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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 20 Jan 2010 12:35:56 -0700

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/Jan/20/t1264016196j9lj0w4ns7v79ib.htm/, Retrieved Thu, 12 Feb 2026 12:29:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72320, Retrieved Thu, 12 Feb 2026 12:29:04 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W62

Estimated Impact

437

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

-       [Exponential Smoothing] [] [2010-01-20 19:35:56] [461523bf9c5715e033e9a40193969321] [Current]

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Dataseries X:

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Histogram

Boxplots

0,62
0,62
0,62
0,63
0,62
0,63
0,63
0,62
0,63
0,63
0,63
0,64
0,64
0,64
0,64
0,64
0,64
0,64
0,64
0,63
0,64
0,64
0,64
0,64
0,64
0,64
0,64
0,64
0,64
0,64
0,64
0,64
0,65
0,65
0,65
0,65
0,65
0,65
0,66
0,66
0,66
0,66
0,68
0,69
0,7
0,7
0,7
0,7
0,7
0,7
0,7
0,7
0,7
0,71
0,7
0,71
0,7
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,7
0,7
0,7
0,7
0,7
0,7
0,7
0,7
0,7
0,71
0,71
0,7
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,7
0,7
0,68
0,68
0,69
0,69
0,7
0,7
0,7
0,7
0,7
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,76
0,77
0,78
0,85
0,89
0,9
0,91
0,91
0,91
0,9
0,89
0,88
0,87
0,86
0,87
0,87
0,87
0,85

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72320&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]1 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=72320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72320&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999923349407294
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999923349407294 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72320&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]0.999923349407294[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72320&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	0.999923349407294
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	0.62	0.62	0
3	0.62	0.62	0
4	0.63	0.62	0.01
5	0.62	0.629999233494073	-0.00999923349407295
6	0.63	0.620000766447174	0.00999923355282606
7	0.63	0.629999233552822	7.66447178390806e-07
8	0.62	0.629999999941251	-0.00999999994125134
9	0.63	0.620000766505923	0.0099992334940775
10	0.63	0.629999233552826	7.66447173949913e-07
11	0.63	0.629999999941251	5.87486725933672e-11
12	0.64	0.629999999999995	0.0100000000000046
13	0.64	0.639999233494073	7.66505927063399e-07
14	0.64	0.639999999941247	5.87531134854657e-11
15	0.64	0.639999999999995	4.55191440096314e-15
16	0.64	0.64	0
17	0.64	0.64	0
18	0.64	0.64	0
19	0.64	0.64	0
20	0.63	0.64	-0.01
21	0.64	0.630000766505927	0.00999923349407295
22	0.64	0.639999233552826	7.66447173949913e-07
23	0.64	0.639999999941251	5.87486725933672e-11
24	0.64	0.639999999999995	4.55191440096314e-15
25	0.64	0.64	0
26	0.64	0.64	0
27	0.64	0.64	0
28	0.64	0.64	0
29	0.64	0.64	0
30	0.64	0.64	0
31	0.64	0.64	0
32	0.64	0.64	0
33	0.65	0.64	0.01
34	0.65	0.649999233494073	7.66505927063399e-07
35	0.65	0.649999999941247	5.87531134854657e-11
36	0.65	0.649999999999995	4.55191440096314e-15
37	0.65	0.65	0
38	0.65	0.65	0
39	0.66	0.65	0.01
40	0.66	0.659999233494073	7.66505927063399e-07
41	0.66	0.659999999941247	5.87531134854657e-11
42	0.66	0.659999999999995	4.55191440096314e-15
43	0.68	0.66	0.02
44	0.69	0.679998466988146	0.0100015330118540
45	0.7	0.689999233376567	0.0100007666234333
46	0.7	0.699999233435311	7.66564689169691e-07
47	0.7	0.699999999941242	5.87576653998667e-11
48	0.7	0.699999999999995	4.55191440096314e-15
49	0.7	0.7	0
50	0.7	0.7	0
51	0.7	0.7	0
52	0.7	0.7	0
53	0.7	0.7	0
54	0.71	0.7	0.01
55	0.7	0.709999233494073	-0.00999923349407295
56	0.71	0.700000766447174	0.00999923355282606
57	0.7	0.709999233552822	-0.00999923355282162
58	0.71	0.700000766447178	0.00999923355282162
59	0.71	0.709999233552822	7.66447178390806e-07
60	0.71	0.709999999941251	5.87486725933672e-11
61	0.71	0.709999999999995	4.55191440096314e-15
62	0.71	0.71	0
63	0.71	0.71	0
64	0.71	0.71	0
65	0.71	0.71	0
66	0.71	0.71	0
67	0.71	0.71	0
68	0.71	0.71	0
69	0.71	0.71	0
70	0.71	0.71	0
71	0.7	0.71	-0.01
72	0.7	0.700000766505927	-7.66505927063399e-07
73	0.7	0.700000000058753	-5.87531134854657e-11
74	0.7	0.700000000000005	-4.55191440096314e-15
75	0.7	0.7	0
76	0.7	0.7	0
77	0.7	0.7	0
78	0.7	0.7	0
79	0.7	0.7	0
80	0.71	0.7	0.01
81	0.71	0.709999233494073	7.66505927063399e-07
82	0.7	0.709999999941247	-0.0099999999412469
83	0.71	0.700000766505922	0.0099992334940775
84	0.71	0.709999233552826	7.66447173949913e-07
85	0.71	0.709999999941251	5.87486725933672e-11
86	0.71	0.709999999999995	4.55191440096314e-15
87	0.71	0.71	0
88	0.71	0.71	0
89	0.71	0.71	0
90	0.71	0.71	0
91	0.71	0.71	0
92	0.71	0.71	0
93	0.71	0.71	0
94	0.71	0.71	0
95	0.7	0.71	-0.01
96	0.7	0.700000766505927	-7.66505927063399e-07
97	0.68	0.700000000058753	-0.020000000058753
98	0.68	0.680001533011859	-1.53301185867871e-06
99	0.69	0.680000000117506	0.00999999988249367
100	0.69	0.689999233494082	7.66505918070592e-07
101	0.7	0.689999999941247	0.0100000000587531
102	0.7	0.699999233494068	7.66505931615313e-07
103	0.7	0.699999999941247	5.87531134854657e-11
104	0.7	0.699999999999995	4.55191440096314e-15
105	0.7	0.7	0
106	0.71	0.7	0.01
107	0.71	0.709999233494073	7.66505927063399e-07
108	0.71	0.709999999941247	5.87531134854657e-11
109	0.71	0.709999999999995	4.55191440096314e-15
110	0.71	0.71	0
111	0.71	0.71	0
112	0.71	0.71	0
113	0.71	0.71	0
114	0.71	0.71	0
115	0.76	0.71	0.05
116	0.77	0.759996167470365	0.0100038325296353
117	0.78	0.769999233200307	0.0100007667996928
118	0.85	0.779999233435297	0.0700007665647027
119	0.89	0.849994634399753	0.0400053656002471
120	0.9	0.889996933565015	0.0100030664349847
121	0.91	0.899999233259029	0.0100007667409712
122	0.91	0.909999233435302	7.66564698162497e-07
123	0.91	0.909999999941242	5.87576653998667e-11
124	0.9	0.909999999999995	-0.00999999999999546
125	0.89	0.900000766505927	-0.0100007665059271
126	0.88	0.89000076656468	-0.0100007665646802
127	0.87	0.880000766564685	-0.0100007665646847
128	0.86	0.870000766564685	-0.0100007665646847
129	0.87	0.860000766564685	0.00999923343531528
130	0.87	0.86999923355283	7.66447169397999e-07
131	0.87	0.869999999941251	5.87486725933672e-11
132	0.85	0.869999999999995	-0.0199999999999955

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 0.62 & 0.62 & 0 \tabularnewline
3 & 0.62 & 0.62 & 0 \tabularnewline
4 & 0.63 & 0.62 & 0.01 \tabularnewline
5 & 0.62 & 0.629999233494073 & -0.00999923349407295 \tabularnewline
6 & 0.63 & 0.620000766447174 & 0.00999923355282606 \tabularnewline
7 & 0.63 & 0.629999233552822 & 7.66447178390806e-07 \tabularnewline
8 & 0.62 & 0.629999999941251 & -0.00999999994125134 \tabularnewline
9 & 0.63 & 0.620000766505923 & 0.0099992334940775 \tabularnewline
10 & 0.63 & 0.629999233552826 & 7.66447173949913e-07 \tabularnewline
11 & 0.63 & 0.629999999941251 & 5.87486725933672e-11 \tabularnewline
12 & 0.64 & 0.629999999999995 & 0.0100000000000046 \tabularnewline
13 & 0.64 & 0.639999233494073 & 7.66505927063399e-07 \tabularnewline
14 & 0.64 & 0.639999999941247 & 5.87531134854657e-11 \tabularnewline
15 & 0.64 & 0.639999999999995 & 4.55191440096314e-15 \tabularnewline
16 & 0.64 & 0.64 & 0 \tabularnewline
17 & 0.64 & 0.64 & 0 \tabularnewline
18 & 0.64 & 0.64 & 0 \tabularnewline
19 & 0.64 & 0.64 & 0 \tabularnewline
20 & 0.63 & 0.64 & -0.01 \tabularnewline
21 & 0.64 & 0.630000766505927 & 0.00999923349407295 \tabularnewline
22 & 0.64 & 0.639999233552826 & 7.66447173949913e-07 \tabularnewline
23 & 0.64 & 0.639999999941251 & 5.87486725933672e-11 \tabularnewline
24 & 0.64 & 0.639999999999995 & 4.55191440096314e-15 \tabularnewline
25 & 0.64 & 0.64 & 0 \tabularnewline
26 & 0.64 & 0.64 & 0 \tabularnewline
27 & 0.64 & 0.64 & 0 \tabularnewline
28 & 0.64 & 0.64 & 0 \tabularnewline
29 & 0.64 & 0.64 & 0 \tabularnewline
30 & 0.64 & 0.64 & 0 \tabularnewline
31 & 0.64 & 0.64 & 0 \tabularnewline
32 & 0.64 & 0.64 & 0 \tabularnewline
33 & 0.65 & 0.64 & 0.01 \tabularnewline
34 & 0.65 & 0.649999233494073 & 7.66505927063399e-07 \tabularnewline
35 & 0.65 & 0.649999999941247 & 5.87531134854657e-11 \tabularnewline
36 & 0.65 & 0.649999999999995 & 4.55191440096314e-15 \tabularnewline
37 & 0.65 & 0.65 & 0 \tabularnewline
38 & 0.65 & 0.65 & 0 \tabularnewline
39 & 0.66 & 0.65 & 0.01 \tabularnewline
40 & 0.66 & 0.659999233494073 & 7.66505927063399e-07 \tabularnewline
41 & 0.66 & 0.659999999941247 & 5.87531134854657e-11 \tabularnewline
42 & 0.66 & 0.659999999999995 & 4.55191440096314e-15 \tabularnewline
43 & 0.68 & 0.66 & 0.02 \tabularnewline
44 & 0.69 & 0.679998466988146 & 0.0100015330118540 \tabularnewline
45 & 0.7 & 0.689999233376567 & 0.0100007666234333 \tabularnewline
46 & 0.7 & 0.699999233435311 & 7.66564689169691e-07 \tabularnewline
47 & 0.7 & 0.699999999941242 & 5.87576653998667e-11 \tabularnewline
48 & 0.7 & 0.699999999999995 & 4.55191440096314e-15 \tabularnewline
49 & 0.7 & 0.7 & 0 \tabularnewline
50 & 0.7 & 0.7 & 0 \tabularnewline
51 & 0.7 & 0.7 & 0 \tabularnewline
52 & 0.7 & 0.7 & 0 \tabularnewline
53 & 0.7 & 0.7 & 0 \tabularnewline
54 & 0.71 & 0.7 & 0.01 \tabularnewline
55 & 0.7 & 0.709999233494073 & -0.00999923349407295 \tabularnewline
56 & 0.71 & 0.700000766447174 & 0.00999923355282606 \tabularnewline
57 & 0.7 & 0.709999233552822 & -0.00999923355282162 \tabularnewline
58 & 0.71 & 0.700000766447178 & 0.00999923355282162 \tabularnewline
59 & 0.71 & 0.709999233552822 & 7.66447178390806e-07 \tabularnewline
60 & 0.71 & 0.709999999941251 & 5.87486725933672e-11 \tabularnewline
61 & 0.71 & 0.709999999999995 & 4.55191440096314e-15 \tabularnewline
62 & 0.71 & 0.71 & 0 \tabularnewline
63 & 0.71 & 0.71 & 0 \tabularnewline
64 & 0.71 & 0.71 & 0 \tabularnewline
65 & 0.71 & 0.71 & 0 \tabularnewline
66 & 0.71 & 0.71 & 0 \tabularnewline
67 & 0.71 & 0.71 & 0 \tabularnewline
68 & 0.71 & 0.71 & 0 \tabularnewline
69 & 0.71 & 0.71 & 0 \tabularnewline
70 & 0.71 & 0.71 & 0 \tabularnewline
71 & 0.7 & 0.71 & -0.01 \tabularnewline
72 & 0.7 & 0.700000766505927 & -7.66505927063399e-07 \tabularnewline
73 & 0.7 & 0.700000000058753 & -5.87531134854657e-11 \tabularnewline
74 & 0.7 & 0.700000000000005 & -4.55191440096314e-15 \tabularnewline
75 & 0.7 & 0.7 & 0 \tabularnewline
76 & 0.7 & 0.7 & 0 \tabularnewline
77 & 0.7 & 0.7 & 0 \tabularnewline
78 & 0.7 & 0.7 & 0 \tabularnewline
79 & 0.7 & 0.7 & 0 \tabularnewline
80 & 0.71 & 0.7 & 0.01 \tabularnewline
81 & 0.71 & 0.709999233494073 & 7.66505927063399e-07 \tabularnewline
82 & 0.7 & 0.709999999941247 & -0.0099999999412469 \tabularnewline
83 & 0.71 & 0.700000766505922 & 0.0099992334940775 \tabularnewline
84 & 0.71 & 0.709999233552826 & 7.66447173949913e-07 \tabularnewline
85 & 0.71 & 0.709999999941251 & 5.87486725933672e-11 \tabularnewline
86 & 0.71 & 0.709999999999995 & 4.55191440096314e-15 \tabularnewline
87 & 0.71 & 0.71 & 0 \tabularnewline
88 & 0.71 & 0.71 & 0 \tabularnewline
89 & 0.71 & 0.71 & 0 \tabularnewline
90 & 0.71 & 0.71 & 0 \tabularnewline
91 & 0.71 & 0.71 & 0 \tabularnewline
92 & 0.71 & 0.71 & 0 \tabularnewline
93 & 0.71 & 0.71 & 0 \tabularnewline
94 & 0.71 & 0.71 & 0 \tabularnewline
95 & 0.7 & 0.71 & -0.01 \tabularnewline
96 & 0.7 & 0.700000766505927 & -7.66505927063399e-07 \tabularnewline
97 & 0.68 & 0.700000000058753 & -0.020000000058753 \tabularnewline
98 & 0.68 & 0.680001533011859 & -1.53301185867871e-06 \tabularnewline
99 & 0.69 & 0.680000000117506 & 0.00999999988249367 \tabularnewline
100 & 0.69 & 0.689999233494082 & 7.66505918070592e-07 \tabularnewline
101 & 0.7 & 0.689999999941247 & 0.0100000000587531 \tabularnewline
102 & 0.7 & 0.699999233494068 & 7.66505931615313e-07 \tabularnewline
103 & 0.7 & 0.699999999941247 & 5.87531134854657e-11 \tabularnewline
104 & 0.7 & 0.699999999999995 & 4.55191440096314e-15 \tabularnewline
105 & 0.7 & 0.7 & 0 \tabularnewline
106 & 0.71 & 0.7 & 0.01 \tabularnewline
107 & 0.71 & 0.709999233494073 & 7.66505927063399e-07 \tabularnewline
108 & 0.71 & 0.709999999941247 & 5.87531134854657e-11 \tabularnewline
109 & 0.71 & 0.709999999999995 & 4.55191440096314e-15 \tabularnewline
110 & 0.71 & 0.71 & 0 \tabularnewline
111 & 0.71 & 0.71 & 0 \tabularnewline
112 & 0.71 & 0.71 & 0 \tabularnewline
113 & 0.71 & 0.71 & 0 \tabularnewline
114 & 0.71 & 0.71 & 0 \tabularnewline
115 & 0.76 & 0.71 & 0.05 \tabularnewline
116 & 0.77 & 0.759996167470365 & 0.0100038325296353 \tabularnewline
117 & 0.78 & 0.769999233200307 & 0.0100007667996928 \tabularnewline
118 & 0.85 & 0.779999233435297 & 0.0700007665647027 \tabularnewline
119 & 0.89 & 0.849994634399753 & 0.0400053656002471 \tabularnewline
120 & 0.9 & 0.889996933565015 & 0.0100030664349847 \tabularnewline
121 & 0.91 & 0.899999233259029 & 0.0100007667409712 \tabularnewline
122 & 0.91 & 0.909999233435302 & 7.66564698162497e-07 \tabularnewline
123 & 0.91 & 0.909999999941242 & 5.87576653998667e-11 \tabularnewline
124 & 0.9 & 0.909999999999995 & -0.00999999999999546 \tabularnewline
125 & 0.89 & 0.900000766505927 & -0.0100007665059271 \tabularnewline
126 & 0.88 & 0.89000076656468 & -0.0100007665646802 \tabularnewline
127 & 0.87 & 0.880000766564685 & -0.0100007665646847 \tabularnewline
128 & 0.86 & 0.870000766564685 & -0.0100007665646847 \tabularnewline
129 & 0.87 & 0.860000766564685 & 0.00999923343531528 \tabularnewline
130 & 0.87 & 0.86999923355283 & 7.66447169397999e-07 \tabularnewline
131 & 0.87 & 0.869999999941251 & 5.87486725933672e-11 \tabularnewline
132 & 0.85 & 0.869999999999995 & -0.0199999999999955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72320&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]2[/C][C]0.62[/C][C]0.62[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.62[/C][C]0.62[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.63[/C][C]0.62[/C][C]0.01[/C][/ROW]
[ROW][C]5[/C][C]0.62[/C][C]0.629999233494073[/C][C]-0.00999923349407295[/C][/ROW]
[ROW][C]6[/C][C]0.63[/C][C]0.620000766447174[/C][C]0.00999923355282606[/C][/ROW]
[ROW][C]7[/C][C]0.63[/C][C]0.629999233552822[/C][C]7.66447178390806e-07[/C][/ROW]
[ROW][C]8[/C][C]0.62[/C][C]0.629999999941251[/C][C]-0.00999999994125134[/C][/ROW]
[ROW][C]9[/C][C]0.63[/C][C]0.620000766505923[/C][C]0.0099992334940775[/C][/ROW]
[ROW][C]10[/C][C]0.63[/C][C]0.629999233552826[/C][C]7.66447173949913e-07[/C][/ROW]
[ROW][C]11[/C][C]0.63[/C][C]0.629999999941251[/C][C]5.87486725933672e-11[/C][/ROW]
[ROW][C]12[/C][C]0.64[/C][C]0.629999999999995[/C][C]0.0100000000000046[/C][/ROW]
[ROW][C]13[/C][C]0.64[/C][C]0.639999233494073[/C][C]7.66505927063399e-07[/C][/ROW]
[ROW][C]14[/C][C]0.64[/C][C]0.639999999941247[/C][C]5.87531134854657e-11[/C][/ROW]
[ROW][C]15[/C][C]0.64[/C][C]0.639999999999995[/C][C]4.55191440096314e-15[/C][/ROW]
[ROW][C]16[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.63[/C][C]0.64[/C][C]-0.01[/C][/ROW]
[ROW][C]21[/C][C]0.64[/C][C]0.630000766505927[/C][C]0.00999923349407295[/C][/ROW]
[ROW][C]22[/C][C]0.64[/C][C]0.639999233552826[/C][C]7.66447173949913e-07[/C][/ROW]
[ROW][C]23[/C][C]0.64[/C][C]0.639999999941251[/C][C]5.87486725933672e-11[/C][/ROW]
[ROW][C]24[/C][C]0.64[/C][C]0.639999999999995[/C][C]4.55191440096314e-15[/C][/ROW]
[ROW][C]25[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]0.64[/C][C]0.64[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]0.65[/C][C]0.64[/C][C]0.01[/C][/ROW]
[ROW][C]34[/C][C]0.65[/C][C]0.649999233494073[/C][C]7.66505927063399e-07[/C][/ROW]
[ROW][C]35[/C][C]0.65[/C][C]0.649999999941247[/C][C]5.87531134854657e-11[/C][/ROW]
[ROW][C]36[/C][C]0.65[/C][C]0.649999999999995[/C][C]4.55191440096314e-15[/C][/ROW]
[ROW][C]37[/C][C]0.65[/C][C]0.65[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]0.65[/C][C]0.65[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]0.66[/C][C]0.65[/C][C]0.01[/C][/ROW]
[ROW][C]40[/C][C]0.66[/C][C]0.659999233494073[/C][C]7.66505927063399e-07[/C][/ROW]
[ROW][C]41[/C][C]0.66[/C][C]0.659999999941247[/C][C]5.87531134854657e-11[/C][/ROW]
[ROW][C]42[/C][C]0.66[/C][C]0.659999999999995[/C][C]4.55191440096314e-15[/C][/ROW]
[ROW][C]43[/C][C]0.68[/C][C]0.66[/C][C]0.02[/C][/ROW]
[ROW][C]44[/C][C]0.69[/C][C]0.679998466988146[/C][C]0.0100015330118540[/C][/ROW]
[ROW][C]45[/C][C]0.7[/C][C]0.689999233376567[/C][C]0.0100007666234333[/C][/ROW]
[ROW][C]46[/C][C]0.7[/C][C]0.699999233435311[/C][C]7.66564689169691e-07[/C][/ROW]
[ROW][C]47[/C][C]0.7[/C][C]0.699999999941242[/C][C]5.87576653998667e-11[/C][/ROW]
[ROW][C]48[/C][C]0.7[/C][C]0.699999999999995[/C][C]4.55191440096314e-15[/C][/ROW]
[ROW][C]49[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]53[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]0.71[/C][C]0.7[/C][C]0.01[/C][/ROW]
[ROW][C]55[/C][C]0.7[/C][C]0.709999233494073[/C][C]-0.00999923349407295[/C][/ROW]
[ROW][C]56[/C][C]0.71[/C][C]0.700000766447174[/C][C]0.00999923355282606[/C][/ROW]
[ROW][C]57[/C][C]0.7[/C][C]0.709999233552822[/C][C]-0.00999923355282162[/C][/ROW]
[ROW][C]58[/C][C]0.71[/C][C]0.700000766447178[/C][C]0.00999923355282162[/C][/ROW]
[ROW][C]59[/C][C]0.71[/C][C]0.709999233552822[/C][C]7.66447178390806e-07[/C][/ROW]
[ROW][C]60[/C][C]0.71[/C][C]0.709999999941251[/C][C]5.87486725933672e-11[/C][/ROW]
[ROW][C]61[/C][C]0.71[/C][C]0.709999999999995[/C][C]4.55191440096314e-15[/C][/ROW]
[ROW][C]62[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]64[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]68[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]0.7[/C][C]0.71[/C][C]-0.01[/C][/ROW]
[ROW][C]72[/C][C]0.7[/C][C]0.700000766505927[/C][C]-7.66505927063399e-07[/C][/ROW]
[ROW][C]73[/C][C]0.7[/C][C]0.700000000058753[/C][C]-5.87531134854657e-11[/C][/ROW]
[ROW][C]74[/C][C]0.7[/C][C]0.700000000000005[/C][C]-4.55191440096314e-15[/C][/ROW]
[ROW][C]75[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]76[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]77[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]78[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]79[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]80[/C][C]0.71[/C][C]0.7[/C][C]0.01[/C][/ROW]
[ROW][C]81[/C][C]0.71[/C][C]0.709999233494073[/C][C]7.66505927063399e-07[/C][/ROW]
[ROW][C]82[/C][C]0.7[/C][C]0.709999999941247[/C][C]-0.0099999999412469[/C][/ROW]
[ROW][C]83[/C][C]0.71[/C][C]0.700000766505922[/C][C]0.0099992334940775[/C][/ROW]
[ROW][C]84[/C][C]0.71[/C][C]0.709999233552826[/C][C]7.66447173949913e-07[/C][/ROW]
[ROW][C]85[/C][C]0.71[/C][C]0.709999999941251[/C][C]5.87486725933672e-11[/C][/ROW]
[ROW][C]86[/C][C]0.71[/C][C]0.709999999999995[/C][C]4.55191440096314e-15[/C][/ROW]
[ROW][C]87[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]88[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]89[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]90[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]91[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]92[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]93[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]94[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]95[/C][C]0.7[/C][C]0.71[/C][C]-0.01[/C][/ROW]
[ROW][C]96[/C][C]0.7[/C][C]0.700000766505927[/C][C]-7.66505927063399e-07[/C][/ROW]
[ROW][C]97[/C][C]0.68[/C][C]0.700000000058753[/C][C]-0.020000000058753[/C][/ROW]
[ROW][C]98[/C][C]0.68[/C][C]0.680001533011859[/C][C]-1.53301185867871e-06[/C][/ROW]
[ROW][C]99[/C][C]0.69[/C][C]0.680000000117506[/C][C]0.00999999988249367[/C][/ROW]
[ROW][C]100[/C][C]0.69[/C][C]0.689999233494082[/C][C]7.66505918070592e-07[/C][/ROW]
[ROW][C]101[/C][C]0.7[/C][C]0.689999999941247[/C][C]0.0100000000587531[/C][/ROW]
[ROW][C]102[/C][C]0.7[/C][C]0.699999233494068[/C][C]7.66505931615313e-07[/C][/ROW]
[ROW][C]103[/C][C]0.7[/C][C]0.699999999941247[/C][C]5.87531134854657e-11[/C][/ROW]
[ROW][C]104[/C][C]0.7[/C][C]0.699999999999995[/C][C]4.55191440096314e-15[/C][/ROW]
[ROW][C]105[/C][C]0.7[/C][C]0.7[/C][C]0[/C][/ROW]
[ROW][C]106[/C][C]0.71[/C][C]0.7[/C][C]0.01[/C][/ROW]
[ROW][C]107[/C][C]0.71[/C][C]0.709999233494073[/C][C]7.66505927063399e-07[/C][/ROW]
[ROW][C]108[/C][C]0.71[/C][C]0.709999999941247[/C][C]5.87531134854657e-11[/C][/ROW]
[ROW][C]109[/C][C]0.71[/C][C]0.709999999999995[/C][C]4.55191440096314e-15[/C][/ROW]
[ROW][C]110[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]111[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]112[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]113[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]114[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]115[/C][C]0.76[/C][C]0.71[/C][C]0.05[/C][/ROW]
[ROW][C]116[/C][C]0.77[/C][C]0.759996167470365[/C][C]0.0100038325296353[/C][/ROW]
[ROW][C]117[/C][C]0.78[/C][C]0.769999233200307[/C][C]0.0100007667996928[/C][/ROW]
[ROW][C]118[/C][C]0.85[/C][C]0.779999233435297[/C][C]0.0700007665647027[/C][/ROW]
[ROW][C]119[/C][C]0.89[/C][C]0.849994634399753[/C][C]0.0400053656002471[/C][/ROW]
[ROW][C]120[/C][C]0.9[/C][C]0.889996933565015[/C][C]0.0100030664349847[/C][/ROW]
[ROW][C]121[/C][C]0.91[/C][C]0.899999233259029[/C][C]0.0100007667409712[/C][/ROW]
[ROW][C]122[/C][C]0.91[/C][C]0.909999233435302[/C][C]7.66564698162497e-07[/C][/ROW]
[ROW][C]123[/C][C]0.91[/C][C]0.909999999941242[/C][C]5.87576653998667e-11[/C][/ROW]
[ROW][C]124[/C][C]0.9[/C][C]0.909999999999995[/C][C]-0.00999999999999546[/C][/ROW]
[ROW][C]125[/C][C]0.89[/C][C]0.900000766505927[/C][C]-0.0100007665059271[/C][/ROW]
[ROW][C]126[/C][C]0.88[/C][C]0.89000076656468[/C][C]-0.0100007665646802[/C][/ROW]
[ROW][C]127[/C][C]0.87[/C][C]0.880000766564685[/C][C]-0.0100007665646847[/C][/ROW]
[ROW][C]128[/C][C]0.86[/C][C]0.870000766564685[/C][C]-0.0100007665646847[/C][/ROW]
[ROW][C]129[/C][C]0.87[/C][C]0.860000766564685[/C][C]0.00999923343531528[/C][/ROW]
[ROW][C]130[/C][C]0.87[/C][C]0.86999923355283[/C][C]7.66447169397999e-07[/C][/ROW]
[ROW][C]131[/C][C]0.87[/C][C]0.869999999941251[/C][C]5.87486725933672e-11[/C][/ROW]
[ROW][C]132[/C][C]0.85[/C][C]0.869999999999995[/C][C]-0.0199999999999955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72320&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72320&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
2	0.62	0.62	0
3	0.62	0.62	0
4	0.63	0.62	0.01
5	0.62	0.629999233494073	-0.00999923349407295
6	0.63	0.620000766447174	0.00999923355282606
7	0.63	0.629999233552822	7.66447178390806e-07
8	0.62	0.629999999941251	-0.00999999994125134
9	0.63	0.620000766505923	0.0099992334940775
10	0.63	0.629999233552826	7.66447173949913e-07
11	0.63	0.629999999941251	5.87486725933672e-11
12	0.64	0.629999999999995	0.0100000000000046
13	0.64	0.639999233494073	7.66505927063399e-07
14	0.64	0.639999999941247	5.87531134854657e-11
15	0.64	0.639999999999995	4.55191440096314e-15
16	0.64	0.64	0
17	0.64	0.64	0
18	0.64	0.64	0
19	0.64	0.64	0
20	0.63	0.64	-0.01
21	0.64	0.630000766505927	0.00999923349407295
22	0.64	0.639999233552826	7.66447173949913e-07
23	0.64	0.639999999941251	5.87486725933672e-11
24	0.64	0.639999999999995	4.55191440096314e-15
25	0.64	0.64	0
26	0.64	0.64	0
27	0.64	0.64	0
28	0.64	0.64	0
29	0.64	0.64	0
30	0.64	0.64	0
31	0.64	0.64	0
32	0.64	0.64	0
33	0.65	0.64	0.01
34	0.65	0.649999233494073	7.66505927063399e-07
35	0.65	0.649999999941247	5.87531134854657e-11
36	0.65	0.649999999999995	4.55191440096314e-15
37	0.65	0.65	0
38	0.65	0.65	0
39	0.66	0.65	0.01
40	0.66	0.659999233494073	7.66505927063399e-07
41	0.66	0.659999999941247	5.87531134854657e-11
42	0.66	0.659999999999995	4.55191440096314e-15
43	0.68	0.66	0.02
44	0.69	0.679998466988146	0.0100015330118540
45	0.7	0.689999233376567	0.0100007666234333
46	0.7	0.699999233435311	7.66564689169691e-07
47	0.7	0.699999999941242	5.87576653998667e-11
48	0.7	0.699999999999995	4.55191440096314e-15
49	0.7	0.7	0
50	0.7	0.7	0
51	0.7	0.7	0
52	0.7	0.7	0
53	0.7	0.7	0
54	0.71	0.7	0.01
55	0.7	0.709999233494073	-0.00999923349407295
56	0.71	0.700000766447174	0.00999923355282606
57	0.7	0.709999233552822	-0.00999923355282162
58	0.71	0.700000766447178	0.00999923355282162
59	0.71	0.709999233552822	7.66447178390806e-07
60	0.71	0.709999999941251	5.87486725933672e-11
61	0.71	0.709999999999995	4.55191440096314e-15
62	0.71	0.71	0
63	0.71	0.71	0
64	0.71	0.71	0
65	0.71	0.71	0
66	0.71	0.71	0
67	0.71	0.71	0
68	0.71	0.71	0
69	0.71	0.71	0
70	0.71	0.71	0
71	0.7	0.71	-0.01
72	0.7	0.700000766505927	-7.66505927063399e-07
73	0.7	0.700000000058753	-5.87531134854657e-11
74	0.7	0.700000000000005	-4.55191440096314e-15
75	0.7	0.7	0
76	0.7	0.7	0
77	0.7	0.7	0
78	0.7	0.7	0
79	0.7	0.7	0
80	0.71	0.7	0.01
81	0.71	0.709999233494073	7.66505927063399e-07
82	0.7	0.709999999941247	-0.0099999999412469
83	0.71	0.700000766505922	0.0099992334940775
84	0.71	0.709999233552826	7.66447173949913e-07
85	0.71	0.709999999941251	5.87486725933672e-11
86	0.71	0.709999999999995	4.55191440096314e-15
87	0.71	0.71	0
88	0.71	0.71	0
89	0.71	0.71	0
90	0.71	0.71	0
91	0.71	0.71	0
92	0.71	0.71	0
93	0.71	0.71	0
94	0.71	0.71	0
95	0.7	0.71	-0.01
96	0.7	0.700000766505927	-7.66505927063399e-07
97	0.68	0.700000000058753	-0.020000000058753
98	0.68	0.680001533011859	-1.53301185867871e-06
99	0.69	0.680000000117506	0.00999999988249367
100	0.69	0.689999233494082	7.66505918070592e-07
101	0.7	0.689999999941247	0.0100000000587531
102	0.7	0.699999233494068	7.66505931615313e-07
103	0.7	0.699999999941247	5.87531134854657e-11
104	0.7	0.699999999999995	4.55191440096314e-15
105	0.7	0.7	0
106	0.71	0.7	0.01
107	0.71	0.709999233494073	7.66505927063399e-07
108	0.71	0.709999999941247	5.87531134854657e-11
109	0.71	0.709999999999995	4.55191440096314e-15
110	0.71	0.71	0
111	0.71	0.71	0
112	0.71	0.71	0
113	0.71	0.71	0
114	0.71	0.71	0
115	0.76	0.71	0.05
116	0.77	0.759996167470365	0.0100038325296353
117	0.78	0.769999233200307	0.0100007667996928
118	0.85	0.779999233435297	0.0700007665647027
119	0.89	0.849994634399753	0.0400053656002471
120	0.9	0.889996933565015	0.0100030664349847
121	0.91	0.899999233259029	0.0100007667409712
122	0.91	0.909999233435302	7.66564698162497e-07
123	0.91	0.909999999941242	5.87576653998667e-11
124	0.9	0.909999999999995	-0.00999999999999546
125	0.89	0.900000766505927	-0.0100007665059271
126	0.88	0.89000076656468	-0.0100007665646802
127	0.87	0.880000766564685	-0.0100007665646847
128	0.86	0.870000766564685	-0.0100007665646847
129	0.87	0.860000766564685	0.00999923343531528
130	0.87	0.86999923355283	7.66447169397999e-07
131	0.87	0.869999999941251	5.87486725933672e-11
132	0.85	0.869999999999995	-0.0199999999999955

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	0.850001533011854	0.830179436859045	0.869823629164664
134	0.850001533011854	0.82196993013796	0.878033135885747
135	0.850001533011854	0.815670409763872	0.884332656259836
136	0.850001533011854	0.810359619747525	0.889643446276183
137	0.850001533011854	0.805680696478176	0.894322369545532
138	0.850001533011854	0.80145061319736	0.898552452826348
139	0.850001533011854	0.79756064172822	0.902442424295488
140	0.850001533011854	0.793939938828221	0.906063127195487
141	0.850001533011854	0.790539296203954	0.909463769819754
142	0.850001533011854	0.787322885371791	0.912680180651917
143	0.850001533011854	0.78426365858793	0.915739407435778
144	0.850001533011854	0.78134060236302	0.918662463660689

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 0.850001533011854 & 0.830179436859045 & 0.869823629164664 \tabularnewline
134 & 0.850001533011854 & 0.82196993013796 & 0.878033135885747 \tabularnewline
135 & 0.850001533011854 & 0.815670409763872 & 0.884332656259836 \tabularnewline
136 & 0.850001533011854 & 0.810359619747525 & 0.889643446276183 \tabularnewline
137 & 0.850001533011854 & 0.805680696478176 & 0.894322369545532 \tabularnewline
138 & 0.850001533011854 & 0.80145061319736 & 0.898552452826348 \tabularnewline
139 & 0.850001533011854 & 0.79756064172822 & 0.902442424295488 \tabularnewline
140 & 0.850001533011854 & 0.793939938828221 & 0.906063127195487 \tabularnewline
141 & 0.850001533011854 & 0.790539296203954 & 0.909463769819754 \tabularnewline
142 & 0.850001533011854 & 0.787322885371791 & 0.912680180651917 \tabularnewline
143 & 0.850001533011854 & 0.78426365858793 & 0.915739407435778 \tabularnewline
144 & 0.850001533011854 & 0.78134060236302 & 0.918662463660689 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72320&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]133[/C][C]0.850001533011854[/C][C]0.830179436859045[/C][C]0.869823629164664[/C][/ROW]
[ROW][C]134[/C][C]0.850001533011854[/C][C]0.82196993013796[/C][C]0.878033135885747[/C][/ROW]
[ROW][C]135[/C][C]0.850001533011854[/C][C]0.815670409763872[/C][C]0.884332656259836[/C][/ROW]
[ROW][C]136[/C][C]0.850001533011854[/C][C]0.810359619747525[/C][C]0.889643446276183[/C][/ROW]
[ROW][C]137[/C][C]0.850001533011854[/C][C]0.805680696478176[/C][C]0.894322369545532[/C][/ROW]
[ROW][C]138[/C][C]0.850001533011854[/C][C]0.80145061319736[/C][C]0.898552452826348[/C][/ROW]
[ROW][C]139[/C][C]0.850001533011854[/C][C]0.79756064172822[/C][C]0.902442424295488[/C][/ROW]
[ROW][C]140[/C][C]0.850001533011854[/C][C]0.793939938828221[/C][C]0.906063127195487[/C][/ROW]
[ROW][C]141[/C][C]0.850001533011854[/C][C]0.790539296203954[/C][C]0.909463769819754[/C][/ROW]
[ROW][C]142[/C][C]0.850001533011854[/C][C]0.787322885371791[/C][C]0.912680180651917[/C][/ROW]
[ROW][C]143[/C][C]0.850001533011854[/C][C]0.78426365858793[/C][C]0.915739407435778[/C][/ROW]
[ROW][C]144[/C][C]0.850001533011854[/C][C]0.78134060236302[/C][C]0.918662463660689[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72320&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72320&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
133	0.850001533011854	0.830179436859045	0.869823629164664
134	0.850001533011854	0.82196993013796	0.878033135885747
135	0.850001533011854	0.815670409763872	0.884332656259836
136	0.850001533011854	0.810359619747525	0.889643446276183
137	0.850001533011854	0.805680696478176	0.894322369545532
138	0.850001533011854	0.80145061319736	0.898552452826348
139	0.850001533011854	0.79756064172822	0.902442424295488
140	0.850001533011854	0.793939938828221	0.906063127195487
141	0.850001533011854	0.790539296203954	0.909463769819754
142	0.850001533011854	0.787322885371791	0.912680180651917
143	0.850001533011854	0.78426365858793	0.915739407435778
144	0.850001533011854	0.78134060236302	0.918662463660689

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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