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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 01 Jun 2008 12:28:49 -0600

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/2008/Jun/01/t1212345024ji2cxsrwm4x8moq.htm/, Retrieved Sat, 18 May 2024 15:55:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13729, Retrieved Sat, 18 May 2024 15:55:19 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

238

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

-     [Histogram] [Studio 100 Maximu...] [2008-02-20 11:35:46] [f3999b06b4bdaaef0aae42cfc0c31daa]
- RMPD    [Exponential Smoothing] [exponential smoot...] [2008-06-01 18:28:49] [d41d8cd98f00b204e9800998ecf8427e] [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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13729&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13729&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13729&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

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

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13729&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13729&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13729&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.9643	0.9834	-0.0191
4	0.947	0.9643	-0.0173000000000001
5	0.906	0.947	-0.0409999999999999
6	0.9492	0.906	0.0432
7	0.9397	0.9492	-0.00950000000000006
8	0.9041	0.9397	-0.0356
9	0.8721	0.9041	-0.032
10	0.8552	0.8721	-0.0169000000000000
11	0.8564	0.8552	0.00120000000000009
12	0.8973	0.8564	0.0408999999999999
13	0.9383	0.8973	0.041
14	0.9217	0.9383	-0.0166000000000001
15	0.9095	0.9217	-0.0122
16	0.892	0.9095	-0.0175000000000000
17	0.8742	0.892	-0.0178000000000000
18	0.8532	0.8742	-0.021
19	0.8607	0.8532	0.00750000000000006
20	0.9005	0.8607	0.0397999999999999
21	0.9111	0.9005	0.0106000000000001
22	0.9059	0.9111	-0.00519999999999998
23	0.8883	0.9059	-0.0176000000000001
24	0.8924	0.8883	0.00409999999999999
25	0.8833	0.8924	-0.0091
26	0.87	0.8833	-0.0133000000000000
27	0.8758	0.87	0.00580000000000003
28	0.8858	0.8758	0.01
29	0.917	0.8858	0.0312
30	0.9554	0.917	0.0384
31	0.9922	0.9554	0.0367999999999999
32	0.9778	0.9922	-0.0144000000000000
33	0.9808	0.9778	0.003
34	0.9811	0.9808	0.000299999999999967
35	1.0014	0.9811	0.0203000000000001
36	1.0183	1.0014	0.0168999999999999
37	1.0622	1.0183	0.043900
38	1.0773	1.0622	0.0150999999999999
39	1.0807	1.0773	0.00340000000000007
40	1.0848	1.0807	0.00409999999999999
41	1.1582	1.0848	0.0733999999999999
42	1.1663	1.1582	0.0081
43	1.1372	1.1663	-0.0290999999999999
44	1.1139	1.1372	-0.0233000000000001
45	1.1222	1.1139	0.0083000000000002
46	1.1692	1.1222	0.0469999999999999
47	1.1702	1.1692	0.00099999999999989
48	1.2286	1.1702	0.0584
49	1.2613	1.2286	0.0327000000000002
50	1.2646	1.2613	0.00329999999999986
51	1.2262	1.2646	-0.0384
52	1.1985	1.2262	-0.0277000000000001
53	1.2007	1.1985	0.00220000000000020
54	1.2138	1.2007	0.0130999999999999
55	1.2266	1.2138	0.0127999999999999
56	1.2176	1.2266	-0.0089999999999999
57	1.2218	1.2176	0.00419999999999998
58	1.249	1.2218	0.0272000000000001
59	1.2991	1.249	0.0500999999999998
60	1.3408	1.2991	0.0417000000000001
61	1.3119	1.3408	-0.0288999999999999
62	1.3014	1.3119	-0.0105000000000002
63	1.3201	1.3014	0.0187000000000002
64	1.2938	1.3201	-0.0263
65	1.2694	1.2938	-0.0244
66	1.2165	1.2694	-0.0529000000000002
67	1.2037	1.2165	-0.0127999999999999
68	1.2292	1.2037	0.0255000000000001
69	1.2256	1.2292	-0.00360000000000005
70	1.2015	1.2256	-0.0241
71	1.1786	1.2015	-0.0228999999999999
72	1.1856	1.1786	0.0069999999999999
73	1.2103	1.1856	0.0246999999999999
74	1.1938	1.2103	-0.0165000000000000
75	1.202	1.1938	0.00819999999999999
76	1.2271	1.202	0.0251000000000001
77	1.277	1.2271	0.0498999999999998
78	1.265	1.277	-0.012
79	1.2684	1.265	0.00340000000000007
80	1.2811	1.2684	0.0126999999999999
81	1.2727	1.2811	-0.00839999999999996
82	1.2611	1.2727	-0.0115999999999998
83	1.2881	1.2611	0.0269999999999999
84	1.3213	1.2881	0.0331999999999999
85	1.2999	1.3213	-0.0213999999999999
86	1.3074	1.2999	0.00749999999999984
87	1.3242	1.3074	0.0168000000000001
88	1.3516	1.3242	0.0273999999999999
89	1.3511	1.3516	-0.000499999999999945
90	1.3419	1.3511	-0.00919999999999987
91	1.3716	1.3419	0.0296999999999998
92	1.3622	1.3716	-0.00939999999999985
93	1.3896	1.3622	0.0273999999999999
94	1.4227	1.3896	0.0331000000000001
95	1.4684	1.4227	0.0456999999999999
96	1.457	1.4684	-0.0113999999999999

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.9643 & 0.9834 & -0.0191 \tabularnewline
4 & 0.947 & 0.9643 & -0.0173000000000001 \tabularnewline
5 & 0.906 & 0.947 & -0.0409999999999999 \tabularnewline
6 & 0.9492 & 0.906 & 0.0432 \tabularnewline
7 & 0.9397 & 0.9492 & -0.00950000000000006 \tabularnewline
8 & 0.9041 & 0.9397 & -0.0356 \tabularnewline
9 & 0.8721 & 0.9041 & -0.032 \tabularnewline
10 & 0.8552 & 0.8721 & -0.0169000000000000 \tabularnewline
11 & 0.8564 & 0.8552 & 0.00120000000000009 \tabularnewline
12 & 0.8973 & 0.8564 & 0.0408999999999999 \tabularnewline
13 & 0.9383 & 0.8973 & 0.041 \tabularnewline
14 & 0.9217 & 0.9383 & -0.0166000000000001 \tabularnewline
15 & 0.9095 & 0.9217 & -0.0122 \tabularnewline
16 & 0.892 & 0.9095 & -0.0175000000000000 \tabularnewline
17 & 0.8742 & 0.892 & -0.0178000000000000 \tabularnewline
18 & 0.8532 & 0.8742 & -0.021 \tabularnewline
19 & 0.8607 & 0.8532 & 0.00750000000000006 \tabularnewline
20 & 0.9005 & 0.8607 & 0.0397999999999999 \tabularnewline
21 & 0.9111 & 0.9005 & 0.0106000000000001 \tabularnewline
22 & 0.9059 & 0.9111 & -0.00519999999999998 \tabularnewline
23 & 0.8883 & 0.9059 & -0.0176000000000001 \tabularnewline
24 & 0.8924 & 0.8883 & 0.00409999999999999 \tabularnewline
25 & 0.8833 & 0.8924 & -0.0091 \tabularnewline
26 & 0.87 & 0.8833 & -0.0133000000000000 \tabularnewline
27 & 0.8758 & 0.87 & 0.00580000000000003 \tabularnewline
28 & 0.8858 & 0.8758 & 0.01 \tabularnewline
29 & 0.917 & 0.8858 & 0.0312 \tabularnewline
30 & 0.9554 & 0.917 & 0.0384 \tabularnewline
31 & 0.9922 & 0.9554 & 0.0367999999999999 \tabularnewline
32 & 0.9778 & 0.9922 & -0.0144000000000000 \tabularnewline
33 & 0.9808 & 0.9778 & 0.003 \tabularnewline
34 & 0.9811 & 0.9808 & 0.000299999999999967 \tabularnewline
35 & 1.0014 & 0.9811 & 0.0203000000000001 \tabularnewline
36 & 1.0183 & 1.0014 & 0.0168999999999999 \tabularnewline
37 & 1.0622 & 1.0183 & 0.043900 \tabularnewline
38 & 1.0773 & 1.0622 & 0.0150999999999999 \tabularnewline
39 & 1.0807 & 1.0773 & 0.00340000000000007 \tabularnewline
40 & 1.0848 & 1.0807 & 0.00409999999999999 \tabularnewline
41 & 1.1582 & 1.0848 & 0.0733999999999999 \tabularnewline
42 & 1.1663 & 1.1582 & 0.0081 \tabularnewline
43 & 1.1372 & 1.1663 & -0.0290999999999999 \tabularnewline
44 & 1.1139 & 1.1372 & -0.0233000000000001 \tabularnewline
45 & 1.1222 & 1.1139 & 0.0083000000000002 \tabularnewline
46 & 1.1692 & 1.1222 & 0.0469999999999999 \tabularnewline
47 & 1.1702 & 1.1692 & 0.00099999999999989 \tabularnewline
48 & 1.2286 & 1.1702 & 0.0584 \tabularnewline
49 & 1.2613 & 1.2286 & 0.0327000000000002 \tabularnewline
50 & 1.2646 & 1.2613 & 0.00329999999999986 \tabularnewline
51 & 1.2262 & 1.2646 & -0.0384 \tabularnewline
52 & 1.1985 & 1.2262 & -0.0277000000000001 \tabularnewline
53 & 1.2007 & 1.1985 & 0.00220000000000020 \tabularnewline
54 & 1.2138 & 1.2007 & 0.0130999999999999 \tabularnewline
55 & 1.2266 & 1.2138 & 0.0127999999999999 \tabularnewline
56 & 1.2176 & 1.2266 & -0.0089999999999999 \tabularnewline
57 & 1.2218 & 1.2176 & 0.00419999999999998 \tabularnewline
58 & 1.249 & 1.2218 & 0.0272000000000001 \tabularnewline
59 & 1.2991 & 1.249 & 0.0500999999999998 \tabularnewline
60 & 1.3408 & 1.2991 & 0.0417000000000001 \tabularnewline
61 & 1.3119 & 1.3408 & -0.0288999999999999 \tabularnewline
62 & 1.3014 & 1.3119 & -0.0105000000000002 \tabularnewline
63 & 1.3201 & 1.3014 & 0.0187000000000002 \tabularnewline
64 & 1.2938 & 1.3201 & -0.0263 \tabularnewline
65 & 1.2694 & 1.2938 & -0.0244 \tabularnewline
66 & 1.2165 & 1.2694 & -0.0529000000000002 \tabularnewline
67 & 1.2037 & 1.2165 & -0.0127999999999999 \tabularnewline
68 & 1.2292 & 1.2037 & 0.0255000000000001 \tabularnewline
69 & 1.2256 & 1.2292 & -0.00360000000000005 \tabularnewline
70 & 1.2015 & 1.2256 & -0.0241 \tabularnewline
71 & 1.1786 & 1.2015 & -0.0228999999999999 \tabularnewline
72 & 1.1856 & 1.1786 & 0.0069999999999999 \tabularnewline
73 & 1.2103 & 1.1856 & 0.0246999999999999 \tabularnewline
74 & 1.1938 & 1.2103 & -0.0165000000000000 \tabularnewline
75 & 1.202 & 1.1938 & 0.00819999999999999 \tabularnewline
76 & 1.2271 & 1.202 & 0.0251000000000001 \tabularnewline
77 & 1.277 & 1.2271 & 0.0498999999999998 \tabularnewline
78 & 1.265 & 1.277 & -0.012 \tabularnewline
79 & 1.2684 & 1.265 & 0.00340000000000007 \tabularnewline
80 & 1.2811 & 1.2684 & 0.0126999999999999 \tabularnewline
81 & 1.2727 & 1.2811 & -0.00839999999999996 \tabularnewline
82 & 1.2611 & 1.2727 & -0.0115999999999998 \tabularnewline
83 & 1.2881 & 1.2611 & 0.0269999999999999 \tabularnewline
84 & 1.3213 & 1.2881 & 0.0331999999999999 \tabularnewline
85 & 1.2999 & 1.3213 & -0.0213999999999999 \tabularnewline
86 & 1.3074 & 1.2999 & 0.00749999999999984 \tabularnewline
87 & 1.3242 & 1.3074 & 0.0168000000000001 \tabularnewline
88 & 1.3516 & 1.3242 & 0.0273999999999999 \tabularnewline
89 & 1.3511 & 1.3516 & -0.000499999999999945 \tabularnewline
90 & 1.3419 & 1.3511 & -0.00919999999999987 \tabularnewline
91 & 1.3716 & 1.3419 & 0.0296999999999998 \tabularnewline
92 & 1.3622 & 1.3716 & -0.00939999999999985 \tabularnewline
93 & 1.3896 & 1.3622 & 0.0273999999999999 \tabularnewline
94 & 1.4227 & 1.3896 & 0.0331000000000001 \tabularnewline
95 & 1.4684 & 1.4227 & 0.0456999999999999 \tabularnewline
96 & 1.457 & 1.4684 & -0.0113999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13729&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]0.9643[/C][C]0.9834[/C][C]-0.0191[/C][/ROW]
[ROW][C]4[/C][C]0.947[/C][C]0.9643[/C][C]-0.0173000000000001[/C][/ROW]
[ROW][C]5[/C][C]0.906[/C][C]0.947[/C][C]-0.0409999999999999[/C][/ROW]
[ROW][C]6[/C][C]0.9492[/C][C]0.906[/C][C]0.0432[/C][/ROW]
[ROW][C]7[/C][C]0.9397[/C][C]0.9492[/C][C]-0.00950000000000006[/C][/ROW]
[ROW][C]8[/C][C]0.9041[/C][C]0.9397[/C][C]-0.0356[/C][/ROW]
[ROW][C]9[/C][C]0.8721[/C][C]0.9041[/C][C]-0.032[/C][/ROW]
[ROW][C]10[/C][C]0.8552[/C][C]0.8721[/C][C]-0.0169000000000000[/C][/ROW]
[ROW][C]11[/C][C]0.8564[/C][C]0.8552[/C][C]0.00120000000000009[/C][/ROW]
[ROW][C]12[/C][C]0.8973[/C][C]0.8564[/C][C]0.0408999999999999[/C][/ROW]
[ROW][C]13[/C][C]0.9383[/C][C]0.8973[/C][C]0.041[/C][/ROW]
[ROW][C]14[/C][C]0.9217[/C][C]0.9383[/C][C]-0.0166000000000001[/C][/ROW]
[ROW][C]15[/C][C]0.9095[/C][C]0.9217[/C][C]-0.0122[/C][/ROW]
[ROW][C]16[/C][C]0.892[/C][C]0.9095[/C][C]-0.0175000000000000[/C][/ROW]
[ROW][C]17[/C][C]0.8742[/C][C]0.892[/C][C]-0.0178000000000000[/C][/ROW]
[ROW][C]18[/C][C]0.8532[/C][C]0.8742[/C][C]-0.021[/C][/ROW]
[ROW][C]19[/C][C]0.8607[/C][C]0.8532[/C][C]0.00750000000000006[/C][/ROW]
[ROW][C]20[/C][C]0.9005[/C][C]0.8607[/C][C]0.0397999999999999[/C][/ROW]
[ROW][C]21[/C][C]0.9111[/C][C]0.9005[/C][C]0.0106000000000001[/C][/ROW]
[ROW][C]22[/C][C]0.9059[/C][C]0.9111[/C][C]-0.00519999999999998[/C][/ROW]
[ROW][C]23[/C][C]0.8883[/C][C]0.9059[/C][C]-0.0176000000000001[/C][/ROW]
[ROW][C]24[/C][C]0.8924[/C][C]0.8883[/C][C]0.00409999999999999[/C][/ROW]
[ROW][C]25[/C][C]0.8833[/C][C]0.8924[/C][C]-0.0091[/C][/ROW]
[ROW][C]26[/C][C]0.87[/C][C]0.8833[/C][C]-0.0133000000000000[/C][/ROW]
[ROW][C]27[/C][C]0.8758[/C][C]0.87[/C][C]0.00580000000000003[/C][/ROW]
[ROW][C]28[/C][C]0.8858[/C][C]0.8758[/C][C]0.01[/C][/ROW]
[ROW][C]29[/C][C]0.917[/C][C]0.8858[/C][C]0.0312[/C][/ROW]
[ROW][C]30[/C][C]0.9554[/C][C]0.917[/C][C]0.0384[/C][/ROW]
[ROW][C]31[/C][C]0.9922[/C][C]0.9554[/C][C]0.0367999999999999[/C][/ROW]
[ROW][C]32[/C][C]0.9778[/C][C]0.9922[/C][C]-0.0144000000000000[/C][/ROW]
[ROW][C]33[/C][C]0.9808[/C][C]0.9778[/C][C]0.003[/C][/ROW]
[ROW][C]34[/C][C]0.9811[/C][C]0.9808[/C][C]0.000299999999999967[/C][/ROW]
[ROW][C]35[/C][C]1.0014[/C][C]0.9811[/C][C]0.0203000000000001[/C][/ROW]
[ROW][C]36[/C][C]1.0183[/C][C]1.0014[/C][C]0.0168999999999999[/C][/ROW]
[ROW][C]37[/C][C]1.0622[/C][C]1.0183[/C][C]0.043900[/C][/ROW]
[ROW][C]38[/C][C]1.0773[/C][C]1.0622[/C][C]0.0150999999999999[/C][/ROW]
[ROW][C]39[/C][C]1.0807[/C][C]1.0773[/C][C]0.00340000000000007[/C][/ROW]
[ROW][C]40[/C][C]1.0848[/C][C]1.0807[/C][C]0.00409999999999999[/C][/ROW]
[ROW][C]41[/C][C]1.1582[/C][C]1.0848[/C][C]0.0733999999999999[/C][/ROW]
[ROW][C]42[/C][C]1.1663[/C][C]1.1582[/C][C]0.0081[/C][/ROW]
[ROW][C]43[/C][C]1.1372[/C][C]1.1663[/C][C]-0.0290999999999999[/C][/ROW]
[ROW][C]44[/C][C]1.1139[/C][C]1.1372[/C][C]-0.0233000000000001[/C][/ROW]
[ROW][C]45[/C][C]1.1222[/C][C]1.1139[/C][C]0.0083000000000002[/C][/ROW]
[ROW][C]46[/C][C]1.1692[/C][C]1.1222[/C][C]0.0469999999999999[/C][/ROW]
[ROW][C]47[/C][C]1.1702[/C][C]1.1692[/C][C]0.00099999999999989[/C][/ROW]
[ROW][C]48[/C][C]1.2286[/C][C]1.1702[/C][C]0.0584[/C][/ROW]
[ROW][C]49[/C][C]1.2613[/C][C]1.2286[/C][C]0.0327000000000002[/C][/ROW]
[ROW][C]50[/C][C]1.2646[/C][C]1.2613[/C][C]0.00329999999999986[/C][/ROW]
[ROW][C]51[/C][C]1.2262[/C][C]1.2646[/C][C]-0.0384[/C][/ROW]
[ROW][C]52[/C][C]1.1985[/C][C]1.2262[/C][C]-0.0277000000000001[/C][/ROW]
[ROW][C]53[/C][C]1.2007[/C][C]1.1985[/C][C]0.00220000000000020[/C][/ROW]
[ROW][C]54[/C][C]1.2138[/C][C]1.2007[/C][C]0.0130999999999999[/C][/ROW]
[ROW][C]55[/C][C]1.2266[/C][C]1.2138[/C][C]0.0127999999999999[/C][/ROW]
[ROW][C]56[/C][C]1.2176[/C][C]1.2266[/C][C]-0.0089999999999999[/C][/ROW]
[ROW][C]57[/C][C]1.2218[/C][C]1.2176[/C][C]0.00419999999999998[/C][/ROW]
[ROW][C]58[/C][C]1.249[/C][C]1.2218[/C][C]0.0272000000000001[/C][/ROW]
[ROW][C]59[/C][C]1.2991[/C][C]1.249[/C][C]0.0500999999999998[/C][/ROW]
[ROW][C]60[/C][C]1.3408[/C][C]1.2991[/C][C]0.0417000000000001[/C][/ROW]
[ROW][C]61[/C][C]1.3119[/C][C]1.3408[/C][C]-0.0288999999999999[/C][/ROW]
[ROW][C]62[/C][C]1.3014[/C][C]1.3119[/C][C]-0.0105000000000002[/C][/ROW]
[ROW][C]63[/C][C]1.3201[/C][C]1.3014[/C][C]0.0187000000000002[/C][/ROW]
[ROW][C]64[/C][C]1.2938[/C][C]1.3201[/C][C]-0.0263[/C][/ROW]
[ROW][C]65[/C][C]1.2694[/C][C]1.2938[/C][C]-0.0244[/C][/ROW]
[ROW][C]66[/C][C]1.2165[/C][C]1.2694[/C][C]-0.0529000000000002[/C][/ROW]
[ROW][C]67[/C][C]1.2037[/C][C]1.2165[/C][C]-0.0127999999999999[/C][/ROW]
[ROW][C]68[/C][C]1.2292[/C][C]1.2037[/C][C]0.0255000000000001[/C][/ROW]
[ROW][C]69[/C][C]1.2256[/C][C]1.2292[/C][C]-0.00360000000000005[/C][/ROW]
[ROW][C]70[/C][C]1.2015[/C][C]1.2256[/C][C]-0.0241[/C][/ROW]
[ROW][C]71[/C][C]1.1786[/C][C]1.2015[/C][C]-0.0228999999999999[/C][/ROW]
[ROW][C]72[/C][C]1.1856[/C][C]1.1786[/C][C]0.0069999999999999[/C][/ROW]
[ROW][C]73[/C][C]1.2103[/C][C]1.1856[/C][C]0.0246999999999999[/C][/ROW]
[ROW][C]74[/C][C]1.1938[/C][C]1.2103[/C][C]-0.0165000000000000[/C][/ROW]
[ROW][C]75[/C][C]1.202[/C][C]1.1938[/C][C]0.00819999999999999[/C][/ROW]
[ROW][C]76[/C][C]1.2271[/C][C]1.202[/C][C]0.0251000000000001[/C][/ROW]
[ROW][C]77[/C][C]1.277[/C][C]1.2271[/C][C]0.0498999999999998[/C][/ROW]
[ROW][C]78[/C][C]1.265[/C][C]1.277[/C][C]-0.012[/C][/ROW]
[ROW][C]79[/C][C]1.2684[/C][C]1.265[/C][C]0.00340000000000007[/C][/ROW]
[ROW][C]80[/C][C]1.2811[/C][C]1.2684[/C][C]0.0126999999999999[/C][/ROW]
[ROW][C]81[/C][C]1.2727[/C][C]1.2811[/C][C]-0.00839999999999996[/C][/ROW]
[ROW][C]82[/C][C]1.2611[/C][C]1.2727[/C][C]-0.0115999999999998[/C][/ROW]
[ROW][C]83[/C][C]1.2881[/C][C]1.2611[/C][C]0.0269999999999999[/C][/ROW]
[ROW][C]84[/C][C]1.3213[/C][C]1.2881[/C][C]0.0331999999999999[/C][/ROW]
[ROW][C]85[/C][C]1.2999[/C][C]1.3213[/C][C]-0.0213999999999999[/C][/ROW]
[ROW][C]86[/C][C]1.3074[/C][C]1.2999[/C][C]0.00749999999999984[/C][/ROW]
[ROW][C]87[/C][C]1.3242[/C][C]1.3074[/C][C]0.0168000000000001[/C][/ROW]
[ROW][C]88[/C][C]1.3516[/C][C]1.3242[/C][C]0.0273999999999999[/C][/ROW]
[ROW][C]89[/C][C]1.3511[/C][C]1.3516[/C][C]-0.000499999999999945[/C][/ROW]
[ROW][C]90[/C][C]1.3419[/C][C]1.3511[/C][C]-0.00919999999999987[/C][/ROW]
[ROW][C]91[/C][C]1.3716[/C][C]1.3419[/C][C]0.0296999999999998[/C][/ROW]
[ROW][C]92[/C][C]1.3622[/C][C]1.3716[/C][C]-0.00939999999999985[/C][/ROW]
[ROW][C]93[/C][C]1.3896[/C][C]1.3622[/C][C]0.0273999999999999[/C][/ROW]
[ROW][C]94[/C][C]1.4227[/C][C]1.3896[/C][C]0.0331000000000001[/C][/ROW]
[ROW][C]95[/C][C]1.4684[/C][C]1.4227[/C][C]0.0456999999999999[/C][/ROW]
[ROW][C]96[/C][C]1.457[/C][C]1.4684[/C][C]-0.0113999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13729&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13729&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	0.9643	0.9834	-0.0191
4	0.947	0.9643	-0.0173000000000001
5	0.906	0.947	-0.0409999999999999
6	0.9492	0.906	0.0432
7	0.9397	0.9492	-0.00950000000000006
8	0.9041	0.9397	-0.0356
9	0.8721	0.9041	-0.032
10	0.8552	0.8721	-0.0169000000000000
11	0.8564	0.8552	0.00120000000000009
12	0.8973	0.8564	0.0408999999999999
13	0.9383	0.8973	0.041
14	0.9217	0.9383	-0.0166000000000001
15	0.9095	0.9217	-0.0122
16	0.892	0.9095	-0.0175000000000000
17	0.8742	0.892	-0.0178000000000000
18	0.8532	0.8742	-0.021
19	0.8607	0.8532	0.00750000000000006
20	0.9005	0.8607	0.0397999999999999
21	0.9111	0.9005	0.0106000000000001
22	0.9059	0.9111	-0.00519999999999998
23	0.8883	0.9059	-0.0176000000000001
24	0.8924	0.8883	0.00409999999999999
25	0.8833	0.8924	-0.0091
26	0.87	0.8833	-0.0133000000000000
27	0.8758	0.87	0.00580000000000003
28	0.8858	0.8758	0.01
29	0.917	0.8858	0.0312
30	0.9554	0.917	0.0384
31	0.9922	0.9554	0.0367999999999999
32	0.9778	0.9922	-0.0144000000000000
33	0.9808	0.9778	0.003
34	0.9811	0.9808	0.000299999999999967
35	1.0014	0.9811	0.0203000000000001
36	1.0183	1.0014	0.0168999999999999
37	1.0622	1.0183	0.043900
38	1.0773	1.0622	0.0150999999999999
39	1.0807	1.0773	0.00340000000000007
40	1.0848	1.0807	0.00409999999999999
41	1.1582	1.0848	0.0733999999999999
42	1.1663	1.1582	0.0081
43	1.1372	1.1663	-0.0290999999999999
44	1.1139	1.1372	-0.0233000000000001
45	1.1222	1.1139	0.0083000000000002
46	1.1692	1.1222	0.0469999999999999
47	1.1702	1.1692	0.00099999999999989
48	1.2286	1.1702	0.0584
49	1.2613	1.2286	0.0327000000000002
50	1.2646	1.2613	0.00329999999999986
51	1.2262	1.2646	-0.0384
52	1.1985	1.2262	-0.0277000000000001
53	1.2007	1.1985	0.00220000000000020
54	1.2138	1.2007	0.0130999999999999
55	1.2266	1.2138	0.0127999999999999
56	1.2176	1.2266	-0.0089999999999999
57	1.2218	1.2176	0.00419999999999998
58	1.249	1.2218	0.0272000000000001
59	1.2991	1.249	0.0500999999999998
60	1.3408	1.2991	0.0417000000000001
61	1.3119	1.3408	-0.0288999999999999
62	1.3014	1.3119	-0.0105000000000002
63	1.3201	1.3014	0.0187000000000002
64	1.2938	1.3201	-0.0263
65	1.2694	1.2938	-0.0244
66	1.2165	1.2694	-0.0529000000000002
67	1.2037	1.2165	-0.0127999999999999
68	1.2292	1.2037	0.0255000000000001
69	1.2256	1.2292	-0.00360000000000005
70	1.2015	1.2256	-0.0241
71	1.1786	1.2015	-0.0228999999999999
72	1.1856	1.1786	0.0069999999999999
73	1.2103	1.1856	0.0246999999999999
74	1.1938	1.2103	-0.0165000000000000
75	1.202	1.1938	0.00819999999999999
76	1.2271	1.202	0.0251000000000001
77	1.277	1.2271	0.0498999999999998
78	1.265	1.277	-0.012
79	1.2684	1.265	0.00340000000000007
80	1.2811	1.2684	0.0126999999999999
81	1.2727	1.2811	-0.00839999999999996
82	1.2611	1.2727	-0.0115999999999998
83	1.2881	1.2611	0.0269999999999999
84	1.3213	1.2881	0.0331999999999999
85	1.2999	1.3213	-0.0213999999999999
86	1.3074	1.2999	0.00749999999999984
87	1.3242	1.3074	0.0168000000000001
88	1.3516	1.3242	0.0273999999999999
89	1.3511	1.3516	-0.000499999999999945
90	1.3419	1.3511	-0.00919999999999987
91	1.3716	1.3419	0.0296999999999998
92	1.3622	1.3716	-0.00939999999999985
93	1.3896	1.3622	0.0273999999999999
94	1.4227	1.3896	0.0331000000000001
95	1.4684	1.4227	0.0456999999999999
96	1.457	1.4684	-0.0113999999999999

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	1.457	1.40702233492418	1.50697766507582
98	1.457	1.38632090823403	1.52767909176597
99	1.457	1.37043614484501	1.54356385515499
100	1.457	1.35704466984835	1.55695533015165
101	1.457	1.34524654353374	1.56875345646626
102	1.457	1.33458022202852	1.57941977797148
103	1.457	1.32477152710169	1.58922847289831
104	1.457	1.31564181646806	1.59835818353194
105	1.457	1.30706700477253	1.60693299522747
106	1.457	1.29895674622335	1.61504325377665
107	1.457	1.29124283704544	1.62275716295456
108	1.457	1.28387228969003	1.63012771030997

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 1.457 & 1.40702233492418 & 1.50697766507582 \tabularnewline
98 & 1.457 & 1.38632090823403 & 1.52767909176597 \tabularnewline
99 & 1.457 & 1.37043614484501 & 1.54356385515499 \tabularnewline
100 & 1.457 & 1.35704466984835 & 1.55695533015165 \tabularnewline
101 & 1.457 & 1.34524654353374 & 1.56875345646626 \tabularnewline
102 & 1.457 & 1.33458022202852 & 1.57941977797148 \tabularnewline
103 & 1.457 & 1.32477152710169 & 1.58922847289831 \tabularnewline
104 & 1.457 & 1.31564181646806 & 1.59835818353194 \tabularnewline
105 & 1.457 & 1.30706700477253 & 1.60693299522747 \tabularnewline
106 & 1.457 & 1.29895674622335 & 1.61504325377665 \tabularnewline
107 & 1.457 & 1.29124283704544 & 1.62275716295456 \tabularnewline
108 & 1.457 & 1.28387228969003 & 1.63012771030997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13729&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]97[/C][C]1.457[/C][C]1.40702233492418[/C][C]1.50697766507582[/C][/ROW]
[ROW][C]98[/C][C]1.457[/C][C]1.38632090823403[/C][C]1.52767909176597[/C][/ROW]
[ROW][C]99[/C][C]1.457[/C][C]1.37043614484501[/C][C]1.54356385515499[/C][/ROW]
[ROW][C]100[/C][C]1.457[/C][C]1.35704466984835[/C][C]1.55695533015165[/C][/ROW]
[ROW][C]101[/C][C]1.457[/C][C]1.34524654353374[/C][C]1.56875345646626[/C][/ROW]
[ROW][C]102[/C][C]1.457[/C][C]1.33458022202852[/C][C]1.57941977797148[/C][/ROW]
[ROW][C]103[/C][C]1.457[/C][C]1.32477152710169[/C][C]1.58922847289831[/C][/ROW]
[ROW][C]104[/C][C]1.457[/C][C]1.31564181646806[/C][C]1.59835818353194[/C][/ROW]
[ROW][C]105[/C][C]1.457[/C][C]1.30706700477253[/C][C]1.60693299522747[/C][/ROW]
[ROW][C]106[/C][C]1.457[/C][C]1.29895674622335[/C][C]1.61504325377665[/C][/ROW]
[ROW][C]107[/C][C]1.457[/C][C]1.29124283704544[/C][C]1.62275716295456[/C][/ROW]
[ROW][C]108[/C][C]1.457[/C][C]1.28387228969003[/C][C]1.63012771030997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13729&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13729&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
97	1.457	1.40702233492418	1.50697766507582
98	1.457	1.38632090823403	1.52767909176597
99	1.457	1.37043614484501	1.54356385515499
100	1.457	1.35704466984835	1.55695533015165
101	1.457	1.34524654353374	1.56875345646626
102	1.457	1.33458022202852	1.57941977797148
103	1.457	1.32477152710169	1.58922847289831
104	1.457	1.31564181646806	1.59835818353194
105	1.457	1.30706700477253	1.60693299522747
106	1.457	1.29895674622335	1.61504325377665
107	1.457	1.29124283704544	1.62275716295456
108	1.457	1.28387228969003	1.63012771030997

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 = additive ; par2 = 12 ;

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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