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Author

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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 21 Dec 2012 06:31:18 -0500

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/2012/Dec/21/t13560894852dqk16gf639wqa0.htm/, Retrieved Thu, 02 May 2024 15:56:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203497, Retrieved Thu, 02 May 2024 15:56:47 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

105

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D  [Exponential Smoothing] [...] [2012-11-24 22:27:08] [0883bf8f4217d775edf6393676d58a73]
-    D      [Exponential Smoothing] [Single] [2012-12-21 11:31:18] [b650a28572edc4a1d205c228043a3295] [Current]
- R PD        [Exponential Smoothing] [double] [2012-12-21 11:32:59] [0604709baf8ca89a71bc0fcadc3cdffd] 
-   P           [Exponential Smoothing] [triple] [2012-12-21 11:34:02] [0604709baf8ca89a71bc0fcadc3cdffd] 
- RMPD          [Histogram] [] [2012-12-21 13:41:38] [0604709baf8ca89a71bc0fcadc3cdffd] 

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Dataseries X:

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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	4 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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203497&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]4 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=203497&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203497&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	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.933090814754979
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.933090814754979 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203497&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]0.933090814754979[/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=203497&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203497&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	0.933090814754979
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1.4721	1.4761	-0.004
3	1.487	1.47236763674098	0.01463236325902
4	1.5167	1.48602096049613	0.0306790395038701
5	1.5812	1.5146472904627	0.0665527095373037
6	1.554	1.57674701242901	-0.0227470124290103
7	1.5508	1.55552198406838	-0.00472198406838364
8	1.5764	1.55111594410676	0.0252840558932446
9	1.5611	1.57470826442049	-0.0136082644204936
10	1.4735	1.56201051788497	-0.0885105178849739
11	1.4303	1.4794221666373	-0.0491221666372985
12	1.2757	1.43358672414717	-0.157886724147172
13	1.2727	1.28626407207369	-0.0135640720736927
14	1.3917	1.27360756101106	0.118092438988944
15	1.2816	1.38379853112365	-0.102198531123652
16	1.2644	1.28843802045072	-0.0240380204507216
17	1.3308	1.26600836436326	0.0647916356367391
18	1.3275	1.32646484444885	0.00103515555114631
19	1.4098	1.32743073858547	0.082369261414529
20	1.4134	1.40428873982952	0.00911126017048036
21	1.4138	1.41279037300544	0.00100962699456231
22	1.4272	1.41373244668039	0.0134675533196076
23	1.4643	1.42629889698014	0.0380011030198588
24	1.48	1.46175737715853	0.0182426228414709
25	1.5023	1.47877940096895	0.023520599031055
26	1.4406	1.50072625588236	-0.0601262558823572
27	1.3966	1.44462299879292	-0.0480229987929222
28	1.357	1.39981317972226	-0.0428131797222571
29	1.3479	1.35986459497296	-0.0119645949729648
30	1.3315	1.34870054130143	-0.017200541301428
31	1.2307	1.33265087420425	-0.101950874204252
32	1.2271	1.23752144992802	-0.010421449928024
33	1.3028	1.22779729072376	0.075002709276244
34	1.268	1.29778162983116	-0.0297816298311573
35	1.3648	1.26999266458727	0.0948073354127286
36	1.3857	1.35845651843228	0.0272434815677169
37	1.2998	1.38387716084507	-0.0840771608450661
38	1.3362	1.30542553432986	0.0307744656701421
39	1.3692	1.33414090557566	0.0350590944243401
40	1.3834	1.36685422455664	0.0165457754433609
41	1.4207	1.38229293564584	0.0384070643541625
42	1.486	1.41813021461641	0.0678697853835899
43	1.4385	1.48145888795723	-0.0429588879572296
44	1.4453	1.44137434419225	0.00392565580774984
45	1.426	1.44503733756835	-0.0190373375683512
46	1.445	1.42727377274593	0.0177262272540673
47	1.3503	1.44381395257696	-0.0935139525769624
48	1.4001	1.35655694237597	0.0435430576240339
49	1.3418	1.3971865694913	-0.0553865694912987
50	1.2939	1.34550587023818	-0.0516058702381796
51	1.3176	1.2973529067315	0.0202470932685033
52	1.3443	1.31624528348582	0.0280547165141753
53	1.3356	1.34242288177576	-0.00682288177575674
54	1.3214	1.33605651346064	-0.0146565134606389
55	1.2403	1.32238065537418	-0.082080655374184
56	1.259	1.24579194977546	0.013208050224536
57	1.2284	1.2581162601208	-0.029716260120801
58	1.2611	1.23038829075321	0.0307117092467883
59	1.293	1.25904510455682	0.0339548954431843
60	1.2993	1.29072810561082	0.00857189438918327
61	1.2986	1.29872646153041	-0.000126461530413291

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.4721 & 1.4761 & -0.004 \tabularnewline
3 & 1.487 & 1.47236763674098 & 0.01463236325902 \tabularnewline
4 & 1.5167 & 1.48602096049613 & 0.0306790395038701 \tabularnewline
5 & 1.5812 & 1.5146472904627 & 0.0665527095373037 \tabularnewline
6 & 1.554 & 1.57674701242901 & -0.0227470124290103 \tabularnewline
7 & 1.5508 & 1.55552198406838 & -0.00472198406838364 \tabularnewline
8 & 1.5764 & 1.55111594410676 & 0.0252840558932446 \tabularnewline
9 & 1.5611 & 1.57470826442049 & -0.0136082644204936 \tabularnewline
10 & 1.4735 & 1.56201051788497 & -0.0885105178849739 \tabularnewline
11 & 1.4303 & 1.4794221666373 & -0.0491221666372985 \tabularnewline
12 & 1.2757 & 1.43358672414717 & -0.157886724147172 \tabularnewline
13 & 1.2727 & 1.28626407207369 & -0.0135640720736927 \tabularnewline
14 & 1.3917 & 1.27360756101106 & 0.118092438988944 \tabularnewline
15 & 1.2816 & 1.38379853112365 & -0.102198531123652 \tabularnewline
16 & 1.2644 & 1.28843802045072 & -0.0240380204507216 \tabularnewline
17 & 1.3308 & 1.26600836436326 & 0.0647916356367391 \tabularnewline
18 & 1.3275 & 1.32646484444885 & 0.00103515555114631 \tabularnewline
19 & 1.4098 & 1.32743073858547 & 0.082369261414529 \tabularnewline
20 & 1.4134 & 1.40428873982952 & 0.00911126017048036 \tabularnewline
21 & 1.4138 & 1.41279037300544 & 0.00100962699456231 \tabularnewline
22 & 1.4272 & 1.41373244668039 & 0.0134675533196076 \tabularnewline
23 & 1.4643 & 1.42629889698014 & 0.0380011030198588 \tabularnewline
24 & 1.48 & 1.46175737715853 & 0.0182426228414709 \tabularnewline
25 & 1.5023 & 1.47877940096895 & 0.023520599031055 \tabularnewline
26 & 1.4406 & 1.50072625588236 & -0.0601262558823572 \tabularnewline
27 & 1.3966 & 1.44462299879292 & -0.0480229987929222 \tabularnewline
28 & 1.357 & 1.39981317972226 & -0.0428131797222571 \tabularnewline
29 & 1.3479 & 1.35986459497296 & -0.0119645949729648 \tabularnewline
30 & 1.3315 & 1.34870054130143 & -0.017200541301428 \tabularnewline
31 & 1.2307 & 1.33265087420425 & -0.101950874204252 \tabularnewline
32 & 1.2271 & 1.23752144992802 & -0.010421449928024 \tabularnewline
33 & 1.3028 & 1.22779729072376 & 0.075002709276244 \tabularnewline
34 & 1.268 & 1.29778162983116 & -0.0297816298311573 \tabularnewline
35 & 1.3648 & 1.26999266458727 & 0.0948073354127286 \tabularnewline
36 & 1.3857 & 1.35845651843228 & 0.0272434815677169 \tabularnewline
37 & 1.2998 & 1.38387716084507 & -0.0840771608450661 \tabularnewline
38 & 1.3362 & 1.30542553432986 & 0.0307744656701421 \tabularnewline
39 & 1.3692 & 1.33414090557566 & 0.0350590944243401 \tabularnewline
40 & 1.3834 & 1.36685422455664 & 0.0165457754433609 \tabularnewline
41 & 1.4207 & 1.38229293564584 & 0.0384070643541625 \tabularnewline
42 & 1.486 & 1.41813021461641 & 0.0678697853835899 \tabularnewline
43 & 1.4385 & 1.48145888795723 & -0.0429588879572296 \tabularnewline
44 & 1.4453 & 1.44137434419225 & 0.00392565580774984 \tabularnewline
45 & 1.426 & 1.44503733756835 & -0.0190373375683512 \tabularnewline
46 & 1.445 & 1.42727377274593 & 0.0177262272540673 \tabularnewline
47 & 1.3503 & 1.44381395257696 & -0.0935139525769624 \tabularnewline
48 & 1.4001 & 1.35655694237597 & 0.0435430576240339 \tabularnewline
49 & 1.3418 & 1.3971865694913 & -0.0553865694912987 \tabularnewline
50 & 1.2939 & 1.34550587023818 & -0.0516058702381796 \tabularnewline
51 & 1.3176 & 1.2973529067315 & 0.0202470932685033 \tabularnewline
52 & 1.3443 & 1.31624528348582 & 0.0280547165141753 \tabularnewline
53 & 1.3356 & 1.34242288177576 & -0.00682288177575674 \tabularnewline
54 & 1.3214 & 1.33605651346064 & -0.0146565134606389 \tabularnewline
55 & 1.2403 & 1.32238065537418 & -0.082080655374184 \tabularnewline
56 & 1.259 & 1.24579194977546 & 0.013208050224536 \tabularnewline
57 & 1.2284 & 1.2581162601208 & -0.029716260120801 \tabularnewline
58 & 1.2611 & 1.23038829075321 & 0.0307117092467883 \tabularnewline
59 & 1.293 & 1.25904510455682 & 0.0339548954431843 \tabularnewline
60 & 1.2993 & 1.29072810561082 & 0.00857189438918327 \tabularnewline
61 & 1.2986 & 1.29872646153041 & -0.000126461530413291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203497&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]1.4721[/C][C]1.4761[/C][C]-0.004[/C][/ROW]
[ROW][C]3[/C][C]1.487[/C][C]1.47236763674098[/C][C]0.01463236325902[/C][/ROW]
[ROW][C]4[/C][C]1.5167[/C][C]1.48602096049613[/C][C]0.0306790395038701[/C][/ROW]
[ROW][C]5[/C][C]1.5812[/C][C]1.5146472904627[/C][C]0.0665527095373037[/C][/ROW]
[ROW][C]6[/C][C]1.554[/C][C]1.57674701242901[/C][C]-0.0227470124290103[/C][/ROW]
[ROW][C]7[/C][C]1.5508[/C][C]1.55552198406838[/C][C]-0.00472198406838364[/C][/ROW]
[ROW][C]8[/C][C]1.5764[/C][C]1.55111594410676[/C][C]0.0252840558932446[/C][/ROW]
[ROW][C]9[/C][C]1.5611[/C][C]1.57470826442049[/C][C]-0.0136082644204936[/C][/ROW]
[ROW][C]10[/C][C]1.4735[/C][C]1.56201051788497[/C][C]-0.0885105178849739[/C][/ROW]
[ROW][C]11[/C][C]1.4303[/C][C]1.4794221666373[/C][C]-0.0491221666372985[/C][/ROW]
[ROW][C]12[/C][C]1.2757[/C][C]1.43358672414717[/C][C]-0.157886724147172[/C][/ROW]
[ROW][C]13[/C][C]1.2727[/C][C]1.28626407207369[/C][C]-0.0135640720736927[/C][/ROW]
[ROW][C]14[/C][C]1.3917[/C][C]1.27360756101106[/C][C]0.118092438988944[/C][/ROW]
[ROW][C]15[/C][C]1.2816[/C][C]1.38379853112365[/C][C]-0.102198531123652[/C][/ROW]
[ROW][C]16[/C][C]1.2644[/C][C]1.28843802045072[/C][C]-0.0240380204507216[/C][/ROW]
[ROW][C]17[/C][C]1.3308[/C][C]1.26600836436326[/C][C]0.0647916356367391[/C][/ROW]
[ROW][C]18[/C][C]1.3275[/C][C]1.32646484444885[/C][C]0.00103515555114631[/C][/ROW]
[ROW][C]19[/C][C]1.4098[/C][C]1.32743073858547[/C][C]0.082369261414529[/C][/ROW]
[ROW][C]20[/C][C]1.4134[/C][C]1.40428873982952[/C][C]0.00911126017048036[/C][/ROW]
[ROW][C]21[/C][C]1.4138[/C][C]1.41279037300544[/C][C]0.00100962699456231[/C][/ROW]
[ROW][C]22[/C][C]1.4272[/C][C]1.41373244668039[/C][C]0.0134675533196076[/C][/ROW]
[ROW][C]23[/C][C]1.4643[/C][C]1.42629889698014[/C][C]0.0380011030198588[/C][/ROW]
[ROW][C]24[/C][C]1.48[/C][C]1.46175737715853[/C][C]0.0182426228414709[/C][/ROW]
[ROW][C]25[/C][C]1.5023[/C][C]1.47877940096895[/C][C]0.023520599031055[/C][/ROW]
[ROW][C]26[/C][C]1.4406[/C][C]1.50072625588236[/C][C]-0.0601262558823572[/C][/ROW]
[ROW][C]27[/C][C]1.3966[/C][C]1.44462299879292[/C][C]-0.0480229987929222[/C][/ROW]
[ROW][C]28[/C][C]1.357[/C][C]1.39981317972226[/C][C]-0.0428131797222571[/C][/ROW]
[ROW][C]29[/C][C]1.3479[/C][C]1.35986459497296[/C][C]-0.0119645949729648[/C][/ROW]
[ROW][C]30[/C][C]1.3315[/C][C]1.34870054130143[/C][C]-0.017200541301428[/C][/ROW]
[ROW][C]31[/C][C]1.2307[/C][C]1.33265087420425[/C][C]-0.101950874204252[/C][/ROW]
[ROW][C]32[/C][C]1.2271[/C][C]1.23752144992802[/C][C]-0.010421449928024[/C][/ROW]
[ROW][C]33[/C][C]1.3028[/C][C]1.22779729072376[/C][C]0.075002709276244[/C][/ROW]
[ROW][C]34[/C][C]1.268[/C][C]1.29778162983116[/C][C]-0.0297816298311573[/C][/ROW]
[ROW][C]35[/C][C]1.3648[/C][C]1.26999266458727[/C][C]0.0948073354127286[/C][/ROW]
[ROW][C]36[/C][C]1.3857[/C][C]1.35845651843228[/C][C]0.0272434815677169[/C][/ROW]
[ROW][C]37[/C][C]1.2998[/C][C]1.38387716084507[/C][C]-0.0840771608450661[/C][/ROW]
[ROW][C]38[/C][C]1.3362[/C][C]1.30542553432986[/C][C]0.0307744656701421[/C][/ROW]
[ROW][C]39[/C][C]1.3692[/C][C]1.33414090557566[/C][C]0.0350590944243401[/C][/ROW]
[ROW][C]40[/C][C]1.3834[/C][C]1.36685422455664[/C][C]0.0165457754433609[/C][/ROW]
[ROW][C]41[/C][C]1.4207[/C][C]1.38229293564584[/C][C]0.0384070643541625[/C][/ROW]
[ROW][C]42[/C][C]1.486[/C][C]1.41813021461641[/C][C]0.0678697853835899[/C][/ROW]
[ROW][C]43[/C][C]1.4385[/C][C]1.48145888795723[/C][C]-0.0429588879572296[/C][/ROW]
[ROW][C]44[/C][C]1.4453[/C][C]1.44137434419225[/C][C]0.00392565580774984[/C][/ROW]
[ROW][C]45[/C][C]1.426[/C][C]1.44503733756835[/C][C]-0.0190373375683512[/C][/ROW]
[ROW][C]46[/C][C]1.445[/C][C]1.42727377274593[/C][C]0.0177262272540673[/C][/ROW]
[ROW][C]47[/C][C]1.3503[/C][C]1.44381395257696[/C][C]-0.0935139525769624[/C][/ROW]
[ROW][C]48[/C][C]1.4001[/C][C]1.35655694237597[/C][C]0.0435430576240339[/C][/ROW]
[ROW][C]49[/C][C]1.3418[/C][C]1.3971865694913[/C][C]-0.0553865694912987[/C][/ROW]
[ROW][C]50[/C][C]1.2939[/C][C]1.34550587023818[/C][C]-0.0516058702381796[/C][/ROW]
[ROW][C]51[/C][C]1.3176[/C][C]1.2973529067315[/C][C]0.0202470932685033[/C][/ROW]
[ROW][C]52[/C][C]1.3443[/C][C]1.31624528348582[/C][C]0.0280547165141753[/C][/ROW]
[ROW][C]53[/C][C]1.3356[/C][C]1.34242288177576[/C][C]-0.00682288177575674[/C][/ROW]
[ROW][C]54[/C][C]1.3214[/C][C]1.33605651346064[/C][C]-0.0146565134606389[/C][/ROW]
[ROW][C]55[/C][C]1.2403[/C][C]1.32238065537418[/C][C]-0.082080655374184[/C][/ROW]
[ROW][C]56[/C][C]1.259[/C][C]1.24579194977546[/C][C]0.013208050224536[/C][/ROW]
[ROW][C]57[/C][C]1.2284[/C][C]1.2581162601208[/C][C]-0.029716260120801[/C][/ROW]
[ROW][C]58[/C][C]1.2611[/C][C]1.23038829075321[/C][C]0.0307117092467883[/C][/ROW]
[ROW][C]59[/C][C]1.293[/C][C]1.25904510455682[/C][C]0.0339548954431843[/C][/ROW]
[ROW][C]60[/C][C]1.2993[/C][C]1.29072810561082[/C][C]0.00857189438918327[/C][/ROW]
[ROW][C]61[/C][C]1.2986[/C][C]1.29872646153041[/C][C]-0.000126461530413291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203497&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203497&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	1.4721	1.4761	-0.004
3	1.487	1.47236763674098	0.01463236325902
4	1.5167	1.48602096049613	0.0306790395038701
5	1.5812	1.5146472904627	0.0665527095373037
6	1.554	1.57674701242901	-0.0227470124290103
7	1.5508	1.55552198406838	-0.00472198406838364
8	1.5764	1.55111594410676	0.0252840558932446
9	1.5611	1.57470826442049	-0.0136082644204936
10	1.4735	1.56201051788497	-0.0885105178849739
11	1.4303	1.4794221666373	-0.0491221666372985
12	1.2757	1.43358672414717	-0.157886724147172
13	1.2727	1.28626407207369	-0.0135640720736927
14	1.3917	1.27360756101106	0.118092438988944
15	1.2816	1.38379853112365	-0.102198531123652
16	1.2644	1.28843802045072	-0.0240380204507216
17	1.3308	1.26600836436326	0.0647916356367391
18	1.3275	1.32646484444885	0.00103515555114631
19	1.4098	1.32743073858547	0.082369261414529
20	1.4134	1.40428873982952	0.00911126017048036
21	1.4138	1.41279037300544	0.00100962699456231
22	1.4272	1.41373244668039	0.0134675533196076
23	1.4643	1.42629889698014	0.0380011030198588
24	1.48	1.46175737715853	0.0182426228414709
25	1.5023	1.47877940096895	0.023520599031055
26	1.4406	1.50072625588236	-0.0601262558823572
27	1.3966	1.44462299879292	-0.0480229987929222
28	1.357	1.39981317972226	-0.0428131797222571
29	1.3479	1.35986459497296	-0.0119645949729648
30	1.3315	1.34870054130143	-0.017200541301428
31	1.2307	1.33265087420425	-0.101950874204252
32	1.2271	1.23752144992802	-0.010421449928024
33	1.3028	1.22779729072376	0.075002709276244
34	1.268	1.29778162983116	-0.0297816298311573
35	1.3648	1.26999266458727	0.0948073354127286
36	1.3857	1.35845651843228	0.0272434815677169
37	1.2998	1.38387716084507	-0.0840771608450661
38	1.3362	1.30542553432986	0.0307744656701421
39	1.3692	1.33414090557566	0.0350590944243401
40	1.3834	1.36685422455664	0.0165457754433609
41	1.4207	1.38229293564584	0.0384070643541625
42	1.486	1.41813021461641	0.0678697853835899
43	1.4385	1.48145888795723	-0.0429588879572296
44	1.4453	1.44137434419225	0.00392565580774984
45	1.426	1.44503733756835	-0.0190373375683512
46	1.445	1.42727377274593	0.0177262272540673
47	1.3503	1.44381395257696	-0.0935139525769624
48	1.4001	1.35655694237597	0.0435430576240339
49	1.3418	1.3971865694913	-0.0553865694912987
50	1.2939	1.34550587023818	-0.0516058702381796
51	1.3176	1.2973529067315	0.0202470932685033
52	1.3443	1.31624528348582	0.0280547165141753
53	1.3356	1.34242288177576	-0.00682288177575674
54	1.3214	1.33605651346064	-0.0146565134606389
55	1.2403	1.32238065537418	-0.082080655374184
56	1.259	1.24579194977546	0.013208050224536
57	1.2284	1.2581162601208	-0.029716260120801
58	1.2611	1.23038829075321	0.0307117092467883
59	1.293	1.25904510455682	0.0339548954431843
60	1.2993	1.29072810561082	0.00857189438918327
61	1.2986	1.29872646153041	-0.000126461530413291

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
62	1.29860846143796	1.19617936725679	1.40103755561914
63	1.29860846143796	1.1585141231385	1.43870279973743
64	1.29860846143796	1.12901740061118	1.46819952226475
65	1.29860846143796	1.1039399426653	1.49327698021063
66	1.29860846143796	1.08174321182445	1.51547371105148
67	1.29860846143796	1.06161639241724	1.53560053045869
68	1.29860846143796	1.04306992213809	1.55414700073784
69	1.29860846143796	1.02578131953984	1.57143560333609
70	1.29860846143796	1.00952481671711	1.58769210615881
71	1.29860846143796	0.994135050556358	1.60308187231957
72	1.29860846143796	0.979486600352471	1.61773032252346
73	1.29860846143796	0.965481658986618	1.63173526388931

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 1.29860846143796 & 1.19617936725679 & 1.40103755561914 \tabularnewline
63 & 1.29860846143796 & 1.1585141231385 & 1.43870279973743 \tabularnewline
64 & 1.29860846143796 & 1.12901740061118 & 1.46819952226475 \tabularnewline
65 & 1.29860846143796 & 1.1039399426653 & 1.49327698021063 \tabularnewline
66 & 1.29860846143796 & 1.08174321182445 & 1.51547371105148 \tabularnewline
67 & 1.29860846143796 & 1.06161639241724 & 1.53560053045869 \tabularnewline
68 & 1.29860846143796 & 1.04306992213809 & 1.55414700073784 \tabularnewline
69 & 1.29860846143796 & 1.02578131953984 & 1.57143560333609 \tabularnewline
70 & 1.29860846143796 & 1.00952481671711 & 1.58769210615881 \tabularnewline
71 & 1.29860846143796 & 0.994135050556358 & 1.60308187231957 \tabularnewline
72 & 1.29860846143796 & 0.979486600352471 & 1.61773032252346 \tabularnewline
73 & 1.29860846143796 & 0.965481658986618 & 1.63173526388931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203497&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]62[/C][C]1.29860846143796[/C][C]1.19617936725679[/C][C]1.40103755561914[/C][/ROW]
[ROW][C]63[/C][C]1.29860846143796[/C][C]1.1585141231385[/C][C]1.43870279973743[/C][/ROW]
[ROW][C]64[/C][C]1.29860846143796[/C][C]1.12901740061118[/C][C]1.46819952226475[/C][/ROW]
[ROW][C]65[/C][C]1.29860846143796[/C][C]1.1039399426653[/C][C]1.49327698021063[/C][/ROW]
[ROW][C]66[/C][C]1.29860846143796[/C][C]1.08174321182445[/C][C]1.51547371105148[/C][/ROW]
[ROW][C]67[/C][C]1.29860846143796[/C][C]1.06161639241724[/C][C]1.53560053045869[/C][/ROW]
[ROW][C]68[/C][C]1.29860846143796[/C][C]1.04306992213809[/C][C]1.55414700073784[/C][/ROW]
[ROW][C]69[/C][C]1.29860846143796[/C][C]1.02578131953984[/C][C]1.57143560333609[/C][/ROW]
[ROW][C]70[/C][C]1.29860846143796[/C][C]1.00952481671711[/C][C]1.58769210615881[/C][/ROW]
[ROW][C]71[/C][C]1.29860846143796[/C][C]0.994135050556358[/C][C]1.60308187231957[/C][/ROW]
[ROW][C]72[/C][C]1.29860846143796[/C][C]0.979486600352471[/C][C]1.61773032252346[/C][/ROW]
[ROW][C]73[/C][C]1.29860846143796[/C][C]0.965481658986618[/C][C]1.63173526388931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203497&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203497&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
62	1.29860846143796	1.19617936725679	1.40103755561914
63	1.29860846143796	1.1585141231385	1.43870279973743
64	1.29860846143796	1.12901740061118	1.46819952226475
65	1.29860846143796	1.1039399426653	1.49327698021063
66	1.29860846143796	1.08174321182445	1.51547371105148
67	1.29860846143796	1.06161639241724	1.53560053045869
68	1.29860846143796	1.04306992213809	1.55414700073784
69	1.29860846143796	1.02578131953984	1.57143560333609
70	1.29860846143796	1.00952481671711	1.58769210615881
71	1.29860846143796	0.994135050556358	1.60308187231957
72	1.29860846143796	0.979486600352471	1.61773032252346
73	1.29860846143796	0.965481658986618	1.63173526388931

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 = 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code