/ROW]
[ROW][C]65[/C][C]511[/C][C]525[/C][C]-14[/C][/ROW]
[ROW][C]66[/C][C]499[/C][C]510[/C][C]-11[/C][/ROW]
[ROW][C]67[/C][C]555[/C][C]498[/C][C]57[/C][/ROW]
[ROW][C]68[/C][C]565[/C][C]554[/C][C]11[/C][/ROW]
[ROW][C]69[/C][C]542[/C][C]564[/C][C]-22[/C][/ROW]
[ROW][C]70[/C][C]527[/C][C]541[/C][C]-14[/C][/ROW]
[ROW][C]71[/C][C]510[/C][C]526[/C][C]-16[/C][/ROW]
[ROW][C]72[/C][C]514[/C][C]509[/C][C]5[/C][/ROW]
[ROW][C]73[/C][C]517[/C][C]513[/C][C]4[/C][/ROW]
[ROW][C]74[/C][C]508[/C][C]516[/C][C]-8[/C][/ROW]
[ROW][C]75[/C][C]493[/C][C]507[/C][C]-14[/C][/ROW]
[ROW][C]76[/C][C]490[/C][C]492[/C][C]-2[/C][/ROW]
[ROW][C]77[/C][C]469[/C][C]489[/C][C]-20[/C][/ROW]
[ROW][C]78[/C][C]478[/C][C]468[/C][C]10[/C][/ROW]
[ROW][C]79[/C][C]528[/C][C]477[/C][C]51[/C][/ROW]
[ROW][C]80[/C][C]534[/C][C]527[/C][C]7[/C][/ROW]
[ROW][C]81[/C][C]518[/C][C]533[/C][C]-15[/C][/ROW]
[ROW][C]82[/C][C]506[/C][C]517[/C][C]-11[/C][/ROW]
[ROW][C]83[/C][C]502[/C][C]505[/C][C]-3[/C][/ROW]
[ROW][C]84[/C][C]516[/C][C]501[/C][C]15[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121826&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121826&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
3470474-4
4461469-8
5455460-5
64564542
751745562
85255169
9523524-1
10519522-3
11509518-9
125125084
135195118
14517518-1
15510516-6
165095090
17501508-7
185075007
1956950663
2058056812
21578579-1
22565577-12
23547564-17
245555469
255625548
265615610
27555560-5
28544554-10
29537543-6
305435367
3159454252
3261159318
336136103
34611612-1
35594610-16
365955932
37591594-3
38589590-1
39584588-4
40573583-10
41567572-5
425695663
4362156853
446296209
456286280
46612627-15
47595611-16
485975943
49593596-3
50590592-2
51580589-9
52574579-5
535735730
545735721
5562057248
566266197
57620625-5
58588619-31
59566587-21
60557565-8
615615565
62549560-11
63532548-16
64526531-5
65511525-14
66499510-11
6755549857
6856555411
69542564-22
70527541-14
71510526-16
725145095
735175134
74508516-8
75493507-14
76490492-2
77469489-20
7847846810
7952847751
805345277
81518533-15
82506517-11
83502505-3
8451650115







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85515477.949966289217552.050033710783
86514461.603339839831566.396660160169
87513448.827459190785577.172540809215
88512437.899932578435586.100067421565
89511428.153606054031593.846393945969
90510419.246322455667600.753677544333
91509410.974824734709607.025175265291
92508403.206679679661612.793320320339
93507395.849898867652618.150101132348
94506388.837506087906623.162493912094
95505382.118939711315627.881060288685
96504375.654918381569632.34508161843

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 515 & 477.949966289217 & 552.050033710783 \tabularnewline
86 & 514 & 461.603339839831 & 566.396660160169 \tabularnewline
87 & 513 & 448.827459190785 & 577.172540809215 \tabularnewline
88 & 512 & 437.899932578435 & 586.100067421565 \tabularnewline
89 & 511 & 428.153606054031 & 593.846393945969 \tabularnewline
90 & 510 & 419.246322455667 & 600.753677544333 \tabularnewline
91 & 509 & 410.974824734709 & 607.025175265291 \tabularnewline
92 & 508 & 403.206679679661 & 612.793320320339 \tabularnewline
93 & 507 & 395.849898867652 & 618.150101132348 \tabularnewline
94 & 506 & 388.837506087906 & 623.162493912094 \tabularnewline
95 & 505 & 382.118939711315 & 627.881060288685 \tabularnewline
96 & 504 & 375.654918381569 & 632.34508161843 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121826&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]85[/C][C]515[/C][C]477.949966289217[/C][C]552.050033710783[/C][/ROW]
[ROW][C]86[/C][C]514[/C][C]461.603339839831[/C][C]566.396660160169[/C][/ROW]
[ROW][C]87[/C][C]513[/C][C]448.827459190785[/C][C]577.172540809215[/C][/ROW]
[ROW][C]88[/C][C]512[/C][C]437.899932578435[/C][C]586.100067421565[/C][/ROW]
[ROW][C]89[/C][C]511[/C][C]428.153606054031[/C][C]593.846393945969[/C][/ROW]
[ROW][C]90[/C][C]510[/C][C]419.246322455667[/C][C]600.753677544333[/C][/ROW]
[ROW][C]91[/C][C]509[/C][C]410.974824734709[/C][C]607.025175265291[/C][/ROW]
[ROW][C]92[/C][C]508[/C][C]403.206679679661[/C][C]612.793320320339[/C][/ROW]
[ROW][C]93[/C][C]507[/C][C]395.849898867652[/C][C]618.150101132348[/C][/ROW]
[ROW][C]94[/C][C]506[/C][C]388.837506087906[/C][C]623.162493912094[/C][/ROW]
[ROW][C]95[/C][C]505[/C][C]382.118939711315[/C][C]627.881060288685[/C][/ROW]
[ROW][C]96[/C][C]504[/C][C]375.654918381569[/C][C]632.34508161843[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121826&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121826&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
85515477.949966289217552.050033710783
86514461.603339839831566.396660160169
87513448.827459190785577.172540809215
88512437.899932578435586.100067421565
89511428.153606054031593.846393945969
90510419.246322455667600.753677544333
91509410.974824734709607.025175265291
92508403.206679679661612.793320320339
93507395.849898867652618.150101132348
94506388.837506087906623.162493912094
95505382.118939711315627.881060288685
96504375.654918381569632.34508161843



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')