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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 15:22:29 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/28/t1338233020yivzi64kf2mb2cu.htm/, Retrieved Thu, 02 May 2024 03:55:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167862, Retrieved Thu, 02 May 2024 03:55:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [werkloosheid] [2012-05-28 19:22:29] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
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
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167862&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167862&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167862&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.79958475419847
beta0.193045695066485
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.79958475419847 \tabularnewline
beta & 0.193045695066485 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167862&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]0.79958475419847[/C][/ROW]
[ROW][C]beta[/C][C]0.193045695066485[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167862&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167862&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
alpha0.79958475419847
beta0.193045695066485
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13561590.546981204633-29.5469812046326
14549550.566515007488-1.56651500748819
15532528.4009440458433.59905595415728
16526521.9307476645484.06925233545155
17511506.6639765235284.33602347647212
18499494.6229454888664.37705451113408
19555555.847983051436-0.84798305143579
20565555.6399387328969.36006126710379
21542554.934355304029-12.9343553040294
22527512.09226197200914.9077380279912
23510502.9429701353287.05702986467196
24514501.11804935079412.8819506492059
25517512.5604760180534.43952398194654
26508513.205218529442-5.20521852944228
27493496.958756256623-3.95875625662285
28490490.428704291724-0.428704291724216
29469477.392640972135-8.39264097213533
30478458.87794187312319.1220581268767
31528533.671226221265-5.67122622126544
32534536.522681524719-2.52268152471947
33518525.64089322074-7.6408932207396
34506497.4845621994178.51543780058267
35502485.42586670513416.5741332948663
36516496.87049980646419.1295001935357
37528517.07911743426810.9208825657322
38533527.3473173444975.65268265550299
39536527.5484148575218.45158514247873
40537541.569643617947-4.56964361794655
41524531.537952250634-7.53795225063357
42536527.9703915554788.02960844452218
43587603.781085025389-16.7810850253885
44597606.280141932036-9.28014193203649
45581593.635888992656-12.6358889926557
46564567.442330632014-3.44233063201432
47558548.3276397113549.67236028864556
48575556.10409726572918.8959027342714
49580576.0188123647013.98118763529874
50575579.735140389586-4.73514038958615
51563570.311248097787-7.31124809778737
52552565.465453061588-13.4654530615879
53537542.492282748867-5.4922827488673
54545539.1973341950075.80266580499278
55601603.669495171766-2.66949517176567
56604615.998794895717-11.9987948957166
57586596.696682227465-10.6966822274646
58564570.45415763852-6.4541576385202
59549547.8730315794361.12696842056425
60551545.6113006227235.38869937727691

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 561 & 590.546981204633 & -29.5469812046326 \tabularnewline
14 & 549 & 550.566515007488 & -1.56651500748819 \tabularnewline
15 & 532 & 528.400944045843 & 3.59905595415728 \tabularnewline
16 & 526 & 521.930747664548 & 4.06925233545155 \tabularnewline
17 & 511 & 506.663976523528 & 4.33602347647212 \tabularnewline
18 & 499 & 494.622945488866 & 4.37705451113408 \tabularnewline
19 & 555 & 555.847983051436 & -0.84798305143579 \tabularnewline
20 & 565 & 555.639938732896 & 9.36006126710379 \tabularnewline
21 & 542 & 554.934355304029 & -12.9343553040294 \tabularnewline
22 & 527 & 512.092261972009 & 14.9077380279912 \tabularnewline
23 & 510 & 502.942970135328 & 7.05702986467196 \tabularnewline
24 & 514 & 501.118049350794 & 12.8819506492059 \tabularnewline
25 & 517 & 512.560476018053 & 4.43952398194654 \tabularnewline
26 & 508 & 513.205218529442 & -5.20521852944228 \tabularnewline
27 & 493 & 496.958756256623 & -3.95875625662285 \tabularnewline
28 & 490 & 490.428704291724 & -0.428704291724216 \tabularnewline
29 & 469 & 477.392640972135 & -8.39264097213533 \tabularnewline
30 & 478 & 458.877941873123 & 19.1220581268767 \tabularnewline
31 & 528 & 533.671226221265 & -5.67122622126544 \tabularnewline
32 & 534 & 536.522681524719 & -2.52268152471947 \tabularnewline
33 & 518 & 525.64089322074 & -7.6408932207396 \tabularnewline
34 & 506 & 497.484562199417 & 8.51543780058267 \tabularnewline
35 & 502 & 485.425866705134 & 16.5741332948663 \tabularnewline
36 & 516 & 496.870499806464 & 19.1295001935357 \tabularnewline
37 & 528 & 517.079117434268 & 10.9208825657322 \tabularnewline
38 & 533 & 527.347317344497 & 5.65268265550299 \tabularnewline
39 & 536 & 527.548414857521 & 8.45158514247873 \tabularnewline
40 & 537 & 541.569643617947 & -4.56964361794655 \tabularnewline
41 & 524 & 531.537952250634 & -7.53795225063357 \tabularnewline
42 & 536 & 527.970391555478 & 8.02960844452218 \tabularnewline
43 & 587 & 603.781085025389 & -16.7810850253885 \tabularnewline
44 & 597 & 606.280141932036 & -9.28014193203649 \tabularnewline
45 & 581 & 593.635888992656 & -12.6358889926557 \tabularnewline
46 & 564 & 567.442330632014 & -3.44233063201432 \tabularnewline
47 & 558 & 548.327639711354 & 9.67236028864556 \tabularnewline
48 & 575 & 556.104097265729 & 18.8959027342714 \tabularnewline
49 & 580 & 576.018812364701 & 3.98118763529874 \tabularnewline
50 & 575 & 579.735140389586 & -4.73514038958615 \tabularnewline
51 & 563 & 570.311248097787 & -7.31124809778737 \tabularnewline
52 & 552 & 565.465453061588 & -13.4654530615879 \tabularnewline
53 & 537 & 542.492282748867 & -5.4922827488673 \tabularnewline
54 & 545 & 539.197334195007 & 5.80266580499278 \tabularnewline
55 & 601 & 603.669495171766 & -2.66949517176567 \tabularnewline
56 & 604 & 615.998794895717 & -11.9987948957166 \tabularnewline
57 & 586 & 596.696682227465 & -10.6966822274646 \tabularnewline
58 & 564 & 570.45415763852 & -6.4541576385202 \tabularnewline
59 & 549 & 547.873031579436 & 1.12696842056425 \tabularnewline
60 & 551 & 545.611300622723 & 5.38869937727691 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167862&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]561[/C][C]590.546981204633[/C][C]-29.5469812046326[/C][/ROW]
[ROW][C]14[/C][C]549[/C][C]550.566515007488[/C][C]-1.56651500748819[/C][/ROW]
[ROW][C]15[/C][C]532[/C][C]528.400944045843[/C][C]3.59905595415728[/C][/ROW]
[ROW][C]16[/C][C]526[/C][C]521.930747664548[/C][C]4.06925233545155[/C][/ROW]
[ROW][C]17[/C][C]511[/C][C]506.663976523528[/C][C]4.33602347647212[/C][/ROW]
[ROW][C]18[/C][C]499[/C][C]494.622945488866[/C][C]4.37705451113408[/C][/ROW]
[ROW][C]19[/C][C]555[/C][C]555.847983051436[/C][C]-0.84798305143579[/C][/ROW]
[ROW][C]20[/C][C]565[/C][C]555.639938732896[/C][C]9.36006126710379[/C][/ROW]
[ROW][C]21[/C][C]542[/C][C]554.934355304029[/C][C]-12.9343553040294[/C][/ROW]
[ROW][C]22[/C][C]527[/C][C]512.092261972009[/C][C]14.9077380279912[/C][/ROW]
[ROW][C]23[/C][C]510[/C][C]502.942970135328[/C][C]7.05702986467196[/C][/ROW]
[ROW][C]24[/C][C]514[/C][C]501.118049350794[/C][C]12.8819506492059[/C][/ROW]
[ROW][C]25[/C][C]517[/C][C]512.560476018053[/C][C]4.43952398194654[/C][/ROW]
[ROW][C]26[/C][C]508[/C][C]513.205218529442[/C][C]-5.20521852944228[/C][/ROW]
[ROW][C]27[/C][C]493[/C][C]496.958756256623[/C][C]-3.95875625662285[/C][/ROW]
[ROW][C]28[/C][C]490[/C][C]490.428704291724[/C][C]-0.428704291724216[/C][/ROW]
[ROW][C]29[/C][C]469[/C][C]477.392640972135[/C][C]-8.39264097213533[/C][/ROW]
[ROW][C]30[/C][C]478[/C][C]458.877941873123[/C][C]19.1220581268767[/C][/ROW]
[ROW][C]31[/C][C]528[/C][C]533.671226221265[/C][C]-5.67122622126544[/C][/ROW]
[ROW][C]32[/C][C]534[/C][C]536.522681524719[/C][C]-2.52268152471947[/C][/ROW]
[ROW][C]33[/C][C]518[/C][C]525.64089322074[/C][C]-7.6408932207396[/C][/ROW]
[ROW][C]34[/C][C]506[/C][C]497.484562199417[/C][C]8.51543780058267[/C][/ROW]
[ROW][C]35[/C][C]502[/C][C]485.425866705134[/C][C]16.5741332948663[/C][/ROW]
[ROW][C]36[/C][C]516[/C][C]496.870499806464[/C][C]19.1295001935357[/C][/ROW]
[ROW][C]37[/C][C]528[/C][C]517.079117434268[/C][C]10.9208825657322[/C][/ROW]
[ROW][C]38[/C][C]533[/C][C]527.347317344497[/C][C]5.65268265550299[/C][/ROW]
[ROW][C]39[/C][C]536[/C][C]527.548414857521[/C][C]8.45158514247873[/C][/ROW]
[ROW][C]40[/C][C]537[/C][C]541.569643617947[/C][C]-4.56964361794655[/C][/ROW]
[ROW][C]41[/C][C]524[/C][C]531.537952250634[/C][C]-7.53795225063357[/C][/ROW]
[ROW][C]42[/C][C]536[/C][C]527.970391555478[/C][C]8.02960844452218[/C][/ROW]
[ROW][C]43[/C][C]587[/C][C]603.781085025389[/C][C]-16.7810850253885[/C][/ROW]
[ROW][C]44[/C][C]597[/C][C]606.280141932036[/C][C]-9.28014193203649[/C][/ROW]
[ROW][C]45[/C][C]581[/C][C]593.635888992656[/C][C]-12.6358889926557[/C][/ROW]
[ROW][C]46[/C][C]564[/C][C]567.442330632014[/C][C]-3.44233063201432[/C][/ROW]
[ROW][C]47[/C][C]558[/C][C]548.327639711354[/C][C]9.67236028864556[/C][/ROW]
[ROW][C]48[/C][C]575[/C][C]556.104097265729[/C][C]18.8959027342714[/C][/ROW]
[ROW][C]49[/C][C]580[/C][C]576.018812364701[/C][C]3.98118763529874[/C][/ROW]
[ROW][C]50[/C][C]575[/C][C]579.735140389586[/C][C]-4.73514038958615[/C][/ROW]
[ROW][C]51[/C][C]563[/C][C]570.311248097787[/C][C]-7.31124809778737[/C][/ROW]
[ROW][C]52[/C][C]552[/C][C]565.465453061588[/C][C]-13.4654530615879[/C][/ROW]
[ROW][C]53[/C][C]537[/C][C]542.492282748867[/C][C]-5.4922827488673[/C][/ROW]
[ROW][C]54[/C][C]545[/C][C]539.197334195007[/C][C]5.80266580499278[/C][/ROW]
[ROW][C]55[/C][C]601[/C][C]603.669495171766[/C][C]-2.66949517176567[/C][/ROW]
[ROW][C]56[/C][C]604[/C][C]615.998794895717[/C][C]-11.9987948957166[/C][/ROW]
[ROW][C]57[/C][C]586[/C][C]596.696682227465[/C][C]-10.6966822274646[/C][/ROW]
[ROW][C]58[/C][C]564[/C][C]570.45415763852[/C][C]-6.4541576385202[/C][/ROW]
[ROW][C]59[/C][C]549[/C][C]547.873031579436[/C][C]1.12696842056425[/C][/ROW]
[ROW][C]60[/C][C]551[/C][C]545.611300622723[/C][C]5.38869937727691[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167862&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167862&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
13561590.546981204633-29.5469812046326
14549550.566515007488-1.56651500748819
15532528.4009440458433.59905595415728
16526521.9307476645484.06925233545155
17511506.6639765235284.33602347647212
18499494.6229454888664.37705451113408
19555555.847983051436-0.84798305143579
20565555.6399387328969.36006126710379
21542554.934355304029-12.9343553040294
22527512.09226197200914.9077380279912
23510502.9429701353287.05702986467196
24514501.11804935079412.8819506492059
25517512.5604760180534.43952398194654
26508513.205218529442-5.20521852944228
27493496.958756256623-3.95875625662285
28490490.428704291724-0.428704291724216
29469477.392640972135-8.39264097213533
30478458.87794187312319.1220581268767
31528533.671226221265-5.67122622126544
32534536.522681524719-2.52268152471947
33518525.64089322074-7.6408932207396
34506497.4845621994178.51543780058267
35502485.42586670513416.5741332948663
36516496.87049980646419.1295001935357
37528517.07911743426810.9208825657322
38533527.3473173444975.65268265550299
39536527.5484148575218.45158514247873
40537541.569643617947-4.56964361794655
41524531.537952250634-7.53795225063357
42536527.9703915554788.02960844452218
43587603.781085025389-16.7810850253885
44597606.280141932036-9.28014193203649
45581593.635888992656-12.6358889926557
46564567.442330632014-3.44233063201432
47558548.3276397113549.67236028864556
48575556.10409726572918.8959027342714
49580576.0188123647013.98118763529874
50575579.735140389586-4.73514038958615
51563570.311248097787-7.31124809778737
52552565.465453061588-13.4654530615879
53537542.492282748867-5.4922827488673
54545539.1973341950075.80266580499278
55601603.669495171766-2.66949517176567
56604615.998794895717-11.9987948957166
57586596.696682227465-10.6966822274646
58564570.45415763852-6.4541576385202
59549547.8730315794361.12696842056425
60551545.6113006227235.38869937727691







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61544.832880915595524.673850505436564.991911325754
62536.447860528201508.733650055583564.162071000818
63524.287027815378489.169572977466559.404482653291
64518.704895800046475.696730652613561.713060947478
65505.400446278617454.893540770781555.907351786453
66506.006369919352446.498826629447565.513913209257
67556.250640125665481.088483826616631.412796424714
68564.462784803227477.705490131918651.220079474537
69553.93573126906457.989638400904649.881824137217
70537.904844737237433.755460445062642.054229029411
71523.587190581746411.064671417049636.109709746443
72522.060470777005399.727754475117644.393187078894

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 544.832880915595 & 524.673850505436 & 564.991911325754 \tabularnewline
62 & 536.447860528201 & 508.733650055583 & 564.162071000818 \tabularnewline
63 & 524.287027815378 & 489.169572977466 & 559.404482653291 \tabularnewline
64 & 518.704895800046 & 475.696730652613 & 561.713060947478 \tabularnewline
65 & 505.400446278617 & 454.893540770781 & 555.907351786453 \tabularnewline
66 & 506.006369919352 & 446.498826629447 & 565.513913209257 \tabularnewline
67 & 556.250640125665 & 481.088483826616 & 631.412796424714 \tabularnewline
68 & 564.462784803227 & 477.705490131918 & 651.220079474537 \tabularnewline
69 & 553.93573126906 & 457.989638400904 & 649.881824137217 \tabularnewline
70 & 537.904844737237 & 433.755460445062 & 642.054229029411 \tabularnewline
71 & 523.587190581746 & 411.064671417049 & 636.109709746443 \tabularnewline
72 & 522.060470777005 & 399.727754475117 & 644.393187078894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167862&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]544.832880915595[/C][C]524.673850505436[/C][C]564.991911325754[/C][/ROW]
[ROW][C]62[/C][C]536.447860528201[/C][C]508.733650055583[/C][C]564.162071000818[/C][/ROW]
[ROW][C]63[/C][C]524.287027815378[/C][C]489.169572977466[/C][C]559.404482653291[/C][/ROW]
[ROW][C]64[/C][C]518.704895800046[/C][C]475.696730652613[/C][C]561.713060947478[/C][/ROW]
[ROW][C]65[/C][C]505.400446278617[/C][C]454.893540770781[/C][C]555.907351786453[/C][/ROW]
[ROW][C]66[/C][C]506.006369919352[/C][C]446.498826629447[/C][C]565.513913209257[/C][/ROW]
[ROW][C]67[/C][C]556.250640125665[/C][C]481.088483826616[/C][C]631.412796424714[/C][/ROW]
[ROW][C]68[/C][C]564.462784803227[/C][C]477.705490131918[/C][C]651.220079474537[/C][/ROW]
[ROW][C]69[/C][C]553.93573126906[/C][C]457.989638400904[/C][C]649.881824137217[/C][/ROW]
[ROW][C]70[/C][C]537.904844737237[/C][C]433.755460445062[/C][C]642.054229029411[/C][/ROW]
[ROW][C]71[/C][C]523.587190581746[/C][C]411.064671417049[/C][C]636.109709746443[/C][/ROW]
[ROW][C]72[/C][C]522.060470777005[/C][C]399.727754475117[/C][C]644.393187078894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167862&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167862&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
61544.832880915595524.673850505436564.991911325754
62536.447860528201508.733650055583564.162071000818
63524.287027815378489.169572977466559.404482653291
64518.704895800046475.696730652613561.713060947478
65505.400446278617454.893540770781555.907351786453
66506.006369919352446.498826629447565.513913209257
67556.250640125665481.088483826616631.412796424714
68564.462784803227477.705490131918651.220079474537
69553.93573126906457.989638400904649.881824137217
70537.904844737237433.755460445062642.054229029411
71523.587190581746411.064671417049636.109709746443
72522.060470777005399.727754475117644.393187078894



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=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')