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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 01 Dec 2014 20:51:05 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/01/t1417467105defgv51cercxs5g.htm/, Retrieved Thu, 16 May 2024 14:28:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=262277, Retrieved Thu, 16 May 2024 14:28:18 +0000

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No (this computation is public)

User-defined keywords

Simon Dewilde

Estimated Impact

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

-       [Exponential Smoothing] [] [2014-12-01 20:51:05] [1a08c6aa6bf9a3504070a6066c5cb670] [Current]

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Dataseries X:

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1.64
1.65
1.65
1.66
1.67
1.67
1.68
1.68
1.69
1.7
1.71
1.72
1.72
1.73
1.73
1.73
1.73
1.74
1.75
1.75
1.75
1.76
1.76
1.76
1.77
1.78
1.78
1.79
1.79
1.79
1.79
1.79
1.83
1.83
1.83
1.83
1.84
1.84
1.84
1.85
1.85
1.85
1.86
1.86
1.86
1.87
1.87
1.88
1.88
1.88
1.89
1.89
1.9
1.91
1.91
1.91
1.91
1.91
1.92
1.92
1.92
1.93
1.94
1.94
1.94
1.95
1.95
1.95
1.95
1.96
1.96
1.97

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=262277&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=262277&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262277&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	0.939167065058845
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.939167065058845 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262277&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]0.939167065058845[/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=262277&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262277&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	0.939167065058845
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.72	1.68491558440345	0.0350844155965495
14	1.73	1.72759622199974	0.00240377800026481
15	1.73	1.73000797515438	-7.97515438466512e-06
16	1.73	1.73056985097477	-0.000569850974768249
17	1.73	1.73101740679385	-0.00101740679384577
18	1.74	1.74188143418988	-0.00188143418987763
19	1.75	1.74651803131961	0.00348196868038997
20	1.75	1.74842019625172	0.00157980374827837
21	1.75	1.75894882192327	-0.00894882192327229
22	1.76	1.75999869560158	1.30439842438435e-06
23	1.76	1.77031509806378	-0.0103150980637776
24	1.76	1.77091668015477	-0.0109166801547695
25	1.77	1.76244912450363	0.00755087549637445
26	1.78	1.77734472844091	0.00265527155908973
27	1.78	1.77968547756334	0.000314522436658526
28	1.79	1.78037081166564	0.00962918833436022
29	1.79	1.79021201066867	-0.000212010668666274
30	1.79	1.80199482701111	-0.0119948270111054
31	1.79	1.79749291302592	-0.00749291302591715
32	1.79	1.78880946573565	0.00119053426435412
33	1.83	1.79839429704202	0.0316057029579806
34	1.83	1.83827363039905	-0.00827363039904672
35	1.83	1.840351682073	-0.0103516820730021
36	1.83	1.84106502673061	-0.0110650267306054
37	1.84	1.83347196224155	0.00652803775844757
38	1.84	1.84718398917516	-0.00718398917516083
39	1.84	1.83994219880739	5.78011926120059e-05
40	1.85	1.84079471464947	0.00920528535053089
41	1.85	1.84946153379772	0.000538466202275156
42	1.85	1.86141861170986	-0.011418611709858
43	1.86	1.85777963708689	0.00222036291310967
44	1.86	1.85848656093317	0.00151343906683277
45	1.86	1.8703781109894	-0.0103781109894034
46	1.87	1.86843630939288	0.00156369060711614
47	1.87	1.87971368012028	-0.00971368012028195
48	1.88	1.88108526459125	-0.00108526459124536
49	1.88	1.88388660689518	-0.00388660689518017
50	1.88	1.88700694353739	-0.00700694353739406
51	1.89	1.88024821507616	0.00975178492383622
52	1.89	1.89064571393006	-0.000645713930057745
53	1.9	1.88940255661194	0.0105974433880613
54	1.91	1.91021287093528	-0.000212870935280662
55	1.91	1.91800356734156	-0.00800356734156438
56	1.91	1.90887623652645	0.00112376347354726
57	1.91	1.9197873771952	-0.00978737719520129
58	1.91	1.91920729945508	-0.00920729945508025
59	1.92	1.91975675500988	0.000243244990120628
60	1.92	1.93114934677094	-0.011149346770944
61	1.92	1.92428595193769	-0.00428595193769299
62	1.93	1.92686102037314	0.00313897962685705
63	1.94	1.93052199366966	0.00947800633034057
64	1.94	1.93990016779947	9.98322005307806e-05
65	1.94	1.93989215203244	0.000107847967561137
66	1.95	1.95029096766467	-0.000290967664666519
67	1.95	1.95757325075522	-0.00757325075521598
68	1.95	1.94926535402809	0.000734645971908643
69	1.95	1.95922035056526	-0.00922035056525927
70	1.96	1.95927088015334	0.000729119846662574
71	1.96	1.96983680183603	-0.00983680183603464
72	1.97	1.971168828938	-0.00116882893800008

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.72 & 1.68491558440345 & 0.0350844155965495 \tabularnewline
14 & 1.73 & 1.72759622199974 & 0.00240377800026481 \tabularnewline
15 & 1.73 & 1.73000797515438 & -7.97515438466512e-06 \tabularnewline
16 & 1.73 & 1.73056985097477 & -0.000569850974768249 \tabularnewline
17 & 1.73 & 1.73101740679385 & -0.00101740679384577 \tabularnewline
18 & 1.74 & 1.74188143418988 & -0.00188143418987763 \tabularnewline
19 & 1.75 & 1.74651803131961 & 0.00348196868038997 \tabularnewline
20 & 1.75 & 1.74842019625172 & 0.00157980374827837 \tabularnewline
21 & 1.75 & 1.75894882192327 & -0.00894882192327229 \tabularnewline
22 & 1.76 & 1.75999869560158 & 1.30439842438435e-06 \tabularnewline
23 & 1.76 & 1.77031509806378 & -0.0103150980637776 \tabularnewline
24 & 1.76 & 1.77091668015477 & -0.0109166801547695 \tabularnewline
25 & 1.77 & 1.76244912450363 & 0.00755087549637445 \tabularnewline
26 & 1.78 & 1.77734472844091 & 0.00265527155908973 \tabularnewline
27 & 1.78 & 1.77968547756334 & 0.000314522436658526 \tabularnewline
28 & 1.79 & 1.78037081166564 & 0.00962918833436022 \tabularnewline
29 & 1.79 & 1.79021201066867 & -0.000212010668666274 \tabularnewline
30 & 1.79 & 1.80199482701111 & -0.0119948270111054 \tabularnewline
31 & 1.79 & 1.79749291302592 & -0.00749291302591715 \tabularnewline
32 & 1.79 & 1.78880946573565 & 0.00119053426435412 \tabularnewline
33 & 1.83 & 1.79839429704202 & 0.0316057029579806 \tabularnewline
34 & 1.83 & 1.83827363039905 & -0.00827363039904672 \tabularnewline
35 & 1.83 & 1.840351682073 & -0.0103516820730021 \tabularnewline
36 & 1.83 & 1.84106502673061 & -0.0110650267306054 \tabularnewline
37 & 1.84 & 1.83347196224155 & 0.00652803775844757 \tabularnewline
38 & 1.84 & 1.84718398917516 & -0.00718398917516083 \tabularnewline
39 & 1.84 & 1.83994219880739 & 5.78011926120059e-05 \tabularnewline
40 & 1.85 & 1.84079471464947 & 0.00920528535053089 \tabularnewline
41 & 1.85 & 1.84946153379772 & 0.000538466202275156 \tabularnewline
42 & 1.85 & 1.86141861170986 & -0.011418611709858 \tabularnewline
43 & 1.86 & 1.85777963708689 & 0.00222036291310967 \tabularnewline
44 & 1.86 & 1.85848656093317 & 0.00151343906683277 \tabularnewline
45 & 1.86 & 1.8703781109894 & -0.0103781109894034 \tabularnewline
46 & 1.87 & 1.86843630939288 & 0.00156369060711614 \tabularnewline
47 & 1.87 & 1.87971368012028 & -0.00971368012028195 \tabularnewline
48 & 1.88 & 1.88108526459125 & -0.00108526459124536 \tabularnewline
49 & 1.88 & 1.88388660689518 & -0.00388660689518017 \tabularnewline
50 & 1.88 & 1.88700694353739 & -0.00700694353739406 \tabularnewline
51 & 1.89 & 1.88024821507616 & 0.00975178492383622 \tabularnewline
52 & 1.89 & 1.89064571393006 & -0.000645713930057745 \tabularnewline
53 & 1.9 & 1.88940255661194 & 0.0105974433880613 \tabularnewline
54 & 1.91 & 1.91021287093528 & -0.000212870935280662 \tabularnewline
55 & 1.91 & 1.91800356734156 & -0.00800356734156438 \tabularnewline
56 & 1.91 & 1.90887623652645 & 0.00112376347354726 \tabularnewline
57 & 1.91 & 1.9197873771952 & -0.00978737719520129 \tabularnewline
58 & 1.91 & 1.91920729945508 & -0.00920729945508025 \tabularnewline
59 & 1.92 & 1.91975675500988 & 0.000243244990120628 \tabularnewline
60 & 1.92 & 1.93114934677094 & -0.011149346770944 \tabularnewline
61 & 1.92 & 1.92428595193769 & -0.00428595193769299 \tabularnewline
62 & 1.93 & 1.92686102037314 & 0.00313897962685705 \tabularnewline
63 & 1.94 & 1.93052199366966 & 0.00947800633034057 \tabularnewline
64 & 1.94 & 1.93990016779947 & 9.98322005307806e-05 \tabularnewline
65 & 1.94 & 1.93989215203244 & 0.000107847967561137 \tabularnewline
66 & 1.95 & 1.95029096766467 & -0.000290967664666519 \tabularnewline
67 & 1.95 & 1.95757325075522 & -0.00757325075521598 \tabularnewline
68 & 1.95 & 1.94926535402809 & 0.000734645971908643 \tabularnewline
69 & 1.95 & 1.95922035056526 & -0.00922035056525927 \tabularnewline
70 & 1.96 & 1.95927088015334 & 0.000729119846662574 \tabularnewline
71 & 1.96 & 1.96983680183603 & -0.00983680183603464 \tabularnewline
72 & 1.97 & 1.971168828938 & -0.00116882893800008 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262277&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]1.72[/C][C]1.68491558440345[/C][C]0.0350844155965495[/C][/ROW]
[ROW][C]14[/C][C]1.73[/C][C]1.72759622199974[/C][C]0.00240377800026481[/C][/ROW]
[ROW][C]15[/C][C]1.73[/C][C]1.73000797515438[/C][C]-7.97515438466512e-06[/C][/ROW]
[ROW][C]16[/C][C]1.73[/C][C]1.73056985097477[/C][C]-0.000569850974768249[/C][/ROW]
[ROW][C]17[/C][C]1.73[/C][C]1.73101740679385[/C][C]-0.00101740679384577[/C][/ROW]
[ROW][C]18[/C][C]1.74[/C][C]1.74188143418988[/C][C]-0.00188143418987763[/C][/ROW]
[ROW][C]19[/C][C]1.75[/C][C]1.74651803131961[/C][C]0.00348196868038997[/C][/ROW]
[ROW][C]20[/C][C]1.75[/C][C]1.74842019625172[/C][C]0.00157980374827837[/C][/ROW]
[ROW][C]21[/C][C]1.75[/C][C]1.75894882192327[/C][C]-0.00894882192327229[/C][/ROW]
[ROW][C]22[/C][C]1.76[/C][C]1.75999869560158[/C][C]1.30439842438435e-06[/C][/ROW]
[ROW][C]23[/C][C]1.76[/C][C]1.77031509806378[/C][C]-0.0103150980637776[/C][/ROW]
[ROW][C]24[/C][C]1.76[/C][C]1.77091668015477[/C][C]-0.0109166801547695[/C][/ROW]
[ROW][C]25[/C][C]1.77[/C][C]1.76244912450363[/C][C]0.00755087549637445[/C][/ROW]
[ROW][C]26[/C][C]1.78[/C][C]1.77734472844091[/C][C]0.00265527155908973[/C][/ROW]
[ROW][C]27[/C][C]1.78[/C][C]1.77968547756334[/C][C]0.000314522436658526[/C][/ROW]
[ROW][C]28[/C][C]1.79[/C][C]1.78037081166564[/C][C]0.00962918833436022[/C][/ROW]
[ROW][C]29[/C][C]1.79[/C][C]1.79021201066867[/C][C]-0.000212010668666274[/C][/ROW]
[ROW][C]30[/C][C]1.79[/C][C]1.80199482701111[/C][C]-0.0119948270111054[/C][/ROW]
[ROW][C]31[/C][C]1.79[/C][C]1.79749291302592[/C][C]-0.00749291302591715[/C][/ROW]
[ROW][C]32[/C][C]1.79[/C][C]1.78880946573565[/C][C]0.00119053426435412[/C][/ROW]
[ROW][C]33[/C][C]1.83[/C][C]1.79839429704202[/C][C]0.0316057029579806[/C][/ROW]
[ROW][C]34[/C][C]1.83[/C][C]1.83827363039905[/C][C]-0.00827363039904672[/C][/ROW]
[ROW][C]35[/C][C]1.83[/C][C]1.840351682073[/C][C]-0.0103516820730021[/C][/ROW]
[ROW][C]36[/C][C]1.83[/C][C]1.84106502673061[/C][C]-0.0110650267306054[/C][/ROW]
[ROW][C]37[/C][C]1.84[/C][C]1.83347196224155[/C][C]0.00652803775844757[/C][/ROW]
[ROW][C]38[/C][C]1.84[/C][C]1.84718398917516[/C][C]-0.00718398917516083[/C][/ROW]
[ROW][C]39[/C][C]1.84[/C][C]1.83994219880739[/C][C]5.78011926120059e-05[/C][/ROW]
[ROW][C]40[/C][C]1.85[/C][C]1.84079471464947[/C][C]0.00920528535053089[/C][/ROW]
[ROW][C]41[/C][C]1.85[/C][C]1.84946153379772[/C][C]0.000538466202275156[/C][/ROW]
[ROW][C]42[/C][C]1.85[/C][C]1.86141861170986[/C][C]-0.011418611709858[/C][/ROW]
[ROW][C]43[/C][C]1.86[/C][C]1.85777963708689[/C][C]0.00222036291310967[/C][/ROW]
[ROW][C]44[/C][C]1.86[/C][C]1.85848656093317[/C][C]0.00151343906683277[/C][/ROW]
[ROW][C]45[/C][C]1.86[/C][C]1.8703781109894[/C][C]-0.0103781109894034[/C][/ROW]
[ROW][C]46[/C][C]1.87[/C][C]1.86843630939288[/C][C]0.00156369060711614[/C][/ROW]
[ROW][C]47[/C][C]1.87[/C][C]1.87971368012028[/C][C]-0.00971368012028195[/C][/ROW]
[ROW][C]48[/C][C]1.88[/C][C]1.88108526459125[/C][C]-0.00108526459124536[/C][/ROW]
[ROW][C]49[/C][C]1.88[/C][C]1.88388660689518[/C][C]-0.00388660689518017[/C][/ROW]
[ROW][C]50[/C][C]1.88[/C][C]1.88700694353739[/C][C]-0.00700694353739406[/C][/ROW]
[ROW][C]51[/C][C]1.89[/C][C]1.88024821507616[/C][C]0.00975178492383622[/C][/ROW]
[ROW][C]52[/C][C]1.89[/C][C]1.89064571393006[/C][C]-0.000645713930057745[/C][/ROW]
[ROW][C]53[/C][C]1.9[/C][C]1.88940255661194[/C][C]0.0105974433880613[/C][/ROW]
[ROW][C]54[/C][C]1.91[/C][C]1.91021287093528[/C][C]-0.000212870935280662[/C][/ROW]
[ROW][C]55[/C][C]1.91[/C][C]1.91800356734156[/C][C]-0.00800356734156438[/C][/ROW]
[ROW][C]56[/C][C]1.91[/C][C]1.90887623652645[/C][C]0.00112376347354726[/C][/ROW]
[ROW][C]57[/C][C]1.91[/C][C]1.9197873771952[/C][C]-0.00978737719520129[/C][/ROW]
[ROW][C]58[/C][C]1.91[/C][C]1.91920729945508[/C][C]-0.00920729945508025[/C][/ROW]
[ROW][C]59[/C][C]1.92[/C][C]1.91975675500988[/C][C]0.000243244990120628[/C][/ROW]
[ROW][C]60[/C][C]1.92[/C][C]1.93114934677094[/C][C]-0.011149346770944[/C][/ROW]
[ROW][C]61[/C][C]1.92[/C][C]1.92428595193769[/C][C]-0.00428595193769299[/C][/ROW]
[ROW][C]62[/C][C]1.93[/C][C]1.92686102037314[/C][C]0.00313897962685705[/C][/ROW]
[ROW][C]63[/C][C]1.94[/C][C]1.93052199366966[/C][C]0.00947800633034057[/C][/ROW]
[ROW][C]64[/C][C]1.94[/C][C]1.93990016779947[/C][C]9.98322005307806e-05[/C][/ROW]
[ROW][C]65[/C][C]1.94[/C][C]1.93989215203244[/C][C]0.000107847967561137[/C][/ROW]
[ROW][C]66[/C][C]1.95[/C][C]1.95029096766467[/C][C]-0.000290967664666519[/C][/ROW]
[ROW][C]67[/C][C]1.95[/C][C]1.95757325075522[/C][C]-0.00757325075521598[/C][/ROW]
[ROW][C]68[/C][C]1.95[/C][C]1.94926535402809[/C][C]0.000734645971908643[/C][/ROW]
[ROW][C]69[/C][C]1.95[/C][C]1.95922035056526[/C][C]-0.00922035056525927[/C][/ROW]
[ROW][C]70[/C][C]1.96[/C][C]1.95927088015334[/C][C]0.000729119846662574[/C][/ROW]
[ROW][C]71[/C][C]1.96[/C][C]1.96983680183603[/C][C]-0.00983680183603464[/C][/ROW]
[ROW][C]72[/C][C]1.97[/C][C]1.971168828938[/C][C]-0.00116882893800008[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262277&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262277&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	1.72	1.68491558440345	0.0350844155965495
14	1.73	1.72759622199974	0.00240377800026481
15	1.73	1.73000797515438	-7.97515438466512e-06
16	1.73	1.73056985097477	-0.000569850974768249
17	1.73	1.73101740679385	-0.00101740679384577
18	1.74	1.74188143418988	-0.00188143418987763
19	1.75	1.74651803131961	0.00348196868038997
20	1.75	1.74842019625172	0.00157980374827837
21	1.75	1.75894882192327	-0.00894882192327229
22	1.76	1.75999869560158	1.30439842438435e-06
23	1.76	1.77031509806378	-0.0103150980637776
24	1.76	1.77091668015477	-0.0109166801547695
25	1.77	1.76244912450363	0.00755087549637445
26	1.78	1.77734472844091	0.00265527155908973
27	1.78	1.77968547756334	0.000314522436658526
28	1.79	1.78037081166564	0.00962918833436022
29	1.79	1.79021201066867	-0.000212010668666274
30	1.79	1.80199482701111	-0.0119948270111054
31	1.79	1.79749291302592	-0.00749291302591715
32	1.79	1.78880946573565	0.00119053426435412
33	1.83	1.79839429704202	0.0316057029579806
34	1.83	1.83827363039905	-0.00827363039904672
35	1.83	1.840351682073	-0.0103516820730021
36	1.83	1.84106502673061	-0.0110650267306054
37	1.84	1.83347196224155	0.00652803775844757
38	1.84	1.84718398917516	-0.00718398917516083
39	1.84	1.83994219880739	5.78011926120059e-05
40	1.85	1.84079471464947	0.00920528535053089
41	1.85	1.84946153379772	0.000538466202275156
42	1.85	1.86141861170986	-0.011418611709858
43	1.86	1.85777963708689	0.00222036291310967
44	1.86	1.85848656093317	0.00151343906683277
45	1.86	1.8703781109894	-0.0103781109894034
46	1.87	1.86843630939288	0.00156369060711614
47	1.87	1.87971368012028	-0.00971368012028195
48	1.88	1.88108526459125	-0.00108526459124536
49	1.88	1.88388660689518	-0.00388660689518017
50	1.88	1.88700694353739	-0.00700694353739406
51	1.89	1.88024821507616	0.00975178492383622
52	1.89	1.89064571393006	-0.000645713930057745
53	1.9	1.88940255661194	0.0105974433880613
54	1.91	1.91021287093528	-0.000212870935280662
55	1.91	1.91800356734156	-0.00800356734156438
56	1.91	1.90887623652645	0.00112376347354726
57	1.91	1.9197873771952	-0.00978737719520129
58	1.91	1.91920729945508	-0.00920729945508025
59	1.92	1.91975675500988	0.000243244990120628
60	1.92	1.93114934677094	-0.011149346770944
61	1.92	1.92428595193769	-0.00428595193769299
62	1.93	1.92686102037314	0.00313897962685705
63	1.94	1.93052199366966	0.00947800633034057
64	1.94	1.93990016779947	9.98322005307806e-05
65	1.94	1.93989215203244	0.000107847967561137
66	1.95	1.95029096766467	-0.000290967664666519
67	1.95	1.95757325075522	-0.00757325075521598
68	1.95	1.94926535402809	0.000734645971908643
69	1.95	1.95922035056526	-0.00922035056525927
70	1.96	1.95927088015334	0.000729119846662574
71	1.96	1.96983680183603	-0.00983680183603464
72	1.97	1.971168828938	-0.00116882893800008

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.97405494728495	1.95656766876692	1.99154222580298
74	1.98114764765253	1.95714879375755	2.00514650154751
75	1.98212468986962	1.95308731949716	2.01116206024208
76	1.98190804780457	1.94861844683371	2.01519764877542
77	1.98168469706491	1.94464833963754	2.01872105449229
78	1.99205917727824	1.95146464205479	2.03265371250169
79	1.99920334185284	1.95538325568586	2.04302342801982
80	1.99835593835775	1.95168803927756	2.04502383743795
81	2.00708974255641	1.95754747666298	2.05663200844985
82	2.01651464483669	1.96423206541814	2.06879722425523
83	2.02585565386833	1.97096237493899	2.08074893279768
84	2.03713823411587	-1.11400430519535	5.1882807734271

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.97405494728495 & 1.95656766876692 & 1.99154222580298 \tabularnewline
74 & 1.98114764765253 & 1.95714879375755 & 2.00514650154751 \tabularnewline
75 & 1.98212468986962 & 1.95308731949716 & 2.01116206024208 \tabularnewline
76 & 1.98190804780457 & 1.94861844683371 & 2.01519764877542 \tabularnewline
77 & 1.98168469706491 & 1.94464833963754 & 2.01872105449229 \tabularnewline
78 & 1.99205917727824 & 1.95146464205479 & 2.03265371250169 \tabularnewline
79 & 1.99920334185284 & 1.95538325568586 & 2.04302342801982 \tabularnewline
80 & 1.99835593835775 & 1.95168803927756 & 2.04502383743795 \tabularnewline
81 & 2.00708974255641 & 1.95754747666298 & 2.05663200844985 \tabularnewline
82 & 2.01651464483669 & 1.96423206541814 & 2.06879722425523 \tabularnewline
83 & 2.02585565386833 & 1.97096237493899 & 2.08074893279768 \tabularnewline
84 & 2.03713823411587 & -1.11400430519535 & 5.1882807734271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262277&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]1.97405494728495[/C][C]1.95656766876692[/C][C]1.99154222580298[/C][/ROW]
[ROW][C]74[/C][C]1.98114764765253[/C][C]1.95714879375755[/C][C]2.00514650154751[/C][/ROW]
[ROW][C]75[/C][C]1.98212468986962[/C][C]1.95308731949716[/C][C]2.01116206024208[/C][/ROW]
[ROW][C]76[/C][C]1.98190804780457[/C][C]1.94861844683371[/C][C]2.01519764877542[/C][/ROW]
[ROW][C]77[/C][C]1.98168469706491[/C][C]1.94464833963754[/C][C]2.01872105449229[/C][/ROW]
[ROW][C]78[/C][C]1.99205917727824[/C][C]1.95146464205479[/C][C]2.03265371250169[/C][/ROW]
[ROW][C]79[/C][C]1.99920334185284[/C][C]1.95538325568586[/C][C]2.04302342801982[/C][/ROW]
[ROW][C]80[/C][C]1.99835593835775[/C][C]1.95168803927756[/C][C]2.04502383743795[/C][/ROW]
[ROW][C]81[/C][C]2.00708974255641[/C][C]1.95754747666298[/C][C]2.05663200844985[/C][/ROW]
[ROW][C]82[/C][C]2.01651464483669[/C][C]1.96423206541814[/C][C]2.06879722425523[/C][/ROW]
[ROW][C]83[/C][C]2.02585565386833[/C][C]1.97096237493899[/C][C]2.08074893279768[/C][/ROW]
[ROW][C]84[/C][C]2.03713823411587[/C][C]-1.11400430519535[/C][C]5.1882807734271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262277&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262277&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	1.97405494728495	1.95656766876692	1.99154222580298
74	1.98114764765253	1.95714879375755	2.00514650154751
75	1.98212468986962	1.95308731949716	2.01116206024208
76	1.98190804780457	1.94861844683371	2.01519764877542
77	1.98168469706491	1.94464833963754	2.01872105449229
78	1.99205917727824	1.95146464205479	2.03265371250169
79	1.99920334185284	1.95538325568586	2.04302342801982
80	1.99835593835775	1.95168803927756	2.04502383743795
81	2.00708974255641	1.95754747666298	2.05663200844985
82	2.01651464483669	1.96423206541814	2.06879722425523
83	2.02585565386833	1.97096237493899	2.08074893279768
84	2.03713823411587	-1.11400430519535	5.1882807734271

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