Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 06 Aug 2009 06:29:02 -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/Aug/06/t12495618716b00l7qbbo4lwyg.htm/, Retrieved Fri, 03 May 2024 16:59:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42522, Retrieved Fri, 03 May 2024 16:59:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact226
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [datareeks-diesel-...] [2009-08-06 12:29:02] [dd4d1946c4ef9dfd99dff91c071853fb] [Current]
Feedback Forum

Post a new message
Dataseries X:
0.9
0.92
0.92
0.95
1.06
1.17
1.23
1.26
1.37
1.37
1.31
1.21
1.2
1.11
1.11
1.11
1.17
1.08
1.05
1.03
1.04
1.02
1.01
1.01
0.98
0.96
0.94
0.99
0.99
0.98
1.02
1.06
1.06
1.06
1.06
1.06
1.04
1.02
1.01
1
1.04
1.09
1.08
1.06
1.06
1.03
0.97
0.98
0.93
0.88
0.86
0.9
0.91
0.93
0.89
0.88
0.83
0.81
0.83
0.8
0.76
0.73
0.74
0.74
0.75
0.74
0.74
0.73
0.71
0.71
0.7
0.75
0.81
0.78
0.75




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42522&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42522&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42522&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.740843693108228
beta0.000554454471247304
gamma0.450293672392732

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.740843693108228 \tabularnewline
beta & 0.000554454471247304 \tabularnewline
gamma & 0.450293672392732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42522&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]0.740843693108228[/C][/ROW]
[ROW][C]beta[/C][C]0.000554454471247304[/C][/ROW]
[ROW][C]gamma[/C][C]0.450293672392732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42522&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42522&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
alpha0.740843693108228
beta0.000554454471247304
gamma0.450293672392732







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.21.161664751731530.0383352482684693
141.111.11048182758549-0.000481827585486538
151.111.12609336529116-0.016093365291155
161.111.13552443884904-0.0255244388490383
171.171.19875697194969-0.0287569719496918
181.081.10112236822382-0.0211223682238153
191.051.15936563629937-0.109365636299373
201.031.07821459605905-0.0482145960590488
211.041.11066661232524-0.0706666123252446
221.021.03781221644680-0.0178122164468011
231.010.963391435853550.0466085641464503
241.010.9144187579460760.095581242053924
250.980.983244042236231-0.00324404223623131
260.960.9106000030638730.0493999969361271
270.940.958278315643581-0.0182783156435813
280.990.9608725220707380.0291274779292622
290.991.05367732483681-0.0636773248368059
300.980.9408185685215420.0391814314784582
311.021.02518372932378-0.00518372932378131
321.061.027601560044420.0323984399555795
331.061.11784165612741-0.0578416561274149
341.061.06053473495978-0.000534734959778849
351.061.004598389397420.0554016106025763
361.060.9640931867830260.0959068132169737
371.041.021425955494930.0185740445050708
381.020.9676975776747240.0523024223252759
391.011.010201972984-0.000201972984000598
4011.03373930406097-0.0337393040609708
411.041.07040711324789-0.0304071132478891
421.090.9918284325837960.0981715674162041
431.081.12010601808364-0.0401060180836366
441.061.10224633879243-0.042246338792427
451.061.12737485710197-0.0673748571019677
461.031.06974637423657-0.0397463742365749
470.970.991854741482205-0.0218547414822046
480.980.9032238090096620.0767761909903376
490.930.938657811286493-0.00865781128649246
500.880.8742719059868170.00572809401318297
510.860.875597507870825-0.0155975078708248
520.90.8799059719022270.0200940280977733
530.910.949210822775277-0.0392108227752772
540.930.8824919876970470.0475080123029529
550.890.950131155584487-0.0601311555844871
560.880.91391975302273-0.0339197530227293
570.830.931794663105861-0.101794663105861
580.810.851117320899683-0.0411173208996831
590.830.7823208318399620.0476791681600379
600.80.764874516141550.0351254838584500
610.760.763981764720434-0.00398176472043377
620.730.7138308033058640.0161691966941364
630.740.7201878057472370.0198121942527628
640.740.750916546259799-0.0109165462597992
650.750.780812834208565-0.0308128342085650
660.740.7338047520482930.00619524795170745
670.740.752581318434594-0.0125813184345943
680.730.751333491674163-0.0213334916741627
690.710.762536726688223-0.0525367266882226
700.710.723925320678525-0.0139253206785247
710.70.6880043538423620.0119956461576380
720.750.6497853941980460.100214605801954
730.810.6947687600246620.115231239975338
740.780.7343171822439260.0456828177560741
750.750.763043868236371-0.0130438682363715

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.2 & 1.16166475173153 & 0.0383352482684693 \tabularnewline
14 & 1.11 & 1.11048182758549 & -0.000481827585486538 \tabularnewline
15 & 1.11 & 1.12609336529116 & -0.016093365291155 \tabularnewline
16 & 1.11 & 1.13552443884904 & -0.0255244388490383 \tabularnewline
17 & 1.17 & 1.19875697194969 & -0.0287569719496918 \tabularnewline
18 & 1.08 & 1.10112236822382 & -0.0211223682238153 \tabularnewline
19 & 1.05 & 1.15936563629937 & -0.109365636299373 \tabularnewline
20 & 1.03 & 1.07821459605905 & -0.0482145960590488 \tabularnewline
21 & 1.04 & 1.11066661232524 & -0.0706666123252446 \tabularnewline
22 & 1.02 & 1.03781221644680 & -0.0178122164468011 \tabularnewline
23 & 1.01 & 0.96339143585355 & 0.0466085641464503 \tabularnewline
24 & 1.01 & 0.914418757946076 & 0.095581242053924 \tabularnewline
25 & 0.98 & 0.983244042236231 & -0.00324404223623131 \tabularnewline
26 & 0.96 & 0.910600003063873 & 0.0493999969361271 \tabularnewline
27 & 0.94 & 0.958278315643581 & -0.0182783156435813 \tabularnewline
28 & 0.99 & 0.960872522070738 & 0.0291274779292622 \tabularnewline
29 & 0.99 & 1.05367732483681 & -0.0636773248368059 \tabularnewline
30 & 0.98 & 0.940818568521542 & 0.0391814314784582 \tabularnewline
31 & 1.02 & 1.02518372932378 & -0.00518372932378131 \tabularnewline
32 & 1.06 & 1.02760156004442 & 0.0323984399555795 \tabularnewline
33 & 1.06 & 1.11784165612741 & -0.0578416561274149 \tabularnewline
34 & 1.06 & 1.06053473495978 & -0.000534734959778849 \tabularnewline
35 & 1.06 & 1.00459838939742 & 0.0554016106025763 \tabularnewline
36 & 1.06 & 0.964093186783026 & 0.0959068132169737 \tabularnewline
37 & 1.04 & 1.02142595549493 & 0.0185740445050708 \tabularnewline
38 & 1.02 & 0.967697577674724 & 0.0523024223252759 \tabularnewline
39 & 1.01 & 1.010201972984 & -0.000201972984000598 \tabularnewline
40 & 1 & 1.03373930406097 & -0.0337393040609708 \tabularnewline
41 & 1.04 & 1.07040711324789 & -0.0304071132478891 \tabularnewline
42 & 1.09 & 0.991828432583796 & 0.0981715674162041 \tabularnewline
43 & 1.08 & 1.12010601808364 & -0.0401060180836366 \tabularnewline
44 & 1.06 & 1.10224633879243 & -0.042246338792427 \tabularnewline
45 & 1.06 & 1.12737485710197 & -0.0673748571019677 \tabularnewline
46 & 1.03 & 1.06974637423657 & -0.0397463742365749 \tabularnewline
47 & 0.97 & 0.991854741482205 & -0.0218547414822046 \tabularnewline
48 & 0.98 & 0.903223809009662 & 0.0767761909903376 \tabularnewline
49 & 0.93 & 0.938657811286493 & -0.00865781128649246 \tabularnewline
50 & 0.88 & 0.874271905986817 & 0.00572809401318297 \tabularnewline
51 & 0.86 & 0.875597507870825 & -0.0155975078708248 \tabularnewline
52 & 0.9 & 0.879905971902227 & 0.0200940280977733 \tabularnewline
53 & 0.91 & 0.949210822775277 & -0.0392108227752772 \tabularnewline
54 & 0.93 & 0.882491987697047 & 0.0475080123029529 \tabularnewline
55 & 0.89 & 0.950131155584487 & -0.0601311555844871 \tabularnewline
56 & 0.88 & 0.91391975302273 & -0.0339197530227293 \tabularnewline
57 & 0.83 & 0.931794663105861 & -0.101794663105861 \tabularnewline
58 & 0.81 & 0.851117320899683 & -0.0411173208996831 \tabularnewline
59 & 0.83 & 0.782320831839962 & 0.0476791681600379 \tabularnewline
60 & 0.8 & 0.76487451614155 & 0.0351254838584500 \tabularnewline
61 & 0.76 & 0.763981764720434 & -0.00398176472043377 \tabularnewline
62 & 0.73 & 0.713830803305864 & 0.0161691966941364 \tabularnewline
63 & 0.74 & 0.720187805747237 & 0.0198121942527628 \tabularnewline
64 & 0.74 & 0.750916546259799 & -0.0109165462597992 \tabularnewline
65 & 0.75 & 0.780812834208565 & -0.0308128342085650 \tabularnewline
66 & 0.74 & 0.733804752048293 & 0.00619524795170745 \tabularnewline
67 & 0.74 & 0.752581318434594 & -0.0125813184345943 \tabularnewline
68 & 0.73 & 0.751333491674163 & -0.0213334916741627 \tabularnewline
69 & 0.71 & 0.762536726688223 & -0.0525367266882226 \tabularnewline
70 & 0.71 & 0.723925320678525 & -0.0139253206785247 \tabularnewline
71 & 0.7 & 0.688004353842362 & 0.0119956461576380 \tabularnewline
72 & 0.75 & 0.649785394198046 & 0.100214605801954 \tabularnewline
73 & 0.81 & 0.694768760024662 & 0.115231239975338 \tabularnewline
74 & 0.78 & 0.734317182243926 & 0.0456828177560741 \tabularnewline
75 & 0.75 & 0.763043868236371 & -0.0130438682363715 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42522&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]1.2[/C][C]1.16166475173153[/C][C]0.0383352482684693[/C][/ROW]
[ROW][C]14[/C][C]1.11[/C][C]1.11048182758549[/C][C]-0.000481827585486538[/C][/ROW]
[ROW][C]15[/C][C]1.11[/C][C]1.12609336529116[/C][C]-0.016093365291155[/C][/ROW]
[ROW][C]16[/C][C]1.11[/C][C]1.13552443884904[/C][C]-0.0255244388490383[/C][/ROW]
[ROW][C]17[/C][C]1.17[/C][C]1.19875697194969[/C][C]-0.0287569719496918[/C][/ROW]
[ROW][C]18[/C][C]1.08[/C][C]1.10112236822382[/C][C]-0.0211223682238153[/C][/ROW]
[ROW][C]19[/C][C]1.05[/C][C]1.15936563629937[/C][C]-0.109365636299373[/C][/ROW]
[ROW][C]20[/C][C]1.03[/C][C]1.07821459605905[/C][C]-0.0482145960590488[/C][/ROW]
[ROW][C]21[/C][C]1.04[/C][C]1.11066661232524[/C][C]-0.0706666123252446[/C][/ROW]
[ROW][C]22[/C][C]1.02[/C][C]1.03781221644680[/C][C]-0.0178122164468011[/C][/ROW]
[ROW][C]23[/C][C]1.01[/C][C]0.96339143585355[/C][C]0.0466085641464503[/C][/ROW]
[ROW][C]24[/C][C]1.01[/C][C]0.914418757946076[/C][C]0.095581242053924[/C][/ROW]
[ROW][C]25[/C][C]0.98[/C][C]0.983244042236231[/C][C]-0.00324404223623131[/C][/ROW]
[ROW][C]26[/C][C]0.96[/C][C]0.910600003063873[/C][C]0.0493999969361271[/C][/ROW]
[ROW][C]27[/C][C]0.94[/C][C]0.958278315643581[/C][C]-0.0182783156435813[/C][/ROW]
[ROW][C]28[/C][C]0.99[/C][C]0.960872522070738[/C][C]0.0291274779292622[/C][/ROW]
[ROW][C]29[/C][C]0.99[/C][C]1.05367732483681[/C][C]-0.0636773248368059[/C][/ROW]
[ROW][C]30[/C][C]0.98[/C][C]0.940818568521542[/C][C]0.0391814314784582[/C][/ROW]
[ROW][C]31[/C][C]1.02[/C][C]1.02518372932378[/C][C]-0.00518372932378131[/C][/ROW]
[ROW][C]32[/C][C]1.06[/C][C]1.02760156004442[/C][C]0.0323984399555795[/C][/ROW]
[ROW][C]33[/C][C]1.06[/C][C]1.11784165612741[/C][C]-0.0578416561274149[/C][/ROW]
[ROW][C]34[/C][C]1.06[/C][C]1.06053473495978[/C][C]-0.000534734959778849[/C][/ROW]
[ROW][C]35[/C][C]1.06[/C][C]1.00459838939742[/C][C]0.0554016106025763[/C][/ROW]
[ROW][C]36[/C][C]1.06[/C][C]0.964093186783026[/C][C]0.0959068132169737[/C][/ROW]
[ROW][C]37[/C][C]1.04[/C][C]1.02142595549493[/C][C]0.0185740445050708[/C][/ROW]
[ROW][C]38[/C][C]1.02[/C][C]0.967697577674724[/C][C]0.0523024223252759[/C][/ROW]
[ROW][C]39[/C][C]1.01[/C][C]1.010201972984[/C][C]-0.000201972984000598[/C][/ROW]
[ROW][C]40[/C][C]1[/C][C]1.03373930406097[/C][C]-0.0337393040609708[/C][/ROW]
[ROW][C]41[/C][C]1.04[/C][C]1.07040711324789[/C][C]-0.0304071132478891[/C][/ROW]
[ROW][C]42[/C][C]1.09[/C][C]0.991828432583796[/C][C]0.0981715674162041[/C][/ROW]
[ROW][C]43[/C][C]1.08[/C][C]1.12010601808364[/C][C]-0.0401060180836366[/C][/ROW]
[ROW][C]44[/C][C]1.06[/C][C]1.10224633879243[/C][C]-0.042246338792427[/C][/ROW]
[ROW][C]45[/C][C]1.06[/C][C]1.12737485710197[/C][C]-0.0673748571019677[/C][/ROW]
[ROW][C]46[/C][C]1.03[/C][C]1.06974637423657[/C][C]-0.0397463742365749[/C][/ROW]
[ROW][C]47[/C][C]0.97[/C][C]0.991854741482205[/C][C]-0.0218547414822046[/C][/ROW]
[ROW][C]48[/C][C]0.98[/C][C]0.903223809009662[/C][C]0.0767761909903376[/C][/ROW]
[ROW][C]49[/C][C]0.93[/C][C]0.938657811286493[/C][C]-0.00865781128649246[/C][/ROW]
[ROW][C]50[/C][C]0.88[/C][C]0.874271905986817[/C][C]0.00572809401318297[/C][/ROW]
[ROW][C]51[/C][C]0.86[/C][C]0.875597507870825[/C][C]-0.0155975078708248[/C][/ROW]
[ROW][C]52[/C][C]0.9[/C][C]0.879905971902227[/C][C]0.0200940280977733[/C][/ROW]
[ROW][C]53[/C][C]0.91[/C][C]0.949210822775277[/C][C]-0.0392108227752772[/C][/ROW]
[ROW][C]54[/C][C]0.93[/C][C]0.882491987697047[/C][C]0.0475080123029529[/C][/ROW]
[ROW][C]55[/C][C]0.89[/C][C]0.950131155584487[/C][C]-0.0601311555844871[/C][/ROW]
[ROW][C]56[/C][C]0.88[/C][C]0.91391975302273[/C][C]-0.0339197530227293[/C][/ROW]
[ROW][C]57[/C][C]0.83[/C][C]0.931794663105861[/C][C]-0.101794663105861[/C][/ROW]
[ROW][C]58[/C][C]0.81[/C][C]0.851117320899683[/C][C]-0.0411173208996831[/C][/ROW]
[ROW][C]59[/C][C]0.83[/C][C]0.782320831839962[/C][C]0.0476791681600379[/C][/ROW]
[ROW][C]60[/C][C]0.8[/C][C]0.76487451614155[/C][C]0.0351254838584500[/C][/ROW]
[ROW][C]61[/C][C]0.76[/C][C]0.763981764720434[/C][C]-0.00398176472043377[/C][/ROW]
[ROW][C]62[/C][C]0.73[/C][C]0.713830803305864[/C][C]0.0161691966941364[/C][/ROW]
[ROW][C]63[/C][C]0.74[/C][C]0.720187805747237[/C][C]0.0198121942527628[/C][/ROW]
[ROW][C]64[/C][C]0.74[/C][C]0.750916546259799[/C][C]-0.0109165462597992[/C][/ROW]
[ROW][C]65[/C][C]0.75[/C][C]0.780812834208565[/C][C]-0.0308128342085650[/C][/ROW]
[ROW][C]66[/C][C]0.74[/C][C]0.733804752048293[/C][C]0.00619524795170745[/C][/ROW]
[ROW][C]67[/C][C]0.74[/C][C]0.752581318434594[/C][C]-0.0125813184345943[/C][/ROW]
[ROW][C]68[/C][C]0.73[/C][C]0.751333491674163[/C][C]-0.0213334916741627[/C][/ROW]
[ROW][C]69[/C][C]0.71[/C][C]0.762536726688223[/C][C]-0.0525367266882226[/C][/ROW]
[ROW][C]70[/C][C]0.71[/C][C]0.723925320678525[/C][C]-0.0139253206785247[/C][/ROW]
[ROW][C]71[/C][C]0.7[/C][C]0.688004353842362[/C][C]0.0119956461576380[/C][/ROW]
[ROW][C]72[/C][C]0.75[/C][C]0.649785394198046[/C][C]0.100214605801954[/C][/ROW]
[ROW][C]73[/C][C]0.81[/C][C]0.694768760024662[/C][C]0.115231239975338[/C][/ROW]
[ROW][C]74[/C][C]0.78[/C][C]0.734317182243926[/C][C]0.0456828177560741[/C][/ROW]
[ROW][C]75[/C][C]0.75[/C][C]0.763043868236371[/C][C]-0.0130438682363715[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42522&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42522&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
131.21.161664751731530.0383352482684693
141.111.11048182758549-0.000481827585486538
151.111.12609336529116-0.016093365291155
161.111.13552443884904-0.0255244388490383
171.171.19875697194969-0.0287569719496918
181.081.10112236822382-0.0211223682238153
191.051.15936563629937-0.109365636299373
201.031.07821459605905-0.0482145960590488
211.041.11066661232524-0.0706666123252446
221.021.03781221644680-0.0178122164468011
231.010.963391435853550.0466085641464503
241.010.9144187579460760.095581242053924
250.980.983244042236231-0.00324404223623131
260.960.9106000030638730.0493999969361271
270.940.958278315643581-0.0182783156435813
280.990.9608725220707380.0291274779292622
290.991.05367732483681-0.0636773248368059
300.980.9408185685215420.0391814314784582
311.021.02518372932378-0.00518372932378131
321.061.027601560044420.0323984399555795
331.061.11784165612741-0.0578416561274149
341.061.06053473495978-0.000534734959778849
351.061.004598389397420.0554016106025763
361.060.9640931867830260.0959068132169737
371.041.021425955494930.0185740445050708
381.020.9676975776747240.0523024223252759
391.011.010201972984-0.000201972984000598
4011.03373930406097-0.0337393040609708
411.041.07040711324789-0.0304071132478891
421.090.9918284325837960.0981715674162041
431.081.12010601808364-0.0401060180836366
441.061.10224633879243-0.042246338792427
451.061.12737485710197-0.0673748571019677
461.031.06974637423657-0.0397463742365749
470.970.991854741482205-0.0218547414822046
480.980.9032238090096620.0767761909903376
490.930.938657811286493-0.00865781128649246
500.880.8742719059868170.00572809401318297
510.860.875597507870825-0.0155975078708248
520.90.8799059719022270.0200940280977733
530.910.949210822775277-0.0392108227752772
540.930.8824919876970470.0475080123029529
550.890.950131155584487-0.0601311555844871
560.880.91391975302273-0.0339197530227293
570.830.931794663105861-0.101794663105861
580.810.851117320899683-0.0411173208996831
590.830.7823208318399620.0476791681600379
600.80.764874516141550.0351254838584500
610.760.763981764720434-0.00398176472043377
620.730.7138308033058640.0161691966941364
630.740.7201878057472370.0198121942527628
640.740.750916546259799-0.0109165462597992
650.750.780812834208565-0.0308128342085650
660.740.7338047520482930.00619524795170745
670.740.752581318434594-0.0125813184345943
680.730.751333491674163-0.0213334916741627
690.710.762536726688223-0.0525367266882226
700.710.723925320678525-0.0139253206785247
710.70.6880043538423620.0119956461576380
720.750.6497853941980460.100214605801954
730.810.6947687600246620.115231239975338
740.780.7343171822439260.0456828177560741
750.750.763043868236371-0.0130438682363715







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
760.7663005390258380.6844408754141170.848160202637559
770.8033301203922070.6924375947997850.91422264598463
780.7826853606314160.6525127353778660.912857985884966
790.7958482504838610.645003391154710.946693109813012
800.8039490794632820.6348751344033270.973023024523237
810.8300175459379360.6405531656660431.01948192620983
820.8368545348621690.6316198475420091.04208922218233
830.8117021589945560.5985012160269711.02490310196214
840.7687676395903250.5526552085503560.984880070630294
850.7388541730388810.5173181523396750.960390193738088
860.6879962814880510.4675751050298680.908417457946235
870.676634038171737-10.309184276063211.6624523524067

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 0.766300539025838 & 0.684440875414117 & 0.848160202637559 \tabularnewline
77 & 0.803330120392207 & 0.692437594799785 & 0.91422264598463 \tabularnewline
78 & 0.782685360631416 & 0.652512735377866 & 0.912857985884966 \tabularnewline
79 & 0.795848250483861 & 0.64500339115471 & 0.946693109813012 \tabularnewline
80 & 0.803949079463282 & 0.634875134403327 & 0.973023024523237 \tabularnewline
81 & 0.830017545937936 & 0.640553165666043 & 1.01948192620983 \tabularnewline
82 & 0.836854534862169 & 0.631619847542009 & 1.04208922218233 \tabularnewline
83 & 0.811702158994556 & 0.598501216026971 & 1.02490310196214 \tabularnewline
84 & 0.768767639590325 & 0.552655208550356 & 0.984880070630294 \tabularnewline
85 & 0.738854173038881 & 0.517318152339675 & 0.960390193738088 \tabularnewline
86 & 0.687996281488051 & 0.467575105029868 & 0.908417457946235 \tabularnewline
87 & 0.676634038171737 & -10.3091842760632 & 11.6624523524067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42522&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]76[/C][C]0.766300539025838[/C][C]0.684440875414117[/C][C]0.848160202637559[/C][/ROW]
[ROW][C]77[/C][C]0.803330120392207[/C][C]0.692437594799785[/C][C]0.91422264598463[/C][/ROW]
[ROW][C]78[/C][C]0.782685360631416[/C][C]0.652512735377866[/C][C]0.912857985884966[/C][/ROW]
[ROW][C]79[/C][C]0.795848250483861[/C][C]0.64500339115471[/C][C]0.946693109813012[/C][/ROW]
[ROW][C]80[/C][C]0.803949079463282[/C][C]0.634875134403327[/C][C]0.973023024523237[/C][/ROW]
[ROW][C]81[/C][C]0.830017545937936[/C][C]0.640553165666043[/C][C]1.01948192620983[/C][/ROW]
[ROW][C]82[/C][C]0.836854534862169[/C][C]0.631619847542009[/C][C]1.04208922218233[/C][/ROW]
[ROW][C]83[/C][C]0.811702158994556[/C][C]0.598501216026971[/C][C]1.02490310196214[/C][/ROW]
[ROW][C]84[/C][C]0.768767639590325[/C][C]0.552655208550356[/C][C]0.984880070630294[/C][/ROW]
[ROW][C]85[/C][C]0.738854173038881[/C][C]0.517318152339675[/C][C]0.960390193738088[/C][/ROW]
[ROW][C]86[/C][C]0.687996281488051[/C][C]0.467575105029868[/C][C]0.908417457946235[/C][/ROW]
[ROW][C]87[/C][C]0.676634038171737[/C][C]-10.3091842760632[/C][C]11.6624523524067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42522&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42522&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
760.7663005390258380.6844408754141170.848160202637559
770.8033301203922070.6924375947997850.91422264598463
780.7826853606314160.6525127353778660.912857985884966
790.7958482504838610.645003391154710.946693109813012
800.8039490794632820.6348751344033270.973023024523237
810.8300175459379360.6405531656660431.01948192620983
820.8368545348621690.6316198475420091.04208922218233
830.8117021589945560.5985012160269711.02490310196214
840.7687676395903250.5526552085503560.984880070630294
850.7388541730388810.5173181523396750.960390193738088
860.6879962814880510.4675751050298680.908417457946235
870.676634038171737-10.309184276063211.6624523524067



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')