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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 14 Aug 2010 11:29:56 +0000

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/2010/Aug/14/t1281785434kbrck1g00vnzxlz.htm/, Retrieved Mon, 06 May 2024 09:53:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78787, Retrieved Mon, 06 May 2024 09:53:18 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Reuben Vermoet

Estimated Impact

166

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

-       [Exponential Smoothing] [Tijdreeks 2 - sta...] [2010-08-14 11:29:56] [2c3906e099e396db093769aeca236bf5] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78787&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78787&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78787&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	'Gwilym Jenkins' @ 72.249.127.135

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=78787&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=78787&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78787&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	170	170	0
4	168	169	-1
5	166	167	-1
6	165	165	0
7	166	164	2
8	168	165	3
9	169	167	2
10	169	168	1
11	170	168	2
12	172	169	3
13	173	171	2
14	172	172	0
15	165	171	-6
16	152	164	-12
17	148	151	-3
18	145	147	-2
19	141	144	-3
20	149	140	9
21	146	148	-2
22	144	145	-1
23	149	143	6
24	150	148	2
25	149	149	0
26	156	148	8
27	150	155	-5
28	137	149	-12
29	130	136	-6
30	126	129	-3
31	125	125	0
32	123	124	-1
33	117	122	-5
34	111	116	-5
35	114	110	4
36	121	113	8
37	122	120	2
38	131	121	10
39	125	130	-5
40	116	124	-8
41	106	115	-9
42	98	105	-7
43	99	97	2
44	96	98	-2
45	95	95	0
46	83	94	-11
47	85	82	3
48	98	84	14
49	102	97	5
50	110	101	9
51	101	109	-8
52	90	100	-10
53	88	89	-1
54	83	87	-4
55	88	82	6
56	85	87	-2
57	86	84	2
58	80	85	-5
59	79	79	0
60	97	78	19
61	105	96	9
62	116	104	12
63	99	115	-16
64	87	98	-11
65	82	86	-4
66	81	81	0
67	85	80	5
68	84	84	0
69	78	83	-5
70	77	77	0
71	79	76	3
72	85	78	7
73	96	84	12
74	108	95	13
75	98	107	-9
76	86	97	-11
77	80	85	-5
78	74	79	-5
79	75	73	2
80	82	74	8
81	71	81	-10
82	66	70	-4
83	71	65	6
84	75	70	5

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 170 & 170 & 0 \tabularnewline
4 & 168 & 169 & -1 \tabularnewline
5 & 166 & 167 & -1 \tabularnewline
6 & 165 & 165 & 0 \tabularnewline
7 & 166 & 164 & 2 \tabularnewline
8 & 168 & 165 & 3 \tabularnewline
9 & 169 & 167 & 2 \tabularnewline
10 & 169 & 168 & 1 \tabularnewline
11 & 170 & 168 & 2 \tabularnewline
12 & 172 & 169 & 3 \tabularnewline
13 & 173 & 171 & 2 \tabularnewline
14 & 172 & 172 & 0 \tabularnewline
15 & 165 & 171 & -6 \tabularnewline
16 & 152 & 164 & -12 \tabularnewline
17 & 148 & 151 & -3 \tabularnewline
18 & 145 & 147 & -2 \tabularnewline
19 & 141 & 144 & -3 \tabularnewline
20 & 149 & 140 & 9 \tabularnewline
21 & 146 & 148 & -2 \tabularnewline
22 & 144 & 145 & -1 \tabularnewline
23 & 149 & 143 & 6 \tabularnewline
24 & 150 & 148 & 2 \tabularnewline
25 & 149 & 149 & 0 \tabularnewline
26 & 156 & 148 & 8 \tabularnewline
27 & 150 & 155 & -5 \tabularnewline
28 & 137 & 149 & -12 \tabularnewline
29 & 130 & 136 & -6 \tabularnewline
30 & 126 & 129 & -3 \tabularnewline
31 & 125 & 125 & 0 \tabularnewline
32 & 123 & 124 & -1 \tabularnewline
33 & 117 & 122 & -5 \tabularnewline
34 & 111 & 116 & -5 \tabularnewline
35 & 114 & 110 & 4 \tabularnewline
36 & 121 & 113 & 8 \tabularnewline
37 & 122 & 120 & 2 \tabularnewline
38 & 131 & 121 & 10 \tabularnewline
39 & 125 & 130 & -5 \tabularnewline
40 & 116 & 124 & -8 \tabularnewline
41 & 106 & 115 & -9 \tabularnewline
42 & 98 & 105 & -7 \tabularnewline
43 & 99 & 97 & 2 \tabularnewline
44 & 96 & 98 & -2 \tabularnewline
45 & 95 & 95 & 0 \tabularnewline
46 & 83 & 94 & -11 \tabularnewline
47 & 85 & 82 & 3 \tabularnewline
48 & 98 & 84 & 14 \tabularnewline
49 & 102 & 97 & 5 \tabularnewline
50 & 110 & 101 & 9 \tabularnewline
51 & 101 & 109 & -8 \tabularnewline
52 & 90 & 100 & -10 \tabularnewline
53 & 88 & 89 & -1 \tabularnewline
54 & 83 & 87 & -4 \tabularnewline
55 & 88 & 82 & 6 \tabularnewline
56 & 85 & 87 & -2 \tabularnewline
57 & 86 & 84 & 2 \tabularnewline
58 & 80 & 85 & -5 \tabularnewline
59 & 79 & 79 & 0 \tabularnewline
60 & 97 & 78 & 19 \tabularnewline
61 & 105 & 96 & 9 \tabularnewline
62 & 116 & 104 & 12 \tabularnewline
63 & 99 & 115 & -16 \tabularnewline
64 & 87 & 98 & -11 \tabularnewline
65 & 82 & 86 & -4 \tabularnewline
66 & 81 & 81 & 0 \tabularnewline
67 & 85 & 80 & 5 \tabularnewline
68 & 84 & 84 & 0 \tabularnewline
69 & 78 & 83 & -5 \tabularnewline
70 & 77 & 77 & 0 \tabularnewline
71 & 79 & 76 & 3 \tabularnewline
72 & 85 & 78 & 7 \tabularnewline
73 & 96 & 84 & 12 \tabularnewline
74 & 108 & 95 & 13 \tabularnewline
75 & 98 & 107 & -9 \tabularnewline
76 & 86 & 97 & -11 \tabularnewline
77 & 80 & 85 & -5 \tabularnewline
78 & 74 & 79 & -5 \tabularnewline
79 & 75 & 73 & 2 \tabularnewline
80 & 82 & 74 & 8 \tabularnewline
81 & 71 & 81 & -10 \tabularnewline
82 & 66 & 70 & -4 \tabularnewline
83 & 71 & 65 & 6 \tabularnewline
84 & 75 & 70 & 5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78787&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]170[/C][C]170[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]168[/C][C]169[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]166[/C][C]167[/C][C]-1[/C][/ROW]
[ROW][C]6[/C][C]165[/C][C]165[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]166[/C][C]164[/C][C]2[/C][/ROW]
[ROW][C]8[/C][C]168[/C][C]165[/C][C]3[/C][/ROW]
[ROW][C]9[/C][C]169[/C][C]167[/C][C]2[/C][/ROW]
[ROW][C]10[/C][C]169[/C][C]168[/C][C]1[/C][/ROW]
[ROW][C]11[/C][C]170[/C][C]168[/C][C]2[/C][/ROW]
[ROW][C]12[/C][C]172[/C][C]169[/C][C]3[/C][/ROW]
[ROW][C]13[/C][C]173[/C][C]171[/C][C]2[/C][/ROW]
[ROW][C]14[/C][C]172[/C][C]172[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]165[/C][C]171[/C][C]-6[/C][/ROW]
[ROW][C]16[/C][C]152[/C][C]164[/C][C]-12[/C][/ROW]
[ROW][C]17[/C][C]148[/C][C]151[/C][C]-3[/C][/ROW]
[ROW][C]18[/C][C]145[/C][C]147[/C][C]-2[/C][/ROW]
[ROW][C]19[/C][C]141[/C][C]144[/C][C]-3[/C][/ROW]
[ROW][C]20[/C][C]149[/C][C]140[/C][C]9[/C][/ROW]
[ROW][C]21[/C][C]146[/C][C]148[/C][C]-2[/C][/ROW]
[ROW][C]22[/C][C]144[/C][C]145[/C][C]-1[/C][/ROW]
[ROW][C]23[/C][C]149[/C][C]143[/C][C]6[/C][/ROW]
[ROW][C]24[/C][C]150[/C][C]148[/C][C]2[/C][/ROW]
[ROW][C]25[/C][C]149[/C][C]149[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]156[/C][C]148[/C][C]8[/C][/ROW]
[ROW][C]27[/C][C]150[/C][C]155[/C][C]-5[/C][/ROW]
[ROW][C]28[/C][C]137[/C][C]149[/C][C]-12[/C][/ROW]
[ROW][C]29[/C][C]130[/C][C]136[/C][C]-6[/C][/ROW]
[ROW][C]30[/C][C]126[/C][C]129[/C][C]-3[/C][/ROW]
[ROW][C]31[/C][C]125[/C][C]125[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]123[/C][C]124[/C][C]-1[/C][/ROW]
[ROW][C]33[/C][C]117[/C][C]122[/C][C]-5[/C][/ROW]
[ROW][C]34[/C][C]111[/C][C]116[/C][C]-5[/C][/ROW]
[ROW][C]35[/C][C]114[/C][C]110[/C][C]4[/C][/ROW]
[ROW][C]36[/C][C]121[/C][C]113[/C][C]8[/C][/ROW]
[ROW][C]37[/C][C]122[/C][C]120[/C][C]2[/C][/ROW]
[ROW][C]38[/C][C]131[/C][C]121[/C][C]10[/C][/ROW]
[ROW][C]39[/C][C]125[/C][C]130[/C][C]-5[/C][/ROW]
[ROW][C]40[/C][C]116[/C][C]124[/C][C]-8[/C][/ROW]
[ROW][C]41[/C][C]106[/C][C]115[/C][C]-9[/C][/ROW]
[ROW][C]42[/C][C]98[/C][C]105[/C][C]-7[/C][/ROW]
[ROW][C]43[/C][C]99[/C][C]97[/C][C]2[/C][/ROW]
[ROW][C]44[/C][C]96[/C][C]98[/C][C]-2[/C][/ROW]
[ROW][C]45[/C][C]95[/C][C]95[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]83[/C][C]94[/C][C]-11[/C][/ROW]
[ROW][C]47[/C][C]85[/C][C]82[/C][C]3[/C][/ROW]
[ROW][C]48[/C][C]98[/C][C]84[/C][C]14[/C][/ROW]
[ROW][C]49[/C][C]102[/C][C]97[/C][C]5[/C][/ROW]
[ROW][C]50[/C][C]110[/C][C]101[/C][C]9[/C][/ROW]
[ROW][C]51[/C][C]101[/C][C]109[/C][C]-8[/C][/ROW]
[ROW][C]52[/C][C]90[/C][C]100[/C][C]-10[/C][/ROW]
[ROW][C]53[/C][C]88[/C][C]89[/C][C]-1[/C][/ROW]
[ROW][C]54[/C][C]83[/C][C]87[/C][C]-4[/C][/ROW]
[ROW][C]55[/C][C]88[/C][C]82[/C][C]6[/C][/ROW]
[ROW][C]56[/C][C]85[/C][C]87[/C][C]-2[/C][/ROW]
[ROW][C]57[/C][C]86[/C][C]84[/C][C]2[/C][/ROW]
[ROW][C]58[/C][C]80[/C][C]85[/C][C]-5[/C][/ROW]
[ROW][C]59[/C][C]79[/C][C]79[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]97[/C][C]78[/C][C]19[/C][/ROW]
[ROW][C]61[/C][C]105[/C][C]96[/C][C]9[/C][/ROW]
[ROW][C]62[/C][C]116[/C][C]104[/C][C]12[/C][/ROW]
[ROW][C]63[/C][C]99[/C][C]115[/C][C]-16[/C][/ROW]
[ROW][C]64[/C][C]87[/C][C]98[/C][C]-11[/C][/ROW]
[ROW][C]65[/C][C]82[/C][C]86[/C][C]-4[/C][/ROW]
[ROW][C]66[/C][C]81[/C][C]81[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]85[/C][C]80[/C][C]5[/C][/ROW]
[ROW][C]68[/C][C]84[/C][C]84[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]78[/C][C]83[/C][C]-5[/C][/ROW]
[ROW][C]70[/C][C]77[/C][C]77[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]79[/C][C]76[/C][C]3[/C][/ROW]
[ROW][C]72[/C][C]85[/C][C]78[/C][C]7[/C][/ROW]
[ROW][C]73[/C][C]96[/C][C]84[/C][C]12[/C][/ROW]
[ROW][C]74[/C][C]108[/C][C]95[/C][C]13[/C][/ROW]
[ROW][C]75[/C][C]98[/C][C]107[/C][C]-9[/C][/ROW]
[ROW][C]76[/C][C]86[/C][C]97[/C][C]-11[/C][/ROW]
[ROW][C]77[/C][C]80[/C][C]85[/C][C]-5[/C][/ROW]
[ROW][C]78[/C][C]74[/C][C]79[/C][C]-5[/C][/ROW]
[ROW][C]79[/C][C]75[/C][C]73[/C][C]2[/C][/ROW]
[ROW][C]80[/C][C]82[/C][C]74[/C][C]8[/C][/ROW]
[ROW][C]81[/C][C]71[/C][C]81[/C][C]-10[/C][/ROW]
[ROW][C]82[/C][C]66[/C][C]70[/C][C]-4[/C][/ROW]
[ROW][C]83[/C][C]71[/C][C]65[/C][C]6[/C][/ROW]
[ROW][C]84[/C][C]75[/C][C]70[/C][C]5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78787&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78787&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	170	170	0
4	168	169	-1
5	166	167	-1
6	165	165	0
7	166	164	2
8	168	165	3
9	169	167	2
10	169	168	1
11	170	168	2
12	172	169	3
13	173	171	2
14	172	172	0
15	165	171	-6
16	152	164	-12
17	148	151	-3
18	145	147	-2
19	141	144	-3
20	149	140	9
21	146	148	-2
22	144	145	-1
23	149	143	6
24	150	148	2
25	149	149	0
26	156	148	8
27	150	155	-5
28	137	149	-12
29	130	136	-6
30	126	129	-3
31	125	125	0
32	123	124	-1
33	117	122	-5
34	111	116	-5
35	114	110	4
36	121	113	8
37	122	120	2
38	131	121	10
39	125	130	-5
40	116	124	-8
41	106	115	-9
42	98	105	-7
43	99	97	2
44	96	98	-2
45	95	95	0
46	83	94	-11
47	85	82	3
48	98	84	14
49	102	97	5
50	110	101	9
51	101	109	-8
52	90	100	-10
53	88	89	-1
54	83	87	-4
55	88	82	6
56	85	87	-2
57	86	84	2
58	80	85	-5
59	79	79	0
60	97	78	19
61	105	96	9
62	116	104	12
63	99	115	-16
64	87	98	-11
65	82	86	-4
66	81	81	0
67	85	80	5
68	84	84	0
69	78	83	-5
70	77	77	0
71	79	76	3
72	85	78	7
73	96	84	12
74	108	95	13
75	98	107	-9
76	86	97	-11
77	80	85	-5
78	74	79	-5
79	75	73	2
80	82	74	8
81	71	81	-10
82	66	70	-4
83	71	65	6
84	75	70	5

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	74	60.7862995379728	87.2137004620272
86	73	54.3130055974654	91.6869944025346
87	72	49.1131994437725	94.8868005562275
88	71	44.5725990759455	97.4274009240545
89	70	40.4532675325867	99.5467324674133
90	69	36.6331762540549	101.366823745945
91	68	33.0398346785766	102.960165321423
92	67	29.6260111949309	104.373988805069
93	66	26.3588986139182	105.641101386082
94	65	23.2146102207746	106.785389779225
95	64	20.1751134753098	107.824886524690
96	63	17.2263988875449	108.773601112455

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 74 & 60.7862995379728 & 87.2137004620272 \tabularnewline
86 & 73 & 54.3130055974654 & 91.6869944025346 \tabularnewline
87 & 72 & 49.1131994437725 & 94.8868005562275 \tabularnewline
88 & 71 & 44.5725990759455 & 97.4274009240545 \tabularnewline
89 & 70 & 40.4532675325867 & 99.5467324674133 \tabularnewline
90 & 69 & 36.6331762540549 & 101.366823745945 \tabularnewline
91 & 68 & 33.0398346785766 & 102.960165321423 \tabularnewline
92 & 67 & 29.6260111949309 & 104.373988805069 \tabularnewline
93 & 66 & 26.3588986139182 & 105.641101386082 \tabularnewline
94 & 65 & 23.2146102207746 & 106.785389779225 \tabularnewline
95 & 64 & 20.1751134753098 & 107.824886524690 \tabularnewline
96 & 63 & 17.2263988875449 & 108.773601112455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78787&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]74[/C][C]60.7862995379728[/C][C]87.2137004620272[/C][/ROW]
[ROW][C]86[/C][C]73[/C][C]54.3130055974654[/C][C]91.6869944025346[/C][/ROW]
[ROW][C]87[/C][C]72[/C][C]49.1131994437725[/C][C]94.8868005562275[/C][/ROW]
[ROW][C]88[/C][C]71[/C][C]44.5725990759455[/C][C]97.4274009240545[/C][/ROW]
[ROW][C]89[/C][C]70[/C][C]40.4532675325867[/C][C]99.5467324674133[/C][/ROW]
[ROW][C]90[/C][C]69[/C][C]36.6331762540549[/C][C]101.366823745945[/C][/ROW]
[ROW][C]91[/C][C]68[/C][C]33.0398346785766[/C][C]102.960165321423[/C][/ROW]
[ROW][C]92[/C][C]67[/C][C]29.6260111949309[/C][C]104.373988805069[/C][/ROW]
[ROW][C]93[/C][C]66[/C][C]26.3588986139182[/C][C]105.641101386082[/C][/ROW]
[ROW][C]94[/C][C]65[/C][C]23.2146102207746[/C][C]106.785389779225[/C][/ROW]
[ROW][C]95[/C][C]64[/C][C]20.1751134753098[/C][C]107.824886524690[/C][/ROW]
[ROW][C]96[/C][C]63[/C][C]17.2263988875449[/C][C]108.773601112455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78787&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78787&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	74	60.7862995379728	87.2137004620272
86	73	54.3130055974654	91.6869944025346
87	72	49.1131994437725	94.8868005562275
88	71	44.5725990759455	97.4274009240545
89	70	40.4532675325867	99.5467324674133
90	69	36.6331762540549	101.366823745945
91	68	33.0398346785766	102.960165321423
92	67	29.6260111949309	104.373988805069
93	66	26.3588986139182	105.641101386082
94	65	23.2146102207746	106.785389779225
95	64	20.1751134753098	107.824886524690
96	63	17.2263988875449	108.773601112455

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