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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 03 May 2017 20:15:23 +0100

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/2017/May/03/t1493838942e7udx0kn3wj9wop.htm/, Retrieved Fri, 17 May 2024 06:59:32 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 06:59:32 +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	'Herman Ole Andreas Wold' @ wold.wessa.net

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

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.626892786049989
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.626892786049989 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \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]0.626892786049989[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/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	0.626892786049989
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	99.87	100.085707799145	-0.215707799145335
14	100.51	100.564015061374	-0.0540150613743151
15	100.27	100.314936334469	-0.0449363344686304
16	100.04	100.112798995967	-0.0727989959666644
17	99.23	99.3065280893047	-0.0765280893047304
18	99.32	99.3258361075973	-0.00583610759730391
19	99.95	99.0857104192539	0.864289580746117
20	100.23	101.009393581223	-0.779393581223061
21	101.02	101.304746959735	-0.284746959735244
22	99.83	100.681024070235	-0.851024070235468
23	99.61	99.1018894785912	0.508110521408767
24	100.12	99.0602032243864	1.05979677561359
25	99.83	99.5022163004725	0.327783699527529
26	100.03	100.381563189405	-0.351563189404658
27	100.07	99.9493410260361	0.120658973963941
28	100.46	99.8406184317895	0.619381568210542
29	100.43	99.4668791758283	0.963120824171696
30	100.68	100.164311286347	0.515688713652594
31	101.8	100.575775917556	1.22422408244428
32	101.21	102.111829376911	-0.90182937691111
33	100.63	102.514984861185	-1.88498486118526
34	100.55	100.67680230028	-0.126802300280289
35	99.76	100.058780032593	-0.298780032592759
36	98.8	99.7170980322334	-0.917098032233397
37	96.59	98.6466906551071	-2.05669065510705
38	97.59	97.7777585475625	-0.187758547562538
39	98.79	97.6244138282262	1.16558617177385
40	98.79	98.3568255539073	0.433174446092721
41	99.65	97.9946059924963	1.65539400750373
42	99.78	98.9590790194345	0.820920980565461
43	100.05	99.8262512142751	0.223748785724879
44	99.22	99.941868044567	-0.721868044567017
45	97.72	100.091017586238	-2.37101758623842
46	97.55	98.6041352131282	-1.05413521312818
47	98.14	97.340608499545	0.799391500454959
48	97.95	97.4566634049177	0.493336595082326
49	97.24	96.8452570922923	0.394742907707709
50	97.02	98.2104230524648	-1.19042305246482
51	97.57	97.9334578659224	-0.363457865922371
52	98.07	97.4340548163858	0.635945183614226
53	98.86	97.6549697029423	1.20503029705772
54	99.57	98.0257650625059	1.54423493749412
55	100.14	99.1235683051289	1.01643169487107
56	99.88	99.3832958717752	0.496704128224749
57	99.79	99.6810499269711	0.108950073028893
58	100.59	100.240179702424	0.349820297576144
59	100.55	100.548346758523	0.00165324147668855
60	101.42	100.050114011127	1.36988598887294

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 99.87 & 100.085707799145 & -0.215707799145335 \tabularnewline
14 & 100.51 & 100.564015061374 & -0.0540150613743151 \tabularnewline
15 & 100.27 & 100.314936334469 & -0.0449363344686304 \tabularnewline
16 & 100.04 & 100.112798995967 & -0.0727989959666644 \tabularnewline
17 & 99.23 & 99.3065280893047 & -0.0765280893047304 \tabularnewline
18 & 99.32 & 99.3258361075973 & -0.00583610759730391 \tabularnewline
19 & 99.95 & 99.0857104192539 & 0.864289580746117 \tabularnewline
20 & 100.23 & 101.009393581223 & -0.779393581223061 \tabularnewline
21 & 101.02 & 101.304746959735 & -0.284746959735244 \tabularnewline
22 & 99.83 & 100.681024070235 & -0.851024070235468 \tabularnewline
23 & 99.61 & 99.1018894785912 & 0.508110521408767 \tabularnewline
24 & 100.12 & 99.0602032243864 & 1.05979677561359 \tabularnewline
25 & 99.83 & 99.5022163004725 & 0.327783699527529 \tabularnewline
26 & 100.03 & 100.381563189405 & -0.351563189404658 \tabularnewline
27 & 100.07 & 99.9493410260361 & 0.120658973963941 \tabularnewline
28 & 100.46 & 99.8406184317895 & 0.619381568210542 \tabularnewline
29 & 100.43 & 99.4668791758283 & 0.963120824171696 \tabularnewline
30 & 100.68 & 100.164311286347 & 0.515688713652594 \tabularnewline
31 & 101.8 & 100.575775917556 & 1.22422408244428 \tabularnewline
32 & 101.21 & 102.111829376911 & -0.90182937691111 \tabularnewline
33 & 100.63 & 102.514984861185 & -1.88498486118526 \tabularnewline
34 & 100.55 & 100.67680230028 & -0.126802300280289 \tabularnewline
35 & 99.76 & 100.058780032593 & -0.298780032592759 \tabularnewline
36 & 98.8 & 99.7170980322334 & -0.917098032233397 \tabularnewline
37 & 96.59 & 98.6466906551071 & -2.05669065510705 \tabularnewline
38 & 97.59 & 97.7777585475625 & -0.187758547562538 \tabularnewline
39 & 98.79 & 97.6244138282262 & 1.16558617177385 \tabularnewline
40 & 98.79 & 98.3568255539073 & 0.433174446092721 \tabularnewline
41 & 99.65 & 97.9946059924963 & 1.65539400750373 \tabularnewline
42 & 99.78 & 98.9590790194345 & 0.820920980565461 \tabularnewline
43 & 100.05 & 99.8262512142751 & 0.223748785724879 \tabularnewline
44 & 99.22 & 99.941868044567 & -0.721868044567017 \tabularnewline
45 & 97.72 & 100.091017586238 & -2.37101758623842 \tabularnewline
46 & 97.55 & 98.6041352131282 & -1.05413521312818 \tabularnewline
47 & 98.14 & 97.340608499545 & 0.799391500454959 \tabularnewline
48 & 97.95 & 97.4566634049177 & 0.493336595082326 \tabularnewline
49 & 97.24 & 96.8452570922923 & 0.394742907707709 \tabularnewline
50 & 97.02 & 98.2104230524648 & -1.19042305246482 \tabularnewline
51 & 97.57 & 97.9334578659224 & -0.363457865922371 \tabularnewline
52 & 98.07 & 97.4340548163858 & 0.635945183614226 \tabularnewline
53 & 98.86 & 97.6549697029423 & 1.20503029705772 \tabularnewline
54 & 99.57 & 98.0257650625059 & 1.54423493749412 \tabularnewline
55 & 100.14 & 99.1235683051289 & 1.01643169487107 \tabularnewline
56 & 99.88 & 99.3832958717752 & 0.496704128224749 \tabularnewline
57 & 99.79 & 99.6810499269711 & 0.108950073028893 \tabularnewline
58 & 100.59 & 100.240179702424 & 0.349820297576144 \tabularnewline
59 & 100.55 & 100.548346758523 & 0.00165324147668855 \tabularnewline
60 & 101.42 & 100.050114011127 & 1.36988598887294 \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]13[/C][C]99.87[/C][C]100.085707799145[/C][C]-0.215707799145335[/C][/ROW]
[ROW][C]14[/C][C]100.51[/C][C]100.564015061374[/C][C]-0.0540150613743151[/C][/ROW]
[ROW][C]15[/C][C]100.27[/C][C]100.314936334469[/C][C]-0.0449363344686304[/C][/ROW]
[ROW][C]16[/C][C]100.04[/C][C]100.112798995967[/C][C]-0.0727989959666644[/C][/ROW]
[ROW][C]17[/C][C]99.23[/C][C]99.3065280893047[/C][C]-0.0765280893047304[/C][/ROW]
[ROW][C]18[/C][C]99.32[/C][C]99.3258361075973[/C][C]-0.00583610759730391[/C][/ROW]
[ROW][C]19[/C][C]99.95[/C][C]99.0857104192539[/C][C]0.864289580746117[/C][/ROW]
[ROW][C]20[/C][C]100.23[/C][C]101.009393581223[/C][C]-0.779393581223061[/C][/ROW]
[ROW][C]21[/C][C]101.02[/C][C]101.304746959735[/C][C]-0.284746959735244[/C][/ROW]
[ROW][C]22[/C][C]99.83[/C][C]100.681024070235[/C][C]-0.851024070235468[/C][/ROW]
[ROW][C]23[/C][C]99.61[/C][C]99.1018894785912[/C][C]0.508110521408767[/C][/ROW]
[ROW][C]24[/C][C]100.12[/C][C]99.0602032243864[/C][C]1.05979677561359[/C][/ROW]
[ROW][C]25[/C][C]99.83[/C][C]99.5022163004725[/C][C]0.327783699527529[/C][/ROW]
[ROW][C]26[/C][C]100.03[/C][C]100.381563189405[/C][C]-0.351563189404658[/C][/ROW]
[ROW][C]27[/C][C]100.07[/C][C]99.9493410260361[/C][C]0.120658973963941[/C][/ROW]
[ROW][C]28[/C][C]100.46[/C][C]99.8406184317895[/C][C]0.619381568210542[/C][/ROW]
[ROW][C]29[/C][C]100.43[/C][C]99.4668791758283[/C][C]0.963120824171696[/C][/ROW]
[ROW][C]30[/C][C]100.68[/C][C]100.164311286347[/C][C]0.515688713652594[/C][/ROW]
[ROW][C]31[/C][C]101.8[/C][C]100.575775917556[/C][C]1.22422408244428[/C][/ROW]
[ROW][C]32[/C][C]101.21[/C][C]102.111829376911[/C][C]-0.90182937691111[/C][/ROW]
[ROW][C]33[/C][C]100.63[/C][C]102.514984861185[/C][C]-1.88498486118526[/C][/ROW]
[ROW][C]34[/C][C]100.55[/C][C]100.67680230028[/C][C]-0.126802300280289[/C][/ROW]
[ROW][C]35[/C][C]99.76[/C][C]100.058780032593[/C][C]-0.298780032592759[/C][/ROW]
[ROW][C]36[/C][C]98.8[/C][C]99.7170980322334[/C][C]-0.917098032233397[/C][/ROW]
[ROW][C]37[/C][C]96.59[/C][C]98.6466906551071[/C][C]-2.05669065510705[/C][/ROW]
[ROW][C]38[/C][C]97.59[/C][C]97.7777585475625[/C][C]-0.187758547562538[/C][/ROW]
[ROW][C]39[/C][C]98.79[/C][C]97.6244138282262[/C][C]1.16558617177385[/C][/ROW]
[ROW][C]40[/C][C]98.79[/C][C]98.3568255539073[/C][C]0.433174446092721[/C][/ROW]
[ROW][C]41[/C][C]99.65[/C][C]97.9946059924963[/C][C]1.65539400750373[/C][/ROW]
[ROW][C]42[/C][C]99.78[/C][C]98.9590790194345[/C][C]0.820920980565461[/C][/ROW]
[ROW][C]43[/C][C]100.05[/C][C]99.8262512142751[/C][C]0.223748785724879[/C][/ROW]
[ROW][C]44[/C][C]99.22[/C][C]99.941868044567[/C][C]-0.721868044567017[/C][/ROW]
[ROW][C]45[/C][C]97.72[/C][C]100.091017586238[/C][C]-2.37101758623842[/C][/ROW]
[ROW][C]46[/C][C]97.55[/C][C]98.6041352131282[/C][C]-1.05413521312818[/C][/ROW]
[ROW][C]47[/C][C]98.14[/C][C]97.340608499545[/C][C]0.799391500454959[/C][/ROW]
[ROW][C]48[/C][C]97.95[/C][C]97.4566634049177[/C][C]0.493336595082326[/C][/ROW]
[ROW][C]49[/C][C]97.24[/C][C]96.8452570922923[/C][C]0.394742907707709[/C][/ROW]
[ROW][C]50[/C][C]97.02[/C][C]98.2104230524648[/C][C]-1.19042305246482[/C][/ROW]
[ROW][C]51[/C][C]97.57[/C][C]97.9334578659224[/C][C]-0.363457865922371[/C][/ROW]
[ROW][C]52[/C][C]98.07[/C][C]97.4340548163858[/C][C]0.635945183614226[/C][/ROW]
[ROW][C]53[/C][C]98.86[/C][C]97.6549697029423[/C][C]1.20503029705772[/C][/ROW]
[ROW][C]54[/C][C]99.57[/C][C]98.0257650625059[/C][C]1.54423493749412[/C][/ROW]
[ROW][C]55[/C][C]100.14[/C][C]99.1235683051289[/C][C]1.01643169487107[/C][/ROW]
[ROW][C]56[/C][C]99.88[/C][C]99.3832958717752[/C][C]0.496704128224749[/C][/ROW]
[ROW][C]57[/C][C]99.79[/C][C]99.6810499269711[/C][C]0.108950073028893[/C][/ROW]
[ROW][C]58[/C][C]100.59[/C][C]100.240179702424[/C][C]0.349820297576144[/C][/ROW]
[ROW][C]59[/C][C]100.55[/C][C]100.548346758523[/C][C]0.00165324147668855[/C][/ROW]
[ROW][C]60[/C][C]101.42[/C][C]100.050114011127[/C][C]1.36988598887294[/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
13	99.87	100.085707799145	-0.215707799145335
14	100.51	100.564015061374	-0.0540150613743151
15	100.27	100.314936334469	-0.0449363344686304
16	100.04	100.112798995967	-0.0727989959666644
17	99.23	99.3065280893047	-0.0765280893047304
18	99.32	99.3258361075973	-0.00583610759730391
19	99.95	99.0857104192539	0.864289580746117
20	100.23	101.009393581223	-0.779393581223061
21	101.02	101.304746959735	-0.284746959735244
22	99.83	100.681024070235	-0.851024070235468
23	99.61	99.1018894785912	0.508110521408767
24	100.12	99.0602032243864	1.05979677561359
25	99.83	99.5022163004725	0.327783699527529
26	100.03	100.381563189405	-0.351563189404658
27	100.07	99.9493410260361	0.120658973963941
28	100.46	99.8406184317895	0.619381568210542
29	100.43	99.4668791758283	0.963120824171696
30	100.68	100.164311286347	0.515688713652594
31	101.8	100.575775917556	1.22422408244428
32	101.21	102.111829376911	-0.90182937691111
33	100.63	102.514984861185	-1.88498486118526
34	100.55	100.67680230028	-0.126802300280289
35	99.76	100.058780032593	-0.298780032592759
36	98.8	99.7170980322334	-0.917098032233397
37	96.59	98.6466906551071	-2.05669065510705
38	97.59	97.7777585475625	-0.187758547562538
39	98.79	97.6244138282262	1.16558617177385
40	98.79	98.3568255539073	0.433174446092721
41	99.65	97.9946059924963	1.65539400750373
42	99.78	98.9590790194345	0.820920980565461
43	100.05	99.8262512142751	0.223748785724879
44	99.22	99.941868044567	-0.721868044567017
45	97.72	100.091017586238	-2.37101758623842
46	97.55	98.6041352131282	-1.05413521312818
47	98.14	97.340608499545	0.799391500454959
48	97.95	97.4566634049177	0.493336595082326
49	97.24	96.8452570922923	0.394742907707709
50	97.02	98.2104230524648	-1.19042305246482
51	97.57	97.9334578659224	-0.363457865922371
52	98.07	97.4340548163858	0.635945183614226
53	98.86	97.6549697029423	1.20503029705772
54	99.57	98.0257650625059	1.54423493749412
55	100.14	99.1235683051289	1.01643169487107
56	99.88	99.3832958717752	0.496704128224749
57	99.79	99.6810499269711	0.108950073028893
58	100.59	100.240179702424	0.349820297576144
59	100.55	100.548346758523	0.00165324147668855
60	101.42	100.050114011127	1.36988598887294

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	99.9514241740761	98.1766956531547	101.726152694998
62	100.477691798014	98.3830650758685	102.572318520159
63	101.255540912194	98.8837776678376	103.62730415655
64	101.356871464263	98.7371270741681	103.976615854357
65	101.391446664066	98.5452456079935	104.237647720138
66	101.133376921784	98.077454764114	104.189299079454
67	101.066183224757	97.8140362391653	104.318330210349
68	100.494802989972	97.0576152153445	103.931990764599
69	100.33650297515	96.723739548049	103.949266402251
70	100.917203154186	97.1370101217663	104.697396186605
71	100.87616674903	96.9356516628385	104.816681835222
72	100.887395104895	96.7928305460366	104.981959663754

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 99.9514241740761 & 98.1766956531547 & 101.726152694998 \tabularnewline
62 & 100.477691798014 & 98.3830650758685 & 102.572318520159 \tabularnewline
63 & 101.255540912194 & 98.8837776678376 & 103.62730415655 \tabularnewline
64 & 101.356871464263 & 98.7371270741681 & 103.976615854357 \tabularnewline
65 & 101.391446664066 & 98.5452456079935 & 104.237647720138 \tabularnewline
66 & 101.133376921784 & 98.077454764114 & 104.189299079454 \tabularnewline
67 & 101.066183224757 & 97.8140362391653 & 104.318330210349 \tabularnewline
68 & 100.494802989972 & 97.0576152153445 & 103.931990764599 \tabularnewline
69 & 100.33650297515 & 96.723739548049 & 103.949266402251 \tabularnewline
70 & 100.917203154186 & 97.1370101217663 & 104.697396186605 \tabularnewline
71 & 100.87616674903 & 96.9356516628385 & 104.816681835222 \tabularnewline
72 & 100.887395104895 & 96.7928305460366 & 104.981959663754 \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]99.9514241740761[/C][C]98.1766956531547[/C][C]101.726152694998[/C][/ROW]
[ROW][C]62[/C][C]100.477691798014[/C][C]98.3830650758685[/C][C]102.572318520159[/C][/ROW]
[ROW][C]63[/C][C]101.255540912194[/C][C]98.8837776678376[/C][C]103.62730415655[/C][/ROW]
[ROW][C]64[/C][C]101.356871464263[/C][C]98.7371270741681[/C][C]103.976615854357[/C][/ROW]
[ROW][C]65[/C][C]101.391446664066[/C][C]98.5452456079935[/C][C]104.237647720138[/C][/ROW]
[ROW][C]66[/C][C]101.133376921784[/C][C]98.077454764114[/C][C]104.189299079454[/C][/ROW]
[ROW][C]67[/C][C]101.066183224757[/C][C]97.8140362391653[/C][C]104.318330210349[/C][/ROW]
[ROW][C]68[/C][C]100.494802989972[/C][C]97.0576152153445[/C][C]103.931990764599[/C][/ROW]
[ROW][C]69[/C][C]100.33650297515[/C][C]96.723739548049[/C][C]103.949266402251[/C][/ROW]
[ROW][C]70[/C][C]100.917203154186[/C][C]97.1370101217663[/C][C]104.697396186605[/C][/ROW]
[ROW][C]71[/C][C]100.87616674903[/C][C]96.9356516628385[/C][C]104.816681835222[/C][/ROW]
[ROW][C]72[/C][C]100.887395104895[/C][C]96.7928305460366[/C][C]104.981959663754[/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	99.9514241740761	98.1766956531547	101.726152694998
62	100.477691798014	98.3830650758685	102.572318520159
63	101.255540912194	98.8837776678376	103.62730415655
64	101.356871464263	98.7371270741681	103.976615854357
65	101.391446664066	98.5452456079935	104.237647720138
66	101.133376921784	98.077454764114	104.189299079454
67	101.066183224757	97.8140362391653	104.318330210349
68	100.494802989972	97.0576152153445	103.931990764599
69	100.33650297515	96.723739548049	103.949266402251
70	100.917203154186	97.1370101217663	104.697396186605
71	100.87616674903	96.9356516628385	104.816681835222
72	100.887395104895	96.7928305460366	104.981959663754

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