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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 07:48:47 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t1243950566idl0oshicz8ealm.htm/, Retrieved Fri, 10 May 2024 16:13:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41216, Retrieved Fri, 10 May 2024 16:13:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2009-06-02 13:48:47] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
220206
220115
218444
214912
210705
209673
237041
242081
241878
242621
238545
240337
244752
244576
241572
240541
236089
236997
264579
270349
269645
267037
258113
262813
267413
267366
264777
258863
254844
254868
277267
285351
286602
283042
276687
277915
277128
277103
275037
270150
267140
264993
287259
291186
292300
288186
281477
282656
280190
280408
276836
275216
274352
271311
289802
290726
292300
278506
269826
265861
269034
264176
255198
253353
246057
235372
258556
260993
254663
250643
243422
247105
248541
245039
237080
237085
225554
226839
247934
248333
246969
245098
246263
255765
264319




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41216&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41216&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41216&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.921339261357122
beta0.180937138360347
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.921339261357122 \tabularnewline
beta & 0.180937138360347 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41216&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]0.921339261357122[/C][/ROW]
[ROW][C]beta[/C][C]0.180937138360347[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41216&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41216&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
alpha0.921339261357122
beta0.180937138360347
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13244752232009.03445512812742.9655448717
14244576245522.595096673-946.595096672943
15241572243428.082729499-1856.08272949874
16240541242319.706374761-1778.70637476142
17236089237906.726555531-1817.72655553120
18236997238595.606067781-1598.60606778093
19264579263190.5417467341388.45825326623
20270349270640.247618376-291.247618376219
21269645271309.905570763-1664.90557076276
22267037271333.744620185-4296.74462018523
23258113263303.480405773-5190.48040577321
24262813259381.8809369873431.11906301271
25267413267511.303588251-98.3035882508848
26267366265663.0075641421702.99243585835
27264777263925.961088967851.038911032956
28258863263756.975839852-4893.97583985189
29254844254390.50436265453.495637350221
30254868255487.606934048-619.606934048032
31277267279681.121890495-2414.12189049466
32285351281322.9515482484028.04845175165
33286602284411.856719852190.14328014990
34283042286970.898294348-3928.89829434769
35276687278460.982126856-1773.98212685587
36277915278186.602344273-271.602344273007
37277128281830.95941776-4702.95941775985
38277103274318.311691052784.68830895005
39275037272127.5895796622909.41042033804
40270150272363.026264794-2213.02626479388
41267140265294.0518272051845.94817279465
42264993267228.589519252-2235.58951925213
43287259289161.611821614-1902.61182161386
44291186291236.266110164-50.2661101644044
45292300289198.0200748343101.97992516571
46288186291042.782580104-2856.78258010407
47281477282795.820872853-1318.82087285299
48282656282240.519614241415.480385759322
49280190285465.421224797-5275.4212247968
50280408277214.9759699503193.02403005044
51276836274679.0018309592156.99816904112
52275216272961.5679220902254.43207791046
53274352270215.9565506304136.04344936967
54271311274209.197696483-2898.19769648334
55289802295717.271116954-5915.27111695439
56290726293731.029192182-3005.02919218160
57292300288216.2471080304083.75289196969
58278506289658.346079567-11152.3460795669
59269826271667.936697812-1841.93669781188
60265861268458.487421693-2597.48742169334
61269034265648.8954260953385.10457390529
62264176264676.737756064-500.737756063812
63255198256673.165612966-1475.16561296556
64253353249028.5471335864324.45286641447
65246057246094.824187623-37.8241876228421
66235372242750.084191101-7378.08419110082
67258556256207.4054707872348.59452921333
68260993259755.6010958531237.39890414698
69254663257106.067124817-2443.06712481679
70250643248647.1412752421995.85872475817
71243422243005.791154965416.208845035406
72247105241696.6091268915408.39087310899
73248541247947.539364303593.460635697207
74245039244846.084858005192.915141995181
75237080238269.005756521-1189.00575652113
76237085232255.9966019574829.00339804275
77225554230439.863514258-4885.8635142576
78226839222238.7219305894600.27806941132
79247934249681.810803709-1747.81080370874
80248333250870.055160424-2537.05516042383
81246969245325.8771194361643.12288056378
82245098242534.4907820822563.50921791792
83246263238940.1158519617322.88414803939
84255765247186.6203820748578.37961792576
85264319259307.497804615011.50219538985

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 244752 & 232009.034455128 & 12742.9655448717 \tabularnewline
14 & 244576 & 245522.595096673 & -946.595096672943 \tabularnewline
15 & 241572 & 243428.082729499 & -1856.08272949874 \tabularnewline
16 & 240541 & 242319.706374761 & -1778.70637476142 \tabularnewline
17 & 236089 & 237906.726555531 & -1817.72655553120 \tabularnewline
18 & 236997 & 238595.606067781 & -1598.60606778093 \tabularnewline
19 & 264579 & 263190.541746734 & 1388.45825326623 \tabularnewline
20 & 270349 & 270640.247618376 & -291.247618376219 \tabularnewline
21 & 269645 & 271309.905570763 & -1664.90557076276 \tabularnewline
22 & 267037 & 271333.744620185 & -4296.74462018523 \tabularnewline
23 & 258113 & 263303.480405773 & -5190.48040577321 \tabularnewline
24 & 262813 & 259381.880936987 & 3431.11906301271 \tabularnewline
25 & 267413 & 267511.303588251 & -98.3035882508848 \tabularnewline
26 & 267366 & 265663.007564142 & 1702.99243585835 \tabularnewline
27 & 264777 & 263925.961088967 & 851.038911032956 \tabularnewline
28 & 258863 & 263756.975839852 & -4893.97583985189 \tabularnewline
29 & 254844 & 254390.50436265 & 453.495637350221 \tabularnewline
30 & 254868 & 255487.606934048 & -619.606934048032 \tabularnewline
31 & 277267 & 279681.121890495 & -2414.12189049466 \tabularnewline
32 & 285351 & 281322.951548248 & 4028.04845175165 \tabularnewline
33 & 286602 & 284411.85671985 & 2190.14328014990 \tabularnewline
34 & 283042 & 286970.898294348 & -3928.89829434769 \tabularnewline
35 & 276687 & 278460.982126856 & -1773.98212685587 \tabularnewline
36 & 277915 & 278186.602344273 & -271.602344273007 \tabularnewline
37 & 277128 & 281830.95941776 & -4702.95941775985 \tabularnewline
38 & 277103 & 274318.31169105 & 2784.68830895005 \tabularnewline
39 & 275037 & 272127.589579662 & 2909.41042033804 \tabularnewline
40 & 270150 & 272363.026264794 & -2213.02626479388 \tabularnewline
41 & 267140 & 265294.051827205 & 1845.94817279465 \tabularnewline
42 & 264993 & 267228.589519252 & -2235.58951925213 \tabularnewline
43 & 287259 & 289161.611821614 & -1902.61182161386 \tabularnewline
44 & 291186 & 291236.266110164 & -50.2661101644044 \tabularnewline
45 & 292300 & 289198.020074834 & 3101.97992516571 \tabularnewline
46 & 288186 & 291042.782580104 & -2856.78258010407 \tabularnewline
47 & 281477 & 282795.820872853 & -1318.82087285299 \tabularnewline
48 & 282656 & 282240.519614241 & 415.480385759322 \tabularnewline
49 & 280190 & 285465.421224797 & -5275.4212247968 \tabularnewline
50 & 280408 & 277214.975969950 & 3193.02403005044 \tabularnewline
51 & 276836 & 274679.001830959 & 2156.99816904112 \tabularnewline
52 & 275216 & 272961.567922090 & 2254.43207791046 \tabularnewline
53 & 274352 & 270215.956550630 & 4136.04344936967 \tabularnewline
54 & 271311 & 274209.197696483 & -2898.19769648334 \tabularnewline
55 & 289802 & 295717.271116954 & -5915.27111695439 \tabularnewline
56 & 290726 & 293731.029192182 & -3005.02919218160 \tabularnewline
57 & 292300 & 288216.247108030 & 4083.75289196969 \tabularnewline
58 & 278506 & 289658.346079567 & -11152.3460795669 \tabularnewline
59 & 269826 & 271667.936697812 & -1841.93669781188 \tabularnewline
60 & 265861 & 268458.487421693 & -2597.48742169334 \tabularnewline
61 & 269034 & 265648.895426095 & 3385.10457390529 \tabularnewline
62 & 264176 & 264676.737756064 & -500.737756063812 \tabularnewline
63 & 255198 & 256673.165612966 & -1475.16561296556 \tabularnewline
64 & 253353 & 249028.547133586 & 4324.45286641447 \tabularnewline
65 & 246057 & 246094.824187623 & -37.8241876228421 \tabularnewline
66 & 235372 & 242750.084191101 & -7378.08419110082 \tabularnewline
67 & 258556 & 256207.405470787 & 2348.59452921333 \tabularnewline
68 & 260993 & 259755.601095853 & 1237.39890414698 \tabularnewline
69 & 254663 & 257106.067124817 & -2443.06712481679 \tabularnewline
70 & 250643 & 248647.141275242 & 1995.85872475817 \tabularnewline
71 & 243422 & 243005.791154965 & 416.208845035406 \tabularnewline
72 & 247105 & 241696.609126891 & 5408.39087310899 \tabularnewline
73 & 248541 & 247947.539364303 & 593.460635697207 \tabularnewline
74 & 245039 & 244846.084858005 & 192.915141995181 \tabularnewline
75 & 237080 & 238269.005756521 & -1189.00575652113 \tabularnewline
76 & 237085 & 232255.996601957 & 4829.00339804275 \tabularnewline
77 & 225554 & 230439.863514258 & -4885.8635142576 \tabularnewline
78 & 226839 & 222238.721930589 & 4600.27806941132 \tabularnewline
79 & 247934 & 249681.810803709 & -1747.81080370874 \tabularnewline
80 & 248333 & 250870.055160424 & -2537.05516042383 \tabularnewline
81 & 246969 & 245325.877119436 & 1643.12288056378 \tabularnewline
82 & 245098 & 242534.490782082 & 2563.50921791792 \tabularnewline
83 & 246263 & 238940.115851961 & 7322.88414803939 \tabularnewline
84 & 255765 & 247186.620382074 & 8578.37961792576 \tabularnewline
85 & 264319 & 259307.49780461 & 5011.50219538985 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41216&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]244752[/C][C]232009.034455128[/C][C]12742.9655448717[/C][/ROW]
[ROW][C]14[/C][C]244576[/C][C]245522.595096673[/C][C]-946.595096672943[/C][/ROW]
[ROW][C]15[/C][C]241572[/C][C]243428.082729499[/C][C]-1856.08272949874[/C][/ROW]
[ROW][C]16[/C][C]240541[/C][C]242319.706374761[/C][C]-1778.70637476142[/C][/ROW]
[ROW][C]17[/C][C]236089[/C][C]237906.726555531[/C][C]-1817.72655553120[/C][/ROW]
[ROW][C]18[/C][C]236997[/C][C]238595.606067781[/C][C]-1598.60606778093[/C][/ROW]
[ROW][C]19[/C][C]264579[/C][C]263190.541746734[/C][C]1388.45825326623[/C][/ROW]
[ROW][C]20[/C][C]270349[/C][C]270640.247618376[/C][C]-291.247618376219[/C][/ROW]
[ROW][C]21[/C][C]269645[/C][C]271309.905570763[/C][C]-1664.90557076276[/C][/ROW]
[ROW][C]22[/C][C]267037[/C][C]271333.744620185[/C][C]-4296.74462018523[/C][/ROW]
[ROW][C]23[/C][C]258113[/C][C]263303.480405773[/C][C]-5190.48040577321[/C][/ROW]
[ROW][C]24[/C][C]262813[/C][C]259381.880936987[/C][C]3431.11906301271[/C][/ROW]
[ROW][C]25[/C][C]267413[/C][C]267511.303588251[/C][C]-98.3035882508848[/C][/ROW]
[ROW][C]26[/C][C]267366[/C][C]265663.007564142[/C][C]1702.99243585835[/C][/ROW]
[ROW][C]27[/C][C]264777[/C][C]263925.961088967[/C][C]851.038911032956[/C][/ROW]
[ROW][C]28[/C][C]258863[/C][C]263756.975839852[/C][C]-4893.97583985189[/C][/ROW]
[ROW][C]29[/C][C]254844[/C][C]254390.50436265[/C][C]453.495637350221[/C][/ROW]
[ROW][C]30[/C][C]254868[/C][C]255487.606934048[/C][C]-619.606934048032[/C][/ROW]
[ROW][C]31[/C][C]277267[/C][C]279681.121890495[/C][C]-2414.12189049466[/C][/ROW]
[ROW][C]32[/C][C]285351[/C][C]281322.951548248[/C][C]4028.04845175165[/C][/ROW]
[ROW][C]33[/C][C]286602[/C][C]284411.85671985[/C][C]2190.14328014990[/C][/ROW]
[ROW][C]34[/C][C]283042[/C][C]286970.898294348[/C][C]-3928.89829434769[/C][/ROW]
[ROW][C]35[/C][C]276687[/C][C]278460.982126856[/C][C]-1773.98212685587[/C][/ROW]
[ROW][C]36[/C][C]277915[/C][C]278186.602344273[/C][C]-271.602344273007[/C][/ROW]
[ROW][C]37[/C][C]277128[/C][C]281830.95941776[/C][C]-4702.95941775985[/C][/ROW]
[ROW][C]38[/C][C]277103[/C][C]274318.31169105[/C][C]2784.68830895005[/C][/ROW]
[ROW][C]39[/C][C]275037[/C][C]272127.589579662[/C][C]2909.41042033804[/C][/ROW]
[ROW][C]40[/C][C]270150[/C][C]272363.026264794[/C][C]-2213.02626479388[/C][/ROW]
[ROW][C]41[/C][C]267140[/C][C]265294.051827205[/C][C]1845.94817279465[/C][/ROW]
[ROW][C]42[/C][C]264993[/C][C]267228.589519252[/C][C]-2235.58951925213[/C][/ROW]
[ROW][C]43[/C][C]287259[/C][C]289161.611821614[/C][C]-1902.61182161386[/C][/ROW]
[ROW][C]44[/C][C]291186[/C][C]291236.266110164[/C][C]-50.2661101644044[/C][/ROW]
[ROW][C]45[/C][C]292300[/C][C]289198.020074834[/C][C]3101.97992516571[/C][/ROW]
[ROW][C]46[/C][C]288186[/C][C]291042.782580104[/C][C]-2856.78258010407[/C][/ROW]
[ROW][C]47[/C][C]281477[/C][C]282795.820872853[/C][C]-1318.82087285299[/C][/ROW]
[ROW][C]48[/C][C]282656[/C][C]282240.519614241[/C][C]415.480385759322[/C][/ROW]
[ROW][C]49[/C][C]280190[/C][C]285465.421224797[/C][C]-5275.4212247968[/C][/ROW]
[ROW][C]50[/C][C]280408[/C][C]277214.975969950[/C][C]3193.02403005044[/C][/ROW]
[ROW][C]51[/C][C]276836[/C][C]274679.001830959[/C][C]2156.99816904112[/C][/ROW]
[ROW][C]52[/C][C]275216[/C][C]272961.567922090[/C][C]2254.43207791046[/C][/ROW]
[ROW][C]53[/C][C]274352[/C][C]270215.956550630[/C][C]4136.04344936967[/C][/ROW]
[ROW][C]54[/C][C]271311[/C][C]274209.197696483[/C][C]-2898.19769648334[/C][/ROW]
[ROW][C]55[/C][C]289802[/C][C]295717.271116954[/C][C]-5915.27111695439[/C][/ROW]
[ROW][C]56[/C][C]290726[/C][C]293731.029192182[/C][C]-3005.02919218160[/C][/ROW]
[ROW][C]57[/C][C]292300[/C][C]288216.247108030[/C][C]4083.75289196969[/C][/ROW]
[ROW][C]58[/C][C]278506[/C][C]289658.346079567[/C][C]-11152.3460795669[/C][/ROW]
[ROW][C]59[/C][C]269826[/C][C]271667.936697812[/C][C]-1841.93669781188[/C][/ROW]
[ROW][C]60[/C][C]265861[/C][C]268458.487421693[/C][C]-2597.48742169334[/C][/ROW]
[ROW][C]61[/C][C]269034[/C][C]265648.895426095[/C][C]3385.10457390529[/C][/ROW]
[ROW][C]62[/C][C]264176[/C][C]264676.737756064[/C][C]-500.737756063812[/C][/ROW]
[ROW][C]63[/C][C]255198[/C][C]256673.165612966[/C][C]-1475.16561296556[/C][/ROW]
[ROW][C]64[/C][C]253353[/C][C]249028.547133586[/C][C]4324.45286641447[/C][/ROW]
[ROW][C]65[/C][C]246057[/C][C]246094.824187623[/C][C]-37.8241876228421[/C][/ROW]
[ROW][C]66[/C][C]235372[/C][C]242750.084191101[/C][C]-7378.08419110082[/C][/ROW]
[ROW][C]67[/C][C]258556[/C][C]256207.405470787[/C][C]2348.59452921333[/C][/ROW]
[ROW][C]68[/C][C]260993[/C][C]259755.601095853[/C][C]1237.39890414698[/C][/ROW]
[ROW][C]69[/C][C]254663[/C][C]257106.067124817[/C][C]-2443.06712481679[/C][/ROW]
[ROW][C]70[/C][C]250643[/C][C]248647.141275242[/C][C]1995.85872475817[/C][/ROW]
[ROW][C]71[/C][C]243422[/C][C]243005.791154965[/C][C]416.208845035406[/C][/ROW]
[ROW][C]72[/C][C]247105[/C][C]241696.609126891[/C][C]5408.39087310899[/C][/ROW]
[ROW][C]73[/C][C]248541[/C][C]247947.539364303[/C][C]593.460635697207[/C][/ROW]
[ROW][C]74[/C][C]245039[/C][C]244846.084858005[/C][C]192.915141995181[/C][/ROW]
[ROW][C]75[/C][C]237080[/C][C]238269.005756521[/C][C]-1189.00575652113[/C][/ROW]
[ROW][C]76[/C][C]237085[/C][C]232255.996601957[/C][C]4829.00339804275[/C][/ROW]
[ROW][C]77[/C][C]225554[/C][C]230439.863514258[/C][C]-4885.8635142576[/C][/ROW]
[ROW][C]78[/C][C]226839[/C][C]222238.721930589[/C][C]4600.27806941132[/C][/ROW]
[ROW][C]79[/C][C]247934[/C][C]249681.810803709[/C][C]-1747.81080370874[/C][/ROW]
[ROW][C]80[/C][C]248333[/C][C]250870.055160424[/C][C]-2537.05516042383[/C][/ROW]
[ROW][C]81[/C][C]246969[/C][C]245325.877119436[/C][C]1643.12288056378[/C][/ROW]
[ROW][C]82[/C][C]245098[/C][C]242534.490782082[/C][C]2563.50921791792[/C][/ROW]
[ROW][C]83[/C][C]246263[/C][C]238940.115851961[/C][C]7322.88414803939[/C][/ROW]
[ROW][C]84[/C][C]255765[/C][C]247186.620382074[/C][C]8578.37961792576[/C][/ROW]
[ROW][C]85[/C][C]264319[/C][C]259307.49780461[/C][C]5011.50219538985[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41216&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41216&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
13244752232009.03445512812742.9655448717
14244576245522.595096673-946.595096672943
15241572243428.082729499-1856.08272949874
16240541242319.706374761-1778.70637476142
17236089237906.726555531-1817.72655553120
18236997238595.606067781-1598.60606778093
19264579263190.5417467341388.45825326623
20270349270640.247618376-291.247618376219
21269645271309.905570763-1664.90557076276
22267037271333.744620185-4296.74462018523
23258113263303.480405773-5190.48040577321
24262813259381.8809369873431.11906301271
25267413267511.303588251-98.3035882508848
26267366265663.0075641421702.99243585835
27264777263925.961088967851.038911032956
28258863263756.975839852-4893.97583985189
29254844254390.50436265453.495637350221
30254868255487.606934048-619.606934048032
31277267279681.121890495-2414.12189049466
32285351281322.9515482484028.04845175165
33286602284411.856719852190.14328014990
34283042286970.898294348-3928.89829434769
35276687278460.982126856-1773.98212685587
36277915278186.602344273-271.602344273007
37277128281830.95941776-4702.95941775985
38277103274318.311691052784.68830895005
39275037272127.5895796622909.41042033804
40270150272363.026264794-2213.02626479388
41267140265294.0518272051845.94817279465
42264993267228.589519252-2235.58951925213
43287259289161.611821614-1902.61182161386
44291186291236.266110164-50.2661101644044
45292300289198.0200748343101.97992516571
46288186291042.782580104-2856.78258010407
47281477282795.820872853-1318.82087285299
48282656282240.519614241415.480385759322
49280190285465.421224797-5275.4212247968
50280408277214.9759699503193.02403005044
51276836274679.0018309592156.99816904112
52275216272961.5679220902254.43207791046
53274352270215.9565506304136.04344936967
54271311274209.197696483-2898.19769648334
55289802295717.271116954-5915.27111695439
56290726293731.029192182-3005.02919218160
57292300288216.2471080304083.75289196969
58278506289658.346079567-11152.3460795669
59269826271667.936697812-1841.93669781188
60265861268458.487421693-2597.48742169334
61269034265648.8954260953385.10457390529
62264176264676.737756064-500.737756063812
63255198256673.165612966-1475.16561296556
64253353249028.5471335864324.45286641447
65246057246094.824187623-37.8241876228421
66235372242750.084191101-7378.08419110082
67258556256207.4054707872348.59452921333
68260993259755.6010958531237.39890414698
69254663257106.067124817-2443.06712481679
70250643248647.1412752421995.85872475817
71243422243005.791154965416.208845035406
72247105241696.6091268915408.39087310899
73248541247947.539364303593.460635697207
74245039244846.084858005192.915141995181
75237080238269.005756521-1189.00575652113
76237085232255.9966019574829.00339804275
77225554230439.863514258-4885.8635142576
78226839222238.7219305894600.27806941132
79247934249681.810803709-1747.81080370874
80248333250870.055160424-2537.05516042383
81246969245325.8771194361643.12288056378
82245098242534.4907820822563.50921791792
83246263238940.1158519617322.88414803939
84255765247186.6203820748578.37961792576
85264319259307.497804615011.50219538985







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
86264309.616669019256899.23533014271719.998007898
87261478.499962085250527.572899378272429.427024793
88261264.967743390246899.083236489275630.852250292
89257661.107284032239847.253046961275474.961521103
90258947.787527314237597.395313867280298.179740760
91285126.324277284260127.357876168310125.290678400
92291627.390747517262857.392973076320397.388521957
93292937.033554246260269.239797812325604.827310679
94292617.772331913255924.225203949329311.319459877
95290522.163631672249675.378244173331368.949019171
96294386.059999668249259.9331474339512.186851937
97299158.206183333249628.509089475348687.90327719

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 264309.616669019 & 256899.23533014 & 271719.998007898 \tabularnewline
87 & 261478.499962085 & 250527.572899378 & 272429.427024793 \tabularnewline
88 & 261264.967743390 & 246899.083236489 & 275630.852250292 \tabularnewline
89 & 257661.107284032 & 239847.253046961 & 275474.961521103 \tabularnewline
90 & 258947.787527314 & 237597.395313867 & 280298.179740760 \tabularnewline
91 & 285126.324277284 & 260127.357876168 & 310125.290678400 \tabularnewline
92 & 291627.390747517 & 262857.392973076 & 320397.388521957 \tabularnewline
93 & 292937.033554246 & 260269.239797812 & 325604.827310679 \tabularnewline
94 & 292617.772331913 & 255924.225203949 & 329311.319459877 \tabularnewline
95 & 290522.163631672 & 249675.378244173 & 331368.949019171 \tabularnewline
96 & 294386.059999668 & 249259.9331474 & 339512.186851937 \tabularnewline
97 & 299158.206183333 & 249628.509089475 & 348687.90327719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41216&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]86[/C][C]264309.616669019[/C][C]256899.23533014[/C][C]271719.998007898[/C][/ROW]
[ROW][C]87[/C][C]261478.499962085[/C][C]250527.572899378[/C][C]272429.427024793[/C][/ROW]
[ROW][C]88[/C][C]261264.967743390[/C][C]246899.083236489[/C][C]275630.852250292[/C][/ROW]
[ROW][C]89[/C][C]257661.107284032[/C][C]239847.253046961[/C][C]275474.961521103[/C][/ROW]
[ROW][C]90[/C][C]258947.787527314[/C][C]237597.395313867[/C][C]280298.179740760[/C][/ROW]
[ROW][C]91[/C][C]285126.324277284[/C][C]260127.357876168[/C][C]310125.290678400[/C][/ROW]
[ROW][C]92[/C][C]291627.390747517[/C][C]262857.392973076[/C][C]320397.388521957[/C][/ROW]
[ROW][C]93[/C][C]292937.033554246[/C][C]260269.239797812[/C][C]325604.827310679[/C][/ROW]
[ROW][C]94[/C][C]292617.772331913[/C][C]255924.225203949[/C][C]329311.319459877[/C][/ROW]
[ROW][C]95[/C][C]290522.163631672[/C][C]249675.378244173[/C][C]331368.949019171[/C][/ROW]
[ROW][C]96[/C][C]294386.059999668[/C][C]249259.9331474[/C][C]339512.186851937[/C][/ROW]
[ROW][C]97[/C][C]299158.206183333[/C][C]249628.509089475[/C][C]348687.90327719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41216&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41216&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
86264309.616669019256899.23533014271719.998007898
87261478.499962085250527.572899378272429.427024793
88261264.967743390246899.083236489275630.852250292
89257661.107284032239847.253046961275474.961521103
90258947.787527314237597.395313867280298.179740760
91285126.324277284260127.357876168310125.290678400
92291627.390747517262857.392973076320397.388521957
93292937.033554246260269.239797812325604.827310679
94292617.772331913255924.225203949329311.319459877
95290522.163631672249675.378244173331368.949019171
96294386.059999668249259.9331474339512.186851937
97299158.206183333249628.509089475348687.90327719



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')