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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, 23 Dec 2016 10:21:20 +0100
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/Dec/23/t14824850390w25n4cj8tpa4e9.htm/, Retrieved Fri, 01 Nov 2024 03:29:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302801, Retrieved Fri, 01 Nov 2024 03:29:22 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-23 09:21:20] [070714f07871aeb0c40d04255feda5cb] [Current]
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Dataseries X:
434.50
455.00
448.00
425.51
405.00
392.50
394.00
439.98
445.00
440.00
422.00
418.00
420.00
426.34
421.00
429.00
444.44
462.34
455.00
458.00
459.08
510.05
578.00
590.00
745.00
735.00
687.80
685.76
660.00
669.01
658.06
649.00
595.69
583.37
594.80
606.00
627.42
629.00
614.68
610.99
618.26
642.76
657.00
712.00
730.00
729.47
744.90
745.00
773.64
770.00
780.00
890.00




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302801&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302801&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302801&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0398786733727108
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0398786733727108 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302801&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]0.0398786733727108[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302801&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302801&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
beta0.0398786733727108
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3448475.5-27.5
4425.51467.40333648225-41.8933364822504
5405443.242685800182-38.2426858001817
6392.5421.207618224261-28.7076182242611
7394407.562796493787-13.5627964937873
8439.98408.52193016239131.458069837609
9445455.756436254381-10.756436254381
10440460.347483846338-20.3474838463381
11422454.536053184073-32.5360531840735
12418435.238558546309-17.2385585463086
13420430.551107700624-10.5511077006241
14426.34432.130343522911-5.79034352291058
15421438.239432304845-17.2394323048446
16429432.211946614829-3.21194661482878
17444.44440.0838584448854.35614155511456
18462.34455.6975755911276.64242440887284
19455473.862466664531-18.8624666645315
20458465.770256517413-7.77025651741303
21459.08468.460388995733-9.38038899573291
22510.05469.16631152686340.8836884731369
23578521.76669878575556.233301214245
24590591.959208237547-1.95920823754716
25745603.881077612173141.118922387827
26735764.508713024786-29.5087130247859
27687.8753.331944696421-65.5319446964215
28685.76703.518617678394-17.7586176783943
29660700.770427564447-40.7704275644468
30669.01673.384557000338-4.37455700033843
31658.06682.220105470572-24.1601054705717
32649670.30663251586-21.3066325158604
33595.69660.396952277088-64.706952277088
34583.37604.506524862287-21.1365248622866
35594.8591.3436282910693.45637170893076
36606602.9114638095043.08853619049569
37627.42614.23463053544513.185369464555
38629636.18044557762-7.18044557762039
39614.68637.47409893376-22.79409893376
40610.99622.245100507555-11.2551005075552
41618.26618.1062620306370.15373796936251
42642.76625.38239289690317.3776071030974
43657650.5753888145666.4246111854336
44712665.07159378557746.928406214423
45730721.9430363689048.05696363109621
46729.47740.264337389924-10.7943373899241
47744.9739.3038735348775.59612646512346
48745754.957039634332-9.95703963433152
49773.64754.65996610299518.9800338970051
50770784.056864675377-14.0568646753766
51780779.8562955603430.143704439657199
52890789.862026302754100.137973697246

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 448 & 475.5 & -27.5 \tabularnewline
4 & 425.51 & 467.40333648225 & -41.8933364822504 \tabularnewline
5 & 405 & 443.242685800182 & -38.2426858001817 \tabularnewline
6 & 392.5 & 421.207618224261 & -28.7076182242611 \tabularnewline
7 & 394 & 407.562796493787 & -13.5627964937873 \tabularnewline
8 & 439.98 & 408.521930162391 & 31.458069837609 \tabularnewline
9 & 445 & 455.756436254381 & -10.756436254381 \tabularnewline
10 & 440 & 460.347483846338 & -20.3474838463381 \tabularnewline
11 & 422 & 454.536053184073 & -32.5360531840735 \tabularnewline
12 & 418 & 435.238558546309 & -17.2385585463086 \tabularnewline
13 & 420 & 430.551107700624 & -10.5511077006241 \tabularnewline
14 & 426.34 & 432.130343522911 & -5.79034352291058 \tabularnewline
15 & 421 & 438.239432304845 & -17.2394323048446 \tabularnewline
16 & 429 & 432.211946614829 & -3.21194661482878 \tabularnewline
17 & 444.44 & 440.083858444885 & 4.35614155511456 \tabularnewline
18 & 462.34 & 455.697575591127 & 6.64242440887284 \tabularnewline
19 & 455 & 473.862466664531 & -18.8624666645315 \tabularnewline
20 & 458 & 465.770256517413 & -7.77025651741303 \tabularnewline
21 & 459.08 & 468.460388995733 & -9.38038899573291 \tabularnewline
22 & 510.05 & 469.166311526863 & 40.8836884731369 \tabularnewline
23 & 578 & 521.766698785755 & 56.233301214245 \tabularnewline
24 & 590 & 591.959208237547 & -1.95920823754716 \tabularnewline
25 & 745 & 603.881077612173 & 141.118922387827 \tabularnewline
26 & 735 & 764.508713024786 & -29.5087130247859 \tabularnewline
27 & 687.8 & 753.331944696421 & -65.5319446964215 \tabularnewline
28 & 685.76 & 703.518617678394 & -17.7586176783943 \tabularnewline
29 & 660 & 700.770427564447 & -40.7704275644468 \tabularnewline
30 & 669.01 & 673.384557000338 & -4.37455700033843 \tabularnewline
31 & 658.06 & 682.220105470572 & -24.1601054705717 \tabularnewline
32 & 649 & 670.30663251586 & -21.3066325158604 \tabularnewline
33 & 595.69 & 660.396952277088 & -64.706952277088 \tabularnewline
34 & 583.37 & 604.506524862287 & -21.1365248622866 \tabularnewline
35 & 594.8 & 591.343628291069 & 3.45637170893076 \tabularnewline
36 & 606 & 602.911463809504 & 3.08853619049569 \tabularnewline
37 & 627.42 & 614.234630535445 & 13.185369464555 \tabularnewline
38 & 629 & 636.18044557762 & -7.18044557762039 \tabularnewline
39 & 614.68 & 637.47409893376 & -22.79409893376 \tabularnewline
40 & 610.99 & 622.245100507555 & -11.2551005075552 \tabularnewline
41 & 618.26 & 618.106262030637 & 0.15373796936251 \tabularnewline
42 & 642.76 & 625.382392896903 & 17.3776071030974 \tabularnewline
43 & 657 & 650.575388814566 & 6.4246111854336 \tabularnewline
44 & 712 & 665.071593785577 & 46.928406214423 \tabularnewline
45 & 730 & 721.943036368904 & 8.05696363109621 \tabularnewline
46 & 729.47 & 740.264337389924 & -10.7943373899241 \tabularnewline
47 & 744.9 & 739.303873534877 & 5.59612646512346 \tabularnewline
48 & 745 & 754.957039634332 & -9.95703963433152 \tabularnewline
49 & 773.64 & 754.659966102995 & 18.9800338970051 \tabularnewline
50 & 770 & 784.056864675377 & -14.0568646753766 \tabularnewline
51 & 780 & 779.856295560343 & 0.143704439657199 \tabularnewline
52 & 890 & 789.862026302754 & 100.137973697246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302801&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]448[/C][C]475.5[/C][C]-27.5[/C][/ROW]
[ROW][C]4[/C][C]425.51[/C][C]467.40333648225[/C][C]-41.8933364822504[/C][/ROW]
[ROW][C]5[/C][C]405[/C][C]443.242685800182[/C][C]-38.2426858001817[/C][/ROW]
[ROW][C]6[/C][C]392.5[/C][C]421.207618224261[/C][C]-28.7076182242611[/C][/ROW]
[ROW][C]7[/C][C]394[/C][C]407.562796493787[/C][C]-13.5627964937873[/C][/ROW]
[ROW][C]8[/C][C]439.98[/C][C]408.521930162391[/C][C]31.458069837609[/C][/ROW]
[ROW][C]9[/C][C]445[/C][C]455.756436254381[/C][C]-10.756436254381[/C][/ROW]
[ROW][C]10[/C][C]440[/C][C]460.347483846338[/C][C]-20.3474838463381[/C][/ROW]
[ROW][C]11[/C][C]422[/C][C]454.536053184073[/C][C]-32.5360531840735[/C][/ROW]
[ROW][C]12[/C][C]418[/C][C]435.238558546309[/C][C]-17.2385585463086[/C][/ROW]
[ROW][C]13[/C][C]420[/C][C]430.551107700624[/C][C]-10.5511077006241[/C][/ROW]
[ROW][C]14[/C][C]426.34[/C][C]432.130343522911[/C][C]-5.79034352291058[/C][/ROW]
[ROW][C]15[/C][C]421[/C][C]438.239432304845[/C][C]-17.2394323048446[/C][/ROW]
[ROW][C]16[/C][C]429[/C][C]432.211946614829[/C][C]-3.21194661482878[/C][/ROW]
[ROW][C]17[/C][C]444.44[/C][C]440.083858444885[/C][C]4.35614155511456[/C][/ROW]
[ROW][C]18[/C][C]462.34[/C][C]455.697575591127[/C][C]6.64242440887284[/C][/ROW]
[ROW][C]19[/C][C]455[/C][C]473.862466664531[/C][C]-18.8624666645315[/C][/ROW]
[ROW][C]20[/C][C]458[/C][C]465.770256517413[/C][C]-7.77025651741303[/C][/ROW]
[ROW][C]21[/C][C]459.08[/C][C]468.460388995733[/C][C]-9.38038899573291[/C][/ROW]
[ROW][C]22[/C][C]510.05[/C][C]469.166311526863[/C][C]40.8836884731369[/C][/ROW]
[ROW][C]23[/C][C]578[/C][C]521.766698785755[/C][C]56.233301214245[/C][/ROW]
[ROW][C]24[/C][C]590[/C][C]591.959208237547[/C][C]-1.95920823754716[/C][/ROW]
[ROW][C]25[/C][C]745[/C][C]603.881077612173[/C][C]141.118922387827[/C][/ROW]
[ROW][C]26[/C][C]735[/C][C]764.508713024786[/C][C]-29.5087130247859[/C][/ROW]
[ROW][C]27[/C][C]687.8[/C][C]753.331944696421[/C][C]-65.5319446964215[/C][/ROW]
[ROW][C]28[/C][C]685.76[/C][C]703.518617678394[/C][C]-17.7586176783943[/C][/ROW]
[ROW][C]29[/C][C]660[/C][C]700.770427564447[/C][C]-40.7704275644468[/C][/ROW]
[ROW][C]30[/C][C]669.01[/C][C]673.384557000338[/C][C]-4.37455700033843[/C][/ROW]
[ROW][C]31[/C][C]658.06[/C][C]682.220105470572[/C][C]-24.1601054705717[/C][/ROW]
[ROW][C]32[/C][C]649[/C][C]670.30663251586[/C][C]-21.3066325158604[/C][/ROW]
[ROW][C]33[/C][C]595.69[/C][C]660.396952277088[/C][C]-64.706952277088[/C][/ROW]
[ROW][C]34[/C][C]583.37[/C][C]604.506524862287[/C][C]-21.1365248622866[/C][/ROW]
[ROW][C]35[/C][C]594.8[/C][C]591.343628291069[/C][C]3.45637170893076[/C][/ROW]
[ROW][C]36[/C][C]606[/C][C]602.911463809504[/C][C]3.08853619049569[/C][/ROW]
[ROW][C]37[/C][C]627.42[/C][C]614.234630535445[/C][C]13.185369464555[/C][/ROW]
[ROW][C]38[/C][C]629[/C][C]636.18044557762[/C][C]-7.18044557762039[/C][/ROW]
[ROW][C]39[/C][C]614.68[/C][C]637.47409893376[/C][C]-22.79409893376[/C][/ROW]
[ROW][C]40[/C][C]610.99[/C][C]622.245100507555[/C][C]-11.2551005075552[/C][/ROW]
[ROW][C]41[/C][C]618.26[/C][C]618.106262030637[/C][C]0.15373796936251[/C][/ROW]
[ROW][C]42[/C][C]642.76[/C][C]625.382392896903[/C][C]17.3776071030974[/C][/ROW]
[ROW][C]43[/C][C]657[/C][C]650.575388814566[/C][C]6.4246111854336[/C][/ROW]
[ROW][C]44[/C][C]712[/C][C]665.071593785577[/C][C]46.928406214423[/C][/ROW]
[ROW][C]45[/C][C]730[/C][C]721.943036368904[/C][C]8.05696363109621[/C][/ROW]
[ROW][C]46[/C][C]729.47[/C][C]740.264337389924[/C][C]-10.7943373899241[/C][/ROW]
[ROW][C]47[/C][C]744.9[/C][C]739.303873534877[/C][C]5.59612646512346[/C][/ROW]
[ROW][C]48[/C][C]745[/C][C]754.957039634332[/C][C]-9.95703963433152[/C][/ROW]
[ROW][C]49[/C][C]773.64[/C][C]754.659966102995[/C][C]18.9800338970051[/C][/ROW]
[ROW][C]50[/C][C]770[/C][C]784.056864675377[/C][C]-14.0568646753766[/C][/ROW]
[ROW][C]51[/C][C]780[/C][C]779.856295560343[/C][C]0.143704439657199[/C][/ROW]
[ROW][C]52[/C][C]890[/C][C]789.862026302754[/C][C]100.137973697246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302801&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302801&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
3448475.5-27.5
4425.51467.40333648225-41.8933364822504
5405443.242685800182-38.2426858001817
6392.5421.207618224261-28.7076182242611
7394407.562796493787-13.5627964937873
8439.98408.52193016239131.458069837609
9445455.756436254381-10.756436254381
10440460.347483846338-20.3474838463381
11422454.536053184073-32.5360531840735
12418435.238558546309-17.2385585463086
13420430.551107700624-10.5511077006241
14426.34432.130343522911-5.79034352291058
15421438.239432304845-17.2394323048446
16429432.211946614829-3.21194661482878
17444.44440.0838584448854.35614155511456
18462.34455.6975755911276.64242440887284
19455473.862466664531-18.8624666645315
20458465.770256517413-7.77025651741303
21459.08468.460388995733-9.38038899573291
22510.05469.16631152686340.8836884731369
23578521.76669878575556.233301214245
24590591.959208237547-1.95920823754716
25745603.881077612173141.118922387827
26735764.508713024786-29.5087130247859
27687.8753.331944696421-65.5319446964215
28685.76703.518617678394-17.7586176783943
29660700.770427564447-40.7704275644468
30669.01673.384557000338-4.37455700033843
31658.06682.220105470572-24.1601054705717
32649670.30663251586-21.3066325158604
33595.69660.396952277088-64.706952277088
34583.37604.506524862287-21.1365248622866
35594.8591.3436282910693.45637170893076
36606602.9114638095043.08853619049569
37627.42614.23463053544513.185369464555
38629636.18044557762-7.18044557762039
39614.68637.47409893376-22.79409893376
40610.99622.245100507555-11.2551005075552
41618.26618.1062620306370.15373796936251
42642.76625.38239289690317.3776071030974
43657650.5753888145666.4246111854336
44712665.07159378557746.928406214423
45730721.9430363689048.05696363109621
46729.47740.264337389924-10.7943373899241
47744.9739.3038735348775.59612646512346
48745754.957039634332-9.95703963433152
49773.64754.65996610299518.9800338970051
50770784.056864675377-14.0568646753766
51780779.8562955603430.143704439657199
52890789.862026302754100.137973697246







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
53903.855395848032835.132298162623972.57849353344
54917.710791696063818.5648273986091016.85675599352
55931.566187544095807.7267920923531055.40558299584
56945.421583392127799.6247841594531091.2183826248
57959.276979240158793.1250118691341125.42894661118
58973.13237508819787.6585864466881158.60616372969
59986.987770936222782.8949530207541191.08058885169
601000.84316678425778.6235591006291223.06277446788
611014.69856263229774.7015313192561254.69559394531
621028.55395848032771.027332774241286.08058418639
631042.40935432835767.5262166363351317.29249202036
641056.26475017638764.1416152118851348.38788514088

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
53 & 903.855395848032 & 835.132298162623 & 972.57849353344 \tabularnewline
54 & 917.710791696063 & 818.564827398609 & 1016.85675599352 \tabularnewline
55 & 931.566187544095 & 807.726792092353 & 1055.40558299584 \tabularnewline
56 & 945.421583392127 & 799.624784159453 & 1091.2183826248 \tabularnewline
57 & 959.276979240158 & 793.125011869134 & 1125.42894661118 \tabularnewline
58 & 973.13237508819 & 787.658586446688 & 1158.60616372969 \tabularnewline
59 & 986.987770936222 & 782.894953020754 & 1191.08058885169 \tabularnewline
60 & 1000.84316678425 & 778.623559100629 & 1223.06277446788 \tabularnewline
61 & 1014.69856263229 & 774.701531319256 & 1254.69559394531 \tabularnewline
62 & 1028.55395848032 & 771.02733277424 & 1286.08058418639 \tabularnewline
63 & 1042.40935432835 & 767.526216636335 & 1317.29249202036 \tabularnewline
64 & 1056.26475017638 & 764.141615211885 & 1348.38788514088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302801&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]53[/C][C]903.855395848032[/C][C]835.132298162623[/C][C]972.57849353344[/C][/ROW]
[ROW][C]54[/C][C]917.710791696063[/C][C]818.564827398609[/C][C]1016.85675599352[/C][/ROW]
[ROW][C]55[/C][C]931.566187544095[/C][C]807.726792092353[/C][C]1055.40558299584[/C][/ROW]
[ROW][C]56[/C][C]945.421583392127[/C][C]799.624784159453[/C][C]1091.2183826248[/C][/ROW]
[ROW][C]57[/C][C]959.276979240158[/C][C]793.125011869134[/C][C]1125.42894661118[/C][/ROW]
[ROW][C]58[/C][C]973.13237508819[/C][C]787.658586446688[/C][C]1158.60616372969[/C][/ROW]
[ROW][C]59[/C][C]986.987770936222[/C][C]782.894953020754[/C][C]1191.08058885169[/C][/ROW]
[ROW][C]60[/C][C]1000.84316678425[/C][C]778.623559100629[/C][C]1223.06277446788[/C][/ROW]
[ROW][C]61[/C][C]1014.69856263229[/C][C]774.701531319256[/C][C]1254.69559394531[/C][/ROW]
[ROW][C]62[/C][C]1028.55395848032[/C][C]771.02733277424[/C][C]1286.08058418639[/C][/ROW]
[ROW][C]63[/C][C]1042.40935432835[/C][C]767.526216636335[/C][C]1317.29249202036[/C][/ROW]
[ROW][C]64[/C][C]1056.26475017638[/C][C]764.141615211885[/C][C]1348.38788514088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302801&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302801&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
53903.855395848032835.132298162623972.57849353344
54917.710791696063818.5648273986091016.85675599352
55931.566187544095807.7267920923531055.40558299584
56945.421583392127799.6247841594531091.2183826248
57959.276979240158793.1250118691341125.42894661118
58973.13237508819787.6585864466881158.60616372969
59986.987770936222782.8949530207541191.08058885169
601000.84316678425778.6235591006291223.06277446788
611014.69856263229774.7015313192561254.69559394531
621028.55395848032771.027332774241286.08058418639
631042.40935432835767.5262166363351317.29249202036
641056.26475017638764.1416152118851348.38788514088



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')