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exponential smoothing-prijsindescijfers grondstoffen levensmiddelen-gaelle ...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 27 Nov 2014 11:02:56 +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/2014/Nov/27/t1417086254gmnzljes0q6h121.htm/, Retrieved Sun, 19 May 2024 21:15:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=259614, Retrieved Sun, 19 May 2024 21:15:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2014-11-27 11:02:56] [3acc2e190882a8fff3240b97d842d2ea] [Current]
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Dataseries X:
103,1
113,5
115,7
113,1
112,7
121,9
120,3
108,7
102,8
83,4
79,4
77,8
85,7
83,2
82
86,9
95,7
97,9
89,3
91,5
86,8
91
93,8
96,8
95,7
91,4
88,7
88,2
87,7
89,5
95,6
100,5
106,3
112
117,7
125
132,4
138,1
134,7
136,7
134,3
131,6
129,8
131,9
129,8
119,4
116,7
112,8
116
117,5
118,8
118,7
116,3
115,2
131,7
133,7
132,5
126,9
122,2
120,2
117,9
117,2
116,4
112,3
113,6
114,2
108
102,8
102,8
101,6
100,3
101,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259614&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259614&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999954217891987
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999954217891987 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259614&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]0.999954217891987[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259614&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
alpha0.999954217891987
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2113.5103.110.4
3115.7113.4995238660772.20047613392335
4113.1115.699899257564-2.59989925756396
5112.7113.100119028869-0.40011902886863
6121.9112.7000183182939.19998168170741
7120.3121.899578805445-1.59957880544493
8108.7120.30007323209-11.6000732320896
9102.8108.700531075806-5.90053107580567
1083.4102.800270138751-19.400270138751
1179.483.400888185263-4.00088818526298
1277.879.400183169095-1.60018316909505
1385.777.80007325975877.89992674024131
1483.285.6996383247007-2.49963832470068
158283.2001144387118-1.20011443871178
1686.982.00005494376894.89994505623115
1795.786.89977567018628.80022432981383
1897.995.69959710717922.20040289282082
1989.397.8998992609171-8.5998992609171
2091.589.30039372151692.19960627848315
2186.891.4998992973878-4.69989929738777
229186.80021517129734.19978482870272
2393.890.99980772499732.80019227500266
2496.893.79987180129483.0001281987052
2595.796.7998626478067-1.09986264780675
2691.495.7000503540305-4.30005035403053
2788.791.4001968653698-2.70019686536978
2888.288.7001236207045-0.500123620704542
2987.788.2000228967136-0.500022896713617
3089.587.70002289210231.79997710789773
3195.689.49991759325366.10008240674637
32100.595.59972072536844.90027927463164
33106.3100.4997756548855.80022434511504
34112106.2997344535035.70026554649748
35117.7111.9997390298275.70026097017296
36125117.6997390300377.30026096996343
37132.4124.9996657786647.40033422133625
38138.1132.3996611970995.70033880290063
39134.7138.099739026473-3.39973902647324
40136.7134.7001556472191.99984435278068
41134.3136.69990844291-2.3999084429098
42131.6134.300109872868-2.70010987286756
43129.8131.600123616722-1.80012361672181
44131.9129.8000824134542.09991758654616
45129.8131.899903861346-2.09990386134621
46119.4129.800096138025-10.4000961380254
47116.7119.400476138325-2.70047613832475
48112.8116.70012363349-3.90012363349027
49116112.8001785558813.19982144411854
50117.5115.9998535054291.50014649457098
51118.8117.4999313201311.30006867986886
52118.7118.799940480115-0.0999404801152792
53116.3118.700004575486-2.40000457548585
54115.2116.300109877269-1.10010987726869
55131.7115.20005036534916.4999496346507
56133.7131.6992445975242.00075540247639
57132.5133.6999084012-1.19990840120002
58126.9132.500054934336-5.60005493433601
59122.2126.90025638232-4.70025638231988
60120.2122.200215187645-2.00021518764538
61117.9120.200091574068-2.30009157406776
62117.2117.900105303041-0.700105303040885
63116.4117.200032052297-0.800032052296601
64112.3116.400036627154-4.10003662715384
65113.6112.300187708321.29981229168028
66114.2113.5999404918530.600059508146742
67108114.199972528011-6.19997252801078
68102.8108.000283847812-5.20028384781196
69102.8102.800238079957-0.000238079956830006
70101.6102.8000000109-1.20000001089981
71100.3101.60005493853-1.30005493853011
72101.7100.3000595192561.39994048074439

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 113.5 & 103.1 & 10.4 \tabularnewline
3 & 115.7 & 113.499523866077 & 2.20047613392335 \tabularnewline
4 & 113.1 & 115.699899257564 & -2.59989925756396 \tabularnewline
5 & 112.7 & 113.100119028869 & -0.40011902886863 \tabularnewline
6 & 121.9 & 112.700018318293 & 9.19998168170741 \tabularnewline
7 & 120.3 & 121.899578805445 & -1.59957880544493 \tabularnewline
8 & 108.7 & 120.30007323209 & -11.6000732320896 \tabularnewline
9 & 102.8 & 108.700531075806 & -5.90053107580567 \tabularnewline
10 & 83.4 & 102.800270138751 & -19.400270138751 \tabularnewline
11 & 79.4 & 83.400888185263 & -4.00088818526298 \tabularnewline
12 & 77.8 & 79.400183169095 & -1.60018316909505 \tabularnewline
13 & 85.7 & 77.8000732597587 & 7.89992674024131 \tabularnewline
14 & 83.2 & 85.6996383247007 & -2.49963832470068 \tabularnewline
15 & 82 & 83.2001144387118 & -1.20011443871178 \tabularnewline
16 & 86.9 & 82.0000549437689 & 4.89994505623115 \tabularnewline
17 & 95.7 & 86.8997756701862 & 8.80022432981383 \tabularnewline
18 & 97.9 & 95.6995971071792 & 2.20040289282082 \tabularnewline
19 & 89.3 & 97.8998992609171 & -8.5998992609171 \tabularnewline
20 & 91.5 & 89.3003937215169 & 2.19960627848315 \tabularnewline
21 & 86.8 & 91.4998992973878 & -4.69989929738777 \tabularnewline
22 & 91 & 86.8002151712973 & 4.19978482870272 \tabularnewline
23 & 93.8 & 90.9998077249973 & 2.80019227500266 \tabularnewline
24 & 96.8 & 93.7998718012948 & 3.0001281987052 \tabularnewline
25 & 95.7 & 96.7998626478067 & -1.09986264780675 \tabularnewline
26 & 91.4 & 95.7000503540305 & -4.30005035403053 \tabularnewline
27 & 88.7 & 91.4001968653698 & -2.70019686536978 \tabularnewline
28 & 88.2 & 88.7001236207045 & -0.500123620704542 \tabularnewline
29 & 87.7 & 88.2000228967136 & -0.500022896713617 \tabularnewline
30 & 89.5 & 87.7000228921023 & 1.79997710789773 \tabularnewline
31 & 95.6 & 89.4999175932536 & 6.10008240674637 \tabularnewline
32 & 100.5 & 95.5997207253684 & 4.90027927463164 \tabularnewline
33 & 106.3 & 100.499775654885 & 5.80022434511504 \tabularnewline
34 & 112 & 106.299734453503 & 5.70026554649748 \tabularnewline
35 & 117.7 & 111.999739029827 & 5.70026097017296 \tabularnewline
36 & 125 & 117.699739030037 & 7.30026096996343 \tabularnewline
37 & 132.4 & 124.999665778664 & 7.40033422133625 \tabularnewline
38 & 138.1 & 132.399661197099 & 5.70033880290063 \tabularnewline
39 & 134.7 & 138.099739026473 & -3.39973902647324 \tabularnewline
40 & 136.7 & 134.700155647219 & 1.99984435278068 \tabularnewline
41 & 134.3 & 136.69990844291 & -2.3999084429098 \tabularnewline
42 & 131.6 & 134.300109872868 & -2.70010987286756 \tabularnewline
43 & 129.8 & 131.600123616722 & -1.80012361672181 \tabularnewline
44 & 131.9 & 129.800082413454 & 2.09991758654616 \tabularnewline
45 & 129.8 & 131.899903861346 & -2.09990386134621 \tabularnewline
46 & 119.4 & 129.800096138025 & -10.4000961380254 \tabularnewline
47 & 116.7 & 119.400476138325 & -2.70047613832475 \tabularnewline
48 & 112.8 & 116.70012363349 & -3.90012363349027 \tabularnewline
49 & 116 & 112.800178555881 & 3.19982144411854 \tabularnewline
50 & 117.5 & 115.999853505429 & 1.50014649457098 \tabularnewline
51 & 118.8 & 117.499931320131 & 1.30006867986886 \tabularnewline
52 & 118.7 & 118.799940480115 & -0.0999404801152792 \tabularnewline
53 & 116.3 & 118.700004575486 & -2.40000457548585 \tabularnewline
54 & 115.2 & 116.300109877269 & -1.10010987726869 \tabularnewline
55 & 131.7 & 115.200050365349 & 16.4999496346507 \tabularnewline
56 & 133.7 & 131.699244597524 & 2.00075540247639 \tabularnewline
57 & 132.5 & 133.6999084012 & -1.19990840120002 \tabularnewline
58 & 126.9 & 132.500054934336 & -5.60005493433601 \tabularnewline
59 & 122.2 & 126.90025638232 & -4.70025638231988 \tabularnewline
60 & 120.2 & 122.200215187645 & -2.00021518764538 \tabularnewline
61 & 117.9 & 120.200091574068 & -2.30009157406776 \tabularnewline
62 & 117.2 & 117.900105303041 & -0.700105303040885 \tabularnewline
63 & 116.4 & 117.200032052297 & -0.800032052296601 \tabularnewline
64 & 112.3 & 116.400036627154 & -4.10003662715384 \tabularnewline
65 & 113.6 & 112.30018770832 & 1.29981229168028 \tabularnewline
66 & 114.2 & 113.599940491853 & 0.600059508146742 \tabularnewline
67 & 108 & 114.199972528011 & -6.19997252801078 \tabularnewline
68 & 102.8 & 108.000283847812 & -5.20028384781196 \tabularnewline
69 & 102.8 & 102.800238079957 & -0.000238079956830006 \tabularnewline
70 & 101.6 & 102.8000000109 & -1.20000001089981 \tabularnewline
71 & 100.3 & 101.60005493853 & -1.30005493853011 \tabularnewline
72 & 101.7 & 100.300059519256 & 1.39994048074439 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259614&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]2[/C][C]113.5[/C][C]103.1[/C][C]10.4[/C][/ROW]
[ROW][C]3[/C][C]115.7[/C][C]113.499523866077[/C][C]2.20047613392335[/C][/ROW]
[ROW][C]4[/C][C]113.1[/C][C]115.699899257564[/C][C]-2.59989925756396[/C][/ROW]
[ROW][C]5[/C][C]112.7[/C][C]113.100119028869[/C][C]-0.40011902886863[/C][/ROW]
[ROW][C]6[/C][C]121.9[/C][C]112.700018318293[/C][C]9.19998168170741[/C][/ROW]
[ROW][C]7[/C][C]120.3[/C][C]121.899578805445[/C][C]-1.59957880544493[/C][/ROW]
[ROW][C]8[/C][C]108.7[/C][C]120.30007323209[/C][C]-11.6000732320896[/C][/ROW]
[ROW][C]9[/C][C]102.8[/C][C]108.700531075806[/C][C]-5.90053107580567[/C][/ROW]
[ROW][C]10[/C][C]83.4[/C][C]102.800270138751[/C][C]-19.400270138751[/C][/ROW]
[ROW][C]11[/C][C]79.4[/C][C]83.400888185263[/C][C]-4.00088818526298[/C][/ROW]
[ROW][C]12[/C][C]77.8[/C][C]79.400183169095[/C][C]-1.60018316909505[/C][/ROW]
[ROW][C]13[/C][C]85.7[/C][C]77.8000732597587[/C][C]7.89992674024131[/C][/ROW]
[ROW][C]14[/C][C]83.2[/C][C]85.6996383247007[/C][C]-2.49963832470068[/C][/ROW]
[ROW][C]15[/C][C]82[/C][C]83.2001144387118[/C][C]-1.20011443871178[/C][/ROW]
[ROW][C]16[/C][C]86.9[/C][C]82.0000549437689[/C][C]4.89994505623115[/C][/ROW]
[ROW][C]17[/C][C]95.7[/C][C]86.8997756701862[/C][C]8.80022432981383[/C][/ROW]
[ROW][C]18[/C][C]97.9[/C][C]95.6995971071792[/C][C]2.20040289282082[/C][/ROW]
[ROW][C]19[/C][C]89.3[/C][C]97.8998992609171[/C][C]-8.5998992609171[/C][/ROW]
[ROW][C]20[/C][C]91.5[/C][C]89.3003937215169[/C][C]2.19960627848315[/C][/ROW]
[ROW][C]21[/C][C]86.8[/C][C]91.4998992973878[/C][C]-4.69989929738777[/C][/ROW]
[ROW][C]22[/C][C]91[/C][C]86.8002151712973[/C][C]4.19978482870272[/C][/ROW]
[ROW][C]23[/C][C]93.8[/C][C]90.9998077249973[/C][C]2.80019227500266[/C][/ROW]
[ROW][C]24[/C][C]96.8[/C][C]93.7998718012948[/C][C]3.0001281987052[/C][/ROW]
[ROW][C]25[/C][C]95.7[/C][C]96.7998626478067[/C][C]-1.09986264780675[/C][/ROW]
[ROW][C]26[/C][C]91.4[/C][C]95.7000503540305[/C][C]-4.30005035403053[/C][/ROW]
[ROW][C]27[/C][C]88.7[/C][C]91.4001968653698[/C][C]-2.70019686536978[/C][/ROW]
[ROW][C]28[/C][C]88.2[/C][C]88.7001236207045[/C][C]-0.500123620704542[/C][/ROW]
[ROW][C]29[/C][C]87.7[/C][C]88.2000228967136[/C][C]-0.500022896713617[/C][/ROW]
[ROW][C]30[/C][C]89.5[/C][C]87.7000228921023[/C][C]1.79997710789773[/C][/ROW]
[ROW][C]31[/C][C]95.6[/C][C]89.4999175932536[/C][C]6.10008240674637[/C][/ROW]
[ROW][C]32[/C][C]100.5[/C][C]95.5997207253684[/C][C]4.90027927463164[/C][/ROW]
[ROW][C]33[/C][C]106.3[/C][C]100.499775654885[/C][C]5.80022434511504[/C][/ROW]
[ROW][C]34[/C][C]112[/C][C]106.299734453503[/C][C]5.70026554649748[/C][/ROW]
[ROW][C]35[/C][C]117.7[/C][C]111.999739029827[/C][C]5.70026097017296[/C][/ROW]
[ROW][C]36[/C][C]125[/C][C]117.699739030037[/C][C]7.30026096996343[/C][/ROW]
[ROW][C]37[/C][C]132.4[/C][C]124.999665778664[/C][C]7.40033422133625[/C][/ROW]
[ROW][C]38[/C][C]138.1[/C][C]132.399661197099[/C][C]5.70033880290063[/C][/ROW]
[ROW][C]39[/C][C]134.7[/C][C]138.099739026473[/C][C]-3.39973902647324[/C][/ROW]
[ROW][C]40[/C][C]136.7[/C][C]134.700155647219[/C][C]1.99984435278068[/C][/ROW]
[ROW][C]41[/C][C]134.3[/C][C]136.69990844291[/C][C]-2.3999084429098[/C][/ROW]
[ROW][C]42[/C][C]131.6[/C][C]134.300109872868[/C][C]-2.70010987286756[/C][/ROW]
[ROW][C]43[/C][C]129.8[/C][C]131.600123616722[/C][C]-1.80012361672181[/C][/ROW]
[ROW][C]44[/C][C]131.9[/C][C]129.800082413454[/C][C]2.09991758654616[/C][/ROW]
[ROW][C]45[/C][C]129.8[/C][C]131.899903861346[/C][C]-2.09990386134621[/C][/ROW]
[ROW][C]46[/C][C]119.4[/C][C]129.800096138025[/C][C]-10.4000961380254[/C][/ROW]
[ROW][C]47[/C][C]116.7[/C][C]119.400476138325[/C][C]-2.70047613832475[/C][/ROW]
[ROW][C]48[/C][C]112.8[/C][C]116.70012363349[/C][C]-3.90012363349027[/C][/ROW]
[ROW][C]49[/C][C]116[/C][C]112.800178555881[/C][C]3.19982144411854[/C][/ROW]
[ROW][C]50[/C][C]117.5[/C][C]115.999853505429[/C][C]1.50014649457098[/C][/ROW]
[ROW][C]51[/C][C]118.8[/C][C]117.499931320131[/C][C]1.30006867986886[/C][/ROW]
[ROW][C]52[/C][C]118.7[/C][C]118.799940480115[/C][C]-0.0999404801152792[/C][/ROW]
[ROW][C]53[/C][C]116.3[/C][C]118.700004575486[/C][C]-2.40000457548585[/C][/ROW]
[ROW][C]54[/C][C]115.2[/C][C]116.300109877269[/C][C]-1.10010987726869[/C][/ROW]
[ROW][C]55[/C][C]131.7[/C][C]115.200050365349[/C][C]16.4999496346507[/C][/ROW]
[ROW][C]56[/C][C]133.7[/C][C]131.699244597524[/C][C]2.00075540247639[/C][/ROW]
[ROW][C]57[/C][C]132.5[/C][C]133.6999084012[/C][C]-1.19990840120002[/C][/ROW]
[ROW][C]58[/C][C]126.9[/C][C]132.500054934336[/C][C]-5.60005493433601[/C][/ROW]
[ROW][C]59[/C][C]122.2[/C][C]126.90025638232[/C][C]-4.70025638231988[/C][/ROW]
[ROW][C]60[/C][C]120.2[/C][C]122.200215187645[/C][C]-2.00021518764538[/C][/ROW]
[ROW][C]61[/C][C]117.9[/C][C]120.200091574068[/C][C]-2.30009157406776[/C][/ROW]
[ROW][C]62[/C][C]117.2[/C][C]117.900105303041[/C][C]-0.700105303040885[/C][/ROW]
[ROW][C]63[/C][C]116.4[/C][C]117.200032052297[/C][C]-0.800032052296601[/C][/ROW]
[ROW][C]64[/C][C]112.3[/C][C]116.400036627154[/C][C]-4.10003662715384[/C][/ROW]
[ROW][C]65[/C][C]113.6[/C][C]112.30018770832[/C][C]1.29981229168028[/C][/ROW]
[ROW][C]66[/C][C]114.2[/C][C]113.599940491853[/C][C]0.600059508146742[/C][/ROW]
[ROW][C]67[/C][C]108[/C][C]114.199972528011[/C][C]-6.19997252801078[/C][/ROW]
[ROW][C]68[/C][C]102.8[/C][C]108.000283847812[/C][C]-5.20028384781196[/C][/ROW]
[ROW][C]69[/C][C]102.8[/C][C]102.800238079957[/C][C]-0.000238079956830006[/C][/ROW]
[ROW][C]70[/C][C]101.6[/C][C]102.8000000109[/C][C]-1.20000001089981[/C][/ROW]
[ROW][C]71[/C][C]100.3[/C][C]101.60005493853[/C][C]-1.30005493853011[/C][/ROW]
[ROW][C]72[/C][C]101.7[/C][C]100.300059519256[/C][C]1.39994048074439[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259614&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259614&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
2113.5103.110.4
3115.7113.4995238660772.20047613392335
4113.1115.699899257564-2.59989925756396
5112.7113.100119028869-0.40011902886863
6121.9112.7000183182939.19998168170741
7120.3121.899578805445-1.59957880544493
8108.7120.30007323209-11.6000732320896
9102.8108.700531075806-5.90053107580567
1083.4102.800270138751-19.400270138751
1179.483.400888185263-4.00088818526298
1277.879.400183169095-1.60018316909505
1385.777.80007325975877.89992674024131
1483.285.6996383247007-2.49963832470068
158283.2001144387118-1.20011443871178
1686.982.00005494376894.89994505623115
1795.786.89977567018628.80022432981383
1897.995.69959710717922.20040289282082
1989.397.8998992609171-8.5998992609171
2091.589.30039372151692.19960627848315
2186.891.4998992973878-4.69989929738777
229186.80021517129734.19978482870272
2393.890.99980772499732.80019227500266
2496.893.79987180129483.0001281987052
2595.796.7998626478067-1.09986264780675
2691.495.7000503540305-4.30005035403053
2788.791.4001968653698-2.70019686536978
2888.288.7001236207045-0.500123620704542
2987.788.2000228967136-0.500022896713617
3089.587.70002289210231.79997710789773
3195.689.49991759325366.10008240674637
32100.595.59972072536844.90027927463164
33106.3100.4997756548855.80022434511504
34112106.2997344535035.70026554649748
35117.7111.9997390298275.70026097017296
36125117.6997390300377.30026096996343
37132.4124.9996657786647.40033422133625
38138.1132.3996611970995.70033880290063
39134.7138.099739026473-3.39973902647324
40136.7134.7001556472191.99984435278068
41134.3136.69990844291-2.3999084429098
42131.6134.300109872868-2.70010987286756
43129.8131.600123616722-1.80012361672181
44131.9129.8000824134542.09991758654616
45129.8131.899903861346-2.09990386134621
46119.4129.800096138025-10.4000961380254
47116.7119.400476138325-2.70047613832475
48112.8116.70012363349-3.90012363349027
49116112.8001785558813.19982144411854
50117.5115.9998535054291.50014649457098
51118.8117.4999313201311.30006867986886
52118.7118.799940480115-0.0999404801152792
53116.3118.700004575486-2.40000457548585
54115.2116.300109877269-1.10010987726869
55131.7115.20005036534916.4999496346507
56133.7131.6992445975242.00075540247639
57132.5133.6999084012-1.19990840120002
58126.9132.500054934336-5.60005493433601
59122.2126.90025638232-4.70025638231988
60120.2122.200215187645-2.00021518764538
61117.9120.200091574068-2.30009157406776
62117.2117.900105303041-0.700105303040885
63116.4117.200032052297-0.800032052296601
64112.3116.400036627154-4.10003662715384
65113.6112.300187708321.29981229168028
66114.2113.5999404918530.600059508146742
67108114.199972528011-6.19997252801078
68102.8108.000283847812-5.20028384781196
69102.8102.800238079957-0.000238079956830006
70101.6102.8000000109-1.20000001089981
71100.3101.60005493853-1.30005493853011
72101.7100.3000595192561.39994048074439







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.69993590777491.1249650989073112.27490671664
74101.69993590777486.7450111060846116.654860709463
75101.69993590777483.3841082158573120.01576359969
76101.69993590777480.5507205025685122.849151312979
77101.69993590777478.0544483790386125.345423436509
78101.69993590777475.7976416331854127.602230182362
79101.69993590777473.7222909585796129.677580856968
80101.69993590777471.7905998215453131.609271994002
81101.69993590777469.9763145297727133.423557285775
82101.69993590777468.2603198580856135.139551957462
83101.69993590777466.6281853132231136.771686502324
84101.69993590777465.0686998109375138.33117200461

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.699935907774 & 91.1249650989073 & 112.27490671664 \tabularnewline
74 & 101.699935907774 & 86.7450111060846 & 116.654860709463 \tabularnewline
75 & 101.699935907774 & 83.3841082158573 & 120.01576359969 \tabularnewline
76 & 101.699935907774 & 80.5507205025685 & 122.849151312979 \tabularnewline
77 & 101.699935907774 & 78.0544483790386 & 125.345423436509 \tabularnewline
78 & 101.699935907774 & 75.7976416331854 & 127.602230182362 \tabularnewline
79 & 101.699935907774 & 73.7222909585796 & 129.677580856968 \tabularnewline
80 & 101.699935907774 & 71.7905998215453 & 131.609271994002 \tabularnewline
81 & 101.699935907774 & 69.9763145297727 & 133.423557285775 \tabularnewline
82 & 101.699935907774 & 68.2603198580856 & 135.139551957462 \tabularnewline
83 & 101.699935907774 & 66.6281853132231 & 136.771686502324 \tabularnewline
84 & 101.699935907774 & 65.0686998109375 & 138.33117200461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259614&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]73[/C][C]101.699935907774[/C][C]91.1249650989073[/C][C]112.27490671664[/C][/ROW]
[ROW][C]74[/C][C]101.699935907774[/C][C]86.7450111060846[/C][C]116.654860709463[/C][/ROW]
[ROW][C]75[/C][C]101.699935907774[/C][C]83.3841082158573[/C][C]120.01576359969[/C][/ROW]
[ROW][C]76[/C][C]101.699935907774[/C][C]80.5507205025685[/C][C]122.849151312979[/C][/ROW]
[ROW][C]77[/C][C]101.699935907774[/C][C]78.0544483790386[/C][C]125.345423436509[/C][/ROW]
[ROW][C]78[/C][C]101.699935907774[/C][C]75.7976416331854[/C][C]127.602230182362[/C][/ROW]
[ROW][C]79[/C][C]101.699935907774[/C][C]73.7222909585796[/C][C]129.677580856968[/C][/ROW]
[ROW][C]80[/C][C]101.699935907774[/C][C]71.7905998215453[/C][C]131.609271994002[/C][/ROW]
[ROW][C]81[/C][C]101.699935907774[/C][C]69.9763145297727[/C][C]133.423557285775[/C][/ROW]
[ROW][C]82[/C][C]101.699935907774[/C][C]68.2603198580856[/C][C]135.139551957462[/C][/ROW]
[ROW][C]83[/C][C]101.699935907774[/C][C]66.6281853132231[/C][C]136.771686502324[/C][/ROW]
[ROW][C]84[/C][C]101.699935907774[/C][C]65.0686998109375[/C][C]138.33117200461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259614&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259614&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
73101.69993590777491.1249650989073112.27490671664
74101.69993590777486.7450111060846116.654860709463
75101.69993590777483.3841082158573120.01576359969
76101.69993590777480.5507205025685122.849151312979
77101.69993590777478.0544483790386125.345423436509
78101.69993590777475.7976416331854127.602230182362
79101.69993590777473.7222909585796129.677580856968
80101.69993590777471.7905998215453131.609271994002
81101.69993590777469.9763145297727133.423557285775
82101.69993590777468.2603198580856135.139551957462
83101.69993590777466.6281853132231136.771686502324
84101.69993590777465.0686998109375138.33117200461



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')