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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, 18 May 2011 12:15:22 +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/2011/May/18/t1305720804txrk3nz5fk9oj2s.htm/, Retrieved Tue, 14 May 2024 17:26:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121796, Retrieved Tue, 14 May 2024 17:26:39 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

111

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

-     [Classical Decomposition] [isabelle regnard,...] [2011-05-11 11:49:39] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [Isabelle Regnard,...] [2011-05-18 12:15:22] [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	3 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121796&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121796&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121796&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	3 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999924063401756
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999924063401756 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121796&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]0.999924063401756[/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=121796&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121796&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	0.999924063401756
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	106.22	106.42	-0.200000000000003
3	106.32	106.22001518732	0.0999848126803471
4	105.81	106.319992407493	-0.509992407493442
5	105.92	105.810038727089	0.109961272911448
6	107.54	105.919991649915	1.620008350085
7	107.34	107.539876982077	-0.199876982076773
8	107.24	107.340015177978	-0.100015177978094
9	107.74	107.240007594812	0.499992405187612
10	105.71	107.739962032278	-2.02996203227761
11	105.41	105.710154148411	-0.300154148411295
12	106.22	105.410022792685	0.809977207315029
13	106.32	106.219938493086	0.100061506913775
14	106.12	106.31999240167	-0.199992401669547
15	106.22	106.120015186743	0.0999848132573362
16	105.92	106.219992407493	-0.299992407493392
17	105.71	105.920022780403	-0.210022780402937
18	105.71	105.710015948416	-1.5948415509115e-05
19	105.92	105.710000001211	0.20999999878893
20	105.71	105.919984053314	-0.209984053314471
21	105.41	105.710015945475	-0.300015945474698
22	104.49	105.41002278219	-0.920022782190316
23	101.35	104.4900698634	-3.14006986340038
24	99.72	101.350238446224	-1.63023844622367
25	99.01	99.720123794762	-0.710123794761927
26	97.89	99.0100539243853	-1.12005392438532
27	95.86	97.8900850530849	-2.03008505308487
28	94.95	95.860154157753	-0.910154157753084
29	95.35	94.9500691140106	0.399930885989377
30	95.15	95.349969630609	-0.199969630608976
31	95.46	95.1500151850135	0.309984814986493
32	95.56	95.4599764608076	0.100023539192364
33	95.05	95.5599924045527	-0.50999240455269
34	94.64	95.0500387270883	-0.41003872708832
35	93.63	94.640031136946	-1.01003113694608
36	93.12	93.6300766983287	-0.510076698328646
37	93.53	93.1200387334893	0.409961266510678
38	97.18	93.529968868936	3.650031131064
39	96.27	97.1797228290524	-0.909722829052427
40	95.15	96.270069081257	-1.12006908125697
41	97.08	95.1500850542358	1.92991494576417
42	101.95	97.0798534488241	4.87014655117588
43	103.07	101.949630177638	1.12036982236204
44	103.68	103.069914922927	0.610085077073094
45	102.87	103.679953672215	-0.809953672214604
46	102.56	102.870061505127	-0.310061505126598
47	103.38	102.560023545016	0.819976454984044
48	103.27	103.379937733777	-0.109937733777372
49	102.89	103.270008348298	-0.380008348297523
50	102.69	102.890028856541	-0.20002885654128
51	101.54	102.690015189511	-1.15001518951091
52	102.9	101.540087328241	1.35991267175858
53	101.53	102.899896732858	-1.36989673285781
54	101.96	101.530104025298	0.429895974702148
55	101.99	101.959967355162	0.0300326448379167
56	101.11	101.989997719423	-0.879997719423102
57	101.75	101.110066824033	0.639933175966732
58	101.71	101.749951405652	-0.0399514056515073
59	104.11	101.710003033774	2.39999696622615
60	103.57	104.109817752395	-0.539817752394583
61	103.32	103.570040991924	-0.250040991923782
62	103.64	103.320018987262	0.319981012737671
63	103.68	103.63997570173	0.0400242982696142
64	103.79	103.679996960691	0.110003039309063
65	103.01	103.789991646743	-0.779991646743397
66	101.54	103.010059229912	-1.47005922991232
67	101.9	101.540111631297	0.359888368702869
68	103.68	101.899972671302	1.78002732869847
69	104.62	103.67986483078	0.940135169220127
70	104.11	104.619928609333	-0.509928609333357
71	105.04	104.110038722244	0.929961277756078
72	104.83	105.039929381904	-0.209929381904075
73	105.05	104.830015941323	0.219984058676872
74	104.68	105.049983295159	-0.369983295158903
75	107.32	104.680028095273	2.63997190472715
76	109.9	107.319799529514	2.58020047048592
77	109.77	109.899804068353	-0.129804068353494
78	110.69	109.770009856879	0.919990143120614
79	110.54	110.689930139078	-0.149930139078108
80	110.89	110.540011385185	0.34998861481526
81	110.95	110.889973423055	0.0600265769448356
82	109.73	110.949995441786	-1.21999544178594
83	110.85	109.730092642304	1.11990735769628
84	110.39	110.849914958045	-0.459914958044905
85	110.58	110.390034924377	0.189965075622595
86	110.4	110.579985574698	-0.179985574698364
87	111.07	110.400013667492	0.669986332507719
88	110.86	111.069949123517	-0.209949123517035
89	111.38	110.860015942822	0.519984057177751
90	111.44	111.37996051418	0.0600394858204396
91	110.36	111.439995440806	-1.07999544080567
92	110.06	110.36008201118	-0.300082011179882
93	108.34	110.060022787207	-1.72002278720711
94	107.94	108.340130612679	-0.400130612679376
95	107.39	107.940030384558	-0.550030384557573
96	107.1	107.390041767436	-0.290041767436335
97	107.61	107.100022024785	0.509977975214838
98	107.74	107.609961274007	0.13003872599262
99	106.9	107.739990125302	-0.839990125301497
100	106.71	106.900063785993	-0.190063785992692
101	106.6	106.710014432797	-0.110014432797357
102	108.21	106.600008354122	1.60999164587822
103	110.54	108.209877742711	2.33012225728879
104	110.91	110.539823058442	0.370176941557702
105	109.51	110.909971890022	-1.3999718900223
106	110.27	109.510106309103	0.759893690897016
107	111.39	110.269942296258	1.12005770374192
108	112.13	111.389914946628	0.740085053371857
109	111.64	112.129943800459	-0.489943800458633

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 106.22 & 106.42 & -0.200000000000003 \tabularnewline
3 & 106.32 & 106.22001518732 & 0.0999848126803471 \tabularnewline
4 & 105.81 & 106.319992407493 & -0.509992407493442 \tabularnewline
5 & 105.92 & 105.810038727089 & 0.109961272911448 \tabularnewline
6 & 107.54 & 105.919991649915 & 1.620008350085 \tabularnewline
7 & 107.34 & 107.539876982077 & -0.199876982076773 \tabularnewline
8 & 107.24 & 107.340015177978 & -0.100015177978094 \tabularnewline
9 & 107.74 & 107.240007594812 & 0.499992405187612 \tabularnewline
10 & 105.71 & 107.739962032278 & -2.02996203227761 \tabularnewline
11 & 105.41 & 105.710154148411 & -0.300154148411295 \tabularnewline
12 & 106.22 & 105.410022792685 & 0.809977207315029 \tabularnewline
13 & 106.32 & 106.219938493086 & 0.100061506913775 \tabularnewline
14 & 106.12 & 106.31999240167 & -0.199992401669547 \tabularnewline
15 & 106.22 & 106.120015186743 & 0.0999848132573362 \tabularnewline
16 & 105.92 & 106.219992407493 & -0.299992407493392 \tabularnewline
17 & 105.71 & 105.920022780403 & -0.210022780402937 \tabularnewline
18 & 105.71 & 105.710015948416 & -1.5948415509115e-05 \tabularnewline
19 & 105.92 & 105.710000001211 & 0.20999999878893 \tabularnewline
20 & 105.71 & 105.919984053314 & -0.209984053314471 \tabularnewline
21 & 105.41 & 105.710015945475 & -0.300015945474698 \tabularnewline
22 & 104.49 & 105.41002278219 & -0.920022782190316 \tabularnewline
23 & 101.35 & 104.4900698634 & -3.14006986340038 \tabularnewline
24 & 99.72 & 101.350238446224 & -1.63023844622367 \tabularnewline
25 & 99.01 & 99.720123794762 & -0.710123794761927 \tabularnewline
26 & 97.89 & 99.0100539243853 & -1.12005392438532 \tabularnewline
27 & 95.86 & 97.8900850530849 & -2.03008505308487 \tabularnewline
28 & 94.95 & 95.860154157753 & -0.910154157753084 \tabularnewline
29 & 95.35 & 94.9500691140106 & 0.399930885989377 \tabularnewline
30 & 95.15 & 95.349969630609 & -0.199969630608976 \tabularnewline
31 & 95.46 & 95.1500151850135 & 0.309984814986493 \tabularnewline
32 & 95.56 & 95.4599764608076 & 0.100023539192364 \tabularnewline
33 & 95.05 & 95.5599924045527 & -0.50999240455269 \tabularnewline
34 & 94.64 & 95.0500387270883 & -0.41003872708832 \tabularnewline
35 & 93.63 & 94.640031136946 & -1.01003113694608 \tabularnewline
36 & 93.12 & 93.6300766983287 & -0.510076698328646 \tabularnewline
37 & 93.53 & 93.1200387334893 & 0.409961266510678 \tabularnewline
38 & 97.18 & 93.529968868936 & 3.650031131064 \tabularnewline
39 & 96.27 & 97.1797228290524 & -0.909722829052427 \tabularnewline
40 & 95.15 & 96.270069081257 & -1.12006908125697 \tabularnewline
41 & 97.08 & 95.1500850542358 & 1.92991494576417 \tabularnewline
42 & 101.95 & 97.0798534488241 & 4.87014655117588 \tabularnewline
43 & 103.07 & 101.949630177638 & 1.12036982236204 \tabularnewline
44 & 103.68 & 103.069914922927 & 0.610085077073094 \tabularnewline
45 & 102.87 & 103.679953672215 & -0.809953672214604 \tabularnewline
46 & 102.56 & 102.870061505127 & -0.310061505126598 \tabularnewline
47 & 103.38 & 102.560023545016 & 0.819976454984044 \tabularnewline
48 & 103.27 & 103.379937733777 & -0.109937733777372 \tabularnewline
49 & 102.89 & 103.270008348298 & -0.380008348297523 \tabularnewline
50 & 102.69 & 102.890028856541 & -0.20002885654128 \tabularnewline
51 & 101.54 & 102.690015189511 & -1.15001518951091 \tabularnewline
52 & 102.9 & 101.540087328241 & 1.35991267175858 \tabularnewline
53 & 101.53 & 102.899896732858 & -1.36989673285781 \tabularnewline
54 & 101.96 & 101.530104025298 & 0.429895974702148 \tabularnewline
55 & 101.99 & 101.959967355162 & 0.0300326448379167 \tabularnewline
56 & 101.11 & 101.989997719423 & -0.879997719423102 \tabularnewline
57 & 101.75 & 101.110066824033 & 0.639933175966732 \tabularnewline
58 & 101.71 & 101.749951405652 & -0.0399514056515073 \tabularnewline
59 & 104.11 & 101.710003033774 & 2.39999696622615 \tabularnewline
60 & 103.57 & 104.109817752395 & -0.539817752394583 \tabularnewline
61 & 103.32 & 103.570040991924 & -0.250040991923782 \tabularnewline
62 & 103.64 & 103.320018987262 & 0.319981012737671 \tabularnewline
63 & 103.68 & 103.63997570173 & 0.0400242982696142 \tabularnewline
64 & 103.79 & 103.679996960691 & 0.110003039309063 \tabularnewline
65 & 103.01 & 103.789991646743 & -0.779991646743397 \tabularnewline
66 & 101.54 & 103.010059229912 & -1.47005922991232 \tabularnewline
67 & 101.9 & 101.540111631297 & 0.359888368702869 \tabularnewline
68 & 103.68 & 101.899972671302 & 1.78002732869847 \tabularnewline
69 & 104.62 & 103.67986483078 & 0.940135169220127 \tabularnewline
70 & 104.11 & 104.619928609333 & -0.509928609333357 \tabularnewline
71 & 105.04 & 104.110038722244 & 0.929961277756078 \tabularnewline
72 & 104.83 & 105.039929381904 & -0.209929381904075 \tabularnewline
73 & 105.05 & 104.830015941323 & 0.219984058676872 \tabularnewline
74 & 104.68 & 105.049983295159 & -0.369983295158903 \tabularnewline
75 & 107.32 & 104.680028095273 & 2.63997190472715 \tabularnewline
76 & 109.9 & 107.319799529514 & 2.58020047048592 \tabularnewline
77 & 109.77 & 109.899804068353 & -0.129804068353494 \tabularnewline
78 & 110.69 & 109.770009856879 & 0.919990143120614 \tabularnewline
79 & 110.54 & 110.689930139078 & -0.149930139078108 \tabularnewline
80 & 110.89 & 110.540011385185 & 0.34998861481526 \tabularnewline
81 & 110.95 & 110.889973423055 & 0.0600265769448356 \tabularnewline
82 & 109.73 & 110.949995441786 & -1.21999544178594 \tabularnewline
83 & 110.85 & 109.730092642304 & 1.11990735769628 \tabularnewline
84 & 110.39 & 110.849914958045 & -0.459914958044905 \tabularnewline
85 & 110.58 & 110.390034924377 & 0.189965075622595 \tabularnewline
86 & 110.4 & 110.579985574698 & -0.179985574698364 \tabularnewline
87 & 111.07 & 110.400013667492 & 0.669986332507719 \tabularnewline
88 & 110.86 & 111.069949123517 & -0.209949123517035 \tabularnewline
89 & 111.38 & 110.860015942822 & 0.519984057177751 \tabularnewline
90 & 111.44 & 111.37996051418 & 0.0600394858204396 \tabularnewline
91 & 110.36 & 111.439995440806 & -1.07999544080567 \tabularnewline
92 & 110.06 & 110.36008201118 & -0.300082011179882 \tabularnewline
93 & 108.34 & 110.060022787207 & -1.72002278720711 \tabularnewline
94 & 107.94 & 108.340130612679 & -0.400130612679376 \tabularnewline
95 & 107.39 & 107.940030384558 & -0.550030384557573 \tabularnewline
96 & 107.1 & 107.390041767436 & -0.290041767436335 \tabularnewline
97 & 107.61 & 107.100022024785 & 0.509977975214838 \tabularnewline
98 & 107.74 & 107.609961274007 & 0.13003872599262 \tabularnewline
99 & 106.9 & 107.739990125302 & -0.839990125301497 \tabularnewline
100 & 106.71 & 106.900063785993 & -0.190063785992692 \tabularnewline
101 & 106.6 & 106.710014432797 & -0.110014432797357 \tabularnewline
102 & 108.21 & 106.600008354122 & 1.60999164587822 \tabularnewline
103 & 110.54 & 108.209877742711 & 2.33012225728879 \tabularnewline
104 & 110.91 & 110.539823058442 & 0.370176941557702 \tabularnewline
105 & 109.51 & 110.909971890022 & -1.3999718900223 \tabularnewline
106 & 110.27 & 109.510106309103 & 0.759893690897016 \tabularnewline
107 & 111.39 & 110.269942296258 & 1.12005770374192 \tabularnewline
108 & 112.13 & 111.389914946628 & 0.740085053371857 \tabularnewline
109 & 111.64 & 112.129943800459 & -0.489943800458633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121796&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]106.22[/C][C]106.42[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]3[/C][C]106.32[/C][C]106.22001518732[/C][C]0.0999848126803471[/C][/ROW]
[ROW][C]4[/C][C]105.81[/C][C]106.319992407493[/C][C]-0.509992407493442[/C][/ROW]
[ROW][C]5[/C][C]105.92[/C][C]105.810038727089[/C][C]0.109961272911448[/C][/ROW]
[ROW][C]6[/C][C]107.54[/C][C]105.919991649915[/C][C]1.620008350085[/C][/ROW]
[ROW][C]7[/C][C]107.34[/C][C]107.539876982077[/C][C]-0.199876982076773[/C][/ROW]
[ROW][C]8[/C][C]107.24[/C][C]107.340015177978[/C][C]-0.100015177978094[/C][/ROW]
[ROW][C]9[/C][C]107.74[/C][C]107.240007594812[/C][C]0.499992405187612[/C][/ROW]
[ROW][C]10[/C][C]105.71[/C][C]107.739962032278[/C][C]-2.02996203227761[/C][/ROW]
[ROW][C]11[/C][C]105.41[/C][C]105.710154148411[/C][C]-0.300154148411295[/C][/ROW]
[ROW][C]12[/C][C]106.22[/C][C]105.410022792685[/C][C]0.809977207315029[/C][/ROW]
[ROW][C]13[/C][C]106.32[/C][C]106.219938493086[/C][C]0.100061506913775[/C][/ROW]
[ROW][C]14[/C][C]106.12[/C][C]106.31999240167[/C][C]-0.199992401669547[/C][/ROW]
[ROW][C]15[/C][C]106.22[/C][C]106.120015186743[/C][C]0.0999848132573362[/C][/ROW]
[ROW][C]16[/C][C]105.92[/C][C]106.219992407493[/C][C]-0.299992407493392[/C][/ROW]
[ROW][C]17[/C][C]105.71[/C][C]105.920022780403[/C][C]-0.210022780402937[/C][/ROW]
[ROW][C]18[/C][C]105.71[/C][C]105.710015948416[/C][C]-1.5948415509115e-05[/C][/ROW]
[ROW][C]19[/C][C]105.92[/C][C]105.710000001211[/C][C]0.20999999878893[/C][/ROW]
[ROW][C]20[/C][C]105.71[/C][C]105.919984053314[/C][C]-0.209984053314471[/C][/ROW]
[ROW][C]21[/C][C]105.41[/C][C]105.710015945475[/C][C]-0.300015945474698[/C][/ROW]
[ROW][C]22[/C][C]104.49[/C][C]105.41002278219[/C][C]-0.920022782190316[/C][/ROW]
[ROW][C]23[/C][C]101.35[/C][C]104.4900698634[/C][C]-3.14006986340038[/C][/ROW]
[ROW][C]24[/C][C]99.72[/C][C]101.350238446224[/C][C]-1.63023844622367[/C][/ROW]
[ROW][C]25[/C][C]99.01[/C][C]99.720123794762[/C][C]-0.710123794761927[/C][/ROW]
[ROW][C]26[/C][C]97.89[/C][C]99.0100539243853[/C][C]-1.12005392438532[/C][/ROW]
[ROW][C]27[/C][C]95.86[/C][C]97.8900850530849[/C][C]-2.03008505308487[/C][/ROW]
[ROW][C]28[/C][C]94.95[/C][C]95.860154157753[/C][C]-0.910154157753084[/C][/ROW]
[ROW][C]29[/C][C]95.35[/C][C]94.9500691140106[/C][C]0.399930885989377[/C][/ROW]
[ROW][C]30[/C][C]95.15[/C][C]95.349969630609[/C][C]-0.199969630608976[/C][/ROW]
[ROW][C]31[/C][C]95.46[/C][C]95.1500151850135[/C][C]0.309984814986493[/C][/ROW]
[ROW][C]32[/C][C]95.56[/C][C]95.4599764608076[/C][C]0.100023539192364[/C][/ROW]
[ROW][C]33[/C][C]95.05[/C][C]95.5599924045527[/C][C]-0.50999240455269[/C][/ROW]
[ROW][C]34[/C][C]94.64[/C][C]95.0500387270883[/C][C]-0.41003872708832[/C][/ROW]
[ROW][C]35[/C][C]93.63[/C][C]94.640031136946[/C][C]-1.01003113694608[/C][/ROW]
[ROW][C]36[/C][C]93.12[/C][C]93.6300766983287[/C][C]-0.510076698328646[/C][/ROW]
[ROW][C]37[/C][C]93.53[/C][C]93.1200387334893[/C][C]0.409961266510678[/C][/ROW]
[ROW][C]38[/C][C]97.18[/C][C]93.529968868936[/C][C]3.650031131064[/C][/ROW]
[ROW][C]39[/C][C]96.27[/C][C]97.1797228290524[/C][C]-0.909722829052427[/C][/ROW]
[ROW][C]40[/C][C]95.15[/C][C]96.270069081257[/C][C]-1.12006908125697[/C][/ROW]
[ROW][C]41[/C][C]97.08[/C][C]95.1500850542358[/C][C]1.92991494576417[/C][/ROW]
[ROW][C]42[/C][C]101.95[/C][C]97.0798534488241[/C][C]4.87014655117588[/C][/ROW]
[ROW][C]43[/C][C]103.07[/C][C]101.949630177638[/C][C]1.12036982236204[/C][/ROW]
[ROW][C]44[/C][C]103.68[/C][C]103.069914922927[/C][C]0.610085077073094[/C][/ROW]
[ROW][C]45[/C][C]102.87[/C][C]103.679953672215[/C][C]-0.809953672214604[/C][/ROW]
[ROW][C]46[/C][C]102.56[/C][C]102.870061505127[/C][C]-0.310061505126598[/C][/ROW]
[ROW][C]47[/C][C]103.38[/C][C]102.560023545016[/C][C]0.819976454984044[/C][/ROW]
[ROW][C]48[/C][C]103.27[/C][C]103.379937733777[/C][C]-0.109937733777372[/C][/ROW]
[ROW][C]49[/C][C]102.89[/C][C]103.270008348298[/C][C]-0.380008348297523[/C][/ROW]
[ROW][C]50[/C][C]102.69[/C][C]102.890028856541[/C][C]-0.20002885654128[/C][/ROW]
[ROW][C]51[/C][C]101.54[/C][C]102.690015189511[/C][C]-1.15001518951091[/C][/ROW]
[ROW][C]52[/C][C]102.9[/C][C]101.540087328241[/C][C]1.35991267175858[/C][/ROW]
[ROW][C]53[/C][C]101.53[/C][C]102.899896732858[/C][C]-1.36989673285781[/C][/ROW]
[ROW][C]54[/C][C]101.96[/C][C]101.530104025298[/C][C]0.429895974702148[/C][/ROW]
[ROW][C]55[/C][C]101.99[/C][C]101.959967355162[/C][C]0.0300326448379167[/C][/ROW]
[ROW][C]56[/C][C]101.11[/C][C]101.989997719423[/C][C]-0.879997719423102[/C][/ROW]
[ROW][C]57[/C][C]101.75[/C][C]101.110066824033[/C][C]0.639933175966732[/C][/ROW]
[ROW][C]58[/C][C]101.71[/C][C]101.749951405652[/C][C]-0.0399514056515073[/C][/ROW]
[ROW][C]59[/C][C]104.11[/C][C]101.710003033774[/C][C]2.39999696622615[/C][/ROW]
[ROW][C]60[/C][C]103.57[/C][C]104.109817752395[/C][C]-0.539817752394583[/C][/ROW]
[ROW][C]61[/C][C]103.32[/C][C]103.570040991924[/C][C]-0.250040991923782[/C][/ROW]
[ROW][C]62[/C][C]103.64[/C][C]103.320018987262[/C][C]0.319981012737671[/C][/ROW]
[ROW][C]63[/C][C]103.68[/C][C]103.63997570173[/C][C]0.0400242982696142[/C][/ROW]
[ROW][C]64[/C][C]103.79[/C][C]103.679996960691[/C][C]0.110003039309063[/C][/ROW]
[ROW][C]65[/C][C]103.01[/C][C]103.789991646743[/C][C]-0.779991646743397[/C][/ROW]
[ROW][C]66[/C][C]101.54[/C][C]103.010059229912[/C][C]-1.47005922991232[/C][/ROW]
[ROW][C]67[/C][C]101.9[/C][C]101.540111631297[/C][C]0.359888368702869[/C][/ROW]
[ROW][C]68[/C][C]103.68[/C][C]101.899972671302[/C][C]1.78002732869847[/C][/ROW]
[ROW][C]69[/C][C]104.62[/C][C]103.67986483078[/C][C]0.940135169220127[/C][/ROW]
[ROW][C]70[/C][C]104.11[/C][C]104.619928609333[/C][C]-0.509928609333357[/C][/ROW]
[ROW][C]71[/C][C]105.04[/C][C]104.110038722244[/C][C]0.929961277756078[/C][/ROW]
[ROW][C]72[/C][C]104.83[/C][C]105.039929381904[/C][C]-0.209929381904075[/C][/ROW]
[ROW][C]73[/C][C]105.05[/C][C]104.830015941323[/C][C]0.219984058676872[/C][/ROW]
[ROW][C]74[/C][C]104.68[/C][C]105.049983295159[/C][C]-0.369983295158903[/C][/ROW]
[ROW][C]75[/C][C]107.32[/C][C]104.680028095273[/C][C]2.63997190472715[/C][/ROW]
[ROW][C]76[/C][C]109.9[/C][C]107.319799529514[/C][C]2.58020047048592[/C][/ROW]
[ROW][C]77[/C][C]109.77[/C][C]109.899804068353[/C][C]-0.129804068353494[/C][/ROW]
[ROW][C]78[/C][C]110.69[/C][C]109.770009856879[/C][C]0.919990143120614[/C][/ROW]
[ROW][C]79[/C][C]110.54[/C][C]110.689930139078[/C][C]-0.149930139078108[/C][/ROW]
[ROW][C]80[/C][C]110.89[/C][C]110.540011385185[/C][C]0.34998861481526[/C][/ROW]
[ROW][C]81[/C][C]110.95[/C][C]110.889973423055[/C][C]0.0600265769448356[/C][/ROW]
[ROW][C]82[/C][C]109.73[/C][C]110.949995441786[/C][C]-1.21999544178594[/C][/ROW]
[ROW][C]83[/C][C]110.85[/C][C]109.730092642304[/C][C]1.11990735769628[/C][/ROW]
[ROW][C]84[/C][C]110.39[/C][C]110.849914958045[/C][C]-0.459914958044905[/C][/ROW]
[ROW][C]85[/C][C]110.58[/C][C]110.390034924377[/C][C]0.189965075622595[/C][/ROW]
[ROW][C]86[/C][C]110.4[/C][C]110.579985574698[/C][C]-0.179985574698364[/C][/ROW]
[ROW][C]87[/C][C]111.07[/C][C]110.400013667492[/C][C]0.669986332507719[/C][/ROW]
[ROW][C]88[/C][C]110.86[/C][C]111.069949123517[/C][C]-0.209949123517035[/C][/ROW]
[ROW][C]89[/C][C]111.38[/C][C]110.860015942822[/C][C]0.519984057177751[/C][/ROW]
[ROW][C]90[/C][C]111.44[/C][C]111.37996051418[/C][C]0.0600394858204396[/C][/ROW]
[ROW][C]91[/C][C]110.36[/C][C]111.439995440806[/C][C]-1.07999544080567[/C][/ROW]
[ROW][C]92[/C][C]110.06[/C][C]110.36008201118[/C][C]-0.300082011179882[/C][/ROW]
[ROW][C]93[/C][C]108.34[/C][C]110.060022787207[/C][C]-1.72002278720711[/C][/ROW]
[ROW][C]94[/C][C]107.94[/C][C]108.340130612679[/C][C]-0.400130612679376[/C][/ROW]
[ROW][C]95[/C][C]107.39[/C][C]107.940030384558[/C][C]-0.550030384557573[/C][/ROW]
[ROW][C]96[/C][C]107.1[/C][C]107.390041767436[/C][C]-0.290041767436335[/C][/ROW]
[ROW][C]97[/C][C]107.61[/C][C]107.100022024785[/C][C]0.509977975214838[/C][/ROW]
[ROW][C]98[/C][C]107.74[/C][C]107.609961274007[/C][C]0.13003872599262[/C][/ROW]
[ROW][C]99[/C][C]106.9[/C][C]107.739990125302[/C][C]-0.839990125301497[/C][/ROW]
[ROW][C]100[/C][C]106.71[/C][C]106.900063785993[/C][C]-0.190063785992692[/C][/ROW]
[ROW][C]101[/C][C]106.6[/C][C]106.710014432797[/C][C]-0.110014432797357[/C][/ROW]
[ROW][C]102[/C][C]108.21[/C][C]106.600008354122[/C][C]1.60999164587822[/C][/ROW]
[ROW][C]103[/C][C]110.54[/C][C]108.209877742711[/C][C]2.33012225728879[/C][/ROW]
[ROW][C]104[/C][C]110.91[/C][C]110.539823058442[/C][C]0.370176941557702[/C][/ROW]
[ROW][C]105[/C][C]109.51[/C][C]110.909971890022[/C][C]-1.3999718900223[/C][/ROW]
[ROW][C]106[/C][C]110.27[/C][C]109.510106309103[/C][C]0.759893690897016[/C][/ROW]
[ROW][C]107[/C][C]111.39[/C][C]110.269942296258[/C][C]1.12005770374192[/C][/ROW]
[ROW][C]108[/C][C]112.13[/C][C]111.389914946628[/C][C]0.740085053371857[/C][/ROW]
[ROW][C]109[/C][C]111.64[/C][C]112.129943800459[/C][C]-0.489943800458633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121796&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121796&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	106.22	106.42	-0.200000000000003
3	106.32	106.22001518732	0.0999848126803471
4	105.81	106.319992407493	-0.509992407493442
5	105.92	105.810038727089	0.109961272911448
6	107.54	105.919991649915	1.620008350085
7	107.34	107.539876982077	-0.199876982076773
8	107.24	107.340015177978	-0.100015177978094
9	107.74	107.240007594812	0.499992405187612
10	105.71	107.739962032278	-2.02996203227761
11	105.41	105.710154148411	-0.300154148411295
12	106.22	105.410022792685	0.809977207315029
13	106.32	106.219938493086	0.100061506913775
14	106.12	106.31999240167	-0.199992401669547
15	106.22	106.120015186743	0.0999848132573362
16	105.92	106.219992407493	-0.299992407493392
17	105.71	105.920022780403	-0.210022780402937
18	105.71	105.710015948416	-1.5948415509115e-05
19	105.92	105.710000001211	0.20999999878893
20	105.71	105.919984053314	-0.209984053314471
21	105.41	105.710015945475	-0.300015945474698
22	104.49	105.41002278219	-0.920022782190316
23	101.35	104.4900698634	-3.14006986340038
24	99.72	101.350238446224	-1.63023844622367
25	99.01	99.720123794762	-0.710123794761927
26	97.89	99.0100539243853	-1.12005392438532
27	95.86	97.8900850530849	-2.03008505308487
28	94.95	95.860154157753	-0.910154157753084
29	95.35	94.9500691140106	0.399930885989377
30	95.15	95.349969630609	-0.199969630608976
31	95.46	95.1500151850135	0.309984814986493
32	95.56	95.4599764608076	0.100023539192364
33	95.05	95.5599924045527	-0.50999240455269
34	94.64	95.0500387270883	-0.41003872708832
35	93.63	94.640031136946	-1.01003113694608
36	93.12	93.6300766983287	-0.510076698328646
37	93.53	93.1200387334893	0.409961266510678
38	97.18	93.529968868936	3.650031131064
39	96.27	97.1797228290524	-0.909722829052427
40	95.15	96.270069081257	-1.12006908125697
41	97.08	95.1500850542358	1.92991494576417
42	101.95	97.0798534488241	4.87014655117588
43	103.07	101.949630177638	1.12036982236204
44	103.68	103.069914922927	0.610085077073094
45	102.87	103.679953672215	-0.809953672214604
46	102.56	102.870061505127	-0.310061505126598
47	103.38	102.560023545016	0.819976454984044
48	103.27	103.379937733777	-0.109937733777372
49	102.89	103.270008348298	-0.380008348297523
50	102.69	102.890028856541	-0.20002885654128
51	101.54	102.690015189511	-1.15001518951091
52	102.9	101.540087328241	1.35991267175858
53	101.53	102.899896732858	-1.36989673285781
54	101.96	101.530104025298	0.429895974702148
55	101.99	101.959967355162	0.0300326448379167
56	101.11	101.989997719423	-0.879997719423102
57	101.75	101.110066824033	0.639933175966732
58	101.71	101.749951405652	-0.0399514056515073
59	104.11	101.710003033774	2.39999696622615
60	103.57	104.109817752395	-0.539817752394583
61	103.32	103.570040991924	-0.250040991923782
62	103.64	103.320018987262	0.319981012737671
63	103.68	103.63997570173	0.0400242982696142
64	103.79	103.679996960691	0.110003039309063
65	103.01	103.789991646743	-0.779991646743397
66	101.54	103.010059229912	-1.47005922991232
67	101.9	101.540111631297	0.359888368702869
68	103.68	101.899972671302	1.78002732869847
69	104.62	103.67986483078	0.940135169220127
70	104.11	104.619928609333	-0.509928609333357
71	105.04	104.110038722244	0.929961277756078
72	104.83	105.039929381904	-0.209929381904075
73	105.05	104.830015941323	0.219984058676872
74	104.68	105.049983295159	-0.369983295158903
75	107.32	104.680028095273	2.63997190472715
76	109.9	107.319799529514	2.58020047048592
77	109.77	109.899804068353	-0.129804068353494
78	110.69	109.770009856879	0.919990143120614
79	110.54	110.689930139078	-0.149930139078108
80	110.89	110.540011385185	0.34998861481526
81	110.95	110.889973423055	0.0600265769448356
82	109.73	110.949995441786	-1.21999544178594
83	110.85	109.730092642304	1.11990735769628
84	110.39	110.849914958045	-0.459914958044905
85	110.58	110.390034924377	0.189965075622595
86	110.4	110.579985574698	-0.179985574698364
87	111.07	110.400013667492	0.669986332507719
88	110.86	111.069949123517	-0.209949123517035
89	111.38	110.860015942822	0.519984057177751
90	111.44	111.37996051418	0.0600394858204396
91	110.36	111.439995440806	-1.07999544080567
92	110.06	110.36008201118	-0.300082011179882
93	108.34	110.060022787207	-1.72002278720711
94	107.94	108.340130612679	-0.400130612679376
95	107.39	107.940030384558	-0.550030384557573
96	107.1	107.390041767436	-0.290041767436335
97	107.61	107.100022024785	0.509977975214838
98	107.74	107.609961274007	0.13003872599262
99	106.9	107.739990125302	-0.839990125301497
100	106.71	106.900063785993	-0.190063785992692
101	106.6	106.710014432797	-0.110014432797357
102	108.21	106.600008354122	1.60999164587822
103	110.54	108.209877742711	2.33012225728879
104	110.91	110.539823058442	0.370176941557702
105	109.51	110.909971890022	-1.3999718900223
106	110.27	109.510106309103	0.759893690897016
107	111.39	110.269942296258	1.12005770374192
108	112.13	111.389914946628	0.740085053371857
109	111.64	112.129943800459	-0.489943800458633

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
110	111.640037204666	109.442602820961	113.83747158837
111	111.640037204666	108.532513686428	114.747560722903
112	111.640037204666	107.834161883257	115.445912526074
113	111.640037204666	107.245418733419	116.034655675912
114	111.640037204666	106.726723042765	116.553351366566
115	111.640037204666	106.257784832355	117.022289576976
116	111.640037204666	105.826550716769	117.453523692562
117	111.640037204666	105.425167158505	117.854907250826
118	111.640037204666	105.048179026854	118.231895382477
119	111.640037204666	104.691614449673	118.588459959658
120	111.640037204666	104.352474969748	118.927599439584
121	111.640037204666	104.028431074977	119.251643334354

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
110 & 111.640037204666 & 109.442602820961 & 113.83747158837 \tabularnewline
111 & 111.640037204666 & 108.532513686428 & 114.747560722903 \tabularnewline
112 & 111.640037204666 & 107.834161883257 & 115.445912526074 \tabularnewline
113 & 111.640037204666 & 107.245418733419 & 116.034655675912 \tabularnewline
114 & 111.640037204666 & 106.726723042765 & 116.553351366566 \tabularnewline
115 & 111.640037204666 & 106.257784832355 & 117.022289576976 \tabularnewline
116 & 111.640037204666 & 105.826550716769 & 117.453523692562 \tabularnewline
117 & 111.640037204666 & 105.425167158505 & 117.854907250826 \tabularnewline
118 & 111.640037204666 & 105.048179026854 & 118.231895382477 \tabularnewline
119 & 111.640037204666 & 104.691614449673 & 118.588459959658 \tabularnewline
120 & 111.640037204666 & 104.352474969748 & 118.927599439584 \tabularnewline
121 & 111.640037204666 & 104.028431074977 & 119.251643334354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121796&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]110[/C][C]111.640037204666[/C][C]109.442602820961[/C][C]113.83747158837[/C][/ROW]
[ROW][C]111[/C][C]111.640037204666[/C][C]108.532513686428[/C][C]114.747560722903[/C][/ROW]
[ROW][C]112[/C][C]111.640037204666[/C][C]107.834161883257[/C][C]115.445912526074[/C][/ROW]
[ROW][C]113[/C][C]111.640037204666[/C][C]107.245418733419[/C][C]116.034655675912[/C][/ROW]
[ROW][C]114[/C][C]111.640037204666[/C][C]106.726723042765[/C][C]116.553351366566[/C][/ROW]
[ROW][C]115[/C][C]111.640037204666[/C][C]106.257784832355[/C][C]117.022289576976[/C][/ROW]
[ROW][C]116[/C][C]111.640037204666[/C][C]105.826550716769[/C][C]117.453523692562[/C][/ROW]
[ROW][C]117[/C][C]111.640037204666[/C][C]105.425167158505[/C][C]117.854907250826[/C][/ROW]
[ROW][C]118[/C][C]111.640037204666[/C][C]105.048179026854[/C][C]118.231895382477[/C][/ROW]
[ROW][C]119[/C][C]111.640037204666[/C][C]104.691614449673[/C][C]118.588459959658[/C][/ROW]
[ROW][C]120[/C][C]111.640037204666[/C][C]104.352474969748[/C][C]118.927599439584[/C][/ROW]
[ROW][C]121[/C][C]111.640037204666[/C][C]104.028431074977[/C][C]119.251643334354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121796&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121796&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
110	111.640037204666	109.442602820961	113.83747158837
111	111.640037204666	108.532513686428	114.747560722903
112	111.640037204666	107.834161883257	115.445912526074
113	111.640037204666	107.245418733419	116.034655675912
114	111.640037204666	106.726723042765	116.553351366566
115	111.640037204666	106.257784832355	117.022289576976
116	111.640037204666	105.826550716769	117.453523692562
117	111.640037204666	105.425167158505	117.854907250826
118	111.640037204666	105.048179026854	118.231895382477
119	111.640037204666	104.691614449673	118.588459959658
120	111.640037204666	104.352474969748	118.927599439584
121	111.640037204666	104.028431074977	119.251643334354

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