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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 28 Nov 2016 22:45:19 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/28/t1480373137yamuaxbjet13alz.htm/, Retrieved Sat, 04 May 2024 13:11:55 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 13:11:55 +0200

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Estimated Impact

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999926354804138
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999926354804138 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.999926354804138[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Parameter	Value
alpha	0.999926354804138
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1.3649	1.336	0.0288999999999999
3	1.3999	1.36489787165384	0.0350021283461603
4	1.4442	1.3998974222614	0.0443025777385977
5	1.4349	1.44419673732799	-0.00929673732798508
6	1.4388	1.43490068466004	0.00389931533995846
7	1.4264	1.43879971283416	-0.0123997128341584
8	1.4343	1.42640091317928	0.00789908682071983
9	1.377	1.4342994182702	-0.057299418270204
10	1.3706	1.37700421982688	-0.00640421982688122
11	1.3556	1.37060047164002	-0.0150004716400238
12	1.3179	1.35560110471267	-0.0377011047126719
13	1.2905	1.31790277650524	-0.0274027765052407
14	1.3224	1.29050201808284	0.0318979819171572
15	1.3201	1.32239765086687	-0.00229765086687417
16	1.3162	1.32010016921095	-0.00390016921094816
17	1.2789	1.31620028722873	-0.0373002872287256
18	1.2526	1.27890274698696	-0.0263027469869586
19	1.2288	1.25260193707095	-0.0238019370709537
20	1.24	1.22880175289832	0.0111982471016827
21	1.2856	1.2399991753029	0.0456008246971011
22	1.2974	1.28559664171833	0.0118033582816663
23	1.2828	1.29739913073937	-0.0145991307393678
24	1.3119	1.28280107515584	0.0290989248441573
25	1.3288	1.31189785700398	0.0169021429960194
26	1.3359	1.32879875523837	0.00710124476163165
27	1.2964	1.33589947702744	-0.0394994770274388
28	1.3026	1.29640290894672	0.00619709105327781
29	1.2982	1.30259954361402	-0.00439954361401562
30	1.3189	1.29820032400525	0.0206996759947489
31	1.308	1.31889847556831	-0.010898475568307
32	1.331	1.30800080262037	0.0229991973796322
33	1.3348	1.3309983062196	0.00380169378039574
34	1.3635	1.33479972002352	0.0287002799764831
35	1.3493	1.36349788636226	-0.0141978863622598
36	1.3704	1.34930104560612	0.0210989543938782
37	1.361	1.37039844616337	-0.00939844616337138
38	1.3658	1.36100069215041	0.00479930784959137
39	1.3823	1.36579964655403	0.0165003534459669
40	1.3812	1.38229878482824	-0.00109878482823889
41	1.3732	1.38120008092022	-0.00800008092022386
42	1.3592	1.37320058916753	-0.0140005891675263
43	1.3539	1.35920103107613	-0.00530103107613122
44	1.3316	1.35390039039547	-0.0223003903954719
45	1.2901	1.33160164231662	-0.0415016423166183
46	1.2673	1.29010305639658	-0.0228030563965769
47	1.2472	1.26730167933555	-0.0201016793355544
48	1.2331	1.24720148039211	-0.0141014803921118
49	1.1621	1.23310103850629	-0.0710010385062856
50	1.135	1.16210522888539	-0.027105228885387
51	1.0838	1.13500199616989	-0.05120199616989
52	1.0779	1.08380377078104	-0.00590377078103654
53	1.115	1.07790043478436	0.0370995652156445
54	1.1213	1.11499726779525	0.00630273220474664
55	1.0996	1.12129953583405	-0.0216995358340524
56	1.1139	1.09960159806657	0.0142984019334333
57	1.1221	1.11389894699139	0.00820105300861118
58	1.1235	1.12209939603185	0.00140060396815489
59	1.0736	1.12349989685225	-0.0498998968522462
60	1.0877	1.07360367488768	0.0140963251123225

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.3649 & 1.336 & 0.0288999999999999 \tabularnewline
3 & 1.3999 & 1.36489787165384 & 0.0350021283461603 \tabularnewline
4 & 1.4442 & 1.3998974222614 & 0.0443025777385977 \tabularnewline
5 & 1.4349 & 1.44419673732799 & -0.00929673732798508 \tabularnewline
6 & 1.4388 & 1.43490068466004 & 0.00389931533995846 \tabularnewline
7 & 1.4264 & 1.43879971283416 & -0.0123997128341584 \tabularnewline
8 & 1.4343 & 1.42640091317928 & 0.00789908682071983 \tabularnewline
9 & 1.377 & 1.4342994182702 & -0.057299418270204 \tabularnewline
10 & 1.3706 & 1.37700421982688 & -0.00640421982688122 \tabularnewline
11 & 1.3556 & 1.37060047164002 & -0.0150004716400238 \tabularnewline
12 & 1.3179 & 1.35560110471267 & -0.0377011047126719 \tabularnewline
13 & 1.2905 & 1.31790277650524 & -0.0274027765052407 \tabularnewline
14 & 1.3224 & 1.29050201808284 & 0.0318979819171572 \tabularnewline
15 & 1.3201 & 1.32239765086687 & -0.00229765086687417 \tabularnewline
16 & 1.3162 & 1.32010016921095 & -0.00390016921094816 \tabularnewline
17 & 1.2789 & 1.31620028722873 & -0.0373002872287256 \tabularnewline
18 & 1.2526 & 1.27890274698696 & -0.0263027469869586 \tabularnewline
19 & 1.2288 & 1.25260193707095 & -0.0238019370709537 \tabularnewline
20 & 1.24 & 1.22880175289832 & 0.0111982471016827 \tabularnewline
21 & 1.2856 & 1.2399991753029 & 0.0456008246971011 \tabularnewline
22 & 1.2974 & 1.28559664171833 & 0.0118033582816663 \tabularnewline
23 & 1.2828 & 1.29739913073937 & -0.0145991307393678 \tabularnewline
24 & 1.3119 & 1.28280107515584 & 0.0290989248441573 \tabularnewline
25 & 1.3288 & 1.31189785700398 & 0.0169021429960194 \tabularnewline
26 & 1.3359 & 1.32879875523837 & 0.00710124476163165 \tabularnewline
27 & 1.2964 & 1.33589947702744 & -0.0394994770274388 \tabularnewline
28 & 1.3026 & 1.29640290894672 & 0.00619709105327781 \tabularnewline
29 & 1.2982 & 1.30259954361402 & -0.00439954361401562 \tabularnewline
30 & 1.3189 & 1.29820032400525 & 0.0206996759947489 \tabularnewline
31 & 1.308 & 1.31889847556831 & -0.010898475568307 \tabularnewline
32 & 1.331 & 1.30800080262037 & 0.0229991973796322 \tabularnewline
33 & 1.3348 & 1.3309983062196 & 0.00380169378039574 \tabularnewline
34 & 1.3635 & 1.33479972002352 & 0.0287002799764831 \tabularnewline
35 & 1.3493 & 1.36349788636226 & -0.0141978863622598 \tabularnewline
36 & 1.3704 & 1.34930104560612 & 0.0210989543938782 \tabularnewline
37 & 1.361 & 1.37039844616337 & -0.00939844616337138 \tabularnewline
38 & 1.3658 & 1.36100069215041 & 0.00479930784959137 \tabularnewline
39 & 1.3823 & 1.36579964655403 & 0.0165003534459669 \tabularnewline
40 & 1.3812 & 1.38229878482824 & -0.00109878482823889 \tabularnewline
41 & 1.3732 & 1.38120008092022 & -0.00800008092022386 \tabularnewline
42 & 1.3592 & 1.37320058916753 & -0.0140005891675263 \tabularnewline
43 & 1.3539 & 1.35920103107613 & -0.00530103107613122 \tabularnewline
44 & 1.3316 & 1.35390039039547 & -0.0223003903954719 \tabularnewline
45 & 1.2901 & 1.33160164231662 & -0.0415016423166183 \tabularnewline
46 & 1.2673 & 1.29010305639658 & -0.0228030563965769 \tabularnewline
47 & 1.2472 & 1.26730167933555 & -0.0201016793355544 \tabularnewline
48 & 1.2331 & 1.24720148039211 & -0.0141014803921118 \tabularnewline
49 & 1.1621 & 1.23310103850629 & -0.0710010385062856 \tabularnewline
50 & 1.135 & 1.16210522888539 & -0.027105228885387 \tabularnewline
51 & 1.0838 & 1.13500199616989 & -0.05120199616989 \tabularnewline
52 & 1.0779 & 1.08380377078104 & -0.00590377078103654 \tabularnewline
53 & 1.115 & 1.07790043478436 & 0.0370995652156445 \tabularnewline
54 & 1.1213 & 1.11499726779525 & 0.00630273220474664 \tabularnewline
55 & 1.0996 & 1.12129953583405 & -0.0216995358340524 \tabularnewline
56 & 1.1139 & 1.09960159806657 & 0.0142984019334333 \tabularnewline
57 & 1.1221 & 1.11389894699139 & 0.00820105300861118 \tabularnewline
58 & 1.1235 & 1.12209939603185 & 0.00140060396815489 \tabularnewline
59 & 1.0736 & 1.12349989685225 & -0.0498998968522462 \tabularnewline
60 & 1.0877 & 1.07360367488768 & 0.0140963251123225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1.3649[/C][C]1.336[/C][C]0.0288999999999999[/C][/ROW]
[ROW][C]3[/C][C]1.3999[/C][C]1.36489787165384[/C][C]0.0350021283461603[/C][/ROW]
[ROW][C]4[/C][C]1.4442[/C][C]1.3998974222614[/C][C]0.0443025777385977[/C][/ROW]
[ROW][C]5[/C][C]1.4349[/C][C]1.44419673732799[/C][C]-0.00929673732798508[/C][/ROW]
[ROW][C]6[/C][C]1.4388[/C][C]1.43490068466004[/C][C]0.00389931533995846[/C][/ROW]
[ROW][C]7[/C][C]1.4264[/C][C]1.43879971283416[/C][C]-0.0123997128341584[/C][/ROW]
[ROW][C]8[/C][C]1.4343[/C][C]1.42640091317928[/C][C]0.00789908682071983[/C][/ROW]
[ROW][C]9[/C][C]1.377[/C][C]1.4342994182702[/C][C]-0.057299418270204[/C][/ROW]
[ROW][C]10[/C][C]1.3706[/C][C]1.37700421982688[/C][C]-0.00640421982688122[/C][/ROW]
[ROW][C]11[/C][C]1.3556[/C][C]1.37060047164002[/C][C]-0.0150004716400238[/C][/ROW]
[ROW][C]12[/C][C]1.3179[/C][C]1.35560110471267[/C][C]-0.0377011047126719[/C][/ROW]
[ROW][C]13[/C][C]1.2905[/C][C]1.31790277650524[/C][C]-0.0274027765052407[/C][/ROW]
[ROW][C]14[/C][C]1.3224[/C][C]1.29050201808284[/C][C]0.0318979819171572[/C][/ROW]
[ROW][C]15[/C][C]1.3201[/C][C]1.32239765086687[/C][C]-0.00229765086687417[/C][/ROW]
[ROW][C]16[/C][C]1.3162[/C][C]1.32010016921095[/C][C]-0.00390016921094816[/C][/ROW]
[ROW][C]17[/C][C]1.2789[/C][C]1.31620028722873[/C][C]-0.0373002872287256[/C][/ROW]
[ROW][C]18[/C][C]1.2526[/C][C]1.27890274698696[/C][C]-0.0263027469869586[/C][/ROW]
[ROW][C]19[/C][C]1.2288[/C][C]1.25260193707095[/C][C]-0.0238019370709537[/C][/ROW]
[ROW][C]20[/C][C]1.24[/C][C]1.22880175289832[/C][C]0.0111982471016827[/C][/ROW]
[ROW][C]21[/C][C]1.2856[/C][C]1.2399991753029[/C][C]0.0456008246971011[/C][/ROW]
[ROW][C]22[/C][C]1.2974[/C][C]1.28559664171833[/C][C]0.0118033582816663[/C][/ROW]
[ROW][C]23[/C][C]1.2828[/C][C]1.29739913073937[/C][C]-0.0145991307393678[/C][/ROW]
[ROW][C]24[/C][C]1.3119[/C][C]1.28280107515584[/C][C]0.0290989248441573[/C][/ROW]
[ROW][C]25[/C][C]1.3288[/C][C]1.31189785700398[/C][C]0.0169021429960194[/C][/ROW]
[ROW][C]26[/C][C]1.3359[/C][C]1.32879875523837[/C][C]0.00710124476163165[/C][/ROW]
[ROW][C]27[/C][C]1.2964[/C][C]1.33589947702744[/C][C]-0.0394994770274388[/C][/ROW]
[ROW][C]28[/C][C]1.3026[/C][C]1.29640290894672[/C][C]0.00619709105327781[/C][/ROW]
[ROW][C]29[/C][C]1.2982[/C][C]1.30259954361402[/C][C]-0.00439954361401562[/C][/ROW]
[ROW][C]30[/C][C]1.3189[/C][C]1.29820032400525[/C][C]0.0206996759947489[/C][/ROW]
[ROW][C]31[/C][C]1.308[/C][C]1.31889847556831[/C][C]-0.010898475568307[/C][/ROW]
[ROW][C]32[/C][C]1.331[/C][C]1.30800080262037[/C][C]0.0229991973796322[/C][/ROW]
[ROW][C]33[/C][C]1.3348[/C][C]1.3309983062196[/C][C]0.00380169378039574[/C][/ROW]
[ROW][C]34[/C][C]1.3635[/C][C]1.33479972002352[/C][C]0.0287002799764831[/C][/ROW]
[ROW][C]35[/C][C]1.3493[/C][C]1.36349788636226[/C][C]-0.0141978863622598[/C][/ROW]
[ROW][C]36[/C][C]1.3704[/C][C]1.34930104560612[/C][C]0.0210989543938782[/C][/ROW]
[ROW][C]37[/C][C]1.361[/C][C]1.37039844616337[/C][C]-0.00939844616337138[/C][/ROW]
[ROW][C]38[/C][C]1.3658[/C][C]1.36100069215041[/C][C]0.00479930784959137[/C][/ROW]
[ROW][C]39[/C][C]1.3823[/C][C]1.36579964655403[/C][C]0.0165003534459669[/C][/ROW]
[ROW][C]40[/C][C]1.3812[/C][C]1.38229878482824[/C][C]-0.00109878482823889[/C][/ROW]
[ROW][C]41[/C][C]1.3732[/C][C]1.38120008092022[/C][C]-0.00800008092022386[/C][/ROW]
[ROW][C]42[/C][C]1.3592[/C][C]1.37320058916753[/C][C]-0.0140005891675263[/C][/ROW]
[ROW][C]43[/C][C]1.3539[/C][C]1.35920103107613[/C][C]-0.00530103107613122[/C][/ROW]
[ROW][C]44[/C][C]1.3316[/C][C]1.35390039039547[/C][C]-0.0223003903954719[/C][/ROW]
[ROW][C]45[/C][C]1.2901[/C][C]1.33160164231662[/C][C]-0.0415016423166183[/C][/ROW]
[ROW][C]46[/C][C]1.2673[/C][C]1.29010305639658[/C][C]-0.0228030563965769[/C][/ROW]
[ROW][C]47[/C][C]1.2472[/C][C]1.26730167933555[/C][C]-0.0201016793355544[/C][/ROW]
[ROW][C]48[/C][C]1.2331[/C][C]1.24720148039211[/C][C]-0.0141014803921118[/C][/ROW]
[ROW][C]49[/C][C]1.1621[/C][C]1.23310103850629[/C][C]-0.0710010385062856[/C][/ROW]
[ROW][C]50[/C][C]1.135[/C][C]1.16210522888539[/C][C]-0.027105228885387[/C][/ROW]
[ROW][C]51[/C][C]1.0838[/C][C]1.13500199616989[/C][C]-0.05120199616989[/C][/ROW]
[ROW][C]52[/C][C]1.0779[/C][C]1.08380377078104[/C][C]-0.00590377078103654[/C][/ROW]
[ROW][C]53[/C][C]1.115[/C][C]1.07790043478436[/C][C]0.0370995652156445[/C][/ROW]
[ROW][C]54[/C][C]1.1213[/C][C]1.11499726779525[/C][C]0.00630273220474664[/C][/ROW]
[ROW][C]55[/C][C]1.0996[/C][C]1.12129953583405[/C][C]-0.0216995358340524[/C][/ROW]
[ROW][C]56[/C][C]1.1139[/C][C]1.09960159806657[/C][C]0.0142984019334333[/C][/ROW]
[ROW][C]57[/C][C]1.1221[/C][C]1.11389894699139[/C][C]0.00820105300861118[/C][/ROW]
[ROW][C]58[/C][C]1.1235[/C][C]1.12209939603185[/C][C]0.00140060396815489[/C][/ROW]
[ROW][C]59[/C][C]1.0736[/C][C]1.12349989685225[/C][C]-0.0498998968522462[/C][/ROW]
[ROW][C]60[/C][C]1.0877[/C][C]1.07360367488768[/C][C]0.0140963251123225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
t	Observed	Fitted	Residuals
2	1.3649	1.336	0.0288999999999999
3	1.3999	1.36489787165384	0.0350021283461603
4	1.4442	1.3998974222614	0.0443025777385977
5	1.4349	1.44419673732799	-0.00929673732798508
6	1.4388	1.43490068466004	0.00389931533995846
7	1.4264	1.43879971283416	-0.0123997128341584
8	1.4343	1.42640091317928	0.00789908682071983
9	1.377	1.4342994182702	-0.057299418270204
10	1.3706	1.37700421982688	-0.00640421982688122
11	1.3556	1.37060047164002	-0.0150004716400238
12	1.3179	1.35560110471267	-0.0377011047126719
13	1.2905	1.31790277650524	-0.0274027765052407
14	1.3224	1.29050201808284	0.0318979819171572
15	1.3201	1.32239765086687	-0.00229765086687417
16	1.3162	1.32010016921095	-0.00390016921094816
17	1.2789	1.31620028722873	-0.0373002872287256
18	1.2526	1.27890274698696	-0.0263027469869586
19	1.2288	1.25260193707095	-0.0238019370709537
20	1.24	1.22880175289832	0.0111982471016827
21	1.2856	1.2399991753029	0.0456008246971011
22	1.2974	1.28559664171833	0.0118033582816663
23	1.2828	1.29739913073937	-0.0145991307393678
24	1.3119	1.28280107515584	0.0290989248441573
25	1.3288	1.31189785700398	0.0169021429960194
26	1.3359	1.32879875523837	0.00710124476163165
27	1.2964	1.33589947702744	-0.0394994770274388
28	1.3026	1.29640290894672	0.00619709105327781
29	1.2982	1.30259954361402	-0.00439954361401562
30	1.3189	1.29820032400525	0.0206996759947489
31	1.308	1.31889847556831	-0.010898475568307
32	1.331	1.30800080262037	0.0229991973796322
33	1.3348	1.3309983062196	0.00380169378039574
34	1.3635	1.33479972002352	0.0287002799764831
35	1.3493	1.36349788636226	-0.0141978863622598
36	1.3704	1.34930104560612	0.0210989543938782
37	1.361	1.37039844616337	-0.00939844616337138
38	1.3658	1.36100069215041	0.00479930784959137
39	1.3823	1.36579964655403	0.0165003534459669
40	1.3812	1.38229878482824	-0.00109878482823889
41	1.3732	1.38120008092022	-0.00800008092022386
42	1.3592	1.37320058916753	-0.0140005891675263
43	1.3539	1.35920103107613	-0.00530103107613122
44	1.3316	1.35390039039547	-0.0223003903954719
45	1.2901	1.33160164231662	-0.0415016423166183
46	1.2673	1.29010305639658	-0.0228030563965769
47	1.2472	1.26730167933555	-0.0201016793355544
48	1.2331	1.24720148039211	-0.0141014803921118
49	1.1621	1.23310103850629	-0.0710010385062856
50	1.135	1.16210522888539	-0.027105228885387
51	1.0838	1.13500199616989	-0.05120199616989
52	1.0779	1.08380377078104	-0.00590377078103654
53	1.115	1.07790043478436	0.0370995652156445
54	1.1213	1.11499726779525	0.00630273220474664
55	1.0996	1.12129953583405	-0.0216995358340524
56	1.1139	1.09960159806657	0.0142984019334333
57	1.1221	1.11389894699139	0.00820105300861118
58	1.1235	1.12209939603185	0.00140060396815489
59	1.0736	1.12349989685225	-0.0498998968522462
60	1.0877	1.07360367488768	0.0140963251123225

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.08769896187338	1.03758298130658	1.13781494244018
62	1.08769896187338	1.01682687220669	1.15857105154006
63	1.08769896187338	1.00089979897837	1.17449812476838
64	1.08769896187338	0.987472536890617	1.18792538685614
65	1.08769896187338	0.975642824824237	1.19975509892252
66	1.08769896187338	0.964947915295653	1.2104500084511
67	1.08769896187338	0.955112910489841	1.22028501325691
68	1.08769896187338	0.945958697279901	1.22943922646685
69	1.08769896187338	0.937360862269253	1.2380370614775
70	1.08769896187338	0.92922882027525	1.2461691034715
71	1.08769896187338	0.921494186479644	1.25390373726711
72	1.08769896187338	0.914103832479628	1.26129409126712

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.08769896187338 & 1.03758298130658 & 1.13781494244018 \tabularnewline
62 & 1.08769896187338 & 1.01682687220669 & 1.15857105154006 \tabularnewline
63 & 1.08769896187338 & 1.00089979897837 & 1.17449812476838 \tabularnewline
64 & 1.08769896187338 & 0.987472536890617 & 1.18792538685614 \tabularnewline
65 & 1.08769896187338 & 0.975642824824237 & 1.19975509892252 \tabularnewline
66 & 1.08769896187338 & 0.964947915295653 & 1.2104500084511 \tabularnewline
67 & 1.08769896187338 & 0.955112910489841 & 1.22028501325691 \tabularnewline
68 & 1.08769896187338 & 0.945958697279901 & 1.22943922646685 \tabularnewline
69 & 1.08769896187338 & 0.937360862269253 & 1.2380370614775 \tabularnewline
70 & 1.08769896187338 & 0.92922882027525 & 1.2461691034715 \tabularnewline
71 & 1.08769896187338 & 0.921494186479644 & 1.25390373726711 \tabularnewline
72 & 1.08769896187338 & 0.914103832479628 & 1.26129409126712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]1.08769896187338[/C][C]1.03758298130658[/C][C]1.13781494244018[/C][/ROW]
[ROW][C]62[/C][C]1.08769896187338[/C][C]1.01682687220669[/C][C]1.15857105154006[/C][/ROW]
[ROW][C]63[/C][C]1.08769896187338[/C][C]1.00089979897837[/C][C]1.17449812476838[/C][/ROW]
[ROW][C]64[/C][C]1.08769896187338[/C][C]0.987472536890617[/C][C]1.18792538685614[/C][/ROW]
[ROW][C]65[/C][C]1.08769896187338[/C][C]0.975642824824237[/C][C]1.19975509892252[/C][/ROW]
[ROW][C]66[/C][C]1.08769896187338[/C][C]0.964947915295653[/C][C]1.2104500084511[/C][/ROW]
[ROW][C]67[/C][C]1.08769896187338[/C][C]0.955112910489841[/C][C]1.22028501325691[/C][/ROW]
[ROW][C]68[/C][C]1.08769896187338[/C][C]0.945958697279901[/C][C]1.22943922646685[/C][/ROW]
[ROW][C]69[/C][C]1.08769896187338[/C][C]0.937360862269253[/C][C]1.2380370614775[/C][/ROW]
[ROW][C]70[/C][C]1.08769896187338[/C][C]0.92922882027525[/C][C]1.2461691034715[/C][/ROW]
[ROW][C]71[/C][C]1.08769896187338[/C][C]0.921494186479644[/C][C]1.25390373726711[/C][/ROW]
[ROW][C]72[/C][C]1.08769896187338[/C][C]0.914103832479628[/C][C]1.26129409126712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.08769896187338	1.03758298130658	1.13781494244018
62	1.08769896187338	1.01682687220669	1.15857105154006
63	1.08769896187338	1.00089979897837	1.17449812476838
64	1.08769896187338	0.987472536890617	1.18792538685614
65	1.08769896187338	0.975642824824237	1.19975509892252
66	1.08769896187338	0.964947915295653	1.2104500084511
67	1.08769896187338	0.955112910489841	1.22028501325691
68	1.08769896187338	0.945958697279901	1.22943922646685
69	1.08769896187338	0.937360862269253	1.2380370614775
70	1.08769896187338	0.92922882027525	1.2461691034715
71	1.08769896187338	0.921494186479644	1.25390373726711
72	1.08769896187338	0.914103832479628	1.26129409126712

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code