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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 23 Dec 2013 12:41:07 -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/2013/Dec/23/t1387821540aba00c0n6jb2nk3.htm/, Retrieved Wed, 11 Feb 2026 11:29:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232603, Retrieved Wed, 11 Feb 2026 11:29:42 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

453

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

-       [Exponential Smoothing] [] [2013-12-23 17:41:07] [4a6145c727f9c0eb5ad6c1d4f2919b3e] [Current]
- R PD    [Exponential Smoothing] [] [2014-01-12 23:59:22] [ed8109c700ca2a37c253822187bef503] 

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Dataseries X:

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Histogram

Boxplots

1,94
1,82
1,8
1,79
1,79
1,78
1,81
1,84
1,87
1,87
1,87
1,84
1,82
1,83
1,83
1,82
1,83
1,87
1,88
1,9
1,98
2,03
2,14
2,42
2,73
2,84
2,85
2,94
3,06
3,24
3,18
3,01
2,87
2,73
2,63
2,39
2,26
2,11
2,01
1,99
1,96
1,93
1,98
2,07
2,24
2,31
2,23
2,26
2,28
2,3
2,33
2,26
2,24
2,47
2,55
2,89
3,21
3,21
2,92
2,68
2,4
2,28
2,24
2,2
2,18
2,23
2,24
2,25
2,23
2,25
2,23
2,21
2,17
2,17
2,13
2,12
2,13
2,17
2,33
2,5
2,57
2,59
2,58
2,31

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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232603&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232603&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232603&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	1
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232603&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]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232603&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232603&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	1
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.8	1.7	0.0999999999999999
4	1.79	1.78	0.01
5	1.79	1.78	0.01
6	1.78	1.79	-0.01
7	1.81	1.77	0.04
8	1.84	1.84	0
9	1.87	1.87	0
10	1.87	1.9	-0.03
11	1.87	1.87	0
12	1.84	1.87	-0.03
13	1.82	1.81	0.01
14	1.83	1.8	0.03
15	1.83	1.84	-0.01
16	1.82	1.83	-0.01
17	1.83	1.81	0.02
18	1.87	1.84	0.03
19	1.88	1.91	-0.0300000000000002
20	1.9	1.89	0.0100000000000002
21	1.98	1.92	0.0600000000000001
22	2.03	2.06	-0.0300000000000002
23	2.14	2.08	0.0600000000000005
24	2.42	2.25	0.169999999999999
25	2.73	2.7	0.0300000000000002
26	2.84	3.04	-0.2
27	2.85	2.95	-0.0999999999999996
28	2.94	2.86	0.0799999999999996
29	3.06	3.03	0.0300000000000002
30	3.24	3.18	0.0600000000000001
31	3.18	3.42	-0.24
32	3.01	3.12	-0.11
33	2.87	2.84	0.0300000000000007
34	2.73	2.73	-4.44089209850063e-16
35	2.63	2.59	0.04
36	2.39	2.53	-0.14
37	2.26	2.15	0.109999999999999
38	2.11	2.13	-0.0199999999999996
39	2.01	1.96	0.0499999999999998
40	1.99	1.91	0.0800000000000003
41	1.96	1.97	-0.0100000000000002
42	1.93	1.93	0
43	1.98	1.9	0.0800000000000001
44	2.07	2.03	0.0399999999999996
45	2.24	2.16	0.0800000000000005
46	2.31	2.41	-0.100000000000001
47	2.23	2.38	-0.15
48	2.26	2.15	0.11
49	2.28	2.29	-0.00999999999999979
50	2.3	2.3	0
51	2.33	2.32	0.0100000000000002
52	2.26	2.36	-0.100000000000001
53	2.24	2.19	0.0500000000000007
54	2.47	2.22	0.25
55	2.55	2.7	-0.15
56	2.89	2.63	0.260000000000001
57	3.21	3.23	-0.0200000000000005
58	3.21	3.53	-0.32
59	2.92	3.21	-0.29
60	2.68	2.63	0.0500000000000003
61	2.4	2.44	-0.0400000000000005
62	2.28	2.12	0.16
63	2.24	2.16	0.0800000000000005
64	2.2	2.2	-4.44089209850063e-16
65	2.18	2.16	0.02
66	2.23	2.16	0.0699999999999998
67	2.24	2.28	-0.0399999999999996
68	2.25	2.25	-4.44089209850063e-16
69	2.23	2.26	-0.0299999999999998
70	2.25	2.21	0.04
71	2.23	2.27	-0.04
72	2.21	2.21	0
73	2.17	2.19	-0.02
74	2.17	2.13	0.04
75	2.13	2.17	-0.04
76	2.12	2.09	0.0300000000000002
77	2.13	2.11	0.0199999999999996
78	2.17	2.14	0.0300000000000002
79	2.33	2.21	0.12
80	2.5	2.49	0.00999999999999979
81	2.57	2.67	-0.1
82	2.59	2.64	-0.0499999999999998
83	2.58	2.61	-0.0299999999999998
84	2.31	2.57	-0.26

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.8 & 1.7 & 0.0999999999999999 \tabularnewline
4 & 1.79 & 1.78 & 0.01 \tabularnewline
5 & 1.79 & 1.78 & 0.01 \tabularnewline
6 & 1.78 & 1.79 & -0.01 \tabularnewline
7 & 1.81 & 1.77 & 0.04 \tabularnewline
8 & 1.84 & 1.84 & 0 \tabularnewline
9 & 1.87 & 1.87 & 0 \tabularnewline
10 & 1.87 & 1.9 & -0.03 \tabularnewline
11 & 1.87 & 1.87 & 0 \tabularnewline
12 & 1.84 & 1.87 & -0.03 \tabularnewline
13 & 1.82 & 1.81 & 0.01 \tabularnewline
14 & 1.83 & 1.8 & 0.03 \tabularnewline
15 & 1.83 & 1.84 & -0.01 \tabularnewline
16 & 1.82 & 1.83 & -0.01 \tabularnewline
17 & 1.83 & 1.81 & 0.02 \tabularnewline
18 & 1.87 & 1.84 & 0.03 \tabularnewline
19 & 1.88 & 1.91 & -0.0300000000000002 \tabularnewline
20 & 1.9 & 1.89 & 0.0100000000000002 \tabularnewline
21 & 1.98 & 1.92 & 0.0600000000000001 \tabularnewline
22 & 2.03 & 2.06 & -0.0300000000000002 \tabularnewline
23 & 2.14 & 2.08 & 0.0600000000000005 \tabularnewline
24 & 2.42 & 2.25 & 0.169999999999999 \tabularnewline
25 & 2.73 & 2.7 & 0.0300000000000002 \tabularnewline
26 & 2.84 & 3.04 & -0.2 \tabularnewline
27 & 2.85 & 2.95 & -0.0999999999999996 \tabularnewline
28 & 2.94 & 2.86 & 0.0799999999999996 \tabularnewline
29 & 3.06 & 3.03 & 0.0300000000000002 \tabularnewline
30 & 3.24 & 3.18 & 0.0600000000000001 \tabularnewline
31 & 3.18 & 3.42 & -0.24 \tabularnewline
32 & 3.01 & 3.12 & -0.11 \tabularnewline
33 & 2.87 & 2.84 & 0.0300000000000007 \tabularnewline
34 & 2.73 & 2.73 & -4.44089209850063e-16 \tabularnewline
35 & 2.63 & 2.59 & 0.04 \tabularnewline
36 & 2.39 & 2.53 & -0.14 \tabularnewline
37 & 2.26 & 2.15 & 0.109999999999999 \tabularnewline
38 & 2.11 & 2.13 & -0.0199999999999996 \tabularnewline
39 & 2.01 & 1.96 & 0.0499999999999998 \tabularnewline
40 & 1.99 & 1.91 & 0.0800000000000003 \tabularnewline
41 & 1.96 & 1.97 & -0.0100000000000002 \tabularnewline
42 & 1.93 & 1.93 & 0 \tabularnewline
43 & 1.98 & 1.9 & 0.0800000000000001 \tabularnewline
44 & 2.07 & 2.03 & 0.0399999999999996 \tabularnewline
45 & 2.24 & 2.16 & 0.0800000000000005 \tabularnewline
46 & 2.31 & 2.41 & -0.100000000000001 \tabularnewline
47 & 2.23 & 2.38 & -0.15 \tabularnewline
48 & 2.26 & 2.15 & 0.11 \tabularnewline
49 & 2.28 & 2.29 & -0.00999999999999979 \tabularnewline
50 & 2.3 & 2.3 & 0 \tabularnewline
51 & 2.33 & 2.32 & 0.0100000000000002 \tabularnewline
52 & 2.26 & 2.36 & -0.100000000000001 \tabularnewline
53 & 2.24 & 2.19 & 0.0500000000000007 \tabularnewline
54 & 2.47 & 2.22 & 0.25 \tabularnewline
55 & 2.55 & 2.7 & -0.15 \tabularnewline
56 & 2.89 & 2.63 & 0.260000000000001 \tabularnewline
57 & 3.21 & 3.23 & -0.0200000000000005 \tabularnewline
58 & 3.21 & 3.53 & -0.32 \tabularnewline
59 & 2.92 & 3.21 & -0.29 \tabularnewline
60 & 2.68 & 2.63 & 0.0500000000000003 \tabularnewline
61 & 2.4 & 2.44 & -0.0400000000000005 \tabularnewline
62 & 2.28 & 2.12 & 0.16 \tabularnewline
63 & 2.24 & 2.16 & 0.0800000000000005 \tabularnewline
64 & 2.2 & 2.2 & -4.44089209850063e-16 \tabularnewline
65 & 2.18 & 2.16 & 0.02 \tabularnewline
66 & 2.23 & 2.16 & 0.0699999999999998 \tabularnewline
67 & 2.24 & 2.28 & -0.0399999999999996 \tabularnewline
68 & 2.25 & 2.25 & -4.44089209850063e-16 \tabularnewline
69 & 2.23 & 2.26 & -0.0299999999999998 \tabularnewline
70 & 2.25 & 2.21 & 0.04 \tabularnewline
71 & 2.23 & 2.27 & -0.04 \tabularnewline
72 & 2.21 & 2.21 & 0 \tabularnewline
73 & 2.17 & 2.19 & -0.02 \tabularnewline
74 & 2.17 & 2.13 & 0.04 \tabularnewline
75 & 2.13 & 2.17 & -0.04 \tabularnewline
76 & 2.12 & 2.09 & 0.0300000000000002 \tabularnewline
77 & 2.13 & 2.11 & 0.0199999999999996 \tabularnewline
78 & 2.17 & 2.14 & 0.0300000000000002 \tabularnewline
79 & 2.33 & 2.21 & 0.12 \tabularnewline
80 & 2.5 & 2.49 & 0.00999999999999979 \tabularnewline
81 & 2.57 & 2.67 & -0.1 \tabularnewline
82 & 2.59 & 2.64 & -0.0499999999999998 \tabularnewline
83 & 2.58 & 2.61 & -0.0299999999999998 \tabularnewline
84 & 2.31 & 2.57 & -0.26 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232603&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]3[/C][C]1.8[/C][C]1.7[/C][C]0.0999999999999999[/C][/ROW]
[ROW][C]4[/C][C]1.79[/C][C]1.78[/C][C]0.01[/C][/ROW]
[ROW][C]5[/C][C]1.79[/C][C]1.78[/C][C]0.01[/C][/ROW]
[ROW][C]6[/C][C]1.78[/C][C]1.79[/C][C]-0.01[/C][/ROW]
[ROW][C]7[/C][C]1.81[/C][C]1.77[/C][C]0.04[/C][/ROW]
[ROW][C]8[/C][C]1.84[/C][C]1.84[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]1.87[/C][C]1.87[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]1.87[/C][C]1.9[/C][C]-0.03[/C][/ROW]
[ROW][C]11[/C][C]1.87[/C][C]1.87[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]1.84[/C][C]1.87[/C][C]-0.03[/C][/ROW]
[ROW][C]13[/C][C]1.82[/C][C]1.81[/C][C]0.01[/C][/ROW]
[ROW][C]14[/C][C]1.83[/C][C]1.8[/C][C]0.03[/C][/ROW]
[ROW][C]15[/C][C]1.83[/C][C]1.84[/C][C]-0.01[/C][/ROW]
[ROW][C]16[/C][C]1.82[/C][C]1.83[/C][C]-0.01[/C][/ROW]
[ROW][C]17[/C][C]1.83[/C][C]1.81[/C][C]0.02[/C][/ROW]
[ROW][C]18[/C][C]1.87[/C][C]1.84[/C][C]0.03[/C][/ROW]
[ROW][C]19[/C][C]1.88[/C][C]1.91[/C][C]-0.0300000000000002[/C][/ROW]
[ROW][C]20[/C][C]1.9[/C][C]1.89[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]21[/C][C]1.98[/C][C]1.92[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]22[/C][C]2.03[/C][C]2.06[/C][C]-0.0300000000000002[/C][/ROW]
[ROW][C]23[/C][C]2.14[/C][C]2.08[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]24[/C][C]2.42[/C][C]2.25[/C][C]0.169999999999999[/C][/ROW]
[ROW][C]25[/C][C]2.73[/C][C]2.7[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]26[/C][C]2.84[/C][C]3.04[/C][C]-0.2[/C][/ROW]
[ROW][C]27[/C][C]2.85[/C][C]2.95[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]28[/C][C]2.94[/C][C]2.86[/C][C]0.0799999999999996[/C][/ROW]
[ROW][C]29[/C][C]3.06[/C][C]3.03[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]30[/C][C]3.24[/C][C]3.18[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]31[/C][C]3.18[/C][C]3.42[/C][C]-0.24[/C][/ROW]
[ROW][C]32[/C][C]3.01[/C][C]3.12[/C][C]-0.11[/C][/ROW]
[ROW][C]33[/C][C]2.87[/C][C]2.84[/C][C]0.0300000000000007[/C][/ROW]
[ROW][C]34[/C][C]2.73[/C][C]2.73[/C][C]-4.44089209850063e-16[/C][/ROW]
[ROW][C]35[/C][C]2.63[/C][C]2.59[/C][C]0.04[/C][/ROW]
[ROW][C]36[/C][C]2.39[/C][C]2.53[/C][C]-0.14[/C][/ROW]
[ROW][C]37[/C][C]2.26[/C][C]2.15[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]38[/C][C]2.11[/C][C]2.13[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]39[/C][C]2.01[/C][C]1.96[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]40[/C][C]1.99[/C][C]1.91[/C][C]0.0800000000000003[/C][/ROW]
[ROW][C]41[/C][C]1.96[/C][C]1.97[/C][C]-0.0100000000000002[/C][/ROW]
[ROW][C]42[/C][C]1.93[/C][C]1.93[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]1.98[/C][C]1.9[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]44[/C][C]2.07[/C][C]2.03[/C][C]0.0399999999999996[/C][/ROW]
[ROW][C]45[/C][C]2.24[/C][C]2.16[/C][C]0.0800000000000005[/C][/ROW]
[ROW][C]46[/C][C]2.31[/C][C]2.41[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]47[/C][C]2.23[/C][C]2.38[/C][C]-0.15[/C][/ROW]
[ROW][C]48[/C][C]2.26[/C][C]2.15[/C][C]0.11[/C][/ROW]
[ROW][C]49[/C][C]2.28[/C][C]2.29[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]50[/C][C]2.3[/C][C]2.3[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]2.33[/C][C]2.32[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]52[/C][C]2.26[/C][C]2.36[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]53[/C][C]2.24[/C][C]2.19[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]54[/C][C]2.47[/C][C]2.22[/C][C]0.25[/C][/ROW]
[ROW][C]55[/C][C]2.55[/C][C]2.7[/C][C]-0.15[/C][/ROW]
[ROW][C]56[/C][C]2.89[/C][C]2.63[/C][C]0.260000000000001[/C][/ROW]
[ROW][C]57[/C][C]3.21[/C][C]3.23[/C][C]-0.0200000000000005[/C][/ROW]
[ROW][C]58[/C][C]3.21[/C][C]3.53[/C][C]-0.32[/C][/ROW]
[ROW][C]59[/C][C]2.92[/C][C]3.21[/C][C]-0.29[/C][/ROW]
[ROW][C]60[/C][C]2.68[/C][C]2.63[/C][C]0.0500000000000003[/C][/ROW]
[ROW][C]61[/C][C]2.4[/C][C]2.44[/C][C]-0.0400000000000005[/C][/ROW]
[ROW][C]62[/C][C]2.28[/C][C]2.12[/C][C]0.16[/C][/ROW]
[ROW][C]63[/C][C]2.24[/C][C]2.16[/C][C]0.0800000000000005[/C][/ROW]
[ROW][C]64[/C][C]2.2[/C][C]2.2[/C][C]-4.44089209850063e-16[/C][/ROW]
[ROW][C]65[/C][C]2.18[/C][C]2.16[/C][C]0.02[/C][/ROW]
[ROW][C]66[/C][C]2.23[/C][C]2.16[/C][C]0.0699999999999998[/C][/ROW]
[ROW][C]67[/C][C]2.24[/C][C]2.28[/C][C]-0.0399999999999996[/C][/ROW]
[ROW][C]68[/C][C]2.25[/C][C]2.25[/C][C]-4.44089209850063e-16[/C][/ROW]
[ROW][C]69[/C][C]2.23[/C][C]2.26[/C][C]-0.0299999999999998[/C][/ROW]
[ROW][C]70[/C][C]2.25[/C][C]2.21[/C][C]0.04[/C][/ROW]
[ROW][C]71[/C][C]2.23[/C][C]2.27[/C][C]-0.04[/C][/ROW]
[ROW][C]72[/C][C]2.21[/C][C]2.21[/C][C]0[/C][/ROW]
[ROW][C]73[/C][C]2.17[/C][C]2.19[/C][C]-0.02[/C][/ROW]
[ROW][C]74[/C][C]2.17[/C][C]2.13[/C][C]0.04[/C][/ROW]
[ROW][C]75[/C][C]2.13[/C][C]2.17[/C][C]-0.04[/C][/ROW]
[ROW][C]76[/C][C]2.12[/C][C]2.09[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]77[/C][C]2.13[/C][C]2.11[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]78[/C][C]2.17[/C][C]2.14[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]79[/C][C]2.33[/C][C]2.21[/C][C]0.12[/C][/ROW]
[ROW][C]80[/C][C]2.5[/C][C]2.49[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]81[/C][C]2.57[/C][C]2.67[/C][C]-0.1[/C][/ROW]
[ROW][C]82[/C][C]2.59[/C][C]2.64[/C][C]-0.0499999999999998[/C][/ROW]
[ROW][C]83[/C][C]2.58[/C][C]2.61[/C][C]-0.0299999999999998[/C][/ROW]
[ROW][C]84[/C][C]2.31[/C][C]2.57[/C][C]-0.26[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232603&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232603&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
3	1.8	1.7	0.0999999999999999
4	1.79	1.78	0.01
5	1.79	1.78	0.01
6	1.78	1.79	-0.01
7	1.81	1.77	0.04
8	1.84	1.84	0
9	1.87	1.87	0
10	1.87	1.9	-0.03
11	1.87	1.87	0
12	1.84	1.87	-0.03
13	1.82	1.81	0.01
14	1.83	1.8	0.03
15	1.83	1.84	-0.01
16	1.82	1.83	-0.01
17	1.83	1.81	0.02
18	1.87	1.84	0.03
19	1.88	1.91	-0.0300000000000002
20	1.9	1.89	0.0100000000000002
21	1.98	1.92	0.0600000000000001
22	2.03	2.06	-0.0300000000000002
23	2.14	2.08	0.0600000000000005
24	2.42	2.25	0.169999999999999
25	2.73	2.7	0.0300000000000002
26	2.84	3.04	-0.2
27	2.85	2.95	-0.0999999999999996
28	2.94	2.86	0.0799999999999996
29	3.06	3.03	0.0300000000000002
30	3.24	3.18	0.0600000000000001
31	3.18	3.42	-0.24
32	3.01	3.12	-0.11
33	2.87	2.84	0.0300000000000007
34	2.73	2.73	-4.44089209850063e-16
35	2.63	2.59	0.04
36	2.39	2.53	-0.14
37	2.26	2.15	0.109999999999999
38	2.11	2.13	-0.0199999999999996
39	2.01	1.96	0.0499999999999998
40	1.99	1.91	0.0800000000000003
41	1.96	1.97	-0.0100000000000002
42	1.93	1.93	0
43	1.98	1.9	0.0800000000000001
44	2.07	2.03	0.0399999999999996
45	2.24	2.16	0.0800000000000005
46	2.31	2.41	-0.100000000000001
47	2.23	2.38	-0.15
48	2.26	2.15	0.11
49	2.28	2.29	-0.00999999999999979
50	2.3	2.3	0
51	2.33	2.32	0.0100000000000002
52	2.26	2.36	-0.100000000000001
53	2.24	2.19	0.0500000000000007
54	2.47	2.22	0.25
55	2.55	2.7	-0.15
56	2.89	2.63	0.260000000000001
57	3.21	3.23	-0.0200000000000005
58	3.21	3.53	-0.32
59	2.92	3.21	-0.29
60	2.68	2.63	0.0500000000000003
61	2.4	2.44	-0.0400000000000005
62	2.28	2.12	0.16
63	2.24	2.16	0.0800000000000005
64	2.2	2.2	-4.44089209850063e-16
65	2.18	2.16	0.02
66	2.23	2.16	0.0699999999999998
67	2.24	2.28	-0.0399999999999996
68	2.25	2.25	-4.44089209850063e-16
69	2.23	2.26	-0.0299999999999998
70	2.25	2.21	0.04
71	2.23	2.27	-0.04
72	2.21	2.21	0
73	2.17	2.19	-0.02
74	2.17	2.13	0.04
75	2.13	2.17	-0.04
76	2.12	2.09	0.0300000000000002
77	2.13	2.11	0.0199999999999996
78	2.17	2.14	0.0300000000000002
79	2.33	2.21	0.12
80	2.5	2.49	0.00999999999999979
81	2.57	2.67	-0.1
82	2.59	2.64	-0.0499999999999998
83	2.58	2.61	-0.0299999999999998
84	2.31	2.57	-0.26

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	2.04	1.84660688009918	2.23339311990082
86	1.77	1.337559837521	2.202440162479
87	1.5	0.776389204371834	2.22361079562817
88	1.23	0.17074225764019	2.28925774235981
89	0.96	-0.47424176322318	2.39424176322318
90	0.69	-1.15485278357721	2.53485278357721
91	0.42	-1.86825825367162	2.70825825367162
92	0.15	-2.61220624868864	2.91220624868864
93	-0.12	-3.38485162987806	3.14485162987806
94	-0.39	-4.18464702543132	3.40464702543132
95	-0.66	-5.0102706588713	3.6902706588713
96	-0.93	-5.86057646084438	4.00057646084438

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2.04 & 1.84660688009918 & 2.23339311990082 \tabularnewline
86 & 1.77 & 1.337559837521 & 2.202440162479 \tabularnewline
87 & 1.5 & 0.776389204371834 & 2.22361079562817 \tabularnewline
88 & 1.23 & 0.17074225764019 & 2.28925774235981 \tabularnewline
89 & 0.96 & -0.47424176322318 & 2.39424176322318 \tabularnewline
90 & 0.69 & -1.15485278357721 & 2.53485278357721 \tabularnewline
91 & 0.42 & -1.86825825367162 & 2.70825825367162 \tabularnewline
92 & 0.15 & -2.61220624868864 & 2.91220624868864 \tabularnewline
93 & -0.12 & -3.38485162987806 & 3.14485162987806 \tabularnewline
94 & -0.39 & -4.18464702543132 & 3.40464702543132 \tabularnewline
95 & -0.66 & -5.0102706588713 & 3.6902706588713 \tabularnewline
96 & -0.93 & -5.86057646084438 & 4.00057646084438 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232603&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]85[/C][C]2.04[/C][C]1.84660688009918[/C][C]2.23339311990082[/C][/ROW]
[ROW][C]86[/C][C]1.77[/C][C]1.337559837521[/C][C]2.202440162479[/C][/ROW]
[ROW][C]87[/C][C]1.5[/C][C]0.776389204371834[/C][C]2.22361079562817[/C][/ROW]
[ROW][C]88[/C][C]1.23[/C][C]0.17074225764019[/C][C]2.28925774235981[/C][/ROW]
[ROW][C]89[/C][C]0.96[/C][C]-0.47424176322318[/C][C]2.39424176322318[/C][/ROW]
[ROW][C]90[/C][C]0.69[/C][C]-1.15485278357721[/C][C]2.53485278357721[/C][/ROW]
[ROW][C]91[/C][C]0.42[/C][C]-1.86825825367162[/C][C]2.70825825367162[/C][/ROW]
[ROW][C]92[/C][C]0.15[/C][C]-2.61220624868864[/C][C]2.91220624868864[/C][/ROW]
[ROW][C]93[/C][C]-0.12[/C][C]-3.38485162987806[/C][C]3.14485162987806[/C][/ROW]
[ROW][C]94[/C][C]-0.39[/C][C]-4.18464702543132[/C][C]3.40464702543132[/C][/ROW]
[ROW][C]95[/C][C]-0.66[/C][C]-5.0102706588713[/C][C]3.6902706588713[/C][/ROW]
[ROW][C]96[/C][C]-0.93[/C][C]-5.86057646084438[/C][C]4.00057646084438[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232603&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232603&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
85	2.04	1.84660688009918	2.23339311990082
86	1.77	1.337559837521	2.202440162479
87	1.5	0.776389204371834	2.22361079562817
88	1.23	0.17074225764019	2.28925774235981
89	0.96	-0.47424176322318	2.39424176322318
90	0.69	-1.15485278357721	2.53485278357721
91	0.42	-1.86825825367162	2.70825825367162
92	0.15	-2.61220624868864	2.91220624868864
93	-0.12	-3.38485162987806	3.14485162987806
94	-0.39	-4.18464702543132	3.40464702543132
95	-0.66	-5.0102706588713	3.6902706588713
96	-0.93	-5.86057646084438	4.00057646084438

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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