Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Aug 2010 10:38:03 +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/Aug/15/t1281868780b1f8qy0nn8359cv.htm/, Retrieved Sat, 27 Apr 2024 14:04:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78819, Retrieved Sat, 27 Apr 2024 14:04:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVanhille Olivier
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks 1 - sta...] [2010-08-15 10:38:03] [ddb1c76c3acba5bf82e5ed3b5a08f68d] [Current]
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Dataseries X:
568
567
566
564
584
583
568
558
559
559
560
562
563
552
552
555
575
567
548
541
544
546
551
550
546
532
523
528
555
543
525
517
519
521
520
516
509
494
484
482
508
500
480
467
471
482
481
477
471
455
441
434
459
448
432
414
415
423
425
427
415
399
386
377
397
379
361
350
348
363
367
365
354
327
312
307
335
317
298
286
288
303
310
301
293
264
255
251
279
253
233
226
232
245
250
242
230
196
188
181
212
186
166
155
157
173
182
182
168
131
114
106
134
103
83
74
83
96
95
100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78819&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78819&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78819&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.211128878579708
beta0.136550211331593
gamma0.948390526889117

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.211128878579708 \tabularnewline
beta & 0.136550211331593 \tabularnewline
gamma & 0.948390526889117 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78819&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]0.211128878579708[/C][/ROW]
[ROW][C]beta[/C][C]0.136550211331593[/C][/ROW]
[ROW][C]gamma[/C][C]0.948390526889117[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78819&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78819&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
alpha0.211128878579708
beta0.136550211331593
gamma0.948390526889117







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13563569.188568376069-6.18856837606882
14552557.092262987191-5.09226298719102
15552555.872277613779-3.87227761377858
16555557.631563142701-2.63156314270122
17575576.326932169056-1.32693216905648
18567567.217824756121-0.217824756121104
19548554.336602126659-6.33660212665893
20541541.939179932109-0.939179932109255
21544542.0292331636131.97076683638738
22546541.540476795924.45952320408014
23551542.497402120718.50259787928951
24550545.8447312208214.15526877917864
25546543.222315748822.77768425118052
26532533.881034697877-1.88103469787677
27523534.386132710743-11.3861327107431
28528535.405013300468-7.40501330046845
29555553.848758542991.15124145700997
30543545.944217032109-2.94421703210912
31525527.682525999883-2.68252599988284
32517519.973018099372-2.97301809937187
33519521.630443341301-2.6304433413012
34521521.719244208649-0.719244208648774
35520524.145361001102-4.14536100110195
36516520.742935922923-4.74293592292281
37509514.127753015663-5.12775301566285
38494498.32058844229-4.32058844229005
39484489.817620430112-5.81762043011224
40482493.769527579601-11.7695275796007
41508516.346246663387-8.34624666338732
42500501.751671121325-1.75167112132533
43480482.351137516685-2.35113751668501
44467472.917405498617-5.9174054986172
45471472.547743919449-1.54774391944875
46482472.664484897729.33551510228
47481473.3095233019217.69047669807918
48477470.9594764271176.04052357288293
49471465.644544570225.35545542977979
50455452.2682575590282.73174244097163
51441443.951223454065-2.95122345406514
52434443.954980284937-9.9549802849374
53459469.427907049058-10.4279070490578
54448459.219552722014-11.2195527220143
55432436.990560312967-4.99056031296652
56414423.87432455116-9.87432455115953
57415425.367249342679-10.3672493426792
58423430.938880024783-7.93888002478303
59425425.382576569201-0.382576569201262
60427418.5374361883948.46256381160583
61415411.7349411449823.26505885501803
62399394.4077072780244.59229272197604
63386380.7387201643935.26127983560656
64377375.9802084797141.01979152028554
65397402.476552782214-5.47655278221436
66379391.9241925578-12.9241925577999
67361373.14932327104-12.1493232710396
68350353.815206135173-3.81520613517296
69348355.340649761086-7.34064976108641
70363362.5773921753180.422607824681734
71367363.8901129848873.10988701511332
72365363.9509454147341.04905458526565
73354351.0320121527962.9679878472038
74327333.963796108350-6.9637961083497
75312317.351092009673-5.35109200967321
76307305.8683468490031.13165315099701
77335326.2208896826278.7791103173734
78317312.2101601008314.78983989916918
79298297.3695083185570.63049168144289
80286286.951802005276-0.95180200527642
81288286.5097427626691.49025723733058
82303301.7392178097341.26078219026607
83310305.5837055551654.4162944448347
84301304.760488556107-3.76048855610691
85293292.5050875640140.494912435986237
86264267.656193907221-3.65619390722094
87255253.2157372557211.78426274427881
88251248.5626584196132.43734158038725
89279275.4230877472943.57691225270594
90253257.690154454076-4.69015445407632
91233237.823582251376-4.82358225137577
92226225.0007480064820.99925199351847
93232226.7840969063835.2159030936169
94245242.7223274310762.27767256892363
95250249.2654957712270.734504228772607
96242241.5644411170980.435558882901546
97230233.516648909001-3.51664890900088
98196204.737453854207-8.7374538542073
99188193.170363987551-5.17036398755104
100181187.212915828660-6.21291582865956
101212212.525567674632-0.525567674631645
102186187.049100769234-1.04910076923352
103166167.264095175631-1.26409517563087
104155159.064449885067-4.06444988506726
105157162.302719948844-5.30271994884427
106173172.8879503760110.112049623989037
107182176.8229707096245.17702929037648
108182168.96789082133913.0321091786608
109168160.1175611061627.88243889383835
110131129.6625308524711.33746914752939
111114123.005226209033-9.00522620903251
112106115.461508164519-9.46150816451933
113134144.253040546098-10.2530405460978
114103115.960415475181-12.9604154751810
1158392.7856157490616-9.7856157490616
1167479.7319292067056-5.73192920670564
1178380.68385711077542.31614288922464
1189696.1405340141688-0.140534014168779
11995103.016131166620-8.01613116662014
12010097.07657937831332.92342062168669

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 563 & 569.188568376069 & -6.18856837606882 \tabularnewline
14 & 552 & 557.092262987191 & -5.09226298719102 \tabularnewline
15 & 552 & 555.872277613779 & -3.87227761377858 \tabularnewline
16 & 555 & 557.631563142701 & -2.63156314270122 \tabularnewline
17 & 575 & 576.326932169056 & -1.32693216905648 \tabularnewline
18 & 567 & 567.217824756121 & -0.217824756121104 \tabularnewline
19 & 548 & 554.336602126659 & -6.33660212665893 \tabularnewline
20 & 541 & 541.939179932109 & -0.939179932109255 \tabularnewline
21 & 544 & 542.029233163613 & 1.97076683638738 \tabularnewline
22 & 546 & 541.54047679592 & 4.45952320408014 \tabularnewline
23 & 551 & 542.49740212071 & 8.50259787928951 \tabularnewline
24 & 550 & 545.844731220821 & 4.15526877917864 \tabularnewline
25 & 546 & 543.22231574882 & 2.77768425118052 \tabularnewline
26 & 532 & 533.881034697877 & -1.88103469787677 \tabularnewline
27 & 523 & 534.386132710743 & -11.3861327107431 \tabularnewline
28 & 528 & 535.405013300468 & -7.40501330046845 \tabularnewline
29 & 555 & 553.84875854299 & 1.15124145700997 \tabularnewline
30 & 543 & 545.944217032109 & -2.94421703210912 \tabularnewline
31 & 525 & 527.682525999883 & -2.68252599988284 \tabularnewline
32 & 517 & 519.973018099372 & -2.97301809937187 \tabularnewline
33 & 519 & 521.630443341301 & -2.6304433413012 \tabularnewline
34 & 521 & 521.719244208649 & -0.719244208648774 \tabularnewline
35 & 520 & 524.145361001102 & -4.14536100110195 \tabularnewline
36 & 516 & 520.742935922923 & -4.74293592292281 \tabularnewline
37 & 509 & 514.127753015663 & -5.12775301566285 \tabularnewline
38 & 494 & 498.32058844229 & -4.32058844229005 \tabularnewline
39 & 484 & 489.817620430112 & -5.81762043011224 \tabularnewline
40 & 482 & 493.769527579601 & -11.7695275796007 \tabularnewline
41 & 508 & 516.346246663387 & -8.34624666338732 \tabularnewline
42 & 500 & 501.751671121325 & -1.75167112132533 \tabularnewline
43 & 480 & 482.351137516685 & -2.35113751668501 \tabularnewline
44 & 467 & 472.917405498617 & -5.9174054986172 \tabularnewline
45 & 471 & 472.547743919449 & -1.54774391944875 \tabularnewline
46 & 482 & 472.66448489772 & 9.33551510228 \tabularnewline
47 & 481 & 473.309523301921 & 7.69047669807918 \tabularnewline
48 & 477 & 470.959476427117 & 6.04052357288293 \tabularnewline
49 & 471 & 465.64454457022 & 5.35545542977979 \tabularnewline
50 & 455 & 452.268257559028 & 2.73174244097163 \tabularnewline
51 & 441 & 443.951223454065 & -2.95122345406514 \tabularnewline
52 & 434 & 443.954980284937 & -9.9549802849374 \tabularnewline
53 & 459 & 469.427907049058 & -10.4279070490578 \tabularnewline
54 & 448 & 459.219552722014 & -11.2195527220143 \tabularnewline
55 & 432 & 436.990560312967 & -4.99056031296652 \tabularnewline
56 & 414 & 423.87432455116 & -9.87432455115953 \tabularnewline
57 & 415 & 425.367249342679 & -10.3672493426792 \tabularnewline
58 & 423 & 430.938880024783 & -7.93888002478303 \tabularnewline
59 & 425 & 425.382576569201 & -0.382576569201262 \tabularnewline
60 & 427 & 418.537436188394 & 8.46256381160583 \tabularnewline
61 & 415 & 411.734941144982 & 3.26505885501803 \tabularnewline
62 & 399 & 394.407707278024 & 4.59229272197604 \tabularnewline
63 & 386 & 380.738720164393 & 5.26127983560656 \tabularnewline
64 & 377 & 375.980208479714 & 1.01979152028554 \tabularnewline
65 & 397 & 402.476552782214 & -5.47655278221436 \tabularnewline
66 & 379 & 391.9241925578 & -12.9241925577999 \tabularnewline
67 & 361 & 373.14932327104 & -12.1493232710396 \tabularnewline
68 & 350 & 353.815206135173 & -3.81520613517296 \tabularnewline
69 & 348 & 355.340649761086 & -7.34064976108641 \tabularnewline
70 & 363 & 362.577392175318 & 0.422607824681734 \tabularnewline
71 & 367 & 363.890112984887 & 3.10988701511332 \tabularnewline
72 & 365 & 363.950945414734 & 1.04905458526565 \tabularnewline
73 & 354 & 351.032012152796 & 2.9679878472038 \tabularnewline
74 & 327 & 333.963796108350 & -6.9637961083497 \tabularnewline
75 & 312 & 317.351092009673 & -5.35109200967321 \tabularnewline
76 & 307 & 305.868346849003 & 1.13165315099701 \tabularnewline
77 & 335 & 326.220889682627 & 8.7791103173734 \tabularnewline
78 & 317 & 312.210160100831 & 4.78983989916918 \tabularnewline
79 & 298 & 297.369508318557 & 0.63049168144289 \tabularnewline
80 & 286 & 286.951802005276 & -0.95180200527642 \tabularnewline
81 & 288 & 286.509742762669 & 1.49025723733058 \tabularnewline
82 & 303 & 301.739217809734 & 1.26078219026607 \tabularnewline
83 & 310 & 305.583705555165 & 4.4162944448347 \tabularnewline
84 & 301 & 304.760488556107 & -3.76048855610691 \tabularnewline
85 & 293 & 292.505087564014 & 0.494912435986237 \tabularnewline
86 & 264 & 267.656193907221 & -3.65619390722094 \tabularnewline
87 & 255 & 253.215737255721 & 1.78426274427881 \tabularnewline
88 & 251 & 248.562658419613 & 2.43734158038725 \tabularnewline
89 & 279 & 275.423087747294 & 3.57691225270594 \tabularnewline
90 & 253 & 257.690154454076 & -4.69015445407632 \tabularnewline
91 & 233 & 237.823582251376 & -4.82358225137577 \tabularnewline
92 & 226 & 225.000748006482 & 0.99925199351847 \tabularnewline
93 & 232 & 226.784096906383 & 5.2159030936169 \tabularnewline
94 & 245 & 242.722327431076 & 2.27767256892363 \tabularnewline
95 & 250 & 249.265495771227 & 0.734504228772607 \tabularnewline
96 & 242 & 241.564441117098 & 0.435558882901546 \tabularnewline
97 & 230 & 233.516648909001 & -3.51664890900088 \tabularnewline
98 & 196 & 204.737453854207 & -8.7374538542073 \tabularnewline
99 & 188 & 193.170363987551 & -5.17036398755104 \tabularnewline
100 & 181 & 187.212915828660 & -6.21291582865956 \tabularnewline
101 & 212 & 212.525567674632 & -0.525567674631645 \tabularnewline
102 & 186 & 187.049100769234 & -1.04910076923352 \tabularnewline
103 & 166 & 167.264095175631 & -1.26409517563087 \tabularnewline
104 & 155 & 159.064449885067 & -4.06444988506726 \tabularnewline
105 & 157 & 162.302719948844 & -5.30271994884427 \tabularnewline
106 & 173 & 172.887950376011 & 0.112049623989037 \tabularnewline
107 & 182 & 176.822970709624 & 5.17702929037648 \tabularnewline
108 & 182 & 168.967890821339 & 13.0321091786608 \tabularnewline
109 & 168 & 160.117561106162 & 7.88243889383835 \tabularnewline
110 & 131 & 129.662530852471 & 1.33746914752939 \tabularnewline
111 & 114 & 123.005226209033 & -9.00522620903251 \tabularnewline
112 & 106 & 115.461508164519 & -9.46150816451933 \tabularnewline
113 & 134 & 144.253040546098 & -10.2530405460978 \tabularnewline
114 & 103 & 115.960415475181 & -12.9604154751810 \tabularnewline
115 & 83 & 92.7856157490616 & -9.7856157490616 \tabularnewline
116 & 74 & 79.7319292067056 & -5.73192920670564 \tabularnewline
117 & 83 & 80.6838571107754 & 2.31614288922464 \tabularnewline
118 & 96 & 96.1405340141688 & -0.140534014168779 \tabularnewline
119 & 95 & 103.016131166620 & -8.01613116662014 \tabularnewline
120 & 100 & 97.0765793783133 & 2.92342062168669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78819&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]563[/C][C]569.188568376069[/C][C]-6.18856837606882[/C][/ROW]
[ROW][C]14[/C][C]552[/C][C]557.092262987191[/C][C]-5.09226298719102[/C][/ROW]
[ROW][C]15[/C][C]552[/C][C]555.872277613779[/C][C]-3.87227761377858[/C][/ROW]
[ROW][C]16[/C][C]555[/C][C]557.631563142701[/C][C]-2.63156314270122[/C][/ROW]
[ROW][C]17[/C][C]575[/C][C]576.326932169056[/C][C]-1.32693216905648[/C][/ROW]
[ROW][C]18[/C][C]567[/C][C]567.217824756121[/C][C]-0.217824756121104[/C][/ROW]
[ROW][C]19[/C][C]548[/C][C]554.336602126659[/C][C]-6.33660212665893[/C][/ROW]
[ROW][C]20[/C][C]541[/C][C]541.939179932109[/C][C]-0.939179932109255[/C][/ROW]
[ROW][C]21[/C][C]544[/C][C]542.029233163613[/C][C]1.97076683638738[/C][/ROW]
[ROW][C]22[/C][C]546[/C][C]541.54047679592[/C][C]4.45952320408014[/C][/ROW]
[ROW][C]23[/C][C]551[/C][C]542.49740212071[/C][C]8.50259787928951[/C][/ROW]
[ROW][C]24[/C][C]550[/C][C]545.844731220821[/C][C]4.15526877917864[/C][/ROW]
[ROW][C]25[/C][C]546[/C][C]543.22231574882[/C][C]2.77768425118052[/C][/ROW]
[ROW][C]26[/C][C]532[/C][C]533.881034697877[/C][C]-1.88103469787677[/C][/ROW]
[ROW][C]27[/C][C]523[/C][C]534.386132710743[/C][C]-11.3861327107431[/C][/ROW]
[ROW][C]28[/C][C]528[/C][C]535.405013300468[/C][C]-7.40501330046845[/C][/ROW]
[ROW][C]29[/C][C]555[/C][C]553.84875854299[/C][C]1.15124145700997[/C][/ROW]
[ROW][C]30[/C][C]543[/C][C]545.944217032109[/C][C]-2.94421703210912[/C][/ROW]
[ROW][C]31[/C][C]525[/C][C]527.682525999883[/C][C]-2.68252599988284[/C][/ROW]
[ROW][C]32[/C][C]517[/C][C]519.973018099372[/C][C]-2.97301809937187[/C][/ROW]
[ROW][C]33[/C][C]519[/C][C]521.630443341301[/C][C]-2.6304433413012[/C][/ROW]
[ROW][C]34[/C][C]521[/C][C]521.719244208649[/C][C]-0.719244208648774[/C][/ROW]
[ROW][C]35[/C][C]520[/C][C]524.145361001102[/C][C]-4.14536100110195[/C][/ROW]
[ROW][C]36[/C][C]516[/C][C]520.742935922923[/C][C]-4.74293592292281[/C][/ROW]
[ROW][C]37[/C][C]509[/C][C]514.127753015663[/C][C]-5.12775301566285[/C][/ROW]
[ROW][C]38[/C][C]494[/C][C]498.32058844229[/C][C]-4.32058844229005[/C][/ROW]
[ROW][C]39[/C][C]484[/C][C]489.817620430112[/C][C]-5.81762043011224[/C][/ROW]
[ROW][C]40[/C][C]482[/C][C]493.769527579601[/C][C]-11.7695275796007[/C][/ROW]
[ROW][C]41[/C][C]508[/C][C]516.346246663387[/C][C]-8.34624666338732[/C][/ROW]
[ROW][C]42[/C][C]500[/C][C]501.751671121325[/C][C]-1.75167112132533[/C][/ROW]
[ROW][C]43[/C][C]480[/C][C]482.351137516685[/C][C]-2.35113751668501[/C][/ROW]
[ROW][C]44[/C][C]467[/C][C]472.917405498617[/C][C]-5.9174054986172[/C][/ROW]
[ROW][C]45[/C][C]471[/C][C]472.547743919449[/C][C]-1.54774391944875[/C][/ROW]
[ROW][C]46[/C][C]482[/C][C]472.66448489772[/C][C]9.33551510228[/C][/ROW]
[ROW][C]47[/C][C]481[/C][C]473.309523301921[/C][C]7.69047669807918[/C][/ROW]
[ROW][C]48[/C][C]477[/C][C]470.959476427117[/C][C]6.04052357288293[/C][/ROW]
[ROW][C]49[/C][C]471[/C][C]465.64454457022[/C][C]5.35545542977979[/C][/ROW]
[ROW][C]50[/C][C]455[/C][C]452.268257559028[/C][C]2.73174244097163[/C][/ROW]
[ROW][C]51[/C][C]441[/C][C]443.951223454065[/C][C]-2.95122345406514[/C][/ROW]
[ROW][C]52[/C][C]434[/C][C]443.954980284937[/C][C]-9.9549802849374[/C][/ROW]
[ROW][C]53[/C][C]459[/C][C]469.427907049058[/C][C]-10.4279070490578[/C][/ROW]
[ROW][C]54[/C][C]448[/C][C]459.219552722014[/C][C]-11.2195527220143[/C][/ROW]
[ROW][C]55[/C][C]432[/C][C]436.990560312967[/C][C]-4.99056031296652[/C][/ROW]
[ROW][C]56[/C][C]414[/C][C]423.87432455116[/C][C]-9.87432455115953[/C][/ROW]
[ROW][C]57[/C][C]415[/C][C]425.367249342679[/C][C]-10.3672493426792[/C][/ROW]
[ROW][C]58[/C][C]423[/C][C]430.938880024783[/C][C]-7.93888002478303[/C][/ROW]
[ROW][C]59[/C][C]425[/C][C]425.382576569201[/C][C]-0.382576569201262[/C][/ROW]
[ROW][C]60[/C][C]427[/C][C]418.537436188394[/C][C]8.46256381160583[/C][/ROW]
[ROW][C]61[/C][C]415[/C][C]411.734941144982[/C][C]3.26505885501803[/C][/ROW]
[ROW][C]62[/C][C]399[/C][C]394.407707278024[/C][C]4.59229272197604[/C][/ROW]
[ROW][C]63[/C][C]386[/C][C]380.738720164393[/C][C]5.26127983560656[/C][/ROW]
[ROW][C]64[/C][C]377[/C][C]375.980208479714[/C][C]1.01979152028554[/C][/ROW]
[ROW][C]65[/C][C]397[/C][C]402.476552782214[/C][C]-5.47655278221436[/C][/ROW]
[ROW][C]66[/C][C]379[/C][C]391.9241925578[/C][C]-12.9241925577999[/C][/ROW]
[ROW][C]67[/C][C]361[/C][C]373.14932327104[/C][C]-12.1493232710396[/C][/ROW]
[ROW][C]68[/C][C]350[/C][C]353.815206135173[/C][C]-3.81520613517296[/C][/ROW]
[ROW][C]69[/C][C]348[/C][C]355.340649761086[/C][C]-7.34064976108641[/C][/ROW]
[ROW][C]70[/C][C]363[/C][C]362.577392175318[/C][C]0.422607824681734[/C][/ROW]
[ROW][C]71[/C][C]367[/C][C]363.890112984887[/C][C]3.10988701511332[/C][/ROW]
[ROW][C]72[/C][C]365[/C][C]363.950945414734[/C][C]1.04905458526565[/C][/ROW]
[ROW][C]73[/C][C]354[/C][C]351.032012152796[/C][C]2.9679878472038[/C][/ROW]
[ROW][C]74[/C][C]327[/C][C]333.963796108350[/C][C]-6.9637961083497[/C][/ROW]
[ROW][C]75[/C][C]312[/C][C]317.351092009673[/C][C]-5.35109200967321[/C][/ROW]
[ROW][C]76[/C][C]307[/C][C]305.868346849003[/C][C]1.13165315099701[/C][/ROW]
[ROW][C]77[/C][C]335[/C][C]326.220889682627[/C][C]8.7791103173734[/C][/ROW]
[ROW][C]78[/C][C]317[/C][C]312.210160100831[/C][C]4.78983989916918[/C][/ROW]
[ROW][C]79[/C][C]298[/C][C]297.369508318557[/C][C]0.63049168144289[/C][/ROW]
[ROW][C]80[/C][C]286[/C][C]286.951802005276[/C][C]-0.95180200527642[/C][/ROW]
[ROW][C]81[/C][C]288[/C][C]286.509742762669[/C][C]1.49025723733058[/C][/ROW]
[ROW][C]82[/C][C]303[/C][C]301.739217809734[/C][C]1.26078219026607[/C][/ROW]
[ROW][C]83[/C][C]310[/C][C]305.583705555165[/C][C]4.4162944448347[/C][/ROW]
[ROW][C]84[/C][C]301[/C][C]304.760488556107[/C][C]-3.76048855610691[/C][/ROW]
[ROW][C]85[/C][C]293[/C][C]292.505087564014[/C][C]0.494912435986237[/C][/ROW]
[ROW][C]86[/C][C]264[/C][C]267.656193907221[/C][C]-3.65619390722094[/C][/ROW]
[ROW][C]87[/C][C]255[/C][C]253.215737255721[/C][C]1.78426274427881[/C][/ROW]
[ROW][C]88[/C][C]251[/C][C]248.562658419613[/C][C]2.43734158038725[/C][/ROW]
[ROW][C]89[/C][C]279[/C][C]275.423087747294[/C][C]3.57691225270594[/C][/ROW]
[ROW][C]90[/C][C]253[/C][C]257.690154454076[/C][C]-4.69015445407632[/C][/ROW]
[ROW][C]91[/C][C]233[/C][C]237.823582251376[/C][C]-4.82358225137577[/C][/ROW]
[ROW][C]92[/C][C]226[/C][C]225.000748006482[/C][C]0.99925199351847[/C][/ROW]
[ROW][C]93[/C][C]232[/C][C]226.784096906383[/C][C]5.2159030936169[/C][/ROW]
[ROW][C]94[/C][C]245[/C][C]242.722327431076[/C][C]2.27767256892363[/C][/ROW]
[ROW][C]95[/C][C]250[/C][C]249.265495771227[/C][C]0.734504228772607[/C][/ROW]
[ROW][C]96[/C][C]242[/C][C]241.564441117098[/C][C]0.435558882901546[/C][/ROW]
[ROW][C]97[/C][C]230[/C][C]233.516648909001[/C][C]-3.51664890900088[/C][/ROW]
[ROW][C]98[/C][C]196[/C][C]204.737453854207[/C][C]-8.7374538542073[/C][/ROW]
[ROW][C]99[/C][C]188[/C][C]193.170363987551[/C][C]-5.17036398755104[/C][/ROW]
[ROW][C]100[/C][C]181[/C][C]187.212915828660[/C][C]-6.21291582865956[/C][/ROW]
[ROW][C]101[/C][C]212[/C][C]212.525567674632[/C][C]-0.525567674631645[/C][/ROW]
[ROW][C]102[/C][C]186[/C][C]187.049100769234[/C][C]-1.04910076923352[/C][/ROW]
[ROW][C]103[/C][C]166[/C][C]167.264095175631[/C][C]-1.26409517563087[/C][/ROW]
[ROW][C]104[/C][C]155[/C][C]159.064449885067[/C][C]-4.06444988506726[/C][/ROW]
[ROW][C]105[/C][C]157[/C][C]162.302719948844[/C][C]-5.30271994884427[/C][/ROW]
[ROW][C]106[/C][C]173[/C][C]172.887950376011[/C][C]0.112049623989037[/C][/ROW]
[ROW][C]107[/C][C]182[/C][C]176.822970709624[/C][C]5.17702929037648[/C][/ROW]
[ROW][C]108[/C][C]182[/C][C]168.967890821339[/C][C]13.0321091786608[/C][/ROW]
[ROW][C]109[/C][C]168[/C][C]160.117561106162[/C][C]7.88243889383835[/C][/ROW]
[ROW][C]110[/C][C]131[/C][C]129.662530852471[/C][C]1.33746914752939[/C][/ROW]
[ROW][C]111[/C][C]114[/C][C]123.005226209033[/C][C]-9.00522620903251[/C][/ROW]
[ROW][C]112[/C][C]106[/C][C]115.461508164519[/C][C]-9.46150816451933[/C][/ROW]
[ROW][C]113[/C][C]134[/C][C]144.253040546098[/C][C]-10.2530405460978[/C][/ROW]
[ROW][C]114[/C][C]103[/C][C]115.960415475181[/C][C]-12.9604154751810[/C][/ROW]
[ROW][C]115[/C][C]83[/C][C]92.7856157490616[/C][C]-9.7856157490616[/C][/ROW]
[ROW][C]116[/C][C]74[/C][C]79.7319292067056[/C][C]-5.73192920670564[/C][/ROW]
[ROW][C]117[/C][C]83[/C][C]80.6838571107754[/C][C]2.31614288922464[/C][/ROW]
[ROW][C]118[/C][C]96[/C][C]96.1405340141688[/C][C]-0.140534014168779[/C][/ROW]
[ROW][C]119[/C][C]95[/C][C]103.016131166620[/C][C]-8.01613116662014[/C][/ROW]
[ROW][C]120[/C][C]100[/C][C]97.0765793783133[/C][C]2.92342062168669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78819&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78819&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
13563569.188568376069-6.18856837606882
14552557.092262987191-5.09226298719102
15552555.872277613779-3.87227761377858
16555557.631563142701-2.63156314270122
17575576.326932169056-1.32693216905648
18567567.217824756121-0.217824756121104
19548554.336602126659-6.33660212665893
20541541.939179932109-0.939179932109255
21544542.0292331636131.97076683638738
22546541.540476795924.45952320408014
23551542.497402120718.50259787928951
24550545.8447312208214.15526877917864
25546543.222315748822.77768425118052
26532533.881034697877-1.88103469787677
27523534.386132710743-11.3861327107431
28528535.405013300468-7.40501330046845
29555553.848758542991.15124145700997
30543545.944217032109-2.94421703210912
31525527.682525999883-2.68252599988284
32517519.973018099372-2.97301809937187
33519521.630443341301-2.6304433413012
34521521.719244208649-0.719244208648774
35520524.145361001102-4.14536100110195
36516520.742935922923-4.74293592292281
37509514.127753015663-5.12775301566285
38494498.32058844229-4.32058844229005
39484489.817620430112-5.81762043011224
40482493.769527579601-11.7695275796007
41508516.346246663387-8.34624666338732
42500501.751671121325-1.75167112132533
43480482.351137516685-2.35113751668501
44467472.917405498617-5.9174054986172
45471472.547743919449-1.54774391944875
46482472.664484897729.33551510228
47481473.3095233019217.69047669807918
48477470.9594764271176.04052357288293
49471465.644544570225.35545542977979
50455452.2682575590282.73174244097163
51441443.951223454065-2.95122345406514
52434443.954980284937-9.9549802849374
53459469.427907049058-10.4279070490578
54448459.219552722014-11.2195527220143
55432436.990560312967-4.99056031296652
56414423.87432455116-9.87432455115953
57415425.367249342679-10.3672493426792
58423430.938880024783-7.93888002478303
59425425.382576569201-0.382576569201262
60427418.5374361883948.46256381160583
61415411.7349411449823.26505885501803
62399394.4077072780244.59229272197604
63386380.7387201643935.26127983560656
64377375.9802084797141.01979152028554
65397402.476552782214-5.47655278221436
66379391.9241925578-12.9241925577999
67361373.14932327104-12.1493232710396
68350353.815206135173-3.81520613517296
69348355.340649761086-7.34064976108641
70363362.5773921753180.422607824681734
71367363.8901129848873.10988701511332
72365363.9509454147341.04905458526565
73354351.0320121527962.9679878472038
74327333.963796108350-6.9637961083497
75312317.351092009673-5.35109200967321
76307305.8683468490031.13165315099701
77335326.2208896826278.7791103173734
78317312.2101601008314.78983989916918
79298297.3695083185570.63049168144289
80286286.951802005276-0.95180200527642
81288286.5097427626691.49025723733058
82303301.7392178097341.26078219026607
83310305.5837055551654.4162944448347
84301304.760488556107-3.76048855610691
85293292.5050875640140.494912435986237
86264267.656193907221-3.65619390722094
87255253.2157372557211.78426274427881
88251248.5626584196132.43734158038725
89279275.4230877472943.57691225270594
90253257.690154454076-4.69015445407632
91233237.823582251376-4.82358225137577
92226225.0007480064820.99925199351847
93232226.7840969063835.2159030936169
94245242.7223274310762.27767256892363
95250249.2654957712270.734504228772607
96242241.5644411170980.435558882901546
97230233.516648909001-3.51664890900088
98196204.737453854207-8.7374538542073
99188193.170363987551-5.17036398755104
100181187.212915828660-6.21291582865956
101212212.525567674632-0.525567674631645
102186187.049100769234-1.04910076923352
103166167.264095175631-1.26409517563087
104155159.064449885067-4.06444988506726
105157162.302719948844-5.30271994884427
106173172.8879503760110.112049623989037
107182176.8229707096245.17702929037648
108182168.96789082133913.0321091786608
109168160.1175611061627.88243889383835
110131129.6625308524711.33746914752939
111114123.005226209033-9.00522620903251
112106115.461508164519-9.46150816451933
113134144.253040546098-10.2530405460978
114103115.960415475181-12.9604154751810
1158392.7856157490616-9.7856157490616
1167479.7319292067056-5.73192920670564
1178380.68385711077542.31614288922464
1189696.1405340141688-0.140534014168779
11995103.016131166620-8.01613116662014
12010097.07657937831332.92342062168669







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12180.771961908846969.817078426046791.726845391647
12242.061516889503230.795655561763153.3273782172433
12325.650772366770514.006461673171337.2950830603697
12418.1934722957476.101326730367530.2856178611265
12547.189709069729134.579825564135359.7995925753229
12618.13114301225684.9342874582610131.3279985662527
127-0.46355244000037-14.315013730148813.3879088501480
128-8.66776420319101-23.23919529749325.90366689111118
129-0.568530952970889-15.922597558811314.7855356528695
13012.4102862363036-3.7861560738842328.6067285464914
13113.2765426811373-3.819019394470930.3721047567455
13217.2982210719631-0.75025118722776135.3466933311539

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 80.7719619088469 & 69.8170784260467 & 91.726845391647 \tabularnewline
122 & 42.0615168895032 & 30.7956555617631 & 53.3273782172433 \tabularnewline
123 & 25.6507723667705 & 14.0064616731713 & 37.2950830603697 \tabularnewline
124 & 18.193472295747 & 6.1013267303675 & 30.2856178611265 \tabularnewline
125 & 47.1897090697291 & 34.5798255641353 & 59.7995925753229 \tabularnewline
126 & 18.1311430122568 & 4.93428745826101 & 31.3279985662527 \tabularnewline
127 & -0.46355244000037 & -14.3150137301488 & 13.3879088501480 \tabularnewline
128 & -8.66776420319101 & -23.2391952974932 & 5.90366689111118 \tabularnewline
129 & -0.568530952970889 & -15.9225975588113 & 14.7855356528695 \tabularnewline
130 & 12.4102862363036 & -3.78615607388423 & 28.6067285464914 \tabularnewline
131 & 13.2765426811373 & -3.8190193944709 & 30.3721047567455 \tabularnewline
132 & 17.2982210719631 & -0.750251187227761 & 35.3466933311539 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78819&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]121[/C][C]80.7719619088469[/C][C]69.8170784260467[/C][C]91.726845391647[/C][/ROW]
[ROW][C]122[/C][C]42.0615168895032[/C][C]30.7956555617631[/C][C]53.3273782172433[/C][/ROW]
[ROW][C]123[/C][C]25.6507723667705[/C][C]14.0064616731713[/C][C]37.2950830603697[/C][/ROW]
[ROW][C]124[/C][C]18.193472295747[/C][C]6.1013267303675[/C][C]30.2856178611265[/C][/ROW]
[ROW][C]125[/C][C]47.1897090697291[/C][C]34.5798255641353[/C][C]59.7995925753229[/C][/ROW]
[ROW][C]126[/C][C]18.1311430122568[/C][C]4.93428745826101[/C][C]31.3279985662527[/C][/ROW]
[ROW][C]127[/C][C]-0.46355244000037[/C][C]-14.3150137301488[/C][C]13.3879088501480[/C][/ROW]
[ROW][C]128[/C][C]-8.66776420319101[/C][C]-23.2391952974932[/C][C]5.90366689111118[/C][/ROW]
[ROW][C]129[/C][C]-0.568530952970889[/C][C]-15.9225975588113[/C][C]14.7855356528695[/C][/ROW]
[ROW][C]130[/C][C]12.4102862363036[/C][C]-3.78615607388423[/C][C]28.6067285464914[/C][/ROW]
[ROW][C]131[/C][C]13.2765426811373[/C][C]-3.8190193944709[/C][C]30.3721047567455[/C][/ROW]
[ROW][C]132[/C][C]17.2982210719631[/C][C]-0.750251187227761[/C][C]35.3466933311539[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78819&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78819&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
12180.771961908846969.817078426046791.726845391647
12242.061516889503230.795655561763153.3273782172433
12325.650772366770514.006461673171337.2950830603697
12418.1934722957476.101326730367530.2856178611265
12547.189709069729134.579825564135359.7995925753229
12618.13114301225684.9342874582610131.3279985662527
127-0.46355244000037-14.315013730148813.3879088501480
128-8.66776420319101-23.23919529749325.90366689111118
129-0.568530952970889-15.922597558811314.7855356528695
13012.4102862363036-3.7861560738842328.6067285464914
13113.2765426811373-3.819019394470930.3721047567455
13217.2982210719631-0.75025118722776135.3466933311539



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')