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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 03 Aug 2010 18:02:49 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/03/t1280858593fyuq29dl7o6t8em.htm/, Retrieved Thu, 02 May 2024 17:41:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78287, Retrieved Thu, 02 May 2024 17:41:17 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Lisa Bruggeman

Estimated Impact

108

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

-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2010-08-03 18:02:49] [0e6aef37627b8cf9d1bd74110cef2cca] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78287&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78287&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

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=78287&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=78287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78287&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	160	161	-1
4	158	160	-2
5	156	158	-2
6	155	156	-1
7	156	155	1
8	158	156	2
9	159	158	1
10	159	159	0
11	160	159	1
12	162	160	2
13	152	162	-10
14	157	152	5
15	149	157	-8
16	150	149	1
17	144	150	-6
18	146	144	2
19	151	146	5
20	148	151	-3
21	151	148	3
22	151	151	0
23	145	151	-6
24	140	145	-5
25	139	140	-1
26	144	139	5
27	140	144	-4
28	134	140	-6
29	130	134	-4
30	132	130	2
31	136	132	4
32	137	136	1
33	146	137	9
34	139	146	-7
35	132	139	-7
36	131	132	-1
37	137	131	6
38	145	137	8
39	142	145	-3
40	142	142	0
41	137	142	-5
42	139	137	2
43	139	139	0
44	139	139	0
45	150	139	11
46	146	150	-4
47	138	146	-8
48	134	138	-4
49	137	134	3
50	143	137	6
51	136	143	-7
52	138	136	2
53	129	138	-9
54	132	129	3
55	124	132	-8
56	132	124	8
57	154	132	22
58	145	154	-9
59	136	145	-9
60	132	136	-4
61	135	132	3
62	148	135	13
63	142	148	-6
64	139	142	-3
65	126	139	-13
66	124	126	-2
67	115	124	-9
68	126	115	11
69	147	126	21
70	136	147	-11
71	127	136	-9
72	123	127	-4
73	132	123	9
74	156	132	24
75	153	156	-3
76	147	153	-6
77	129	147	-18
78	119	129	-10
79	108	119	-11
80	121	108	13
81	138	121	17
82	128	138	-10
83	123	128	-5
84	125	123	2

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 160 & 161 & -1 \tabularnewline
4 & 158 & 160 & -2 \tabularnewline
5 & 156 & 158 & -2 \tabularnewline
6 & 155 & 156 & -1 \tabularnewline
7 & 156 & 155 & 1 \tabularnewline
8 & 158 & 156 & 2 \tabularnewline
9 & 159 & 158 & 1 \tabularnewline
10 & 159 & 159 & 0 \tabularnewline
11 & 160 & 159 & 1 \tabularnewline
12 & 162 & 160 & 2 \tabularnewline
13 & 152 & 162 & -10 \tabularnewline
14 & 157 & 152 & 5 \tabularnewline
15 & 149 & 157 & -8 \tabularnewline
16 & 150 & 149 & 1 \tabularnewline
17 & 144 & 150 & -6 \tabularnewline
18 & 146 & 144 & 2 \tabularnewline
19 & 151 & 146 & 5 \tabularnewline
20 & 148 & 151 & -3 \tabularnewline
21 & 151 & 148 & 3 \tabularnewline
22 & 151 & 151 & 0 \tabularnewline
23 & 145 & 151 & -6 \tabularnewline
24 & 140 & 145 & -5 \tabularnewline
25 & 139 & 140 & -1 \tabularnewline
26 & 144 & 139 & 5 \tabularnewline
27 & 140 & 144 & -4 \tabularnewline
28 & 134 & 140 & -6 \tabularnewline
29 & 130 & 134 & -4 \tabularnewline
30 & 132 & 130 & 2 \tabularnewline
31 & 136 & 132 & 4 \tabularnewline
32 & 137 & 136 & 1 \tabularnewline
33 & 146 & 137 & 9 \tabularnewline
34 & 139 & 146 & -7 \tabularnewline
35 & 132 & 139 & -7 \tabularnewline
36 & 131 & 132 & -1 \tabularnewline
37 & 137 & 131 & 6 \tabularnewline
38 & 145 & 137 & 8 \tabularnewline
39 & 142 & 145 & -3 \tabularnewline
40 & 142 & 142 & 0 \tabularnewline
41 & 137 & 142 & -5 \tabularnewline
42 & 139 & 137 & 2 \tabularnewline
43 & 139 & 139 & 0 \tabularnewline
44 & 139 & 139 & 0 \tabularnewline
45 & 150 & 139 & 11 \tabularnewline
46 & 146 & 150 & -4 \tabularnewline
47 & 138 & 146 & -8 \tabularnewline
48 & 134 & 138 & -4 \tabularnewline
49 & 137 & 134 & 3 \tabularnewline
50 & 143 & 137 & 6 \tabularnewline
51 & 136 & 143 & -7 \tabularnewline
52 & 138 & 136 & 2 \tabularnewline
53 & 129 & 138 & -9 \tabularnewline
54 & 132 & 129 & 3 \tabularnewline
55 & 124 & 132 & -8 \tabularnewline
56 & 132 & 124 & 8 \tabularnewline
57 & 154 & 132 & 22 \tabularnewline
58 & 145 & 154 & -9 \tabularnewline
59 & 136 & 145 & -9 \tabularnewline
60 & 132 & 136 & -4 \tabularnewline
61 & 135 & 132 & 3 \tabularnewline
62 & 148 & 135 & 13 \tabularnewline
63 & 142 & 148 & -6 \tabularnewline
64 & 139 & 142 & -3 \tabularnewline
65 & 126 & 139 & -13 \tabularnewline
66 & 124 & 126 & -2 \tabularnewline
67 & 115 & 124 & -9 \tabularnewline
68 & 126 & 115 & 11 \tabularnewline
69 & 147 & 126 & 21 \tabularnewline
70 & 136 & 147 & -11 \tabularnewline
71 & 127 & 136 & -9 \tabularnewline
72 & 123 & 127 & -4 \tabularnewline
73 & 132 & 123 & 9 \tabularnewline
74 & 156 & 132 & 24 \tabularnewline
75 & 153 & 156 & -3 \tabularnewline
76 & 147 & 153 & -6 \tabularnewline
77 & 129 & 147 & -18 \tabularnewline
78 & 119 & 129 & -10 \tabularnewline
79 & 108 & 119 & -11 \tabularnewline
80 & 121 & 108 & 13 \tabularnewline
81 & 138 & 121 & 17 \tabularnewline
82 & 128 & 138 & -10 \tabularnewline
83 & 123 & 128 & -5 \tabularnewline
84 & 125 & 123 & 2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78287&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]160[/C][C]161[/C][C]-1[/C][/ROW]
[ROW][C]4[/C][C]158[/C][C]160[/C][C]-2[/C][/ROW]
[ROW][C]5[/C][C]156[/C][C]158[/C][C]-2[/C][/ROW]
[ROW][C]6[/C][C]155[/C][C]156[/C][C]-1[/C][/ROW]
[ROW][C]7[/C][C]156[/C][C]155[/C][C]1[/C][/ROW]
[ROW][C]8[/C][C]158[/C][C]156[/C][C]2[/C][/ROW]
[ROW][C]9[/C][C]159[/C][C]158[/C][C]1[/C][/ROW]
[ROW][C]10[/C][C]159[/C][C]159[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]160[/C][C]159[/C][C]1[/C][/ROW]
[ROW][C]12[/C][C]162[/C][C]160[/C][C]2[/C][/ROW]
[ROW][C]13[/C][C]152[/C][C]162[/C][C]-10[/C][/ROW]
[ROW][C]14[/C][C]157[/C][C]152[/C][C]5[/C][/ROW]
[ROW][C]15[/C][C]149[/C][C]157[/C][C]-8[/C][/ROW]
[ROW][C]16[/C][C]150[/C][C]149[/C][C]1[/C][/ROW]
[ROW][C]17[/C][C]144[/C][C]150[/C][C]-6[/C][/ROW]
[ROW][C]18[/C][C]146[/C][C]144[/C][C]2[/C][/ROW]
[ROW][C]19[/C][C]151[/C][C]146[/C][C]5[/C][/ROW]
[ROW][C]20[/C][C]148[/C][C]151[/C][C]-3[/C][/ROW]
[ROW][C]21[/C][C]151[/C][C]148[/C][C]3[/C][/ROW]
[ROW][C]22[/C][C]151[/C][C]151[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]145[/C][C]151[/C][C]-6[/C][/ROW]
[ROW][C]24[/C][C]140[/C][C]145[/C][C]-5[/C][/ROW]
[ROW][C]25[/C][C]139[/C][C]140[/C][C]-1[/C][/ROW]
[ROW][C]26[/C][C]144[/C][C]139[/C][C]5[/C][/ROW]
[ROW][C]27[/C][C]140[/C][C]144[/C][C]-4[/C][/ROW]
[ROW][C]28[/C][C]134[/C][C]140[/C][C]-6[/C][/ROW]
[ROW][C]29[/C][C]130[/C][C]134[/C][C]-4[/C][/ROW]
[ROW][C]30[/C][C]132[/C][C]130[/C][C]2[/C][/ROW]
[ROW][C]31[/C][C]136[/C][C]132[/C][C]4[/C][/ROW]
[ROW][C]32[/C][C]137[/C][C]136[/C][C]1[/C][/ROW]
[ROW][C]33[/C][C]146[/C][C]137[/C][C]9[/C][/ROW]
[ROW][C]34[/C][C]139[/C][C]146[/C][C]-7[/C][/ROW]
[ROW][C]35[/C][C]132[/C][C]139[/C][C]-7[/C][/ROW]
[ROW][C]36[/C][C]131[/C][C]132[/C][C]-1[/C][/ROW]
[ROW][C]37[/C][C]137[/C][C]131[/C][C]6[/C][/ROW]
[ROW][C]38[/C][C]145[/C][C]137[/C][C]8[/C][/ROW]
[ROW][C]39[/C][C]142[/C][C]145[/C][C]-3[/C][/ROW]
[ROW][C]40[/C][C]142[/C][C]142[/C][C]0[/C][/ROW]
[ROW][C]41[/C][C]137[/C][C]142[/C][C]-5[/C][/ROW]
[ROW][C]42[/C][C]139[/C][C]137[/C][C]2[/C][/ROW]
[ROW][C]43[/C][C]139[/C][C]139[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]139[/C][C]139[/C][C]0[/C][/ROW]
[ROW][C]45[/C][C]150[/C][C]139[/C][C]11[/C][/ROW]
[ROW][C]46[/C][C]146[/C][C]150[/C][C]-4[/C][/ROW]
[ROW][C]47[/C][C]138[/C][C]146[/C][C]-8[/C][/ROW]
[ROW][C]48[/C][C]134[/C][C]138[/C][C]-4[/C][/ROW]
[ROW][C]49[/C][C]137[/C][C]134[/C][C]3[/C][/ROW]
[ROW][C]50[/C][C]143[/C][C]137[/C][C]6[/C][/ROW]
[ROW][C]51[/C][C]136[/C][C]143[/C][C]-7[/C][/ROW]
[ROW][C]52[/C][C]138[/C][C]136[/C][C]2[/C][/ROW]
[ROW][C]53[/C][C]129[/C][C]138[/C][C]-9[/C][/ROW]
[ROW][C]54[/C][C]132[/C][C]129[/C][C]3[/C][/ROW]
[ROW][C]55[/C][C]124[/C][C]132[/C][C]-8[/C][/ROW]
[ROW][C]56[/C][C]132[/C][C]124[/C][C]8[/C][/ROW]
[ROW][C]57[/C][C]154[/C][C]132[/C][C]22[/C][/ROW]
[ROW][C]58[/C][C]145[/C][C]154[/C][C]-9[/C][/ROW]
[ROW][C]59[/C][C]136[/C][C]145[/C][C]-9[/C][/ROW]
[ROW][C]60[/C][C]132[/C][C]136[/C][C]-4[/C][/ROW]
[ROW][C]61[/C][C]135[/C][C]132[/C][C]3[/C][/ROW]
[ROW][C]62[/C][C]148[/C][C]135[/C][C]13[/C][/ROW]
[ROW][C]63[/C][C]142[/C][C]148[/C][C]-6[/C][/ROW]
[ROW][C]64[/C][C]139[/C][C]142[/C][C]-3[/C][/ROW]
[ROW][C]65[/C][C]126[/C][C]139[/C][C]-13[/C][/ROW]
[ROW][C]66[/C][C]124[/C][C]126[/C][C]-2[/C][/ROW]
[ROW][C]67[/C][C]115[/C][C]124[/C][C]-9[/C][/ROW]
[ROW][C]68[/C][C]126[/C][C]115[/C][C]11[/C][/ROW]
[ROW][C]69[/C][C]147[/C][C]126[/C][C]21[/C][/ROW]
[ROW][C]70[/C][C]136[/C][C]147[/C][C]-11[/C][/ROW]
[ROW][C]71[/C][C]127[/C][C]136[/C][C]-9[/C][/ROW]
[ROW][C]72[/C][C]123[/C][C]127[/C][C]-4[/C][/ROW]
[ROW][C]73[/C][C]132[/C][C]123[/C][C]9[/C][/ROW]
[ROW][C]74[/C][C]156[/C][C]132[/C][C]24[/C][/ROW]
[ROW][C]75[/C][C]153[/C][C]156[/C][C]-3[/C][/ROW]
[ROW][C]76[/C][C]147[/C][C]153[/C][C]-6[/C][/ROW]
[ROW][C]77[/C][C]129[/C][C]147[/C][C]-18[/C][/ROW]
[ROW][C]78[/C][C]119[/C][C]129[/C][C]-10[/C][/ROW]
[ROW][C]79[/C][C]108[/C][C]119[/C][C]-11[/C][/ROW]
[ROW][C]80[/C][C]121[/C][C]108[/C][C]13[/C][/ROW]
[ROW][C]81[/C][C]138[/C][C]121[/C][C]17[/C][/ROW]
[ROW][C]82[/C][C]128[/C][C]138[/C][C]-10[/C][/ROW]
[ROW][C]83[/C][C]123[/C][C]128[/C][C]-5[/C][/ROW]
[ROW][C]84[/C][C]125[/C][C]123[/C][C]2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78287&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78287&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	160	161	-1
4	158	160	-2
5	156	158	-2
6	155	156	-1
7	156	155	1
8	158	156	2
9	159	158	1
10	159	159	0
11	160	159	1
12	162	160	2
13	152	162	-10
14	157	152	5
15	149	157	-8
16	150	149	1
17	144	150	-6
18	146	144	2
19	151	146	5
20	148	151	-3
21	151	148	3
22	151	151	0
23	145	151	-6
24	140	145	-5
25	139	140	-1
26	144	139	5
27	140	144	-4
28	134	140	-6
29	130	134	-4
30	132	130	2
31	136	132	4
32	137	136	1
33	146	137	9
34	139	146	-7
35	132	139	-7
36	131	132	-1
37	137	131	6
38	145	137	8
39	142	145	-3
40	142	142	0
41	137	142	-5
42	139	137	2
43	139	139	0
44	139	139	0
45	150	139	11
46	146	150	-4
47	138	146	-8
48	134	138	-4
49	137	134	3
50	143	137	6
51	136	143	-7
52	138	136	2
53	129	138	-9
54	132	129	3
55	124	132	-8
56	132	124	8
57	154	132	22
58	145	154	-9
59	136	145	-9
60	132	136	-4
61	135	132	3
62	148	135	13
63	142	148	-6
64	139	142	-3
65	126	139	-13
66	124	126	-2
67	115	124	-9
68	126	115	11
69	147	126	21
70	136	147	-11
71	127	136	-9
72	123	127	-4
73	132	123	9
74	156	132	24
75	153	156	-3
76	147	153	-6
77	129	147	-18
78	119	129	-10
79	108	119	-11
80	121	108	13
81	138	121	17
82	128	138	-10
83	123	128	-5
84	125	123	2

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	125	109.511713598514	140.488286401486
86	125	103.096255313099	146.903744686901
87	125	98.1735010304477	151.826498969552
88	125	94.0234271970276	155.976572802972
89	125	90.3671387512912	159.632861248709
90	125	87.0616013262713	162.938398673729
91	125	84.021845947124	165.978154052876
92	125	81.1925106261988	168.807489373801
93	125	78.5351407955413	171.464859204459
94	125	76.0217379182904	173.978262081710
95	125	73.6311653607064	176.368834639294
96	125	71.3470020608955	178.652997939105

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 125 & 109.511713598514 & 140.488286401486 \tabularnewline
86 & 125 & 103.096255313099 & 146.903744686901 \tabularnewline
87 & 125 & 98.1735010304477 & 151.826498969552 \tabularnewline
88 & 125 & 94.0234271970276 & 155.976572802972 \tabularnewline
89 & 125 & 90.3671387512912 & 159.632861248709 \tabularnewline
90 & 125 & 87.0616013262713 & 162.938398673729 \tabularnewline
91 & 125 & 84.021845947124 & 165.978154052876 \tabularnewline
92 & 125 & 81.1925106261988 & 168.807489373801 \tabularnewline
93 & 125 & 78.5351407955413 & 171.464859204459 \tabularnewline
94 & 125 & 76.0217379182904 & 173.978262081710 \tabularnewline
95 & 125 & 73.6311653607064 & 176.368834639294 \tabularnewline
96 & 125 & 71.3470020608955 & 178.652997939105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78287&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]125[/C][C]109.511713598514[/C][C]140.488286401486[/C][/ROW]
[ROW][C]86[/C][C]125[/C][C]103.096255313099[/C][C]146.903744686901[/C][/ROW]
[ROW][C]87[/C][C]125[/C][C]98.1735010304477[/C][C]151.826498969552[/C][/ROW]
[ROW][C]88[/C][C]125[/C][C]94.0234271970276[/C][C]155.976572802972[/C][/ROW]
[ROW][C]89[/C][C]125[/C][C]90.3671387512912[/C][C]159.632861248709[/C][/ROW]
[ROW][C]90[/C][C]125[/C][C]87.0616013262713[/C][C]162.938398673729[/C][/ROW]
[ROW][C]91[/C][C]125[/C][C]84.021845947124[/C][C]165.978154052876[/C][/ROW]
[ROW][C]92[/C][C]125[/C][C]81.1925106261988[/C][C]168.807489373801[/C][/ROW]
[ROW][C]93[/C][C]125[/C][C]78.5351407955413[/C][C]171.464859204459[/C][/ROW]
[ROW][C]94[/C][C]125[/C][C]76.0217379182904[/C][C]173.978262081710[/C][/ROW]
[ROW][C]95[/C][C]125[/C][C]73.6311653607064[/C][C]176.368834639294[/C][/ROW]
[ROW][C]96[/C][C]125[/C][C]71.3470020608955[/C][C]178.652997939105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78287&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78287&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	125	109.511713598514	140.488286401486
86	125	103.096255313099	146.903744686901
87	125	98.1735010304477	151.826498969552
88	125	94.0234271970276	155.976572802972
89	125	90.3671387512912	159.632861248709
90	125	87.0616013262713	162.938398673729
91	125	84.021845947124	165.978154052876
92	125	81.1925106261988	168.807489373801
93	125	78.5351407955413	171.464859204459
94	125	76.0217379182904	173.978262081710
95	125	73.6311653607064	176.368834639294
96	125	71.3470020608955	178.652997939105

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