Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 04 Aug 2010 12:41:06 +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/04/t12809256508xupzezir6zv8m8.htm/, Retrieved Fri, 03 May 2024 09:53:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78307, Retrieved Fri, 03 May 2024 09:53:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBogaerts Yannik
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A stap 32] [2010-08-04 12:41:06] [1596366c2ece8f787477cc7d1246d4c7] [Current]
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Dataseries X:
442
441
440
438
458
457
442
432
433
433
434
436
439
439
441
436
460
453
435
421
412
408
402
409
410
410
416
410
437
431
411
398
394
395
389
404
397
401
402
383
406
400
377
372
362
365
361
372
355
365
367
341
370
366
333
320
298
306
293
313
293
304
304
286
320
313
283
272
251
262
247
268
251
257
261
242
274
272
243
234
217
231
209
226
208
214
222
194
230
226
197
188
175
190
165
176
159
169
170
141
170
164
132
123
113
125
101
99
87
90
89
66
102
97
65
54
33
49
30
34




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78307&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78307&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78307&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.629530665310154
beta0.0694788787378497
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.629530665310154 \tabularnewline
beta & 0.0694788787378497 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78307&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]0.629530665310154[/C][/ROW]
[ROW][C]beta[/C][C]0.0694788787378497[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78307&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78307&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
alpha0.629530665310154
beta0.0694788787378497
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13439439.841079059829-0.841079059829156
14439439.259508768634-0.259508768634248
15441441.616037467087-0.616037467086699
16436437.304508835147-1.3045088351472
17460461.960841675652-1.96084167565243
18453455.201560779497-2.20156077949667
19435432.0694455722132.93055442778683
20421423.171334034321-2.17133403432086
21412421.79978842851-9.79978842851045
22408414.197263075964-6.19726307596392
23402409.549908623796-7.54990862379606
24409404.8041295601034.19587043989679
25410408.6996081380461.30039186195404
26410408.647886735531.35211326447023
27416410.9236621633915.07633783660867
28410409.2263442881740.773655711826166
29437434.3244347373312.67556526266924
30431429.9741678250281.02583217497192
31411410.4956826575330.504317342467289
32398397.7945617589350.205438241064542
33394394.811591114848-0.811591114848
34395394.3136046458210.686395354178842
35389393.911263366435-4.9112633664351
36404395.7061080884848.29389191151591
37397401.816039262232-4.81603926223158
38401398.3727794337132.62722056628746
39402403.326538370803-1.32653837080289
40383396.21989920926-13.2198992092598
41406412.816649016664-6.81664901666426
42400401.067817981349-1.06781798134915
43377379.174787610289-2.17478761028889
44372363.6558578731968.34414212680366
45362364.755147597983-2.75514759798318
46365362.8390562776372.16094372236284
47361360.6061884115350.393811588464587
48372370.1798456129311.82015438706895
49355366.621377684997-11.6213776849968
50365360.6176335429514.3823664570491
51367364.254518067122.74548193288024
52341354.526275390355-13.5262753903546
53370372.510019532484-2.51001953248357
54366364.9981371596521.00186284034771
55333343.484489705345-10.4844897053449
56320325.754383490978-5.75438349097817
57298312.372710826702-14.3727108267021
58306302.9625649985553.03743500144486
59293298.663440651037-5.66344065103664
60313302.72398306516810.2760169348322
61293297.650611134798-4.650611134798
62304300.410516356683.58948364331957
63304301.3536029613942.64639703860615
64286283.942223959272.05777604073046
65320314.9068512557045.09314874429617
66313312.9040567246970.0959432753027158
67283285.946755177542-2.94675517754217
68272274.425928346298-2.42592834629761
69251259.804062899839-8.80406289983927
70262260.4503130417661.54968695823391
71247252.026961520829-5.02696152082945
72268262.4568697832645.54313021673596
73251248.7307328958422.26926710415825
74257259.058875577938-2.05887557793773
75261256.0089675928114.99103240718875
76242239.8703000454552.12969995454466
77274272.0226216641351.97737833586484
78272266.0886652904765.91133470952389
79243241.8010869702211.19891302977894
80234233.4003459662030.599654033796867
81217218.769920540842-1.76992054084209
82231228.4374391692312.56256083076934
83209219.016891746628-10.0168917466282
84226230.804741308723-4.80474130872329
85208209.48219019738-1.48219019737974
86214215.811900131031-1.8119001310308
87222215.5067167665446.49328323345583
88194199.296904609828-5.2969046098284
89230226.435865899453.56413410054984
90226222.7459798554253.25402014457535
91197194.7112530146632.2887469853375
92188186.4937773739461.50622262605393
93175171.3150509916783.68494900832246
94190186.0190607996013.98093920039867
95165172.890595232081-7.89059523208124
96176188.100428425627-12.1004284256267
97159163.249288039178-4.249288039178
98169167.4272134705121.57278652948838
99170172.189988866295-2.18998886629478
100141145.626468186535-4.62646818653459
101170175.980137740149-5.98013774014851
102164165.25939932911-1.25939932910964
103132132.920766727966-0.920766727965685
104123121.1475556217021.85244437829766
105113105.7637343018187.23626569818178
106125121.7381900385053.26180996149512
107101102.652644925829-1.65264492582939
10899119.396361086631-20.3963610866314
1098791.0349430096177-4.03494300961773
1109096.3177401187613-6.31774011876134
1118993.1871045294938-4.18710452949384
1126662.84425581649453.15574418350549
11310296.3165188802075.68348111979296
1149793.91837628037973.08162371962034
1156563.85897742874541.1410225712546
1165453.92226998921670.0777300107833128
1173338.8492822771176-5.84928227711762
1184943.97475044829565.02524955170444
1193023.11700116516226.88299883483781
1203437.6018473752156-3.60184737521563

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 439 & 439.841079059829 & -0.841079059829156 \tabularnewline
14 & 439 & 439.259508768634 & -0.259508768634248 \tabularnewline
15 & 441 & 441.616037467087 & -0.616037467086699 \tabularnewline
16 & 436 & 437.304508835147 & -1.3045088351472 \tabularnewline
17 & 460 & 461.960841675652 & -1.96084167565243 \tabularnewline
18 & 453 & 455.201560779497 & -2.20156077949667 \tabularnewline
19 & 435 & 432.069445572213 & 2.93055442778683 \tabularnewline
20 & 421 & 423.171334034321 & -2.17133403432086 \tabularnewline
21 & 412 & 421.79978842851 & -9.79978842851045 \tabularnewline
22 & 408 & 414.197263075964 & -6.19726307596392 \tabularnewline
23 & 402 & 409.549908623796 & -7.54990862379606 \tabularnewline
24 & 409 & 404.804129560103 & 4.19587043989679 \tabularnewline
25 & 410 & 408.699608138046 & 1.30039186195404 \tabularnewline
26 & 410 & 408.64788673553 & 1.35211326447023 \tabularnewline
27 & 416 & 410.923662163391 & 5.07633783660867 \tabularnewline
28 & 410 & 409.226344288174 & 0.773655711826166 \tabularnewline
29 & 437 & 434.324434737331 & 2.67556526266924 \tabularnewline
30 & 431 & 429.974167825028 & 1.02583217497192 \tabularnewline
31 & 411 & 410.495682657533 & 0.504317342467289 \tabularnewline
32 & 398 & 397.794561758935 & 0.205438241064542 \tabularnewline
33 & 394 & 394.811591114848 & -0.811591114848 \tabularnewline
34 & 395 & 394.313604645821 & 0.686395354178842 \tabularnewline
35 & 389 & 393.911263366435 & -4.9112633664351 \tabularnewline
36 & 404 & 395.706108088484 & 8.29389191151591 \tabularnewline
37 & 397 & 401.816039262232 & -4.81603926223158 \tabularnewline
38 & 401 & 398.372779433713 & 2.62722056628746 \tabularnewline
39 & 402 & 403.326538370803 & -1.32653837080289 \tabularnewline
40 & 383 & 396.21989920926 & -13.2198992092598 \tabularnewline
41 & 406 & 412.816649016664 & -6.81664901666426 \tabularnewline
42 & 400 & 401.067817981349 & -1.06781798134915 \tabularnewline
43 & 377 & 379.174787610289 & -2.17478761028889 \tabularnewline
44 & 372 & 363.655857873196 & 8.34414212680366 \tabularnewline
45 & 362 & 364.755147597983 & -2.75514759798318 \tabularnewline
46 & 365 & 362.839056277637 & 2.16094372236284 \tabularnewline
47 & 361 & 360.606188411535 & 0.393811588464587 \tabularnewline
48 & 372 & 370.179845612931 & 1.82015438706895 \tabularnewline
49 & 355 & 366.621377684997 & -11.6213776849968 \tabularnewline
50 & 365 & 360.617633542951 & 4.3823664570491 \tabularnewline
51 & 367 & 364.25451806712 & 2.74548193288024 \tabularnewline
52 & 341 & 354.526275390355 & -13.5262753903546 \tabularnewline
53 & 370 & 372.510019532484 & -2.51001953248357 \tabularnewline
54 & 366 & 364.998137159652 & 1.00186284034771 \tabularnewline
55 & 333 & 343.484489705345 & -10.4844897053449 \tabularnewline
56 & 320 & 325.754383490978 & -5.75438349097817 \tabularnewline
57 & 298 & 312.372710826702 & -14.3727108267021 \tabularnewline
58 & 306 & 302.962564998555 & 3.03743500144486 \tabularnewline
59 & 293 & 298.663440651037 & -5.66344065103664 \tabularnewline
60 & 313 & 302.723983065168 & 10.2760169348322 \tabularnewline
61 & 293 & 297.650611134798 & -4.650611134798 \tabularnewline
62 & 304 & 300.41051635668 & 3.58948364331957 \tabularnewline
63 & 304 & 301.353602961394 & 2.64639703860615 \tabularnewline
64 & 286 & 283.94222395927 & 2.05777604073046 \tabularnewline
65 & 320 & 314.906851255704 & 5.09314874429617 \tabularnewline
66 & 313 & 312.904056724697 & 0.0959432753027158 \tabularnewline
67 & 283 & 285.946755177542 & -2.94675517754217 \tabularnewline
68 & 272 & 274.425928346298 & -2.42592834629761 \tabularnewline
69 & 251 & 259.804062899839 & -8.80406289983927 \tabularnewline
70 & 262 & 260.450313041766 & 1.54968695823391 \tabularnewline
71 & 247 & 252.026961520829 & -5.02696152082945 \tabularnewline
72 & 268 & 262.456869783264 & 5.54313021673596 \tabularnewline
73 & 251 & 248.730732895842 & 2.26926710415825 \tabularnewline
74 & 257 & 259.058875577938 & -2.05887557793773 \tabularnewline
75 & 261 & 256.008967592811 & 4.99103240718875 \tabularnewline
76 & 242 & 239.870300045455 & 2.12969995454466 \tabularnewline
77 & 274 & 272.022621664135 & 1.97737833586484 \tabularnewline
78 & 272 & 266.088665290476 & 5.91133470952389 \tabularnewline
79 & 243 & 241.801086970221 & 1.19891302977894 \tabularnewline
80 & 234 & 233.400345966203 & 0.599654033796867 \tabularnewline
81 & 217 & 218.769920540842 & -1.76992054084209 \tabularnewline
82 & 231 & 228.437439169231 & 2.56256083076934 \tabularnewline
83 & 209 & 219.016891746628 & -10.0168917466282 \tabularnewline
84 & 226 & 230.804741308723 & -4.80474130872329 \tabularnewline
85 & 208 & 209.48219019738 & -1.48219019737974 \tabularnewline
86 & 214 & 215.811900131031 & -1.8119001310308 \tabularnewline
87 & 222 & 215.506716766544 & 6.49328323345583 \tabularnewline
88 & 194 & 199.296904609828 & -5.2969046098284 \tabularnewline
89 & 230 & 226.43586589945 & 3.56413410054984 \tabularnewline
90 & 226 & 222.745979855425 & 3.25402014457535 \tabularnewline
91 & 197 & 194.711253014663 & 2.2887469853375 \tabularnewline
92 & 188 & 186.493777373946 & 1.50622262605393 \tabularnewline
93 & 175 & 171.315050991678 & 3.68494900832246 \tabularnewline
94 & 190 & 186.019060799601 & 3.98093920039867 \tabularnewline
95 & 165 & 172.890595232081 & -7.89059523208124 \tabularnewline
96 & 176 & 188.100428425627 & -12.1004284256267 \tabularnewline
97 & 159 & 163.249288039178 & -4.249288039178 \tabularnewline
98 & 169 & 167.427213470512 & 1.57278652948838 \tabularnewline
99 & 170 & 172.189988866295 & -2.18998886629478 \tabularnewline
100 & 141 & 145.626468186535 & -4.62646818653459 \tabularnewline
101 & 170 & 175.980137740149 & -5.98013774014851 \tabularnewline
102 & 164 & 165.25939932911 & -1.25939932910964 \tabularnewline
103 & 132 & 132.920766727966 & -0.920766727965685 \tabularnewline
104 & 123 & 121.147555621702 & 1.85244437829766 \tabularnewline
105 & 113 & 105.763734301818 & 7.23626569818178 \tabularnewline
106 & 125 & 121.738190038505 & 3.26180996149512 \tabularnewline
107 & 101 & 102.652644925829 & -1.65264492582939 \tabularnewline
108 & 99 & 119.396361086631 & -20.3963610866314 \tabularnewline
109 & 87 & 91.0349430096177 & -4.03494300961773 \tabularnewline
110 & 90 & 96.3177401187613 & -6.31774011876134 \tabularnewline
111 & 89 & 93.1871045294938 & -4.18710452949384 \tabularnewline
112 & 66 & 62.8442558164945 & 3.15574418350549 \tabularnewline
113 & 102 & 96.316518880207 & 5.68348111979296 \tabularnewline
114 & 97 & 93.9183762803797 & 3.08162371962034 \tabularnewline
115 & 65 & 63.8589774287454 & 1.1410225712546 \tabularnewline
116 & 54 & 53.9222699892167 & 0.0777300107833128 \tabularnewline
117 & 33 & 38.8492822771176 & -5.84928227711762 \tabularnewline
118 & 49 & 43.9747504482956 & 5.02524955170444 \tabularnewline
119 & 30 & 23.1170011651622 & 6.88299883483781 \tabularnewline
120 & 34 & 37.6018473752156 & -3.60184737521563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78307&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]439[/C][C]439.841079059829[/C][C]-0.841079059829156[/C][/ROW]
[ROW][C]14[/C][C]439[/C][C]439.259508768634[/C][C]-0.259508768634248[/C][/ROW]
[ROW][C]15[/C][C]441[/C][C]441.616037467087[/C][C]-0.616037467086699[/C][/ROW]
[ROW][C]16[/C][C]436[/C][C]437.304508835147[/C][C]-1.3045088351472[/C][/ROW]
[ROW][C]17[/C][C]460[/C][C]461.960841675652[/C][C]-1.96084167565243[/C][/ROW]
[ROW][C]18[/C][C]453[/C][C]455.201560779497[/C][C]-2.20156077949667[/C][/ROW]
[ROW][C]19[/C][C]435[/C][C]432.069445572213[/C][C]2.93055442778683[/C][/ROW]
[ROW][C]20[/C][C]421[/C][C]423.171334034321[/C][C]-2.17133403432086[/C][/ROW]
[ROW][C]21[/C][C]412[/C][C]421.79978842851[/C][C]-9.79978842851045[/C][/ROW]
[ROW][C]22[/C][C]408[/C][C]414.197263075964[/C][C]-6.19726307596392[/C][/ROW]
[ROW][C]23[/C][C]402[/C][C]409.549908623796[/C][C]-7.54990862379606[/C][/ROW]
[ROW][C]24[/C][C]409[/C][C]404.804129560103[/C][C]4.19587043989679[/C][/ROW]
[ROW][C]25[/C][C]410[/C][C]408.699608138046[/C][C]1.30039186195404[/C][/ROW]
[ROW][C]26[/C][C]410[/C][C]408.64788673553[/C][C]1.35211326447023[/C][/ROW]
[ROW][C]27[/C][C]416[/C][C]410.923662163391[/C][C]5.07633783660867[/C][/ROW]
[ROW][C]28[/C][C]410[/C][C]409.226344288174[/C][C]0.773655711826166[/C][/ROW]
[ROW][C]29[/C][C]437[/C][C]434.324434737331[/C][C]2.67556526266924[/C][/ROW]
[ROW][C]30[/C][C]431[/C][C]429.974167825028[/C][C]1.02583217497192[/C][/ROW]
[ROW][C]31[/C][C]411[/C][C]410.495682657533[/C][C]0.504317342467289[/C][/ROW]
[ROW][C]32[/C][C]398[/C][C]397.794561758935[/C][C]0.205438241064542[/C][/ROW]
[ROW][C]33[/C][C]394[/C][C]394.811591114848[/C][C]-0.811591114848[/C][/ROW]
[ROW][C]34[/C][C]395[/C][C]394.313604645821[/C][C]0.686395354178842[/C][/ROW]
[ROW][C]35[/C][C]389[/C][C]393.911263366435[/C][C]-4.9112633664351[/C][/ROW]
[ROW][C]36[/C][C]404[/C][C]395.706108088484[/C][C]8.29389191151591[/C][/ROW]
[ROW][C]37[/C][C]397[/C][C]401.816039262232[/C][C]-4.81603926223158[/C][/ROW]
[ROW][C]38[/C][C]401[/C][C]398.372779433713[/C][C]2.62722056628746[/C][/ROW]
[ROW][C]39[/C][C]402[/C][C]403.326538370803[/C][C]-1.32653837080289[/C][/ROW]
[ROW][C]40[/C][C]383[/C][C]396.21989920926[/C][C]-13.2198992092598[/C][/ROW]
[ROW][C]41[/C][C]406[/C][C]412.816649016664[/C][C]-6.81664901666426[/C][/ROW]
[ROW][C]42[/C][C]400[/C][C]401.067817981349[/C][C]-1.06781798134915[/C][/ROW]
[ROW][C]43[/C][C]377[/C][C]379.174787610289[/C][C]-2.17478761028889[/C][/ROW]
[ROW][C]44[/C][C]372[/C][C]363.655857873196[/C][C]8.34414212680366[/C][/ROW]
[ROW][C]45[/C][C]362[/C][C]364.755147597983[/C][C]-2.75514759798318[/C][/ROW]
[ROW][C]46[/C][C]365[/C][C]362.839056277637[/C][C]2.16094372236284[/C][/ROW]
[ROW][C]47[/C][C]361[/C][C]360.606188411535[/C][C]0.393811588464587[/C][/ROW]
[ROW][C]48[/C][C]372[/C][C]370.179845612931[/C][C]1.82015438706895[/C][/ROW]
[ROW][C]49[/C][C]355[/C][C]366.621377684997[/C][C]-11.6213776849968[/C][/ROW]
[ROW][C]50[/C][C]365[/C][C]360.617633542951[/C][C]4.3823664570491[/C][/ROW]
[ROW][C]51[/C][C]367[/C][C]364.25451806712[/C][C]2.74548193288024[/C][/ROW]
[ROW][C]52[/C][C]341[/C][C]354.526275390355[/C][C]-13.5262753903546[/C][/ROW]
[ROW][C]53[/C][C]370[/C][C]372.510019532484[/C][C]-2.51001953248357[/C][/ROW]
[ROW][C]54[/C][C]366[/C][C]364.998137159652[/C][C]1.00186284034771[/C][/ROW]
[ROW][C]55[/C][C]333[/C][C]343.484489705345[/C][C]-10.4844897053449[/C][/ROW]
[ROW][C]56[/C][C]320[/C][C]325.754383490978[/C][C]-5.75438349097817[/C][/ROW]
[ROW][C]57[/C][C]298[/C][C]312.372710826702[/C][C]-14.3727108267021[/C][/ROW]
[ROW][C]58[/C][C]306[/C][C]302.962564998555[/C][C]3.03743500144486[/C][/ROW]
[ROW][C]59[/C][C]293[/C][C]298.663440651037[/C][C]-5.66344065103664[/C][/ROW]
[ROW][C]60[/C][C]313[/C][C]302.723983065168[/C][C]10.2760169348322[/C][/ROW]
[ROW][C]61[/C][C]293[/C][C]297.650611134798[/C][C]-4.650611134798[/C][/ROW]
[ROW][C]62[/C][C]304[/C][C]300.41051635668[/C][C]3.58948364331957[/C][/ROW]
[ROW][C]63[/C][C]304[/C][C]301.353602961394[/C][C]2.64639703860615[/C][/ROW]
[ROW][C]64[/C][C]286[/C][C]283.94222395927[/C][C]2.05777604073046[/C][/ROW]
[ROW][C]65[/C][C]320[/C][C]314.906851255704[/C][C]5.09314874429617[/C][/ROW]
[ROW][C]66[/C][C]313[/C][C]312.904056724697[/C][C]0.0959432753027158[/C][/ROW]
[ROW][C]67[/C][C]283[/C][C]285.946755177542[/C][C]-2.94675517754217[/C][/ROW]
[ROW][C]68[/C][C]272[/C][C]274.425928346298[/C][C]-2.42592834629761[/C][/ROW]
[ROW][C]69[/C][C]251[/C][C]259.804062899839[/C][C]-8.80406289983927[/C][/ROW]
[ROW][C]70[/C][C]262[/C][C]260.450313041766[/C][C]1.54968695823391[/C][/ROW]
[ROW][C]71[/C][C]247[/C][C]252.026961520829[/C][C]-5.02696152082945[/C][/ROW]
[ROW][C]72[/C][C]268[/C][C]262.456869783264[/C][C]5.54313021673596[/C][/ROW]
[ROW][C]73[/C][C]251[/C][C]248.730732895842[/C][C]2.26926710415825[/C][/ROW]
[ROW][C]74[/C][C]257[/C][C]259.058875577938[/C][C]-2.05887557793773[/C][/ROW]
[ROW][C]75[/C][C]261[/C][C]256.008967592811[/C][C]4.99103240718875[/C][/ROW]
[ROW][C]76[/C][C]242[/C][C]239.870300045455[/C][C]2.12969995454466[/C][/ROW]
[ROW][C]77[/C][C]274[/C][C]272.022621664135[/C][C]1.97737833586484[/C][/ROW]
[ROW][C]78[/C][C]272[/C][C]266.088665290476[/C][C]5.91133470952389[/C][/ROW]
[ROW][C]79[/C][C]243[/C][C]241.801086970221[/C][C]1.19891302977894[/C][/ROW]
[ROW][C]80[/C][C]234[/C][C]233.400345966203[/C][C]0.599654033796867[/C][/ROW]
[ROW][C]81[/C][C]217[/C][C]218.769920540842[/C][C]-1.76992054084209[/C][/ROW]
[ROW][C]82[/C][C]231[/C][C]228.437439169231[/C][C]2.56256083076934[/C][/ROW]
[ROW][C]83[/C][C]209[/C][C]219.016891746628[/C][C]-10.0168917466282[/C][/ROW]
[ROW][C]84[/C][C]226[/C][C]230.804741308723[/C][C]-4.80474130872329[/C][/ROW]
[ROW][C]85[/C][C]208[/C][C]209.48219019738[/C][C]-1.48219019737974[/C][/ROW]
[ROW][C]86[/C][C]214[/C][C]215.811900131031[/C][C]-1.8119001310308[/C][/ROW]
[ROW][C]87[/C][C]222[/C][C]215.506716766544[/C][C]6.49328323345583[/C][/ROW]
[ROW][C]88[/C][C]194[/C][C]199.296904609828[/C][C]-5.2969046098284[/C][/ROW]
[ROW][C]89[/C][C]230[/C][C]226.43586589945[/C][C]3.56413410054984[/C][/ROW]
[ROW][C]90[/C][C]226[/C][C]222.745979855425[/C][C]3.25402014457535[/C][/ROW]
[ROW][C]91[/C][C]197[/C][C]194.711253014663[/C][C]2.2887469853375[/C][/ROW]
[ROW][C]92[/C][C]188[/C][C]186.493777373946[/C][C]1.50622262605393[/C][/ROW]
[ROW][C]93[/C][C]175[/C][C]171.315050991678[/C][C]3.68494900832246[/C][/ROW]
[ROW][C]94[/C][C]190[/C][C]186.019060799601[/C][C]3.98093920039867[/C][/ROW]
[ROW][C]95[/C][C]165[/C][C]172.890595232081[/C][C]-7.89059523208124[/C][/ROW]
[ROW][C]96[/C][C]176[/C][C]188.100428425627[/C][C]-12.1004284256267[/C][/ROW]
[ROW][C]97[/C][C]159[/C][C]163.249288039178[/C][C]-4.249288039178[/C][/ROW]
[ROW][C]98[/C][C]169[/C][C]167.427213470512[/C][C]1.57278652948838[/C][/ROW]
[ROW][C]99[/C][C]170[/C][C]172.189988866295[/C][C]-2.18998886629478[/C][/ROW]
[ROW][C]100[/C][C]141[/C][C]145.626468186535[/C][C]-4.62646818653459[/C][/ROW]
[ROW][C]101[/C][C]170[/C][C]175.980137740149[/C][C]-5.98013774014851[/C][/ROW]
[ROW][C]102[/C][C]164[/C][C]165.25939932911[/C][C]-1.25939932910964[/C][/ROW]
[ROW][C]103[/C][C]132[/C][C]132.920766727966[/C][C]-0.920766727965685[/C][/ROW]
[ROW][C]104[/C][C]123[/C][C]121.147555621702[/C][C]1.85244437829766[/C][/ROW]
[ROW][C]105[/C][C]113[/C][C]105.763734301818[/C][C]7.23626569818178[/C][/ROW]
[ROW][C]106[/C][C]125[/C][C]121.738190038505[/C][C]3.26180996149512[/C][/ROW]
[ROW][C]107[/C][C]101[/C][C]102.652644925829[/C][C]-1.65264492582939[/C][/ROW]
[ROW][C]108[/C][C]99[/C][C]119.396361086631[/C][C]-20.3963610866314[/C][/ROW]
[ROW][C]109[/C][C]87[/C][C]91.0349430096177[/C][C]-4.03494300961773[/C][/ROW]
[ROW][C]110[/C][C]90[/C][C]96.3177401187613[/C][C]-6.31774011876134[/C][/ROW]
[ROW][C]111[/C][C]89[/C][C]93.1871045294938[/C][C]-4.18710452949384[/C][/ROW]
[ROW][C]112[/C][C]66[/C][C]62.8442558164945[/C][C]3.15574418350549[/C][/ROW]
[ROW][C]113[/C][C]102[/C][C]96.316518880207[/C][C]5.68348111979296[/C][/ROW]
[ROW][C]114[/C][C]97[/C][C]93.9183762803797[/C][C]3.08162371962034[/C][/ROW]
[ROW][C]115[/C][C]65[/C][C]63.8589774287454[/C][C]1.1410225712546[/C][/ROW]
[ROW][C]116[/C][C]54[/C][C]53.9222699892167[/C][C]0.0777300107833128[/C][/ROW]
[ROW][C]117[/C][C]33[/C][C]38.8492822771176[/C][C]-5.84928227711762[/C][/ROW]
[ROW][C]118[/C][C]49[/C][C]43.9747504482956[/C][C]5.02524955170444[/C][/ROW]
[ROW][C]119[/C][C]30[/C][C]23.1170011651622[/C][C]6.88299883483781[/C][/ROW]
[ROW][C]120[/C][C]34[/C][C]37.6018473752156[/C][C]-3.60184737521563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78307&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78307&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
13439439.841079059829-0.841079059829156
14439439.259508768634-0.259508768634248
15441441.616037467087-0.616037467086699
16436437.304508835147-1.3045088351472
17460461.960841675652-1.96084167565243
18453455.201560779497-2.20156077949667
19435432.0694455722132.93055442778683
20421423.171334034321-2.17133403432086
21412421.79978842851-9.79978842851045
22408414.197263075964-6.19726307596392
23402409.549908623796-7.54990862379606
24409404.8041295601034.19587043989679
25410408.6996081380461.30039186195404
26410408.647886735531.35211326447023
27416410.9236621633915.07633783660867
28410409.2263442881740.773655711826166
29437434.3244347373312.67556526266924
30431429.9741678250281.02583217497192
31411410.4956826575330.504317342467289
32398397.7945617589350.205438241064542
33394394.811591114848-0.811591114848
34395394.3136046458210.686395354178842
35389393.911263366435-4.9112633664351
36404395.7061080884848.29389191151591
37397401.816039262232-4.81603926223158
38401398.3727794337132.62722056628746
39402403.326538370803-1.32653837080289
40383396.21989920926-13.2198992092598
41406412.816649016664-6.81664901666426
42400401.067817981349-1.06781798134915
43377379.174787610289-2.17478761028889
44372363.6558578731968.34414212680366
45362364.755147597983-2.75514759798318
46365362.8390562776372.16094372236284
47361360.6061884115350.393811588464587
48372370.1798456129311.82015438706895
49355366.621377684997-11.6213776849968
50365360.6176335429514.3823664570491
51367364.254518067122.74548193288024
52341354.526275390355-13.5262753903546
53370372.510019532484-2.51001953248357
54366364.9981371596521.00186284034771
55333343.484489705345-10.4844897053449
56320325.754383490978-5.75438349097817
57298312.372710826702-14.3727108267021
58306302.9625649985553.03743500144486
59293298.663440651037-5.66344065103664
60313302.72398306516810.2760169348322
61293297.650611134798-4.650611134798
62304300.410516356683.58948364331957
63304301.3536029613942.64639703860615
64286283.942223959272.05777604073046
65320314.9068512557045.09314874429617
66313312.9040567246970.0959432753027158
67283285.946755177542-2.94675517754217
68272274.425928346298-2.42592834629761
69251259.804062899839-8.80406289983927
70262260.4503130417661.54968695823391
71247252.026961520829-5.02696152082945
72268262.4568697832645.54313021673596
73251248.7307328958422.26926710415825
74257259.058875577938-2.05887557793773
75261256.0089675928114.99103240718875
76242239.8703000454552.12969995454466
77274272.0226216641351.97737833586484
78272266.0886652904765.91133470952389
79243241.8010869702211.19891302977894
80234233.4003459662030.599654033796867
81217218.769920540842-1.76992054084209
82231228.4374391692312.56256083076934
83209219.016891746628-10.0168917466282
84226230.804741308723-4.80474130872329
85208209.48219019738-1.48219019737974
86214215.811900131031-1.8119001310308
87222215.5067167665446.49328323345583
88194199.296904609828-5.2969046098284
89230226.435865899453.56413410054984
90226222.7459798554253.25402014457535
91197194.7112530146632.2887469853375
92188186.4937773739461.50622262605393
93175171.3150509916783.68494900832246
94190186.0190607996013.98093920039867
95165172.890595232081-7.89059523208124
96176188.100428425627-12.1004284256267
97159163.249288039178-4.249288039178
98169167.4272134705121.57278652948838
99170172.189988866295-2.18998886629478
100141145.626468186535-4.62646818653459
101170175.980137740149-5.98013774014851
102164165.25939932911-1.25939932910964
103132132.920766727966-0.920766727965685
104123121.1475556217021.85244437829766
105113105.7637343018187.23626569818178
106125121.7381900385053.26180996149512
107101102.652644925829-1.65264492582939
10899119.396361086631-20.3963610866314
1098791.0349430096177-4.03494300961773
1109096.3177401187613-6.31774011876134
1118993.1871045294938-4.18710452949384
1126662.84425581649453.15574418350549
11310296.3165188802075.68348111979296
1149793.91837628037973.08162371962034
1156563.85897742874541.1410225712546
1165453.92226998921670.0777300107833128
1173338.8492822771176-5.84928227711762
1184943.97475044829565.02524955170444
1193023.11700116516226.88299883483781
1203437.6018473752156-3.60184737521563







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12125.92072362621315.432554480457636.4088927719685
12233.120648748849620.476891545669245.7644059520299
12335.255605601967220.544499263485849.9667119404487
12410.9511541394199-5.7843991119438327.6867073907836
12543.917385399329225.175139932838562.6596308658199
12637.272975416998816.526491200996358.0194596330013
1274.71544596563955-18.042720905992127.4736128372712
128-6.22261549566044-31.006588368358218.5613573770373
129-23.4328408075865-50.26138816761793.39570655244488
130-10.2330751233618-39.128264615271518.6621143685479
131-33.4226193973938-64.4088948828122-2.43634391197549
132-27.3126875305545-60.41621788059275.79084281948378

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 25.920723626213 & 15.4325544804576 & 36.4088927719685 \tabularnewline
122 & 33.1206487488496 & 20.4768915456692 & 45.7644059520299 \tabularnewline
123 & 35.2556056019672 & 20.5444992634858 & 49.9667119404487 \tabularnewline
124 & 10.9511541394199 & -5.78439911194383 & 27.6867073907836 \tabularnewline
125 & 43.9173853993292 & 25.1751399328385 & 62.6596308658199 \tabularnewline
126 & 37.2729754169988 & 16.5264912009963 & 58.0194596330013 \tabularnewline
127 & 4.71544596563955 & -18.0427209059921 & 27.4736128372712 \tabularnewline
128 & -6.22261549566044 & -31.0065883683582 & 18.5613573770373 \tabularnewline
129 & -23.4328408075865 & -50.2613881676179 & 3.39570655244488 \tabularnewline
130 & -10.2330751233618 & -39.1282646152715 & 18.6621143685479 \tabularnewline
131 & -33.4226193973938 & -64.4088948828122 & -2.43634391197549 \tabularnewline
132 & -27.3126875305545 & -60.4162178805927 & 5.79084281948378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78307&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]25.920723626213[/C][C]15.4325544804576[/C][C]36.4088927719685[/C][/ROW]
[ROW][C]122[/C][C]33.1206487488496[/C][C]20.4768915456692[/C][C]45.7644059520299[/C][/ROW]
[ROW][C]123[/C][C]35.2556056019672[/C][C]20.5444992634858[/C][C]49.9667119404487[/C][/ROW]
[ROW][C]124[/C][C]10.9511541394199[/C][C]-5.78439911194383[/C][C]27.6867073907836[/C][/ROW]
[ROW][C]125[/C][C]43.9173853993292[/C][C]25.1751399328385[/C][C]62.6596308658199[/C][/ROW]
[ROW][C]126[/C][C]37.2729754169988[/C][C]16.5264912009963[/C][C]58.0194596330013[/C][/ROW]
[ROW][C]127[/C][C]4.71544596563955[/C][C]-18.0427209059921[/C][C]27.4736128372712[/C][/ROW]
[ROW][C]128[/C][C]-6.22261549566044[/C][C]-31.0065883683582[/C][C]18.5613573770373[/C][/ROW]
[ROW][C]129[/C][C]-23.4328408075865[/C][C]-50.2613881676179[/C][C]3.39570655244488[/C][/ROW]
[ROW][C]130[/C][C]-10.2330751233618[/C][C]-39.1282646152715[/C][C]18.6621143685479[/C][/ROW]
[ROW][C]131[/C][C]-33.4226193973938[/C][C]-64.4088948828122[/C][C]-2.43634391197549[/C][/ROW]
[ROW][C]132[/C][C]-27.3126875305545[/C][C]-60.4162178805927[/C][C]5.79084281948378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78307&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78307&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
12125.92072362621315.432554480457636.4088927719685
12233.120648748849620.476891545669245.7644059520299
12335.255605601967220.544499263485849.9667119404487
12410.9511541394199-5.7843991119438327.6867073907836
12543.917385399329225.175139932838562.6596308658199
12637.272975416998816.526491200996358.0194596330013
1274.71544596563955-18.042720905992127.4736128372712
128-6.22261549566044-31.006588368358218.5613573770373
129-23.4328408075865-50.26138816761793.39570655244488
130-10.2330751233618-39.128264615271518.6621143685479
131-33.4226193973938-64.4088948828122-2.43634391197549
132-27.3126875305545-60.41621788059275.79084281948378



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')