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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

Wed, 23 May 2012 10:39:26 -0400

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/May/23/t1337784019272bk1gmr5jgxgv.htm/, Retrieved Mon, 29 Apr 2024 02:00:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167201, Retrieved Mon, 29 Apr 2024 02:00:49 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

112

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

-       [Exponential Smoothing] [Voorspellen van t...] [2012-05-23 14:39:26] [08ac479f43b71ff391b5d339ed1ce3ff] [Current]

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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=167201&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=167201&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167201&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	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=167201&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=167201&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167201&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	73.97	73.97	0
4	73.97	73.97	0
5	73.97	73.97	0
6	73.97	73.97	0
7	73.96	73.97	-0.0100000000000051
8	74.44	73.95	0.490000000000009
9	75.43	74.92	0.510000000000005
10	75.77	76.42	-0.65000000000002
11	75.82	76.11	-0.289999999999992
12	75.85	75.87	-0.019999999999996
13	75.85	75.88	-0.0300000000000011
14	75.85	75.85	0
15	77.95	75.85	2.10000000000001
16	82.07	80.05	2.01999999999998
17	84.82	86.19	-1.36999999999999
18	85.08	87.57	-2.48999999999999
19	85.34	85.34	0
20	85.65	85.6	0.0499999999999972
21	85.65	85.96	-0.310000000000002
22	85.72	85.65	0.0699999999999932
23	85.73	85.79	-0.0599999999999881
24	85.73	85.74	-0.0100000000000051
25	85.73	85.73	0
26	85.73	85.73	0
27	85.74	85.73	0.00999999999999091
28	86.32	85.75	0.570000000000007
29	87.59	86.9	0.690000000000012
30	87.81	88.86	-1.05000000000001
31	87.87	88.03	-0.159999999999997
32	87.94	87.93	0.00999999999999091
33	87.96	88.01	-0.0499999999999972
34	88.01	87.98	0.0300000000000153
35	88.01	88.06	-0.0500000000000114
36	88.01	88.01	0
37	88.01	88.01	0
38	88.01	88.01	0
39	88.59	88.01	0.579999999999998
40	89.43	89.17	0.260000000000005
41	89.63	90.27	-0.640000000000015
42	89.73	89.83	-0.0999999999999801
43	89.88	89.83	0.0499999999999829
44	89.89	90.03	-0.139999999999986
45	89.9	89.9	0
46	89.91	89.91	-1.4210854715202e-14
47	89.86	89.92	-0.0599999999999881
48	90.07	89.81	0.259999999999991
49	90.17	90.28	-0.109999999999985
50	90.17	90.27	-0.100000000000009
51	90.28	90.17	0.109999999999999
52	90.87	90.39	0.480000000000004
53	92.05	91.46	0.589999999999989
54	92.1	93.23	-1.13
55	92.16	92.15	0.0100000000000051
56	92.22	92.22	0
57	92.25	92.28	-0.0300000000000011
58	92.29	92.28	0.0100000000000051
59	92.29	92.33	-0.0400000000000063
60	92.29	92.29	0

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 73.97 & 73.97 & 0 \tabularnewline
4 & 73.97 & 73.97 & 0 \tabularnewline
5 & 73.97 & 73.97 & 0 \tabularnewline
6 & 73.97 & 73.97 & 0 \tabularnewline
7 & 73.96 & 73.97 & -0.0100000000000051 \tabularnewline
8 & 74.44 & 73.95 & 0.490000000000009 \tabularnewline
9 & 75.43 & 74.92 & 0.510000000000005 \tabularnewline
10 & 75.77 & 76.42 & -0.65000000000002 \tabularnewline
11 & 75.82 & 76.11 & -0.289999999999992 \tabularnewline
12 & 75.85 & 75.87 & -0.019999999999996 \tabularnewline
13 & 75.85 & 75.88 & -0.0300000000000011 \tabularnewline
14 & 75.85 & 75.85 & 0 \tabularnewline
15 & 77.95 & 75.85 & 2.10000000000001 \tabularnewline
16 & 82.07 & 80.05 & 2.01999999999998 \tabularnewline
17 & 84.82 & 86.19 & -1.36999999999999 \tabularnewline
18 & 85.08 & 87.57 & -2.48999999999999 \tabularnewline
19 & 85.34 & 85.34 & 0 \tabularnewline
20 & 85.65 & 85.6 & 0.0499999999999972 \tabularnewline
21 & 85.65 & 85.96 & -0.310000000000002 \tabularnewline
22 & 85.72 & 85.65 & 0.0699999999999932 \tabularnewline
23 & 85.73 & 85.79 & -0.0599999999999881 \tabularnewline
24 & 85.73 & 85.74 & -0.0100000000000051 \tabularnewline
25 & 85.73 & 85.73 & 0 \tabularnewline
26 & 85.73 & 85.73 & 0 \tabularnewline
27 & 85.74 & 85.73 & 0.00999999999999091 \tabularnewline
28 & 86.32 & 85.75 & 0.570000000000007 \tabularnewline
29 & 87.59 & 86.9 & 0.690000000000012 \tabularnewline
30 & 87.81 & 88.86 & -1.05000000000001 \tabularnewline
31 & 87.87 & 88.03 & -0.159999999999997 \tabularnewline
32 & 87.94 & 87.93 & 0.00999999999999091 \tabularnewline
33 & 87.96 & 88.01 & -0.0499999999999972 \tabularnewline
34 & 88.01 & 87.98 & 0.0300000000000153 \tabularnewline
35 & 88.01 & 88.06 & -0.0500000000000114 \tabularnewline
36 & 88.01 & 88.01 & 0 \tabularnewline
37 & 88.01 & 88.01 & 0 \tabularnewline
38 & 88.01 & 88.01 & 0 \tabularnewline
39 & 88.59 & 88.01 & 0.579999999999998 \tabularnewline
40 & 89.43 & 89.17 & 0.260000000000005 \tabularnewline
41 & 89.63 & 90.27 & -0.640000000000015 \tabularnewline
42 & 89.73 & 89.83 & -0.0999999999999801 \tabularnewline
43 & 89.88 & 89.83 & 0.0499999999999829 \tabularnewline
44 & 89.89 & 90.03 & -0.139999999999986 \tabularnewline
45 & 89.9 & 89.9 & 0 \tabularnewline
46 & 89.91 & 89.91 & -1.4210854715202e-14 \tabularnewline
47 & 89.86 & 89.92 & -0.0599999999999881 \tabularnewline
48 & 90.07 & 89.81 & 0.259999999999991 \tabularnewline
49 & 90.17 & 90.28 & -0.109999999999985 \tabularnewline
50 & 90.17 & 90.27 & -0.100000000000009 \tabularnewline
51 & 90.28 & 90.17 & 0.109999999999999 \tabularnewline
52 & 90.87 & 90.39 & 0.480000000000004 \tabularnewline
53 & 92.05 & 91.46 & 0.589999999999989 \tabularnewline
54 & 92.1 & 93.23 & -1.13 \tabularnewline
55 & 92.16 & 92.15 & 0.0100000000000051 \tabularnewline
56 & 92.22 & 92.22 & 0 \tabularnewline
57 & 92.25 & 92.28 & -0.0300000000000011 \tabularnewline
58 & 92.29 & 92.28 & 0.0100000000000051 \tabularnewline
59 & 92.29 & 92.33 & -0.0400000000000063 \tabularnewline
60 & 92.29 & 92.29 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167201&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]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]73.96[/C][C]73.97[/C][C]-0.0100000000000051[/C][/ROW]
[ROW][C]8[/C][C]74.44[/C][C]73.95[/C][C]0.490000000000009[/C][/ROW]
[ROW][C]9[/C][C]75.43[/C][C]74.92[/C][C]0.510000000000005[/C][/ROW]
[ROW][C]10[/C][C]75.77[/C][C]76.42[/C][C]-0.65000000000002[/C][/ROW]
[ROW][C]11[/C][C]75.82[/C][C]76.11[/C][C]-0.289999999999992[/C][/ROW]
[ROW][C]12[/C][C]75.85[/C][C]75.87[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]13[/C][C]75.85[/C][C]75.88[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]14[/C][C]75.85[/C][C]75.85[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]77.95[/C][C]75.85[/C][C]2.10000000000001[/C][/ROW]
[ROW][C]16[/C][C]82.07[/C][C]80.05[/C][C]2.01999999999998[/C][/ROW]
[ROW][C]17[/C][C]84.82[/C][C]86.19[/C][C]-1.36999999999999[/C][/ROW]
[ROW][C]18[/C][C]85.08[/C][C]87.57[/C][C]-2.48999999999999[/C][/ROW]
[ROW][C]19[/C][C]85.34[/C][C]85.34[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]85.65[/C][C]85.6[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]21[/C][C]85.65[/C][C]85.96[/C][C]-0.310000000000002[/C][/ROW]
[ROW][C]22[/C][C]85.72[/C][C]85.65[/C][C]0.0699999999999932[/C][/ROW]
[ROW][C]23[/C][C]85.73[/C][C]85.79[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]24[/C][C]85.73[/C][C]85.74[/C][C]-0.0100000000000051[/C][/ROW]
[ROW][C]25[/C][C]85.73[/C][C]85.73[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]85.73[/C][C]85.73[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]85.74[/C][C]85.73[/C][C]0.00999999999999091[/C][/ROW]
[ROW][C]28[/C][C]86.32[/C][C]85.75[/C][C]0.570000000000007[/C][/ROW]
[ROW][C]29[/C][C]87.59[/C][C]86.9[/C][C]0.690000000000012[/C][/ROW]
[ROW][C]30[/C][C]87.81[/C][C]88.86[/C][C]-1.05000000000001[/C][/ROW]
[ROW][C]31[/C][C]87.87[/C][C]88.03[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]32[/C][C]87.94[/C][C]87.93[/C][C]0.00999999999999091[/C][/ROW]
[ROW][C]33[/C][C]87.96[/C][C]88.01[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]34[/C][C]88.01[/C][C]87.98[/C][C]0.0300000000000153[/C][/ROW]
[ROW][C]35[/C][C]88.01[/C][C]88.06[/C][C]-0.0500000000000114[/C][/ROW]
[ROW][C]36[/C][C]88.01[/C][C]88.01[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]88.01[/C][C]88.01[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]88.01[/C][C]88.01[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]88.59[/C][C]88.01[/C][C]0.579999999999998[/C][/ROW]
[ROW][C]40[/C][C]89.43[/C][C]89.17[/C][C]0.260000000000005[/C][/ROW]
[ROW][C]41[/C][C]89.63[/C][C]90.27[/C][C]-0.640000000000015[/C][/ROW]
[ROW][C]42[/C][C]89.73[/C][C]89.83[/C][C]-0.0999999999999801[/C][/ROW]
[ROW][C]43[/C][C]89.88[/C][C]89.83[/C][C]0.0499999999999829[/C][/ROW]
[ROW][C]44[/C][C]89.89[/C][C]90.03[/C][C]-0.139999999999986[/C][/ROW]
[ROW][C]45[/C][C]89.9[/C][C]89.9[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]89.91[/C][C]89.91[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]47[/C][C]89.86[/C][C]89.92[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]48[/C][C]90.07[/C][C]89.81[/C][C]0.259999999999991[/C][/ROW]
[ROW][C]49[/C][C]90.17[/C][C]90.28[/C][C]-0.109999999999985[/C][/ROW]
[ROW][C]50[/C][C]90.17[/C][C]90.27[/C][C]-0.100000000000009[/C][/ROW]
[ROW][C]51[/C][C]90.28[/C][C]90.17[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]52[/C][C]90.87[/C][C]90.39[/C][C]0.480000000000004[/C][/ROW]
[ROW][C]53[/C][C]92.05[/C][C]91.46[/C][C]0.589999999999989[/C][/ROW]
[ROW][C]54[/C][C]92.1[/C][C]93.23[/C][C]-1.13[/C][/ROW]
[ROW][C]55[/C][C]92.16[/C][C]92.15[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]56[/C][C]92.22[/C][C]92.22[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]92.25[/C][C]92.28[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]58[/C][C]92.29[/C][C]92.28[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]59[/C][C]92.29[/C][C]92.33[/C][C]-0.0400000000000063[/C][/ROW]
[ROW][C]60[/C][C]92.29[/C][C]92.29[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167201&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167201&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	73.97	73.97	0
4	73.97	73.97	0
5	73.97	73.97	0
6	73.97	73.97	0
7	73.96	73.97	-0.0100000000000051
8	74.44	73.95	0.490000000000009
9	75.43	74.92	0.510000000000005
10	75.77	76.42	-0.65000000000002
11	75.82	76.11	-0.289999999999992
12	75.85	75.87	-0.019999999999996
13	75.85	75.88	-0.0300000000000011
14	75.85	75.85	0
15	77.95	75.85	2.10000000000001
16	82.07	80.05	2.01999999999998
17	84.82	86.19	-1.36999999999999
18	85.08	87.57	-2.48999999999999
19	85.34	85.34	0
20	85.65	85.6	0.0499999999999972
21	85.65	85.96	-0.310000000000002
22	85.72	85.65	0.0699999999999932
23	85.73	85.79	-0.0599999999999881
24	85.73	85.74	-0.0100000000000051
25	85.73	85.73	0
26	85.73	85.73	0
27	85.74	85.73	0.00999999999999091
28	86.32	85.75	0.570000000000007
29	87.59	86.9	0.690000000000012
30	87.81	88.86	-1.05000000000001
31	87.87	88.03	-0.159999999999997
32	87.94	87.93	0.00999999999999091
33	87.96	88.01	-0.0499999999999972
34	88.01	87.98	0.0300000000000153
35	88.01	88.06	-0.0500000000000114
36	88.01	88.01	0
37	88.01	88.01	0
38	88.01	88.01	0
39	88.59	88.01	0.579999999999998
40	89.43	89.17	0.260000000000005
41	89.63	90.27	-0.640000000000015
42	89.73	89.83	-0.0999999999999801
43	89.88	89.83	0.0499999999999829
44	89.89	90.03	-0.139999999999986
45	89.9	89.9	0
46	89.91	89.91	-1.4210854715202e-14
47	89.86	89.92	-0.0599999999999881
48	90.07	89.81	0.259999999999991
49	90.17	90.28	-0.109999999999985
50	90.17	90.27	-0.100000000000009
51	90.28	90.17	0.109999999999999
52	90.87	90.39	0.480000000000004
53	92.05	91.46	0.589999999999989
54	92.1	93.23	-1.13
55	92.16	92.15	0.0100000000000051
56	92.22	92.22	0
57	92.25	92.28	-0.0300000000000011
58	92.29	92.28	0.0100000000000051
59	92.29	92.33	-0.0400000000000063
60	92.29	92.29	0

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	92.29	91.0605858957577	93.5194141042424
62	92.29	89.5409464904171	95.0390535095829
63	92.29	87.6899536354575	96.8900463645425
64	92.29	85.5562216259146	99.0237783740854
65	92.29	83.1724209801038	101.407579019896
66	92.29	80.5621369118832	104.017863088117
67	92.29	77.7433761456686	106.836623854331
68	92.29	74.7304543310243	109.849545668976
69	92.29	71.5351011489491	113.044898851051
70	92.29	68.1671533543747	116.412846645625
71	92.29	64.6350135763318	119.944986423668
72	92.29	60.9459674609103	123.63403253909

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 92.29 & 91.0605858957577 & 93.5194141042424 \tabularnewline
62 & 92.29 & 89.5409464904171 & 95.0390535095829 \tabularnewline
63 & 92.29 & 87.6899536354575 & 96.8900463645425 \tabularnewline
64 & 92.29 & 85.5562216259146 & 99.0237783740854 \tabularnewline
65 & 92.29 & 83.1724209801038 & 101.407579019896 \tabularnewline
66 & 92.29 & 80.5621369118832 & 104.017863088117 \tabularnewline
67 & 92.29 & 77.7433761456686 & 106.836623854331 \tabularnewline
68 & 92.29 & 74.7304543310243 & 109.849545668976 \tabularnewline
69 & 92.29 & 71.5351011489491 & 113.044898851051 \tabularnewline
70 & 92.29 & 68.1671533543747 & 116.412846645625 \tabularnewline
71 & 92.29 & 64.6350135763318 & 119.944986423668 \tabularnewline
72 & 92.29 & 60.9459674609103 & 123.63403253909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167201&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]92.29[/C][C]91.0605858957577[/C][C]93.5194141042424[/C][/ROW]
[ROW][C]62[/C][C]92.29[/C][C]89.5409464904171[/C][C]95.0390535095829[/C][/ROW]
[ROW][C]63[/C][C]92.29[/C][C]87.6899536354575[/C][C]96.8900463645425[/C][/ROW]
[ROW][C]64[/C][C]92.29[/C][C]85.5562216259146[/C][C]99.0237783740854[/C][/ROW]
[ROW][C]65[/C][C]92.29[/C][C]83.1724209801038[/C][C]101.407579019896[/C][/ROW]
[ROW][C]66[/C][C]92.29[/C][C]80.5621369118832[/C][C]104.017863088117[/C][/ROW]
[ROW][C]67[/C][C]92.29[/C][C]77.7433761456686[/C][C]106.836623854331[/C][/ROW]
[ROW][C]68[/C][C]92.29[/C][C]74.7304543310243[/C][C]109.849545668976[/C][/ROW]
[ROW][C]69[/C][C]92.29[/C][C]71.5351011489491[/C][C]113.044898851051[/C][/ROW]
[ROW][C]70[/C][C]92.29[/C][C]68.1671533543747[/C][C]116.412846645625[/C][/ROW]
[ROW][C]71[/C][C]92.29[/C][C]64.6350135763318[/C][C]119.944986423668[/C][/ROW]
[ROW][C]72[/C][C]92.29[/C][C]60.9459674609103[/C][C]123.63403253909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167201&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167201&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	92.29	91.0605858957577	93.5194141042424
62	92.29	89.5409464904171	95.0390535095829
63	92.29	87.6899536354575	96.8900463645425
64	92.29	85.5562216259146	99.0237783740854
65	92.29	83.1724209801038	101.407579019896
66	92.29	80.5621369118832	104.017863088117
67	92.29	77.7433761456686	106.836623854331
68	92.29	74.7304543310243	109.849545668976
69	92.29	71.5351011489491	113.044898851051
70	92.29	68.1671533543747	116.412846645625
71	92.29	64.6350135763318	119.944986423668
72	92.29	60.9459674609103	123.63403253909

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