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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 24 Nov 2012 17:32:33 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/24/t1353796372nj4slgcqelidvkq.htm/, Retrieved Sun, 28 Apr 2024 18:59:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=192530, Retrieved Sun, 28 Apr 2024 18:59:15 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

112

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]
- R PD      [Exponential Smoothing] [...] [2012-11-24 22:32:33] [0ce3a3cc7b36ec2616d0d876d7c7ef2d] [Current]
-   P         [Exponential Smoothing] [...] [2012-11-24 22:35:06] [0883bf8f4217d775edf6393676d58a73] 

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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	3 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192530&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192530&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192530&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	3 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0154924408479368
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0154924408479368 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192530&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]0.0154924408479368[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192530&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192530&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	1
beta	0.0154924408479368
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.4718	1.36922168803419	0.102578311965812
14	1.4748	1.47308688656561	0.00171311343439018
15	1.5527	1.55759676020749	-0.00489676020749075
16	1.5751	1.58932923077296	-0.0142292307729635
17	1.5557	1.57981711859024	-0.0241171185902351
18	1.5553	1.57994348555705	-0.0246434855570534
19	1.577	1.48053253114811	0.0964674688518932
20	1.4975	1.56641454770304	-0.0689145477030444
21	1.437	1.52028855981586	-0.0832885598158597
22	1.3322	1.4618607167296	-0.129660716729603
23	1.2732	1.3686477890787	-0.0954477890787013
24	1.3449	1.25148990318567	0.093410096814333
25	1.3239	1.35080372025183	-0.0269037202518294
26	1.2785	1.32084108262391	-0.0423410826239057
27	1.305	1.35626844923925	-0.0512684492392497
28	1.319	1.33588250915538	-0.016882509155379
29	1.365	1.31792929121426	0.0470707087857418
30	1.4016	1.38455853138579	0.0170414686142084
31	1.4088	1.32279337866359	0.0860066213364075
32	1.4268	1.39401333115718	0.0327866688428229
33	1.4562	1.44696294335149	0.00923705664850738
34	1.4816	1.47986854790523	0.0017314520947711
35	1.4914	1.51889120565772	-0.0274912056577208
36	1.4614	1.47158613311356	-0.010186133113564
37	1.4272	1.4675949917155	-0.0403949917154993
38	1.3686	1.42422334136246	-0.0556233413624612
39	1.3569	1.44624493336997	-0.089344933369971
40	1.3406	1.38706909560801	-0.0464690956080078
41	1.2565	1.33835750922638	-0.0818575092263774
42	1.2209	1.27288933660673	-0.0519893366067279
43	1.277	1.13785472821796	0.139145271782042
44	1.2894	1.25879792811031	0.0306020718896893
45	1.3067	1.30611369556555	0.000586304434446738
46	1.3898	1.32678527885232	0.0630147211476766
47	1.3661	1.42445736402559	-0.0583573640255854
48	1.322	1.34317409934871	-0.0211740993487115
49	1.336	1.32491272753371	0.0110872724662903
50	1.3649	1.33053866311323	0.0343613368867743
51	1.3999	1.44145433742573	-0.0415543374257326
52	1.4442	1.42971889264452	0.0144811073554769
53	1.4349	1.44255157367697	-0.00765157367697378
54	1.4388	1.45303303212439	-0.0142330321243895
55	1.4264	1.35808336104945	0.0683166389505505
56	1.4343	1.40942925253732	0.0248707474626801
57	1.377	1.4521562277879	-0.0751562277878961
58	1.3706	1.39705437437454	-0.0264543743745389
59	1.3556	1.4038403648777	-0.0482403648777048
60	1.3179	1.33141383721169	-0.0135138372116876

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.4718 & 1.36922168803419 & 0.102578311965812 \tabularnewline
14 & 1.4748 & 1.47308688656561 & 0.00171311343439018 \tabularnewline
15 & 1.5527 & 1.55759676020749 & -0.00489676020749075 \tabularnewline
16 & 1.5751 & 1.58932923077296 & -0.0142292307729635 \tabularnewline
17 & 1.5557 & 1.57981711859024 & -0.0241171185902351 \tabularnewline
18 & 1.5553 & 1.57994348555705 & -0.0246434855570534 \tabularnewline
19 & 1.577 & 1.48053253114811 & 0.0964674688518932 \tabularnewline
20 & 1.4975 & 1.56641454770304 & -0.0689145477030444 \tabularnewline
21 & 1.437 & 1.52028855981586 & -0.0832885598158597 \tabularnewline
22 & 1.3322 & 1.4618607167296 & -0.129660716729603 \tabularnewline
23 & 1.2732 & 1.3686477890787 & -0.0954477890787013 \tabularnewline
24 & 1.3449 & 1.25148990318567 & 0.093410096814333 \tabularnewline
25 & 1.3239 & 1.35080372025183 & -0.0269037202518294 \tabularnewline
26 & 1.2785 & 1.32084108262391 & -0.0423410826239057 \tabularnewline
27 & 1.305 & 1.35626844923925 & -0.0512684492392497 \tabularnewline
28 & 1.319 & 1.33588250915538 & -0.016882509155379 \tabularnewline
29 & 1.365 & 1.31792929121426 & 0.0470707087857418 \tabularnewline
30 & 1.4016 & 1.38455853138579 & 0.0170414686142084 \tabularnewline
31 & 1.4088 & 1.32279337866359 & 0.0860066213364075 \tabularnewline
32 & 1.4268 & 1.39401333115718 & 0.0327866688428229 \tabularnewline
33 & 1.4562 & 1.44696294335149 & 0.00923705664850738 \tabularnewline
34 & 1.4816 & 1.47986854790523 & 0.0017314520947711 \tabularnewline
35 & 1.4914 & 1.51889120565772 & -0.0274912056577208 \tabularnewline
36 & 1.4614 & 1.47158613311356 & -0.010186133113564 \tabularnewline
37 & 1.4272 & 1.4675949917155 & -0.0403949917154993 \tabularnewline
38 & 1.3686 & 1.42422334136246 & -0.0556233413624612 \tabularnewline
39 & 1.3569 & 1.44624493336997 & -0.089344933369971 \tabularnewline
40 & 1.3406 & 1.38706909560801 & -0.0464690956080078 \tabularnewline
41 & 1.2565 & 1.33835750922638 & -0.0818575092263774 \tabularnewline
42 & 1.2209 & 1.27288933660673 & -0.0519893366067279 \tabularnewline
43 & 1.277 & 1.13785472821796 & 0.139145271782042 \tabularnewline
44 & 1.2894 & 1.25879792811031 & 0.0306020718896893 \tabularnewline
45 & 1.3067 & 1.30611369556555 & 0.000586304434446738 \tabularnewline
46 & 1.3898 & 1.32678527885232 & 0.0630147211476766 \tabularnewline
47 & 1.3661 & 1.42445736402559 & -0.0583573640255854 \tabularnewline
48 & 1.322 & 1.34317409934871 & -0.0211740993487115 \tabularnewline
49 & 1.336 & 1.32491272753371 & 0.0110872724662903 \tabularnewline
50 & 1.3649 & 1.33053866311323 & 0.0343613368867743 \tabularnewline
51 & 1.3999 & 1.44145433742573 & -0.0415543374257326 \tabularnewline
52 & 1.4442 & 1.42971889264452 & 0.0144811073554769 \tabularnewline
53 & 1.4349 & 1.44255157367697 & -0.00765157367697378 \tabularnewline
54 & 1.4388 & 1.45303303212439 & -0.0142330321243895 \tabularnewline
55 & 1.4264 & 1.35808336104945 & 0.0683166389505505 \tabularnewline
56 & 1.4343 & 1.40942925253732 & 0.0248707474626801 \tabularnewline
57 & 1.377 & 1.4521562277879 & -0.0751562277878961 \tabularnewline
58 & 1.3706 & 1.39705437437454 & -0.0264543743745389 \tabularnewline
59 & 1.3556 & 1.4038403648777 & -0.0482403648777048 \tabularnewline
60 & 1.3179 & 1.33141383721169 & -0.0135138372116876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192530&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]1.4718[/C][C]1.36922168803419[/C][C]0.102578311965812[/C][/ROW]
[ROW][C]14[/C][C]1.4748[/C][C]1.47308688656561[/C][C]0.00171311343439018[/C][/ROW]
[ROW][C]15[/C][C]1.5527[/C][C]1.55759676020749[/C][C]-0.00489676020749075[/C][/ROW]
[ROW][C]16[/C][C]1.5751[/C][C]1.58932923077296[/C][C]-0.0142292307729635[/C][/ROW]
[ROW][C]17[/C][C]1.5557[/C][C]1.57981711859024[/C][C]-0.0241171185902351[/C][/ROW]
[ROW][C]18[/C][C]1.5553[/C][C]1.57994348555705[/C][C]-0.0246434855570534[/C][/ROW]
[ROW][C]19[/C][C]1.577[/C][C]1.48053253114811[/C][C]0.0964674688518932[/C][/ROW]
[ROW][C]20[/C][C]1.4975[/C][C]1.56641454770304[/C][C]-0.0689145477030444[/C][/ROW]
[ROW][C]21[/C][C]1.437[/C][C]1.52028855981586[/C][C]-0.0832885598158597[/C][/ROW]
[ROW][C]22[/C][C]1.3322[/C][C]1.4618607167296[/C][C]-0.129660716729603[/C][/ROW]
[ROW][C]23[/C][C]1.2732[/C][C]1.3686477890787[/C][C]-0.0954477890787013[/C][/ROW]
[ROW][C]24[/C][C]1.3449[/C][C]1.25148990318567[/C][C]0.093410096814333[/C][/ROW]
[ROW][C]25[/C][C]1.3239[/C][C]1.35080372025183[/C][C]-0.0269037202518294[/C][/ROW]
[ROW][C]26[/C][C]1.2785[/C][C]1.32084108262391[/C][C]-0.0423410826239057[/C][/ROW]
[ROW][C]27[/C][C]1.305[/C][C]1.35626844923925[/C][C]-0.0512684492392497[/C][/ROW]
[ROW][C]28[/C][C]1.319[/C][C]1.33588250915538[/C][C]-0.016882509155379[/C][/ROW]
[ROW][C]29[/C][C]1.365[/C][C]1.31792929121426[/C][C]0.0470707087857418[/C][/ROW]
[ROW][C]30[/C][C]1.4016[/C][C]1.38455853138579[/C][C]0.0170414686142084[/C][/ROW]
[ROW][C]31[/C][C]1.4088[/C][C]1.32279337866359[/C][C]0.0860066213364075[/C][/ROW]
[ROW][C]32[/C][C]1.4268[/C][C]1.39401333115718[/C][C]0.0327866688428229[/C][/ROW]
[ROW][C]33[/C][C]1.4562[/C][C]1.44696294335149[/C][C]0.00923705664850738[/C][/ROW]
[ROW][C]34[/C][C]1.4816[/C][C]1.47986854790523[/C][C]0.0017314520947711[/C][/ROW]
[ROW][C]35[/C][C]1.4914[/C][C]1.51889120565772[/C][C]-0.0274912056577208[/C][/ROW]
[ROW][C]36[/C][C]1.4614[/C][C]1.47158613311356[/C][C]-0.010186133113564[/C][/ROW]
[ROW][C]37[/C][C]1.4272[/C][C]1.4675949917155[/C][C]-0.0403949917154993[/C][/ROW]
[ROW][C]38[/C][C]1.3686[/C][C]1.42422334136246[/C][C]-0.0556233413624612[/C][/ROW]
[ROW][C]39[/C][C]1.3569[/C][C]1.44624493336997[/C][C]-0.089344933369971[/C][/ROW]
[ROW][C]40[/C][C]1.3406[/C][C]1.38706909560801[/C][C]-0.0464690956080078[/C][/ROW]
[ROW][C]41[/C][C]1.2565[/C][C]1.33835750922638[/C][C]-0.0818575092263774[/C][/ROW]
[ROW][C]42[/C][C]1.2209[/C][C]1.27288933660673[/C][C]-0.0519893366067279[/C][/ROW]
[ROW][C]43[/C][C]1.277[/C][C]1.13785472821796[/C][C]0.139145271782042[/C][/ROW]
[ROW][C]44[/C][C]1.2894[/C][C]1.25879792811031[/C][C]0.0306020718896893[/C][/ROW]
[ROW][C]45[/C][C]1.3067[/C][C]1.30611369556555[/C][C]0.000586304434446738[/C][/ROW]
[ROW][C]46[/C][C]1.3898[/C][C]1.32678527885232[/C][C]0.0630147211476766[/C][/ROW]
[ROW][C]47[/C][C]1.3661[/C][C]1.42445736402559[/C][C]-0.0583573640255854[/C][/ROW]
[ROW][C]48[/C][C]1.322[/C][C]1.34317409934871[/C][C]-0.0211740993487115[/C][/ROW]
[ROW][C]49[/C][C]1.336[/C][C]1.32491272753371[/C][C]0.0110872724662903[/C][/ROW]
[ROW][C]50[/C][C]1.3649[/C][C]1.33053866311323[/C][C]0.0343613368867743[/C][/ROW]
[ROW][C]51[/C][C]1.3999[/C][C]1.44145433742573[/C][C]-0.0415543374257326[/C][/ROW]
[ROW][C]52[/C][C]1.4442[/C][C]1.42971889264452[/C][C]0.0144811073554769[/C][/ROW]
[ROW][C]53[/C][C]1.4349[/C][C]1.44255157367697[/C][C]-0.00765157367697378[/C][/ROW]
[ROW][C]54[/C][C]1.4388[/C][C]1.45303303212439[/C][C]-0.0142330321243895[/C][/ROW]
[ROW][C]55[/C][C]1.4264[/C][C]1.35808336104945[/C][C]0.0683166389505505[/C][/ROW]
[ROW][C]56[/C][C]1.4343[/C][C]1.40942925253732[/C][C]0.0248707474626801[/C][/ROW]
[ROW][C]57[/C][C]1.377[/C][C]1.4521562277879[/C][C]-0.0751562277878961[/C][/ROW]
[ROW][C]58[/C][C]1.3706[/C][C]1.39705437437454[/C][C]-0.0264543743745389[/C][/ROW]
[ROW][C]59[/C][C]1.3556[/C][C]1.4038403648777[/C][C]-0.0482403648777048[/C][/ROW]
[ROW][C]60[/C][C]1.3179[/C][C]1.33141383721169[/C][C]-0.0135138372116876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192530&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192530&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
13	1.4718	1.36922168803419	0.102578311965812
14	1.4748	1.47308688656561	0.00171311343439018
15	1.5527	1.55759676020749	-0.00489676020749075
16	1.5751	1.58932923077296	-0.0142292307729635
17	1.5557	1.57981711859024	-0.0241171185902351
18	1.5553	1.57994348555705	-0.0246434855570534
19	1.577	1.48053253114811	0.0964674688518932
20	1.4975	1.56641454770304	-0.0689145477030444
21	1.437	1.52028855981586	-0.0832885598158597
22	1.3322	1.4618607167296	-0.129660716729603
23	1.2732	1.3686477890787	-0.0954477890787013
24	1.3449	1.25148990318567	0.093410096814333
25	1.3239	1.35080372025183	-0.0269037202518294
26	1.2785	1.32084108262391	-0.0423410826239057
27	1.305	1.35626844923925	-0.0512684492392497
28	1.319	1.33588250915538	-0.016882509155379
29	1.365	1.31792929121426	0.0470707087857418
30	1.4016	1.38455853138579	0.0170414686142084
31	1.4088	1.32279337866359	0.0860066213364075
32	1.4268	1.39401333115718	0.0327866688428229
33	1.4562	1.44696294335149	0.00923705664850738
34	1.4816	1.47986854790523	0.0017314520947711
35	1.4914	1.51889120565772	-0.0274912056577208
36	1.4614	1.47158613311356	-0.010186133113564
37	1.4272	1.4675949917155	-0.0403949917154993
38	1.3686	1.42422334136246	-0.0556233413624612
39	1.3569	1.44624493336997	-0.089344933369971
40	1.3406	1.38706909560801	-0.0464690956080078
41	1.2565	1.33835750922638	-0.0818575092263774
42	1.2209	1.27288933660673	-0.0519893366067279
43	1.277	1.13785472821796	0.139145271782042
44	1.2894	1.25879792811031	0.0306020718896893
45	1.3067	1.30611369556555	0.000586304434446738
46	1.3898	1.32678527885232	0.0630147211476766
47	1.3661	1.42445736402559	-0.0583573640255854
48	1.322	1.34317409934871	-0.0211740993487115
49	1.336	1.32491272753371	0.0110872724662903
50	1.3649	1.33053866311323	0.0343613368867743
51	1.3999	1.44145433742573	-0.0415543374257326
52	1.4442	1.42971889264452	0.0144811073554769
53	1.4349	1.44255157367697	-0.00765157367697378
54	1.4388	1.45303303212439	-0.0142330321243895
55	1.4264	1.35808336104945	0.0683166389505505
56	1.4343	1.40942925253732	0.0248707474626801
57	1.377	1.4521562277879	-0.0751562277878961
58	1.3706	1.39705437437454	-0.0264543743745389
59	1.3556	1.4038403648777	-0.0482403648777048
60	1.3179	1.33141383721169	-0.0135138372116876

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.31967114155472	1.20845310510302	1.43088917800643
62	1.31289644977611	1.15438733924082	1.47140556031141
63	1.38760509133084	1.1919702345253	1.58323994813637
64	1.41622206621889	1.18858426930935	1.64385986312843
65	1.41314737444028	1.15669273127317	1.6696020176074
66	1.42997268266167	1.14690204274379	1.71304332257956
67	1.3481688242164	1.04010241278497	1.65623523564782
68	1.32905246577112	0.997235194168392	1.66086973737385
69	1.34437777399251	0.989795923703727	1.6989596242813
70	1.3630655822139	0.986518623603141	1.73961254082466
71	1.39534922376863	0.997496726083828	1.79320172145342
72	1.37095369865668	0.952347415969675	1.78955998134369

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.31967114155472 & 1.20845310510302 & 1.43088917800643 \tabularnewline
62 & 1.31289644977611 & 1.15438733924082 & 1.47140556031141 \tabularnewline
63 & 1.38760509133084 & 1.1919702345253 & 1.58323994813637 \tabularnewline
64 & 1.41622206621889 & 1.18858426930935 & 1.64385986312843 \tabularnewline
65 & 1.41314737444028 & 1.15669273127317 & 1.6696020176074 \tabularnewline
66 & 1.42997268266167 & 1.14690204274379 & 1.71304332257956 \tabularnewline
67 & 1.3481688242164 & 1.04010241278497 & 1.65623523564782 \tabularnewline
68 & 1.32905246577112 & 0.997235194168392 & 1.66086973737385 \tabularnewline
69 & 1.34437777399251 & 0.989795923703727 & 1.6989596242813 \tabularnewline
70 & 1.3630655822139 & 0.986518623603141 & 1.73961254082466 \tabularnewline
71 & 1.39534922376863 & 0.997496726083828 & 1.79320172145342 \tabularnewline
72 & 1.37095369865668 & 0.952347415969675 & 1.78955998134369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192530&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]1.31967114155472[/C][C]1.20845310510302[/C][C]1.43088917800643[/C][/ROW]
[ROW][C]62[/C][C]1.31289644977611[/C][C]1.15438733924082[/C][C]1.47140556031141[/C][/ROW]
[ROW][C]63[/C][C]1.38760509133084[/C][C]1.1919702345253[/C][C]1.58323994813637[/C][/ROW]
[ROW][C]64[/C][C]1.41622206621889[/C][C]1.18858426930935[/C][C]1.64385986312843[/C][/ROW]
[ROW][C]65[/C][C]1.41314737444028[/C][C]1.15669273127317[/C][C]1.6696020176074[/C][/ROW]
[ROW][C]66[/C][C]1.42997268266167[/C][C]1.14690204274379[/C][C]1.71304332257956[/C][/ROW]
[ROW][C]67[/C][C]1.3481688242164[/C][C]1.04010241278497[/C][C]1.65623523564782[/C][/ROW]
[ROW][C]68[/C][C]1.32905246577112[/C][C]0.997235194168392[/C][C]1.66086973737385[/C][/ROW]
[ROW][C]69[/C][C]1.34437777399251[/C][C]0.989795923703727[/C][C]1.6989596242813[/C][/ROW]
[ROW][C]70[/C][C]1.3630655822139[/C][C]0.986518623603141[/C][C]1.73961254082466[/C][/ROW]
[ROW][C]71[/C][C]1.39534922376863[/C][C]0.997496726083828[/C][C]1.79320172145342[/C][/ROW]
[ROW][C]72[/C][C]1.37095369865668[/C][C]0.952347415969675[/C][C]1.78955998134369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192530&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192530&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	1.31967114155472	1.20845310510302	1.43088917800643
62	1.31289644977611	1.15438733924082	1.47140556031141
63	1.38760509133084	1.1919702345253	1.58323994813637
64	1.41622206621889	1.18858426930935	1.64385986312843
65	1.41314737444028	1.15669273127317	1.6696020176074
66	1.42997268266167	1.14690204274379	1.71304332257956
67	1.3481688242164	1.04010241278497	1.65623523564782
68	1.32905246577112	0.997235194168392	1.66086973737385
69	1.34437777399251	0.989795923703727	1.6989596242813
70	1.3630655822139	0.986518623603141	1.73961254082466
71	1.39534922376863	0.997496726083828	1.79320172145342
72	1.37095369865668	0.952347415969675	1.78955998134369

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 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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