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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 28 Dec 2012 05:21:13 -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/28/t1356690098xyzl4xg0bts069m.htm/, Retrieved Mon, 29 Apr 2024 12:43:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204809, Retrieved Mon, 29 Apr 2024 12:43:17 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

129

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

-       [Exponential Smoothing] [Exponential Smoot...] [2012-12-28 10:21:13] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Histogram

Boxplots

0,75
0,75
0,77
0,78
0,79
1,01
1,16
1,14
1,12
1,1
1,1
1,1
1,1
1,09
1,09
1,1
1,1
1,17
1,15
1,04
0,94
0,88
0,85
0,85
0,85
0,84
0,83
0,8
0,78
1,02
1,19
1,1
0,96
0,87
0,83
0,82
0,81
0,78
0,79
0,8
0,79
0,97
1,01
0,92
0,87
0,84
0,81
0,81
0,83
0,83
0,85
0,88
0,89
1,21
1,32
1,33
1,23
1,16
1,12
1,06
1,08
1,09
1,03
1,04
1,05
1,19
1,14
1,05
0,95
0,87
0,86
0,85

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 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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204809&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204809&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204809&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 Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	0.0933640247397515

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.0933640247397515 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204809&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.0933640247397515[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204809&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204809&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
gamma	0.0933640247397515

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.1	0.971949306883722	0.128050693116278
14	1.09	1.10018059402938	-0.0101805940293789
15	1.09	1.10732374385202	-0.0173237438520151
16	1.1	1.12284092982282	-0.0228409298228189
17	1.1	1.12628557988237	-0.0262855798823682
18	1.17	1.19992382320372	-0.0299238232037207
19	1.15	1.23993237798446	-0.0899323779844634
20	1.04	1.10445777277797	-0.0644577727779709
21	0.94	1.00085698008531	-0.0608569800853145
22	0.88	0.906010069731035	-0.0260100697310353
23	0.85	0.864607189567366	-0.014607189567366
24	0.85	0.840707062438071	0.00929293756192895
25	0.85	0.850935043756226	-0.000935043756226106
26	0.84	0.851429654885878	-0.0114296548858778
27	0.83	0.85466618880266	-0.0246661888026604
28	0.8	0.85640957447208	-0.0564095744720802
29	0.78	0.820749655265172	-0.0407496552651717
30	1.02	0.852744735571289	0.167255264428711
31	1.19	1.08184437545202	0.108155624547984
32	1.1	1.14264635838591	-0.0426463583859114
33	0.96	1.05823811407972	-0.0982381140797211
34	0.87	0.925159542707039	-0.0551595427070388
35	0.83	0.854848476430637	-0.0248484764306367
36	0.82	0.821060711798492	-0.00106071179849232
37	0.81	0.821103393924576	-0.0111033939245762
38	0.78	0.811629504622918	-0.0316295046229176
39	0.79	0.794028375590815	-0.00402837559081515
40	0.8	0.815420135187351	-0.0154201351873511
41	0.79	0.820749655265172	-0.0307496552651717
42	0.97	0.863594082059802	0.106405917940198
43	1.01	1.02914837460787	-0.0191483746078676
44	0.92	0.97079772315018	-0.0507977231501795
45	0.87	0.886094712096502	-0.0160947120965019
46	0.84	0.838986914315023	0.00101308568497727
47	0.81	0.825572337020449	-0.0155723370204489
48	0.81	0.801414361158914	0.00858563884108632
49	0.83	0.81115951064736	0.0188404893526403
50	0.83	0.831529579754398	-0.00152957975439771
51	0.85	0.844559886600686	0.00544011339931383
52	0.88	0.876904294114445	0.0030957058855553
53	0.89	0.902225901829757	-0.0122259018297575
54	1.21	0.972087546944937	0.237912453055063
55	1.32	1.28208917865978	0.0379108213402175
56	1.33	1.26675926161172	0.0632407383882818
57	1.23	1.27819912772494	-0.0481991277249449
58	1.16	1.18367742788309	-0.0236774278830874
59	1.12	1.13785115739578	-0.017851157395784
60	1.06	1.10593279607238	-0.0459327960723825
61	1.08	1.05975659257777	0.0202434074222251
62	1.09	1.0802805188979	0.00971948110210108
63	1.03	1.10732374385202	-0.0773237438520151
64	1.04	1.06135677089573	-0.0213567708957254
65	1.05	1.06517839495893	-0.0151783949589288
66	1.19	1.14567709076115	0.0443229092388469
67	1.14	1.26101077832212	-0.121010778322123
68	1.05	1.09491062637599	-0.044910626375986
69	0.95	1.01042050241772	-0.0604205024177158
70	0.87	0.915584806219037	-0.045584806219037
71	0.86	0.854848476430637	0.00515152356936333
72	0.85	0.85053023775786	-0.000530237757860319

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.1 & 0.971949306883722 & 0.128050693116278 \tabularnewline
14 & 1.09 & 1.10018059402938 & -0.0101805940293789 \tabularnewline
15 & 1.09 & 1.10732374385202 & -0.0173237438520151 \tabularnewline
16 & 1.1 & 1.12284092982282 & -0.0228409298228189 \tabularnewline
17 & 1.1 & 1.12628557988237 & -0.0262855798823682 \tabularnewline
18 & 1.17 & 1.19992382320372 & -0.0299238232037207 \tabularnewline
19 & 1.15 & 1.23993237798446 & -0.0899323779844634 \tabularnewline
20 & 1.04 & 1.10445777277797 & -0.0644577727779709 \tabularnewline
21 & 0.94 & 1.00085698008531 & -0.0608569800853145 \tabularnewline
22 & 0.88 & 0.906010069731035 & -0.0260100697310353 \tabularnewline
23 & 0.85 & 0.864607189567366 & -0.014607189567366 \tabularnewline
24 & 0.85 & 0.840707062438071 & 0.00929293756192895 \tabularnewline
25 & 0.85 & 0.850935043756226 & -0.000935043756226106 \tabularnewline
26 & 0.84 & 0.851429654885878 & -0.0114296548858778 \tabularnewline
27 & 0.83 & 0.85466618880266 & -0.0246661888026604 \tabularnewline
28 & 0.8 & 0.85640957447208 & -0.0564095744720802 \tabularnewline
29 & 0.78 & 0.820749655265172 & -0.0407496552651717 \tabularnewline
30 & 1.02 & 0.852744735571289 & 0.167255264428711 \tabularnewline
31 & 1.19 & 1.08184437545202 & 0.108155624547984 \tabularnewline
32 & 1.1 & 1.14264635838591 & -0.0426463583859114 \tabularnewline
33 & 0.96 & 1.05823811407972 & -0.0982381140797211 \tabularnewline
34 & 0.87 & 0.925159542707039 & -0.0551595427070388 \tabularnewline
35 & 0.83 & 0.854848476430637 & -0.0248484764306367 \tabularnewline
36 & 0.82 & 0.821060711798492 & -0.00106071179849232 \tabularnewline
37 & 0.81 & 0.821103393924576 & -0.0111033939245762 \tabularnewline
38 & 0.78 & 0.811629504622918 & -0.0316295046229176 \tabularnewline
39 & 0.79 & 0.794028375590815 & -0.00402837559081515 \tabularnewline
40 & 0.8 & 0.815420135187351 & -0.0154201351873511 \tabularnewline
41 & 0.79 & 0.820749655265172 & -0.0307496552651717 \tabularnewline
42 & 0.97 & 0.863594082059802 & 0.106405917940198 \tabularnewline
43 & 1.01 & 1.02914837460787 & -0.0191483746078676 \tabularnewline
44 & 0.92 & 0.97079772315018 & -0.0507977231501795 \tabularnewline
45 & 0.87 & 0.886094712096502 & -0.0160947120965019 \tabularnewline
46 & 0.84 & 0.838986914315023 & 0.00101308568497727 \tabularnewline
47 & 0.81 & 0.825572337020449 & -0.0155723370204489 \tabularnewline
48 & 0.81 & 0.801414361158914 & 0.00858563884108632 \tabularnewline
49 & 0.83 & 0.81115951064736 & 0.0188404893526403 \tabularnewline
50 & 0.83 & 0.831529579754398 & -0.00152957975439771 \tabularnewline
51 & 0.85 & 0.844559886600686 & 0.00544011339931383 \tabularnewline
52 & 0.88 & 0.876904294114445 & 0.0030957058855553 \tabularnewline
53 & 0.89 & 0.902225901829757 & -0.0122259018297575 \tabularnewline
54 & 1.21 & 0.972087546944937 & 0.237912453055063 \tabularnewline
55 & 1.32 & 1.28208917865978 & 0.0379108213402175 \tabularnewline
56 & 1.33 & 1.26675926161172 & 0.0632407383882818 \tabularnewline
57 & 1.23 & 1.27819912772494 & -0.0481991277249449 \tabularnewline
58 & 1.16 & 1.18367742788309 & -0.0236774278830874 \tabularnewline
59 & 1.12 & 1.13785115739578 & -0.017851157395784 \tabularnewline
60 & 1.06 & 1.10593279607238 & -0.0459327960723825 \tabularnewline
61 & 1.08 & 1.05975659257777 & 0.0202434074222251 \tabularnewline
62 & 1.09 & 1.0802805188979 & 0.00971948110210108 \tabularnewline
63 & 1.03 & 1.10732374385202 & -0.0773237438520151 \tabularnewline
64 & 1.04 & 1.06135677089573 & -0.0213567708957254 \tabularnewline
65 & 1.05 & 1.06517839495893 & -0.0151783949589288 \tabularnewline
66 & 1.19 & 1.14567709076115 & 0.0443229092388469 \tabularnewline
67 & 1.14 & 1.26101077832212 & -0.121010778322123 \tabularnewline
68 & 1.05 & 1.09491062637599 & -0.044910626375986 \tabularnewline
69 & 0.95 & 1.01042050241772 & -0.0604205024177158 \tabularnewline
70 & 0.87 & 0.915584806219037 & -0.045584806219037 \tabularnewline
71 & 0.86 & 0.854848476430637 & 0.00515152356936333 \tabularnewline
72 & 0.85 & 0.85053023775786 & -0.000530237757860319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204809&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]1.1[/C][C]0.971949306883722[/C][C]0.128050693116278[/C][/ROW]
[ROW][C]14[/C][C]1.09[/C][C]1.10018059402938[/C][C]-0.0101805940293789[/C][/ROW]
[ROW][C]15[/C][C]1.09[/C][C]1.10732374385202[/C][C]-0.0173237438520151[/C][/ROW]
[ROW][C]16[/C][C]1.1[/C][C]1.12284092982282[/C][C]-0.0228409298228189[/C][/ROW]
[ROW][C]17[/C][C]1.1[/C][C]1.12628557988237[/C][C]-0.0262855798823682[/C][/ROW]
[ROW][C]18[/C][C]1.17[/C][C]1.19992382320372[/C][C]-0.0299238232037207[/C][/ROW]
[ROW][C]19[/C][C]1.15[/C][C]1.23993237798446[/C][C]-0.0899323779844634[/C][/ROW]
[ROW][C]20[/C][C]1.04[/C][C]1.10445777277797[/C][C]-0.0644577727779709[/C][/ROW]
[ROW][C]21[/C][C]0.94[/C][C]1.00085698008531[/C][C]-0.0608569800853145[/C][/ROW]
[ROW][C]22[/C][C]0.88[/C][C]0.906010069731035[/C][C]-0.0260100697310353[/C][/ROW]
[ROW][C]23[/C][C]0.85[/C][C]0.864607189567366[/C][C]-0.014607189567366[/C][/ROW]
[ROW][C]24[/C][C]0.85[/C][C]0.840707062438071[/C][C]0.00929293756192895[/C][/ROW]
[ROW][C]25[/C][C]0.85[/C][C]0.850935043756226[/C][C]-0.000935043756226106[/C][/ROW]
[ROW][C]26[/C][C]0.84[/C][C]0.851429654885878[/C][C]-0.0114296548858778[/C][/ROW]
[ROW][C]27[/C][C]0.83[/C][C]0.85466618880266[/C][C]-0.0246661888026604[/C][/ROW]
[ROW][C]28[/C][C]0.8[/C][C]0.85640957447208[/C][C]-0.0564095744720802[/C][/ROW]
[ROW][C]29[/C][C]0.78[/C][C]0.820749655265172[/C][C]-0.0407496552651717[/C][/ROW]
[ROW][C]30[/C][C]1.02[/C][C]0.852744735571289[/C][C]0.167255264428711[/C][/ROW]
[ROW][C]31[/C][C]1.19[/C][C]1.08184437545202[/C][C]0.108155624547984[/C][/ROW]
[ROW][C]32[/C][C]1.1[/C][C]1.14264635838591[/C][C]-0.0426463583859114[/C][/ROW]
[ROW][C]33[/C][C]0.96[/C][C]1.05823811407972[/C][C]-0.0982381140797211[/C][/ROW]
[ROW][C]34[/C][C]0.87[/C][C]0.925159542707039[/C][C]-0.0551595427070388[/C][/ROW]
[ROW][C]35[/C][C]0.83[/C][C]0.854848476430637[/C][C]-0.0248484764306367[/C][/ROW]
[ROW][C]36[/C][C]0.82[/C][C]0.821060711798492[/C][C]-0.00106071179849232[/C][/ROW]
[ROW][C]37[/C][C]0.81[/C][C]0.821103393924576[/C][C]-0.0111033939245762[/C][/ROW]
[ROW][C]38[/C][C]0.78[/C][C]0.811629504622918[/C][C]-0.0316295046229176[/C][/ROW]
[ROW][C]39[/C][C]0.79[/C][C]0.794028375590815[/C][C]-0.00402837559081515[/C][/ROW]
[ROW][C]40[/C][C]0.8[/C][C]0.815420135187351[/C][C]-0.0154201351873511[/C][/ROW]
[ROW][C]41[/C][C]0.79[/C][C]0.820749655265172[/C][C]-0.0307496552651717[/C][/ROW]
[ROW][C]42[/C][C]0.97[/C][C]0.863594082059802[/C][C]0.106405917940198[/C][/ROW]
[ROW][C]43[/C][C]1.01[/C][C]1.02914837460787[/C][C]-0.0191483746078676[/C][/ROW]
[ROW][C]44[/C][C]0.92[/C][C]0.97079772315018[/C][C]-0.0507977231501795[/C][/ROW]
[ROW][C]45[/C][C]0.87[/C][C]0.886094712096502[/C][C]-0.0160947120965019[/C][/ROW]
[ROW][C]46[/C][C]0.84[/C][C]0.838986914315023[/C][C]0.00101308568497727[/C][/ROW]
[ROW][C]47[/C][C]0.81[/C][C]0.825572337020449[/C][C]-0.0155723370204489[/C][/ROW]
[ROW][C]48[/C][C]0.81[/C][C]0.801414361158914[/C][C]0.00858563884108632[/C][/ROW]
[ROW][C]49[/C][C]0.83[/C][C]0.81115951064736[/C][C]0.0188404893526403[/C][/ROW]
[ROW][C]50[/C][C]0.83[/C][C]0.831529579754398[/C][C]-0.00152957975439771[/C][/ROW]
[ROW][C]51[/C][C]0.85[/C][C]0.844559886600686[/C][C]0.00544011339931383[/C][/ROW]
[ROW][C]52[/C][C]0.88[/C][C]0.876904294114445[/C][C]0.0030957058855553[/C][/ROW]
[ROW][C]53[/C][C]0.89[/C][C]0.902225901829757[/C][C]-0.0122259018297575[/C][/ROW]
[ROW][C]54[/C][C]1.21[/C][C]0.972087546944937[/C][C]0.237912453055063[/C][/ROW]
[ROW][C]55[/C][C]1.32[/C][C]1.28208917865978[/C][C]0.0379108213402175[/C][/ROW]
[ROW][C]56[/C][C]1.33[/C][C]1.26675926161172[/C][C]0.0632407383882818[/C][/ROW]
[ROW][C]57[/C][C]1.23[/C][C]1.27819912772494[/C][C]-0.0481991277249449[/C][/ROW]
[ROW][C]58[/C][C]1.16[/C][C]1.18367742788309[/C][C]-0.0236774278830874[/C][/ROW]
[ROW][C]59[/C][C]1.12[/C][C]1.13785115739578[/C][C]-0.017851157395784[/C][/ROW]
[ROW][C]60[/C][C]1.06[/C][C]1.10593279607238[/C][C]-0.0459327960723825[/C][/ROW]
[ROW][C]61[/C][C]1.08[/C][C]1.05975659257777[/C][C]0.0202434074222251[/C][/ROW]
[ROW][C]62[/C][C]1.09[/C][C]1.0802805188979[/C][C]0.00971948110210108[/C][/ROW]
[ROW][C]63[/C][C]1.03[/C][C]1.10732374385202[/C][C]-0.0773237438520151[/C][/ROW]
[ROW][C]64[/C][C]1.04[/C][C]1.06135677089573[/C][C]-0.0213567708957254[/C][/ROW]
[ROW][C]65[/C][C]1.05[/C][C]1.06517839495893[/C][C]-0.0151783949589288[/C][/ROW]
[ROW][C]66[/C][C]1.19[/C][C]1.14567709076115[/C][C]0.0443229092388469[/C][/ROW]
[ROW][C]67[/C][C]1.14[/C][C]1.26101077832212[/C][C]-0.121010778322123[/C][/ROW]
[ROW][C]68[/C][C]1.05[/C][C]1.09491062637599[/C][C]-0.044910626375986[/C][/ROW]
[ROW][C]69[/C][C]0.95[/C][C]1.01042050241772[/C][C]-0.0604205024177158[/C][/ROW]
[ROW][C]70[/C][C]0.87[/C][C]0.915584806219037[/C][C]-0.045584806219037[/C][/ROW]
[ROW][C]71[/C][C]0.86[/C][C]0.854848476430637[/C][C]0.00515152356936333[/C][/ROW]
[ROW][C]72[/C][C]0.85[/C][C]0.85053023775786[/C][C]-0.000530237757860319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204809&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204809&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	1.1	0.971949306883722	0.128050693116278
14	1.09	1.10018059402938	-0.0101805940293789
15	1.09	1.10732374385202	-0.0173237438520151
16	1.1	1.12284092982282	-0.0228409298228189
17	1.1	1.12628557988237	-0.0262855798823682
18	1.17	1.19992382320372	-0.0299238232037207
19	1.15	1.23993237798446	-0.0899323779844634
20	1.04	1.10445777277797	-0.0644577727779709
21	0.94	1.00085698008531	-0.0608569800853145
22	0.88	0.906010069731035	-0.0260100697310353
23	0.85	0.864607189567366	-0.014607189567366
24	0.85	0.840707062438071	0.00929293756192895
25	0.85	0.850935043756226	-0.000935043756226106
26	0.84	0.851429654885878	-0.0114296548858778
27	0.83	0.85466618880266	-0.0246661888026604
28	0.8	0.85640957447208	-0.0564095744720802
29	0.78	0.820749655265172	-0.0407496552651717
30	1.02	0.852744735571289	0.167255264428711
31	1.19	1.08184437545202	0.108155624547984
32	1.1	1.14264635838591	-0.0426463583859114
33	0.96	1.05823811407972	-0.0982381140797211
34	0.87	0.925159542707039	-0.0551595427070388
35	0.83	0.854848476430637	-0.0248484764306367
36	0.82	0.821060711798492	-0.00106071179849232
37	0.81	0.821103393924576	-0.0111033939245762
38	0.78	0.811629504622918	-0.0316295046229176
39	0.79	0.794028375590815	-0.00402837559081515
40	0.8	0.815420135187351	-0.0154201351873511
41	0.79	0.820749655265172	-0.0307496552651717
42	0.97	0.863594082059802	0.106405917940198
43	1.01	1.02914837460787	-0.0191483746078676
44	0.92	0.97079772315018	-0.0507977231501795
45	0.87	0.886094712096502	-0.0160947120965019
46	0.84	0.838986914315023	0.00101308568497727
47	0.81	0.825572337020449	-0.0155723370204489
48	0.81	0.801414361158914	0.00858563884108632
49	0.83	0.81115951064736	0.0188404893526403
50	0.83	0.831529579754398	-0.00152957975439771
51	0.85	0.844559886600686	0.00544011339931383
52	0.88	0.876904294114445	0.0030957058855553
53	0.89	0.902225901829757	-0.0122259018297575
54	1.21	0.972087546944937	0.237912453055063
55	1.32	1.28208917865978	0.0379108213402175
56	1.33	1.26675926161172	0.0632407383882818
57	1.23	1.27819912772494	-0.0481991277249449
58	1.16	1.18367742788309	-0.0236774278830874
59	1.12	1.13785115739578	-0.017851157395784
60	1.06	1.10593279607238	-0.0459327960723825
61	1.08	1.05975659257777	0.0202434074222251
62	1.09	1.0802805188979	0.00971948110210108
63	1.03	1.10732374385202	-0.0773237438520151
64	1.04	1.06135677089573	-0.0213567708957254
65	1.05	1.06517839495893	-0.0151783949589288
66	1.19	1.14567709076115	0.0443229092388469
67	1.14	1.26101077832212	-0.121010778322123
68	1.05	1.09491062637599	-0.044910626375986
69	0.95	1.01042050241772	-0.0604205024177158
70	0.87	0.915584806219037	-0.045584806219037
71	0.86	0.854848476430637	0.00515152356936333
72	0.85	0.85053023775786	-0.000530237757860319

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.850935043756226	0.734258568402536	0.967611519109916
74	0.852360026935884	0.687766260631714	1.01695379324005
75	0.867157605546519	0.663974097283525	1.07034111380951
76	0.894486309884953	0.655813781601243	1.13315883816866
77	0.916979528779726	0.647350678315012	1.18660837924444
78	1.00135857252774	0.686418872158796	1.31629827289669
79	1.06219780189573	0.710366707509612	1.41402889628185
80	1.02063172880622	0.665046203765448	1.37621725384699
81	0.982334090675141	0.622809944623456	1.34185823672683
82	0.9465438459984	0.583072989543637	1.31001470245316
83	0.929545419978673	0.556147448943472	1.30294339101388
84	0.918845923071749	-17.3353402685131	19.1730321146566

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.850935043756226 & 0.734258568402536 & 0.967611519109916 \tabularnewline
74 & 0.852360026935884 & 0.687766260631714 & 1.01695379324005 \tabularnewline
75 & 0.867157605546519 & 0.663974097283525 & 1.07034111380951 \tabularnewline
76 & 0.894486309884953 & 0.655813781601243 & 1.13315883816866 \tabularnewline
77 & 0.916979528779726 & 0.647350678315012 & 1.18660837924444 \tabularnewline
78 & 1.00135857252774 & 0.686418872158796 & 1.31629827289669 \tabularnewline
79 & 1.06219780189573 & 0.710366707509612 & 1.41402889628185 \tabularnewline
80 & 1.02063172880622 & 0.665046203765448 & 1.37621725384699 \tabularnewline
81 & 0.982334090675141 & 0.622809944623456 & 1.34185823672683 \tabularnewline
82 & 0.9465438459984 & 0.583072989543637 & 1.31001470245316 \tabularnewline
83 & 0.929545419978673 & 0.556147448943472 & 1.30294339101388 \tabularnewline
84 & 0.918845923071749 & -17.3353402685131 & 19.1730321146566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204809&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]0.850935043756226[/C][C]0.734258568402536[/C][C]0.967611519109916[/C][/ROW]
[ROW][C]74[/C][C]0.852360026935884[/C][C]0.687766260631714[/C][C]1.01695379324005[/C][/ROW]
[ROW][C]75[/C][C]0.867157605546519[/C][C]0.663974097283525[/C][C]1.07034111380951[/C][/ROW]
[ROW][C]76[/C][C]0.894486309884953[/C][C]0.655813781601243[/C][C]1.13315883816866[/C][/ROW]
[ROW][C]77[/C][C]0.916979528779726[/C][C]0.647350678315012[/C][C]1.18660837924444[/C][/ROW]
[ROW][C]78[/C][C]1.00135857252774[/C][C]0.686418872158796[/C][C]1.31629827289669[/C][/ROW]
[ROW][C]79[/C][C]1.06219780189573[/C][C]0.710366707509612[/C][C]1.41402889628185[/C][/ROW]
[ROW][C]80[/C][C]1.02063172880622[/C][C]0.665046203765448[/C][C]1.37621725384699[/C][/ROW]
[ROW][C]81[/C][C]0.982334090675141[/C][C]0.622809944623456[/C][C]1.34185823672683[/C][/ROW]
[ROW][C]82[/C][C]0.9465438459984[/C][C]0.583072989543637[/C][C]1.31001470245316[/C][/ROW]
[ROW][C]83[/C][C]0.929545419978673[/C][C]0.556147448943472[/C][C]1.30294339101388[/C][/ROW]
[ROW][C]84[/C][C]0.918845923071749[/C][C]-17.3353402685131[/C][C]19.1730321146566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204809&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204809&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
73	0.850935043756226	0.734258568402536	0.967611519109916
74	0.852360026935884	0.687766260631714	1.01695379324005
75	0.867157605546519	0.663974097283525	1.07034111380951
76	0.894486309884953	0.655813781601243	1.13315883816866
77	0.916979528779726	0.647350678315012	1.18660837924444
78	1.00135857252774	0.686418872158796	1.31629827289669
79	1.06219780189573	0.710366707509612	1.41402889628185
80	1.02063172880622	0.665046203765448	1.37621725384699
81	0.982334090675141	0.622809944623456	1.34185823672683
82	0.9465438459984	0.583072989543637	1.31001470245316
83	0.929545419978673	0.556147448943472	1.30294339101388
84	0.918845923071749	-17.3353402685131	19.1730321146566

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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