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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 Jan 2009 13:47:15 -0700
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/Jan/20/t123248457113hds8uzbm3lyi1.htm/, Retrieved Fri, 03 May 2024 22:17:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36932, Retrieved Fri, 03 May 2024 22:17:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact218
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [wisselkoers euro-...] [2009-01-20 20:47:15] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
0,9808
0,9811
1,0014
1,0183
1,0622
1,0773
1,0807
1,0848
1,1582
1,1663
1,1372
1,1139
1,1222
1,1692
1,1702
1,2286
1,2613
1,2646
1,2262
1,1985
1,2007
1,2138
1,2266
1,2176
1,2218
1,249
1,2991
1,3408
1,3119
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
1,4718
1,4748
1,5527
1,575
1,5557
1,5553
1,577
1,4975




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36932&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36932&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36932&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36932&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36932&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36932&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
alpha1
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
20.98110.98080.000299999999999967
31.00140.98110.0203000000000001
41.01831.00140.0168999999999999
51.06221.01830.0439000000000001
61.07731.06220.0150999999999999
71.08071.07730.00340000000000007
81.08481.08070.00409999999999999
91.15821.08480.0733999999999999
101.16631.15820.0081
111.13721.1663-0.0290999999999999
121.11391.1372-0.0233000000000001
131.12221.11390.0083000000000002
141.16921.12220.0469999999999999
151.17021.16920.00099999999999989
161.22861.17020.0584
171.26131.22860.0327000000000002
181.26461.26130.00329999999999986
191.22621.2646-0.0384
201.19851.2262-0.0277000000000001
211.20071.19850.0022000000000002
221.21381.20070.0130999999999999
231.22661.21380.0127999999999999
241.21761.2266-0.0089999999999999
251.22181.21760.00419999999999998
261.2491.22180.0272000000000001
271.29911.2490.0500999999999998
281.34081.29910.0417000000000001
291.31191.3408-0.0288999999999999
301.30141.3119-0.0105000000000002
311.32011.30140.0187000000000002
321.29381.3201-0.0263
331.26941.2938-0.0244
341.21651.2694-0.0529000000000002
351.20371.2165-0.0127999999999999
361.22921.20370.0255000000000001
371.22561.2292-0.00360000000000005
381.20151.2256-0.0241
391.17861.2015-0.0228999999999999
401.18561.17860.0069999999999999
411.21031.18560.0246999999999999
421.19381.2103-0.0165000000000000
431.2021.19380.00819999999999999
441.22711.2020.0251000000000001
451.2771.22710.0498999999999998
461.2651.277-0.012
471.26841.2650.00340000000000007
481.28111.26840.0126999999999999
491.27271.2811-0.00839999999999996
501.26111.2727-0.0115999999999998
511.28811.26110.0269999999999999
521.32131.28810.0331999999999999
531.29991.3213-0.0213999999999999
541.30741.29990.00749999999999984
551.32421.30740.0168000000000001
561.35161.32420.0273999999999999
571.35111.3516-0.000499999999999945
581.34191.3511-0.00919999999999987
591.37161.34190.0296999999999998
601.36221.3716-0.00939999999999985
611.38961.36220.0273999999999999
621.42271.38960.0331000000000001
631.46841.42270.0456999999999999
641.4571.4684-0.0113999999999999
651.47181.4570.0147999999999999
661.47481.47180.00300000000000011
671.55271.47480.0778999999999999
681.5751.55270.0223
691.55571.575-0.0192999999999999
701.55531.5557-0.000400000000000178
711.5771.55530.0217000000000001
721.49751.577-0.0794999999999999

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 0.9811 & 0.9808 & 0.000299999999999967 \tabularnewline
3 & 1.0014 & 0.9811 & 0.0203000000000001 \tabularnewline
4 & 1.0183 & 1.0014 & 0.0168999999999999 \tabularnewline
5 & 1.0622 & 1.0183 & 0.0439000000000001 \tabularnewline
6 & 1.0773 & 1.0622 & 0.0150999999999999 \tabularnewline
7 & 1.0807 & 1.0773 & 0.00340000000000007 \tabularnewline
8 & 1.0848 & 1.0807 & 0.00409999999999999 \tabularnewline
9 & 1.1582 & 1.0848 & 0.0733999999999999 \tabularnewline
10 & 1.1663 & 1.1582 & 0.0081 \tabularnewline
11 & 1.1372 & 1.1663 & -0.0290999999999999 \tabularnewline
12 & 1.1139 & 1.1372 & -0.0233000000000001 \tabularnewline
13 & 1.1222 & 1.1139 & 0.0083000000000002 \tabularnewline
14 & 1.1692 & 1.1222 & 0.0469999999999999 \tabularnewline
15 & 1.1702 & 1.1692 & 0.00099999999999989 \tabularnewline
16 & 1.2286 & 1.1702 & 0.0584 \tabularnewline
17 & 1.2613 & 1.2286 & 0.0327000000000002 \tabularnewline
18 & 1.2646 & 1.2613 & 0.00329999999999986 \tabularnewline
19 & 1.2262 & 1.2646 & -0.0384 \tabularnewline
20 & 1.1985 & 1.2262 & -0.0277000000000001 \tabularnewline
21 & 1.2007 & 1.1985 & 0.0022000000000002 \tabularnewline
22 & 1.2138 & 1.2007 & 0.0130999999999999 \tabularnewline
23 & 1.2266 & 1.2138 & 0.0127999999999999 \tabularnewline
24 & 1.2176 & 1.2266 & -0.0089999999999999 \tabularnewline
25 & 1.2218 & 1.2176 & 0.00419999999999998 \tabularnewline
26 & 1.249 & 1.2218 & 0.0272000000000001 \tabularnewline
27 & 1.2991 & 1.249 & 0.0500999999999998 \tabularnewline
28 & 1.3408 & 1.2991 & 0.0417000000000001 \tabularnewline
29 & 1.3119 & 1.3408 & -0.0288999999999999 \tabularnewline
30 & 1.3014 & 1.3119 & -0.0105000000000002 \tabularnewline
31 & 1.3201 & 1.3014 & 0.0187000000000002 \tabularnewline
32 & 1.2938 & 1.3201 & -0.0263 \tabularnewline
33 & 1.2694 & 1.2938 & -0.0244 \tabularnewline
34 & 1.2165 & 1.2694 & -0.0529000000000002 \tabularnewline
35 & 1.2037 & 1.2165 & -0.0127999999999999 \tabularnewline
36 & 1.2292 & 1.2037 & 0.0255000000000001 \tabularnewline
37 & 1.2256 & 1.2292 & -0.00360000000000005 \tabularnewline
38 & 1.2015 & 1.2256 & -0.0241 \tabularnewline
39 & 1.1786 & 1.2015 & -0.0228999999999999 \tabularnewline
40 & 1.1856 & 1.1786 & 0.0069999999999999 \tabularnewline
41 & 1.2103 & 1.1856 & 0.0246999999999999 \tabularnewline
42 & 1.1938 & 1.2103 & -0.0165000000000000 \tabularnewline
43 & 1.202 & 1.1938 & 0.00819999999999999 \tabularnewline
44 & 1.2271 & 1.202 & 0.0251000000000001 \tabularnewline
45 & 1.277 & 1.2271 & 0.0498999999999998 \tabularnewline
46 & 1.265 & 1.277 & -0.012 \tabularnewline
47 & 1.2684 & 1.265 & 0.00340000000000007 \tabularnewline
48 & 1.2811 & 1.2684 & 0.0126999999999999 \tabularnewline
49 & 1.2727 & 1.2811 & -0.00839999999999996 \tabularnewline
50 & 1.2611 & 1.2727 & -0.0115999999999998 \tabularnewline
51 & 1.2881 & 1.2611 & 0.0269999999999999 \tabularnewline
52 & 1.3213 & 1.2881 & 0.0331999999999999 \tabularnewline
53 & 1.2999 & 1.3213 & -0.0213999999999999 \tabularnewline
54 & 1.3074 & 1.2999 & 0.00749999999999984 \tabularnewline
55 & 1.3242 & 1.3074 & 0.0168000000000001 \tabularnewline
56 & 1.3516 & 1.3242 & 0.0273999999999999 \tabularnewline
57 & 1.3511 & 1.3516 & -0.000499999999999945 \tabularnewline
58 & 1.3419 & 1.3511 & -0.00919999999999987 \tabularnewline
59 & 1.3716 & 1.3419 & 0.0296999999999998 \tabularnewline
60 & 1.3622 & 1.3716 & -0.00939999999999985 \tabularnewline
61 & 1.3896 & 1.3622 & 0.0273999999999999 \tabularnewline
62 & 1.4227 & 1.3896 & 0.0331000000000001 \tabularnewline
63 & 1.4684 & 1.4227 & 0.0456999999999999 \tabularnewline
64 & 1.457 & 1.4684 & -0.0113999999999999 \tabularnewline
65 & 1.4718 & 1.457 & 0.0147999999999999 \tabularnewline
66 & 1.4748 & 1.4718 & 0.00300000000000011 \tabularnewline
67 & 1.5527 & 1.4748 & 0.0778999999999999 \tabularnewline
68 & 1.575 & 1.5527 & 0.0223 \tabularnewline
69 & 1.5557 & 1.575 & -0.0192999999999999 \tabularnewline
70 & 1.5553 & 1.5557 & -0.000400000000000178 \tabularnewline
71 & 1.577 & 1.5553 & 0.0217000000000001 \tabularnewline
72 & 1.4975 & 1.577 & -0.0794999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36932&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]0.9811[/C][C]0.9808[/C][C]0.000299999999999967[/C][/ROW]
[ROW][C]3[/C][C]1.0014[/C][C]0.9811[/C][C]0.0203000000000001[/C][/ROW]
[ROW][C]4[/C][C]1.0183[/C][C]1.0014[/C][C]0.0168999999999999[/C][/ROW]
[ROW][C]5[/C][C]1.0622[/C][C]1.0183[/C][C]0.0439000000000001[/C][/ROW]
[ROW][C]6[/C][C]1.0773[/C][C]1.0622[/C][C]0.0150999999999999[/C][/ROW]
[ROW][C]7[/C][C]1.0807[/C][C]1.0773[/C][C]0.00340000000000007[/C][/ROW]
[ROW][C]8[/C][C]1.0848[/C][C]1.0807[/C][C]0.00409999999999999[/C][/ROW]
[ROW][C]9[/C][C]1.1582[/C][C]1.0848[/C][C]0.0733999999999999[/C][/ROW]
[ROW][C]10[/C][C]1.1663[/C][C]1.1582[/C][C]0.0081[/C][/ROW]
[ROW][C]11[/C][C]1.1372[/C][C]1.1663[/C][C]-0.0290999999999999[/C][/ROW]
[ROW][C]12[/C][C]1.1139[/C][C]1.1372[/C][C]-0.0233000000000001[/C][/ROW]
[ROW][C]13[/C][C]1.1222[/C][C]1.1139[/C][C]0.0083000000000002[/C][/ROW]
[ROW][C]14[/C][C]1.1692[/C][C]1.1222[/C][C]0.0469999999999999[/C][/ROW]
[ROW][C]15[/C][C]1.1702[/C][C]1.1692[/C][C]0.00099999999999989[/C][/ROW]
[ROW][C]16[/C][C]1.2286[/C][C]1.1702[/C][C]0.0584[/C][/ROW]
[ROW][C]17[/C][C]1.2613[/C][C]1.2286[/C][C]0.0327000000000002[/C][/ROW]
[ROW][C]18[/C][C]1.2646[/C][C]1.2613[/C][C]0.00329999999999986[/C][/ROW]
[ROW][C]19[/C][C]1.2262[/C][C]1.2646[/C][C]-0.0384[/C][/ROW]
[ROW][C]20[/C][C]1.1985[/C][C]1.2262[/C][C]-0.0277000000000001[/C][/ROW]
[ROW][C]21[/C][C]1.2007[/C][C]1.1985[/C][C]0.0022000000000002[/C][/ROW]
[ROW][C]22[/C][C]1.2138[/C][C]1.2007[/C][C]0.0130999999999999[/C][/ROW]
[ROW][C]23[/C][C]1.2266[/C][C]1.2138[/C][C]0.0127999999999999[/C][/ROW]
[ROW][C]24[/C][C]1.2176[/C][C]1.2266[/C][C]-0.0089999999999999[/C][/ROW]
[ROW][C]25[/C][C]1.2218[/C][C]1.2176[/C][C]0.00419999999999998[/C][/ROW]
[ROW][C]26[/C][C]1.249[/C][C]1.2218[/C][C]0.0272000000000001[/C][/ROW]
[ROW][C]27[/C][C]1.2991[/C][C]1.249[/C][C]0.0500999999999998[/C][/ROW]
[ROW][C]28[/C][C]1.3408[/C][C]1.2991[/C][C]0.0417000000000001[/C][/ROW]
[ROW][C]29[/C][C]1.3119[/C][C]1.3408[/C][C]-0.0288999999999999[/C][/ROW]
[ROW][C]30[/C][C]1.3014[/C][C]1.3119[/C][C]-0.0105000000000002[/C][/ROW]
[ROW][C]31[/C][C]1.3201[/C][C]1.3014[/C][C]0.0187000000000002[/C][/ROW]
[ROW][C]32[/C][C]1.2938[/C][C]1.3201[/C][C]-0.0263[/C][/ROW]
[ROW][C]33[/C][C]1.2694[/C][C]1.2938[/C][C]-0.0244[/C][/ROW]
[ROW][C]34[/C][C]1.2165[/C][C]1.2694[/C][C]-0.0529000000000002[/C][/ROW]
[ROW][C]35[/C][C]1.2037[/C][C]1.2165[/C][C]-0.0127999999999999[/C][/ROW]
[ROW][C]36[/C][C]1.2292[/C][C]1.2037[/C][C]0.0255000000000001[/C][/ROW]
[ROW][C]37[/C][C]1.2256[/C][C]1.2292[/C][C]-0.00360000000000005[/C][/ROW]
[ROW][C]38[/C][C]1.2015[/C][C]1.2256[/C][C]-0.0241[/C][/ROW]
[ROW][C]39[/C][C]1.1786[/C][C]1.2015[/C][C]-0.0228999999999999[/C][/ROW]
[ROW][C]40[/C][C]1.1856[/C][C]1.1786[/C][C]0.0069999999999999[/C][/ROW]
[ROW][C]41[/C][C]1.2103[/C][C]1.1856[/C][C]0.0246999999999999[/C][/ROW]
[ROW][C]42[/C][C]1.1938[/C][C]1.2103[/C][C]-0.0165000000000000[/C][/ROW]
[ROW][C]43[/C][C]1.202[/C][C]1.1938[/C][C]0.00819999999999999[/C][/ROW]
[ROW][C]44[/C][C]1.2271[/C][C]1.202[/C][C]0.0251000000000001[/C][/ROW]
[ROW][C]45[/C][C]1.277[/C][C]1.2271[/C][C]0.0498999999999998[/C][/ROW]
[ROW][C]46[/C][C]1.265[/C][C]1.277[/C][C]-0.012[/C][/ROW]
[ROW][C]47[/C][C]1.2684[/C][C]1.265[/C][C]0.00340000000000007[/C][/ROW]
[ROW][C]48[/C][C]1.2811[/C][C]1.2684[/C][C]0.0126999999999999[/C][/ROW]
[ROW][C]49[/C][C]1.2727[/C][C]1.2811[/C][C]-0.00839999999999996[/C][/ROW]
[ROW][C]50[/C][C]1.2611[/C][C]1.2727[/C][C]-0.0115999999999998[/C][/ROW]
[ROW][C]51[/C][C]1.2881[/C][C]1.2611[/C][C]0.0269999999999999[/C][/ROW]
[ROW][C]52[/C][C]1.3213[/C][C]1.2881[/C][C]0.0331999999999999[/C][/ROW]
[ROW][C]53[/C][C]1.2999[/C][C]1.3213[/C][C]-0.0213999999999999[/C][/ROW]
[ROW][C]54[/C][C]1.3074[/C][C]1.2999[/C][C]0.00749999999999984[/C][/ROW]
[ROW][C]55[/C][C]1.3242[/C][C]1.3074[/C][C]0.0168000000000001[/C][/ROW]
[ROW][C]56[/C][C]1.3516[/C][C]1.3242[/C][C]0.0273999999999999[/C][/ROW]
[ROW][C]57[/C][C]1.3511[/C][C]1.3516[/C][C]-0.000499999999999945[/C][/ROW]
[ROW][C]58[/C][C]1.3419[/C][C]1.3511[/C][C]-0.00919999999999987[/C][/ROW]
[ROW][C]59[/C][C]1.3716[/C][C]1.3419[/C][C]0.0296999999999998[/C][/ROW]
[ROW][C]60[/C][C]1.3622[/C][C]1.3716[/C][C]-0.00939999999999985[/C][/ROW]
[ROW][C]61[/C][C]1.3896[/C][C]1.3622[/C][C]0.0273999999999999[/C][/ROW]
[ROW][C]62[/C][C]1.4227[/C][C]1.3896[/C][C]0.0331000000000001[/C][/ROW]
[ROW][C]63[/C][C]1.4684[/C][C]1.4227[/C][C]0.0456999999999999[/C][/ROW]
[ROW][C]64[/C][C]1.457[/C][C]1.4684[/C][C]-0.0113999999999999[/C][/ROW]
[ROW][C]65[/C][C]1.4718[/C][C]1.457[/C][C]0.0147999999999999[/C][/ROW]
[ROW][C]66[/C][C]1.4748[/C][C]1.4718[/C][C]0.00300000000000011[/C][/ROW]
[ROW][C]67[/C][C]1.5527[/C][C]1.4748[/C][C]0.0778999999999999[/C][/ROW]
[ROW][C]68[/C][C]1.575[/C][C]1.5527[/C][C]0.0223[/C][/ROW]
[ROW][C]69[/C][C]1.5557[/C][C]1.575[/C][C]-0.0192999999999999[/C][/ROW]
[ROW][C]70[/C][C]1.5553[/C][C]1.5557[/C][C]-0.000400000000000178[/C][/ROW]
[ROW][C]71[/C][C]1.577[/C][C]1.5553[/C][C]0.0217000000000001[/C][/ROW]
[ROW][C]72[/C][C]1.4975[/C][C]1.577[/C][C]-0.0794999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36932&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36932&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
20.98110.98080.000299999999999967
31.00140.98110.0203000000000001
41.01831.00140.0168999999999999
51.06221.01830.0439000000000001
61.07731.06220.0150999999999999
71.08071.07730.00340000000000007
81.08481.08070.00409999999999999
91.15821.08480.0733999999999999
101.16631.15820.0081
111.13721.1663-0.0290999999999999
121.11391.1372-0.0233000000000001
131.12221.11390.0083000000000002
141.16921.12220.0469999999999999
151.17021.16920.00099999999999989
161.22861.17020.0584
171.26131.22860.0327000000000002
181.26461.26130.00329999999999986
191.22621.2646-0.0384
201.19851.2262-0.0277000000000001
211.20071.19850.0022000000000002
221.21381.20070.0130999999999999
231.22661.21380.0127999999999999
241.21761.2266-0.0089999999999999
251.22181.21760.00419999999999998
261.2491.22180.0272000000000001
271.29911.2490.0500999999999998
281.34081.29910.0417000000000001
291.31191.3408-0.0288999999999999
301.30141.3119-0.0105000000000002
311.32011.30140.0187000000000002
321.29381.3201-0.0263
331.26941.2938-0.0244
341.21651.2694-0.0529000000000002
351.20371.2165-0.0127999999999999
361.22921.20370.0255000000000001
371.22561.2292-0.00360000000000005
381.20151.2256-0.0241
391.17861.2015-0.0228999999999999
401.18561.17860.0069999999999999
411.21031.18560.0246999999999999
421.19381.2103-0.0165000000000000
431.2021.19380.00819999999999999
441.22711.2020.0251000000000001
451.2771.22710.0498999999999998
461.2651.277-0.012
471.26841.2650.00340000000000007
481.28111.26840.0126999999999999
491.27271.2811-0.00839999999999996
501.26111.2727-0.0115999999999998
511.28811.26110.0269999999999999
521.32131.28810.0331999999999999
531.29991.3213-0.0213999999999999
541.30741.29990.00749999999999984
551.32421.30740.0168000000000001
561.35161.32420.0273999999999999
571.35111.3516-0.000499999999999945
581.34191.3511-0.00919999999999987
591.37161.34190.0296999999999998
601.36221.3716-0.00939999999999985
611.38961.36220.0273999999999999
621.42271.38960.0331000000000001
631.46841.42270.0456999999999999
641.4571.4684-0.0113999999999999
651.47181.4570.0147999999999999
661.47481.47180.00300000000000011
671.55271.47480.0778999999999999
681.5751.55270.0223
691.55571.575-0.0192999999999999
701.55531.5557-0.000400000000000178
711.5771.55530.0217000000000001
721.49751.577-0.0794999999999999







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731.49751.442654656158091.55234534384192
741.49751.419936970905751.57506302909425
751.49751.402505077907221.59249492209278
761.49751.387809312316171.60719068768383
771.49751.374862082920131.62013791707987
781.49751.363156892819811.63184310718019
791.49751.352392859624471.64260714037553
801.49751.342373941811501.65262605818850
811.49751.332963968474261.66203603152574
821.49751.324063794404461.67093620559554
831.49751.315598572978341.67940142702166
841.49751.307510155814441.68748984418556

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.4975 & 1.44265465615809 & 1.55234534384192 \tabularnewline
74 & 1.4975 & 1.41993697090575 & 1.57506302909425 \tabularnewline
75 & 1.4975 & 1.40250507790722 & 1.59249492209278 \tabularnewline
76 & 1.4975 & 1.38780931231617 & 1.60719068768383 \tabularnewline
77 & 1.4975 & 1.37486208292013 & 1.62013791707987 \tabularnewline
78 & 1.4975 & 1.36315689281981 & 1.63184310718019 \tabularnewline
79 & 1.4975 & 1.35239285962447 & 1.64260714037553 \tabularnewline
80 & 1.4975 & 1.34237394181150 & 1.65262605818850 \tabularnewline
81 & 1.4975 & 1.33296396847426 & 1.66203603152574 \tabularnewline
82 & 1.4975 & 1.32406379440446 & 1.67093620559554 \tabularnewline
83 & 1.4975 & 1.31559857297834 & 1.67940142702166 \tabularnewline
84 & 1.4975 & 1.30751015581444 & 1.68748984418556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36932&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]1.4975[/C][C]1.44265465615809[/C][C]1.55234534384192[/C][/ROW]
[ROW][C]74[/C][C]1.4975[/C][C]1.41993697090575[/C][C]1.57506302909425[/C][/ROW]
[ROW][C]75[/C][C]1.4975[/C][C]1.40250507790722[/C][C]1.59249492209278[/C][/ROW]
[ROW][C]76[/C][C]1.4975[/C][C]1.38780931231617[/C][C]1.60719068768383[/C][/ROW]
[ROW][C]77[/C][C]1.4975[/C][C]1.37486208292013[/C][C]1.62013791707987[/C][/ROW]
[ROW][C]78[/C][C]1.4975[/C][C]1.36315689281981[/C][C]1.63184310718019[/C][/ROW]
[ROW][C]79[/C][C]1.4975[/C][C]1.35239285962447[/C][C]1.64260714037553[/C][/ROW]
[ROW][C]80[/C][C]1.4975[/C][C]1.34237394181150[/C][C]1.65262605818850[/C][/ROW]
[ROW][C]81[/C][C]1.4975[/C][C]1.33296396847426[/C][C]1.66203603152574[/C][/ROW]
[ROW][C]82[/C][C]1.4975[/C][C]1.32406379440446[/C][C]1.67093620559554[/C][/ROW]
[ROW][C]83[/C][C]1.4975[/C][C]1.31559857297834[/C][C]1.67940142702166[/C][/ROW]
[ROW][C]84[/C][C]1.4975[/C][C]1.30751015581444[/C][C]1.68748984418556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36932&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36932&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
731.49751.442654656158091.55234534384192
741.49751.419936970905751.57506302909425
751.49751.402505077907221.59249492209278
761.49751.387809312316171.60719068768383
771.49751.374862082920131.62013791707987
781.49751.363156892819811.63184310718019
791.49751.352392859624471.64260714037553
801.49751.342373941811501.65262605818850
811.49751.332963968474261.66203603152574
821.49751.324063794404461.67093620559554
831.49751.315598572978341.67940142702166
841.49751.307510155814441.68748984418556



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=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')