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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 22 May 2014 08:15:50 -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/2014/May/22/t1400760966j61noe6dnessck4.htm/, Retrieved Thu, 16 May 2024 03:32:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235097, Retrieved Thu, 16 May 2024 03:32:38 +0000

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User-defined keywords

Estimated Impact

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

-       [Exponential Smoothing] [Double eigen reeks] [2014-05-22 12:15:50] [1195732e18620915cb775ad7ef5494bd] [Current]

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Dataseries X:

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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=235097&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=235097&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235097&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	0
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235097&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]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235097&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235097&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	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	227.01	227.81	-0.800000000000011
4	227.26	227.01	0.25
5	227.1	227.26	-0.159999999999997
6	227.59	227.1	0.490000000000009
7	227.59	227.59	0
8	227.7	227.59	0.109999999999985
9	227.75	227.7	0.0500000000000114
10	226.33	227.75	-1.41999999999999
11	225.95	226.33	-0.380000000000024
12	226.33	225.95	0.380000000000024
13	226.33	226.33	0
14	226.22	226.33	-0.110000000000014
15	224.84	226.22	-1.38
16	221.88	224.84	-2.96000000000001
17	222.37	221.88	0.490000000000009
18	221.8	222.37	-0.569999999999993
19	221.8	221.8	0
20	221.8	221.8	0
21	221.9	221.8	0.0999999999999943
22	220.2	221.9	-1.70000000000002
23	219.95	220.2	-0.25
24	220.05	219.95	0.100000000000023
25	220.05	220.05	0
26	220.05	220.05	0
27	220.62	220.05	0.569999999999993
28	221.53	220.62	0.909999999999997
29	221.61	221.53	0.0800000000000125
30	221.5	221.61	-0.110000000000014
31	221.5	221.5	0
32	221.87	221.5	0.370000000000005
33	222.27	221.87	0.400000000000006
34	220.86	222.27	-1.41
35	221.49	220.86	0.629999999999995
36	221.67	221.49	0.179999999999978
37	221.67	221.67	0
38	221.72	221.67	0.0500000000000114
39	221.67	221.72	-0.0500000000000114
40	220.29	221.67	-1.38
41	220.75	220.29	0.460000000000008
42	219.59	220.75	-1.16
43	219.59	219.59	0
44	219.59	219.59	0
45	219.82	219.59	0.22999999999999
46	221.59	219.82	1.77000000000001
47	220.9	221.59	-0.689999999999998
48	221.01	220.9	0.109999999999985
49	221.01	221.01	0
50	219.69	221.01	-1.31999999999999
51	221	219.69	1.31
52	219.82	221	-1.18000000000001
53	218.04	219.82	-1.78
54	217.97	218.04	-0.0699999999999932
55	217.97	217.97	0
56	217.53	217.97	-0.439999999999998
57	217	217.53	-0.530000000000001
58	217.18	217	0.180000000000007
59	217.68	217.18	0.5
60	217.71	217.68	0.0300000000000011
61	217.71	217.71	0
62	218.5	217.71	0.789999999999992
63	218.8	218.5	0.300000000000011
64	218.94	218.8	0.139999999999986
65	220	218.94	1.06
66	219.89	220	-0.110000000000014
67	219.89	219.89	0
68	220.08	219.89	0.190000000000026
69	220.16	220.08	0.0799999999999841
70	221	220.16	0.840000000000003
71	222.16	221	1.16
72	221.5	222.16	-0.659999999999997
73	221.5	221.5	0
74	221.6	221.5	0.0999999999999943
75	221.85	221.6	0.25
76	223.11	221.85	1.26000000000002
77	222.79	223.11	-0.320000000000022
78	222.45	222.79	-0.340000000000003
79	222.45	222.45	0
80	222.4	222.45	-0.0499999999999829
81	223.15	222.4	0.75
82	224.4	223.15	1.25
83	224.24	224.4	-0.159999999999997
84	223.92	224.24	-0.320000000000022

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 227.01 & 227.81 & -0.800000000000011 \tabularnewline
4 & 227.26 & 227.01 & 0.25 \tabularnewline
5 & 227.1 & 227.26 & -0.159999999999997 \tabularnewline
6 & 227.59 & 227.1 & 0.490000000000009 \tabularnewline
7 & 227.59 & 227.59 & 0 \tabularnewline
8 & 227.7 & 227.59 & 0.109999999999985 \tabularnewline
9 & 227.75 & 227.7 & 0.0500000000000114 \tabularnewline
10 & 226.33 & 227.75 & -1.41999999999999 \tabularnewline
11 & 225.95 & 226.33 & -0.380000000000024 \tabularnewline
12 & 226.33 & 225.95 & 0.380000000000024 \tabularnewline
13 & 226.33 & 226.33 & 0 \tabularnewline
14 & 226.22 & 226.33 & -0.110000000000014 \tabularnewline
15 & 224.84 & 226.22 & -1.38 \tabularnewline
16 & 221.88 & 224.84 & -2.96000000000001 \tabularnewline
17 & 222.37 & 221.88 & 0.490000000000009 \tabularnewline
18 & 221.8 & 222.37 & -0.569999999999993 \tabularnewline
19 & 221.8 & 221.8 & 0 \tabularnewline
20 & 221.8 & 221.8 & 0 \tabularnewline
21 & 221.9 & 221.8 & 0.0999999999999943 \tabularnewline
22 & 220.2 & 221.9 & -1.70000000000002 \tabularnewline
23 & 219.95 & 220.2 & -0.25 \tabularnewline
24 & 220.05 & 219.95 & 0.100000000000023 \tabularnewline
25 & 220.05 & 220.05 & 0 \tabularnewline
26 & 220.05 & 220.05 & 0 \tabularnewline
27 & 220.62 & 220.05 & 0.569999999999993 \tabularnewline
28 & 221.53 & 220.62 & 0.909999999999997 \tabularnewline
29 & 221.61 & 221.53 & 0.0800000000000125 \tabularnewline
30 & 221.5 & 221.61 & -0.110000000000014 \tabularnewline
31 & 221.5 & 221.5 & 0 \tabularnewline
32 & 221.87 & 221.5 & 0.370000000000005 \tabularnewline
33 & 222.27 & 221.87 & 0.400000000000006 \tabularnewline
34 & 220.86 & 222.27 & -1.41 \tabularnewline
35 & 221.49 & 220.86 & 0.629999999999995 \tabularnewline
36 & 221.67 & 221.49 & 0.179999999999978 \tabularnewline
37 & 221.67 & 221.67 & 0 \tabularnewline
38 & 221.72 & 221.67 & 0.0500000000000114 \tabularnewline
39 & 221.67 & 221.72 & -0.0500000000000114 \tabularnewline
40 & 220.29 & 221.67 & -1.38 \tabularnewline
41 & 220.75 & 220.29 & 0.460000000000008 \tabularnewline
42 & 219.59 & 220.75 & -1.16 \tabularnewline
43 & 219.59 & 219.59 & 0 \tabularnewline
44 & 219.59 & 219.59 & 0 \tabularnewline
45 & 219.82 & 219.59 & 0.22999999999999 \tabularnewline
46 & 221.59 & 219.82 & 1.77000000000001 \tabularnewline
47 & 220.9 & 221.59 & -0.689999999999998 \tabularnewline
48 & 221.01 & 220.9 & 0.109999999999985 \tabularnewline
49 & 221.01 & 221.01 & 0 \tabularnewline
50 & 219.69 & 221.01 & -1.31999999999999 \tabularnewline
51 & 221 & 219.69 & 1.31 \tabularnewline
52 & 219.82 & 221 & -1.18000000000001 \tabularnewline
53 & 218.04 & 219.82 & -1.78 \tabularnewline
54 & 217.97 & 218.04 & -0.0699999999999932 \tabularnewline
55 & 217.97 & 217.97 & 0 \tabularnewline
56 & 217.53 & 217.97 & -0.439999999999998 \tabularnewline
57 & 217 & 217.53 & -0.530000000000001 \tabularnewline
58 & 217.18 & 217 & 0.180000000000007 \tabularnewline
59 & 217.68 & 217.18 & 0.5 \tabularnewline
60 & 217.71 & 217.68 & 0.0300000000000011 \tabularnewline
61 & 217.71 & 217.71 & 0 \tabularnewline
62 & 218.5 & 217.71 & 0.789999999999992 \tabularnewline
63 & 218.8 & 218.5 & 0.300000000000011 \tabularnewline
64 & 218.94 & 218.8 & 0.139999999999986 \tabularnewline
65 & 220 & 218.94 & 1.06 \tabularnewline
66 & 219.89 & 220 & -0.110000000000014 \tabularnewline
67 & 219.89 & 219.89 & 0 \tabularnewline
68 & 220.08 & 219.89 & 0.190000000000026 \tabularnewline
69 & 220.16 & 220.08 & 0.0799999999999841 \tabularnewline
70 & 221 & 220.16 & 0.840000000000003 \tabularnewline
71 & 222.16 & 221 & 1.16 \tabularnewline
72 & 221.5 & 222.16 & -0.659999999999997 \tabularnewline
73 & 221.5 & 221.5 & 0 \tabularnewline
74 & 221.6 & 221.5 & 0.0999999999999943 \tabularnewline
75 & 221.85 & 221.6 & 0.25 \tabularnewline
76 & 223.11 & 221.85 & 1.26000000000002 \tabularnewline
77 & 222.79 & 223.11 & -0.320000000000022 \tabularnewline
78 & 222.45 & 222.79 & -0.340000000000003 \tabularnewline
79 & 222.45 & 222.45 & 0 \tabularnewline
80 & 222.4 & 222.45 & -0.0499999999999829 \tabularnewline
81 & 223.15 & 222.4 & 0.75 \tabularnewline
82 & 224.4 & 223.15 & 1.25 \tabularnewline
83 & 224.24 & 224.4 & -0.159999999999997 \tabularnewline
84 & 223.92 & 224.24 & -0.320000000000022 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235097&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]227.01[/C][C]227.81[/C][C]-0.800000000000011[/C][/ROW]
[ROW][C]4[/C][C]227.26[/C][C]227.01[/C][C]0.25[/C][/ROW]
[ROW][C]5[/C][C]227.1[/C][C]227.26[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]6[/C][C]227.59[/C][C]227.1[/C][C]0.490000000000009[/C][/ROW]
[ROW][C]7[/C][C]227.59[/C][C]227.59[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]227.7[/C][C]227.59[/C][C]0.109999999999985[/C][/ROW]
[ROW][C]9[/C][C]227.75[/C][C]227.7[/C][C]0.0500000000000114[/C][/ROW]
[ROW][C]10[/C][C]226.33[/C][C]227.75[/C][C]-1.41999999999999[/C][/ROW]
[ROW][C]11[/C][C]225.95[/C][C]226.33[/C][C]-0.380000000000024[/C][/ROW]
[ROW][C]12[/C][C]226.33[/C][C]225.95[/C][C]0.380000000000024[/C][/ROW]
[ROW][C]13[/C][C]226.33[/C][C]226.33[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]226.22[/C][C]226.33[/C][C]-0.110000000000014[/C][/ROW]
[ROW][C]15[/C][C]224.84[/C][C]226.22[/C][C]-1.38[/C][/ROW]
[ROW][C]16[/C][C]221.88[/C][C]224.84[/C][C]-2.96000000000001[/C][/ROW]
[ROW][C]17[/C][C]222.37[/C][C]221.88[/C][C]0.490000000000009[/C][/ROW]
[ROW][C]18[/C][C]221.8[/C][C]222.37[/C][C]-0.569999999999993[/C][/ROW]
[ROW][C]19[/C][C]221.8[/C][C]221.8[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]221.8[/C][C]221.8[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]221.9[/C][C]221.8[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]22[/C][C]220.2[/C][C]221.9[/C][C]-1.70000000000002[/C][/ROW]
[ROW][C]23[/C][C]219.95[/C][C]220.2[/C][C]-0.25[/C][/ROW]
[ROW][C]24[/C][C]220.05[/C][C]219.95[/C][C]0.100000000000023[/C][/ROW]
[ROW][C]25[/C][C]220.05[/C][C]220.05[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]220.05[/C][C]220.05[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]220.62[/C][C]220.05[/C][C]0.569999999999993[/C][/ROW]
[ROW][C]28[/C][C]221.53[/C][C]220.62[/C][C]0.909999999999997[/C][/ROW]
[ROW][C]29[/C][C]221.61[/C][C]221.53[/C][C]0.0800000000000125[/C][/ROW]
[ROW][C]30[/C][C]221.5[/C][C]221.61[/C][C]-0.110000000000014[/C][/ROW]
[ROW][C]31[/C][C]221.5[/C][C]221.5[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]221.87[/C][C]221.5[/C][C]0.370000000000005[/C][/ROW]
[ROW][C]33[/C][C]222.27[/C][C]221.87[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]34[/C][C]220.86[/C][C]222.27[/C][C]-1.41[/C][/ROW]
[ROW][C]35[/C][C]221.49[/C][C]220.86[/C][C]0.629999999999995[/C][/ROW]
[ROW][C]36[/C][C]221.67[/C][C]221.49[/C][C]0.179999999999978[/C][/ROW]
[ROW][C]37[/C][C]221.67[/C][C]221.67[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]221.72[/C][C]221.67[/C][C]0.0500000000000114[/C][/ROW]
[ROW][C]39[/C][C]221.67[/C][C]221.72[/C][C]-0.0500000000000114[/C][/ROW]
[ROW][C]40[/C][C]220.29[/C][C]221.67[/C][C]-1.38[/C][/ROW]
[ROW][C]41[/C][C]220.75[/C][C]220.29[/C][C]0.460000000000008[/C][/ROW]
[ROW][C]42[/C][C]219.59[/C][C]220.75[/C][C]-1.16[/C][/ROW]
[ROW][C]43[/C][C]219.59[/C][C]219.59[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]219.59[/C][C]219.59[/C][C]0[/C][/ROW]
[ROW][C]45[/C][C]219.82[/C][C]219.59[/C][C]0.22999999999999[/C][/ROW]
[ROW][C]46[/C][C]221.59[/C][C]219.82[/C][C]1.77000000000001[/C][/ROW]
[ROW][C]47[/C][C]220.9[/C][C]221.59[/C][C]-0.689999999999998[/C][/ROW]
[ROW][C]48[/C][C]221.01[/C][C]220.9[/C][C]0.109999999999985[/C][/ROW]
[ROW][C]49[/C][C]221.01[/C][C]221.01[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]219.69[/C][C]221.01[/C][C]-1.31999999999999[/C][/ROW]
[ROW][C]51[/C][C]221[/C][C]219.69[/C][C]1.31[/C][/ROW]
[ROW][C]52[/C][C]219.82[/C][C]221[/C][C]-1.18000000000001[/C][/ROW]
[ROW][C]53[/C][C]218.04[/C][C]219.82[/C][C]-1.78[/C][/ROW]
[ROW][C]54[/C][C]217.97[/C][C]218.04[/C][C]-0.0699999999999932[/C][/ROW]
[ROW][C]55[/C][C]217.97[/C][C]217.97[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]217.53[/C][C]217.97[/C][C]-0.439999999999998[/C][/ROW]
[ROW][C]57[/C][C]217[/C][C]217.53[/C][C]-0.530000000000001[/C][/ROW]
[ROW][C]58[/C][C]217.18[/C][C]217[/C][C]0.180000000000007[/C][/ROW]
[ROW][C]59[/C][C]217.68[/C][C]217.18[/C][C]0.5[/C][/ROW]
[ROW][C]60[/C][C]217.71[/C][C]217.68[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]61[/C][C]217.71[/C][C]217.71[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]218.5[/C][C]217.71[/C][C]0.789999999999992[/C][/ROW]
[ROW][C]63[/C][C]218.8[/C][C]218.5[/C][C]0.300000000000011[/C][/ROW]
[ROW][C]64[/C][C]218.94[/C][C]218.8[/C][C]0.139999999999986[/C][/ROW]
[ROW][C]65[/C][C]220[/C][C]218.94[/C][C]1.06[/C][/ROW]
[ROW][C]66[/C][C]219.89[/C][C]220[/C][C]-0.110000000000014[/C][/ROW]
[ROW][C]67[/C][C]219.89[/C][C]219.89[/C][C]0[/C][/ROW]
[ROW][C]68[/C][C]220.08[/C][C]219.89[/C][C]0.190000000000026[/C][/ROW]
[ROW][C]69[/C][C]220.16[/C][C]220.08[/C][C]0.0799999999999841[/C][/ROW]
[ROW][C]70[/C][C]221[/C][C]220.16[/C][C]0.840000000000003[/C][/ROW]
[ROW][C]71[/C][C]222.16[/C][C]221[/C][C]1.16[/C][/ROW]
[ROW][C]72[/C][C]221.5[/C][C]222.16[/C][C]-0.659999999999997[/C][/ROW]
[ROW][C]73[/C][C]221.5[/C][C]221.5[/C][C]0[/C][/ROW]
[ROW][C]74[/C][C]221.6[/C][C]221.5[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]75[/C][C]221.85[/C][C]221.6[/C][C]0.25[/C][/ROW]
[ROW][C]76[/C][C]223.11[/C][C]221.85[/C][C]1.26000000000002[/C][/ROW]
[ROW][C]77[/C][C]222.79[/C][C]223.11[/C][C]-0.320000000000022[/C][/ROW]
[ROW][C]78[/C][C]222.45[/C][C]222.79[/C][C]-0.340000000000003[/C][/ROW]
[ROW][C]79[/C][C]222.45[/C][C]222.45[/C][C]0[/C][/ROW]
[ROW][C]80[/C][C]222.4[/C][C]222.45[/C][C]-0.0499999999999829[/C][/ROW]
[ROW][C]81[/C][C]223.15[/C][C]222.4[/C][C]0.75[/C][/ROW]
[ROW][C]82[/C][C]224.4[/C][C]223.15[/C][C]1.25[/C][/ROW]
[ROW][C]83[/C][C]224.24[/C][C]224.4[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]84[/C][C]223.92[/C][C]224.24[/C][C]-0.320000000000022[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235097&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235097&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	227.01	227.81	-0.800000000000011
4	227.26	227.01	0.25
5	227.1	227.26	-0.159999999999997
6	227.59	227.1	0.490000000000009
7	227.59	227.59	0
8	227.7	227.59	0.109999999999985
9	227.75	227.7	0.0500000000000114
10	226.33	227.75	-1.41999999999999
11	225.95	226.33	-0.380000000000024
12	226.33	225.95	0.380000000000024
13	226.33	226.33	0
14	226.22	226.33	-0.110000000000014
15	224.84	226.22	-1.38
16	221.88	224.84	-2.96000000000001
17	222.37	221.88	0.490000000000009
18	221.8	222.37	-0.569999999999993
19	221.8	221.8	0
20	221.8	221.8	0
21	221.9	221.8	0.0999999999999943
22	220.2	221.9	-1.70000000000002
23	219.95	220.2	-0.25
24	220.05	219.95	0.100000000000023
25	220.05	220.05	0
26	220.05	220.05	0
27	220.62	220.05	0.569999999999993
28	221.53	220.62	0.909999999999997
29	221.61	221.53	0.0800000000000125
30	221.5	221.61	-0.110000000000014
31	221.5	221.5	0
32	221.87	221.5	0.370000000000005
33	222.27	221.87	0.400000000000006
34	220.86	222.27	-1.41
35	221.49	220.86	0.629999999999995
36	221.67	221.49	0.179999999999978
37	221.67	221.67	0
38	221.72	221.67	0.0500000000000114
39	221.67	221.72	-0.0500000000000114
40	220.29	221.67	-1.38
41	220.75	220.29	0.460000000000008
42	219.59	220.75	-1.16
43	219.59	219.59	0
44	219.59	219.59	0
45	219.82	219.59	0.22999999999999
46	221.59	219.82	1.77000000000001
47	220.9	221.59	-0.689999999999998
48	221.01	220.9	0.109999999999985
49	221.01	221.01	0
50	219.69	221.01	-1.31999999999999
51	221	219.69	1.31
52	219.82	221	-1.18000000000001
53	218.04	219.82	-1.78
54	217.97	218.04	-0.0699999999999932
55	217.97	217.97	0
56	217.53	217.97	-0.439999999999998
57	217	217.53	-0.530000000000001
58	217.18	217	0.180000000000007
59	217.68	217.18	0.5
60	217.71	217.68	0.0300000000000011
61	217.71	217.71	0
62	218.5	217.71	0.789999999999992
63	218.8	218.5	0.300000000000011
64	218.94	218.8	0.139999999999986
65	220	218.94	1.06
66	219.89	220	-0.110000000000014
67	219.89	219.89	0
68	220.08	219.89	0.190000000000026
69	220.16	220.08	0.0799999999999841
70	221	220.16	0.840000000000003
71	222.16	221	1.16
72	221.5	222.16	-0.659999999999997
73	221.5	221.5	0
74	221.6	221.5	0.0999999999999943
75	221.85	221.6	0.25
76	223.11	221.85	1.26000000000002
77	222.79	223.11	-0.320000000000022
78	222.45	222.79	-0.340000000000003
79	222.45	222.45	0
80	222.4	222.45	-0.0499999999999829
81	223.15	222.4	0.75
82	224.4	223.15	1.25
83	224.24	224.4	-0.159999999999997
84	223.92	224.24	-0.320000000000022

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	223.92	222.448458873543	225.391541126457
86	223.92	221.838926581374	226.001073418626
87	223.92	221.371216003549	226.468783996451
88	223.92	220.976917747086	226.863082252914
89	223.92	220.629534009555	227.210465990445
90	223.92	220.315475104659	227.524524895341
91	223.92	220.02666813539	227.81333186461
92	223.92	219.757853162749	228.082146837251
93	223.92	219.505376620628	228.334623379372
94	223.92	219.266578369785	228.573421630215
95	223.92	219.039450219965	228.800549780035
96	223.92	218.822432007098	229.017567992902

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 223.92 & 222.448458873543 & 225.391541126457 \tabularnewline
86 & 223.92 & 221.838926581374 & 226.001073418626 \tabularnewline
87 & 223.92 & 221.371216003549 & 226.468783996451 \tabularnewline
88 & 223.92 & 220.976917747086 & 226.863082252914 \tabularnewline
89 & 223.92 & 220.629534009555 & 227.210465990445 \tabularnewline
90 & 223.92 & 220.315475104659 & 227.524524895341 \tabularnewline
91 & 223.92 & 220.02666813539 & 227.81333186461 \tabularnewline
92 & 223.92 & 219.757853162749 & 228.082146837251 \tabularnewline
93 & 223.92 & 219.505376620628 & 228.334623379372 \tabularnewline
94 & 223.92 & 219.266578369785 & 228.573421630215 \tabularnewline
95 & 223.92 & 219.039450219965 & 228.800549780035 \tabularnewline
96 & 223.92 & 218.822432007098 & 229.017567992902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235097&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]223.92[/C][C]222.448458873543[/C][C]225.391541126457[/C][/ROW]
[ROW][C]86[/C][C]223.92[/C][C]221.838926581374[/C][C]226.001073418626[/C][/ROW]
[ROW][C]87[/C][C]223.92[/C][C]221.371216003549[/C][C]226.468783996451[/C][/ROW]
[ROW][C]88[/C][C]223.92[/C][C]220.976917747086[/C][C]226.863082252914[/C][/ROW]
[ROW][C]89[/C][C]223.92[/C][C]220.629534009555[/C][C]227.210465990445[/C][/ROW]
[ROW][C]90[/C][C]223.92[/C][C]220.315475104659[/C][C]227.524524895341[/C][/ROW]
[ROW][C]91[/C][C]223.92[/C][C]220.02666813539[/C][C]227.81333186461[/C][/ROW]
[ROW][C]92[/C][C]223.92[/C][C]219.757853162749[/C][C]228.082146837251[/C][/ROW]
[ROW][C]93[/C][C]223.92[/C][C]219.505376620628[/C][C]228.334623379372[/C][/ROW]
[ROW][C]94[/C][C]223.92[/C][C]219.266578369785[/C][C]228.573421630215[/C][/ROW]
[ROW][C]95[/C][C]223.92[/C][C]219.039450219965[/C][C]228.800549780035[/C][/ROW]
[ROW][C]96[/C][C]223.92[/C][C]218.822432007098[/C][C]229.017567992902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235097&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235097&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	223.92	222.448458873543	225.391541126457
86	223.92	221.838926581374	226.001073418626
87	223.92	221.371216003549	226.468783996451
88	223.92	220.976917747086	226.863082252914
89	223.92	220.629534009555	227.210465990445
90	223.92	220.315475104659	227.524524895341
91	223.92	220.02666813539	227.81333186461
92	223.92	219.757853162749	228.082146837251
93	223.92	219.505376620628	228.334623379372
94	223.92	219.266578369785	228.573421630215
95	223.92	219.039450219965	228.800549780035
96	223.92	218.822432007098	229.017567992902

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