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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 02 May 2017 14:51:42 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/May/02/t1493733219dmv5zn6e5gp5mou.htm/, Retrieved Fri, 17 May 2024 05:03:41 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 05:03:41 +0200

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Estimated Impact

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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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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' @ jenkins.wessa.net

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

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

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	97.75	94.6418563034188	3.10814369658119
14	99.27	99.265659965035	0.00434003496502555
15	100.63	100.708993298368	-0.0789932983682888
16	99.8	99.953159965035	-0.153159965034973
17	99.5	99.674409965035	-0.174409965034968
18	99.72	99.8727432983683	-0.152743298368293
19	99.77	98.940659965035	0.829340034965043
20	100.18	101.427326631702	-1.24732663170163
21	101.11	101.721493298368	-0.611493298368302
22	100.67	101.678993298368	-1.0089932983683
23	101.13	100.492326631702	0.637673368298366
24	100.46	100.434826631702	0.0251733682983684
25	101.6	101.167326631702	0.432673368298381
26	102.3	103.115659965035	-0.815659965034968
27	103.26	103.738993298368	-0.47899329836828
28	104.56	102.583159965035	1.97684003496502
29	104.61	104.434409965035	0.175590034965026
30	104.62	104.982743298368	-0.362743298368287
31	105.03	103.840659965035	1.18934003496504
32	104.93	106.687326631702	-1.75732663170163
33	104.73	106.471493298368	-1.7414932983683
34	104.33	105.298993298368	-0.968993298368304
35	104.6	104.152326631702	0.447673368298368
36	104.41	103.904826631702	0.505173368298372
37	104.63	105.117326631702	-0.48732663170162
38	105.55	106.145659965035	-0.595659965034969
39	106.12	106.988993298368	-0.868993298368281
40	106.62	105.443159965035	1.17684003496502
41	106.72	106.494409965035	0.225590034965023
42	106.52	107.092743298368	-0.572743298368295
43	106.79	105.740659965035	1.04934003496506
44	106.95	108.447326631702	-1.49732663170164
45	106.92	108.491493298368	-1.5714932983683
46	106.74	107.488993298368	-0.748993298368305
47	108.13	106.562326631702	1.56767336829837
48	107.86	107.434826631702	0.425173368298374
49	108.6	108.567326631702	0.0326733682983757
50	110.97	110.115659965035	0.854340034965034
51	111.8	112.408993298368	-0.60899329836829
52	111	111.123159965035	-0.123159965034972
53	113.41	110.874409965035	2.53559003496503
54	114.32	113.782743298368	0.537256701631705
55	111.89	113.540659965035	-1.65065996503495
56	112.48	113.547326631702	-1.06732663170163
57	112.32	114.021493298368	-1.70149329836831
58	110.35	112.888993298368	-2.5389932983683
59	109.77	110.172326631702	-0.402326631701627
60	111.25	109.074826631702	2.17517336829837

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 97.75 & 94.6418563034188 & 3.10814369658119 \tabularnewline
14 & 99.27 & 99.265659965035 & 0.00434003496502555 \tabularnewline
15 & 100.63 & 100.708993298368 & -0.0789932983682888 \tabularnewline
16 & 99.8 & 99.953159965035 & -0.153159965034973 \tabularnewline
17 & 99.5 & 99.674409965035 & -0.174409965034968 \tabularnewline
18 & 99.72 & 99.8727432983683 & -0.152743298368293 \tabularnewline
19 & 99.77 & 98.940659965035 & 0.829340034965043 \tabularnewline
20 & 100.18 & 101.427326631702 & -1.24732663170163 \tabularnewline
21 & 101.11 & 101.721493298368 & -0.611493298368302 \tabularnewline
22 & 100.67 & 101.678993298368 & -1.0089932983683 \tabularnewline
23 & 101.13 & 100.492326631702 & 0.637673368298366 \tabularnewline
24 & 100.46 & 100.434826631702 & 0.0251733682983684 \tabularnewline
25 & 101.6 & 101.167326631702 & 0.432673368298381 \tabularnewline
26 & 102.3 & 103.115659965035 & -0.815659965034968 \tabularnewline
27 & 103.26 & 103.738993298368 & -0.47899329836828 \tabularnewline
28 & 104.56 & 102.583159965035 & 1.97684003496502 \tabularnewline
29 & 104.61 & 104.434409965035 & 0.175590034965026 \tabularnewline
30 & 104.62 & 104.982743298368 & -0.362743298368287 \tabularnewline
31 & 105.03 & 103.840659965035 & 1.18934003496504 \tabularnewline
32 & 104.93 & 106.687326631702 & -1.75732663170163 \tabularnewline
33 & 104.73 & 106.471493298368 & -1.7414932983683 \tabularnewline
34 & 104.33 & 105.298993298368 & -0.968993298368304 \tabularnewline
35 & 104.6 & 104.152326631702 & 0.447673368298368 \tabularnewline
36 & 104.41 & 103.904826631702 & 0.505173368298372 \tabularnewline
37 & 104.63 & 105.117326631702 & -0.48732663170162 \tabularnewline
38 & 105.55 & 106.145659965035 & -0.595659965034969 \tabularnewline
39 & 106.12 & 106.988993298368 & -0.868993298368281 \tabularnewline
40 & 106.62 & 105.443159965035 & 1.17684003496502 \tabularnewline
41 & 106.72 & 106.494409965035 & 0.225590034965023 \tabularnewline
42 & 106.52 & 107.092743298368 & -0.572743298368295 \tabularnewline
43 & 106.79 & 105.740659965035 & 1.04934003496506 \tabularnewline
44 & 106.95 & 108.447326631702 & -1.49732663170164 \tabularnewline
45 & 106.92 & 108.491493298368 & -1.5714932983683 \tabularnewline
46 & 106.74 & 107.488993298368 & -0.748993298368305 \tabularnewline
47 & 108.13 & 106.562326631702 & 1.56767336829837 \tabularnewline
48 & 107.86 & 107.434826631702 & 0.425173368298374 \tabularnewline
49 & 108.6 & 108.567326631702 & 0.0326733682983757 \tabularnewline
50 & 110.97 & 110.115659965035 & 0.854340034965034 \tabularnewline
51 & 111.8 & 112.408993298368 & -0.60899329836829 \tabularnewline
52 & 111 & 111.123159965035 & -0.123159965034972 \tabularnewline
53 & 113.41 & 110.874409965035 & 2.53559003496503 \tabularnewline
54 & 114.32 & 113.782743298368 & 0.537256701631705 \tabularnewline
55 & 111.89 & 113.540659965035 & -1.65065996503495 \tabularnewline
56 & 112.48 & 113.547326631702 & -1.06732663170163 \tabularnewline
57 & 112.32 & 114.021493298368 & -1.70149329836831 \tabularnewline
58 & 110.35 & 112.888993298368 & -2.5389932983683 \tabularnewline
59 & 109.77 & 110.172326631702 & -0.402326631701627 \tabularnewline
60 & 111.25 & 109.074826631702 & 2.17517336829837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]13[/C][C]97.75[/C][C]94.6418563034188[/C][C]3.10814369658119[/C][/ROW]
[ROW][C]14[/C][C]99.27[/C][C]99.265659965035[/C][C]0.00434003496502555[/C][/ROW]
[ROW][C]15[/C][C]100.63[/C][C]100.708993298368[/C][C]-0.0789932983682888[/C][/ROW]
[ROW][C]16[/C][C]99.8[/C][C]99.953159965035[/C][C]-0.153159965034973[/C][/ROW]
[ROW][C]17[/C][C]99.5[/C][C]99.674409965035[/C][C]-0.174409965034968[/C][/ROW]
[ROW][C]18[/C][C]99.72[/C][C]99.8727432983683[/C][C]-0.152743298368293[/C][/ROW]
[ROW][C]19[/C][C]99.77[/C][C]98.940659965035[/C][C]0.829340034965043[/C][/ROW]
[ROW][C]20[/C][C]100.18[/C][C]101.427326631702[/C][C]-1.24732663170163[/C][/ROW]
[ROW][C]21[/C][C]101.11[/C][C]101.721493298368[/C][C]-0.611493298368302[/C][/ROW]
[ROW][C]22[/C][C]100.67[/C][C]101.678993298368[/C][C]-1.0089932983683[/C][/ROW]
[ROW][C]23[/C][C]101.13[/C][C]100.492326631702[/C][C]0.637673368298366[/C][/ROW]
[ROW][C]24[/C][C]100.46[/C][C]100.434826631702[/C][C]0.0251733682983684[/C][/ROW]
[ROW][C]25[/C][C]101.6[/C][C]101.167326631702[/C][C]0.432673368298381[/C][/ROW]
[ROW][C]26[/C][C]102.3[/C][C]103.115659965035[/C][C]-0.815659965034968[/C][/ROW]
[ROW][C]27[/C][C]103.26[/C][C]103.738993298368[/C][C]-0.47899329836828[/C][/ROW]
[ROW][C]28[/C][C]104.56[/C][C]102.583159965035[/C][C]1.97684003496502[/C][/ROW]
[ROW][C]29[/C][C]104.61[/C][C]104.434409965035[/C][C]0.175590034965026[/C][/ROW]
[ROW][C]30[/C][C]104.62[/C][C]104.982743298368[/C][C]-0.362743298368287[/C][/ROW]
[ROW][C]31[/C][C]105.03[/C][C]103.840659965035[/C][C]1.18934003496504[/C][/ROW]
[ROW][C]32[/C][C]104.93[/C][C]106.687326631702[/C][C]-1.75732663170163[/C][/ROW]
[ROW][C]33[/C][C]104.73[/C][C]106.471493298368[/C][C]-1.7414932983683[/C][/ROW]
[ROW][C]34[/C][C]104.33[/C][C]105.298993298368[/C][C]-0.968993298368304[/C][/ROW]
[ROW][C]35[/C][C]104.6[/C][C]104.152326631702[/C][C]0.447673368298368[/C][/ROW]
[ROW][C]36[/C][C]104.41[/C][C]103.904826631702[/C][C]0.505173368298372[/C][/ROW]
[ROW][C]37[/C][C]104.63[/C][C]105.117326631702[/C][C]-0.48732663170162[/C][/ROW]
[ROW][C]38[/C][C]105.55[/C][C]106.145659965035[/C][C]-0.595659965034969[/C][/ROW]
[ROW][C]39[/C][C]106.12[/C][C]106.988993298368[/C][C]-0.868993298368281[/C][/ROW]
[ROW][C]40[/C][C]106.62[/C][C]105.443159965035[/C][C]1.17684003496502[/C][/ROW]
[ROW][C]41[/C][C]106.72[/C][C]106.494409965035[/C][C]0.225590034965023[/C][/ROW]
[ROW][C]42[/C][C]106.52[/C][C]107.092743298368[/C][C]-0.572743298368295[/C][/ROW]
[ROW][C]43[/C][C]106.79[/C][C]105.740659965035[/C][C]1.04934003496506[/C][/ROW]
[ROW][C]44[/C][C]106.95[/C][C]108.447326631702[/C][C]-1.49732663170164[/C][/ROW]
[ROW][C]45[/C][C]106.92[/C][C]108.491493298368[/C][C]-1.5714932983683[/C][/ROW]
[ROW][C]46[/C][C]106.74[/C][C]107.488993298368[/C][C]-0.748993298368305[/C][/ROW]
[ROW][C]47[/C][C]108.13[/C][C]106.562326631702[/C][C]1.56767336829837[/C][/ROW]
[ROW][C]48[/C][C]107.86[/C][C]107.434826631702[/C][C]0.425173368298374[/C][/ROW]
[ROW][C]49[/C][C]108.6[/C][C]108.567326631702[/C][C]0.0326733682983757[/C][/ROW]
[ROW][C]50[/C][C]110.97[/C][C]110.115659965035[/C][C]0.854340034965034[/C][/ROW]
[ROW][C]51[/C][C]111.8[/C][C]112.408993298368[/C][C]-0.60899329836829[/C][/ROW]
[ROW][C]52[/C][C]111[/C][C]111.123159965035[/C][C]-0.123159965034972[/C][/ROW]
[ROW][C]53[/C][C]113.41[/C][C]110.874409965035[/C][C]2.53559003496503[/C][/ROW]
[ROW][C]54[/C][C]114.32[/C][C]113.782743298368[/C][C]0.537256701631705[/C][/ROW]
[ROW][C]55[/C][C]111.89[/C][C]113.540659965035[/C][C]-1.65065996503495[/C][/ROW]
[ROW][C]56[/C][C]112.48[/C][C]113.547326631702[/C][C]-1.06732663170163[/C][/ROW]
[ROW][C]57[/C][C]112.32[/C][C]114.021493298368[/C][C]-1.70149329836831[/C][/ROW]
[ROW][C]58[/C][C]110.35[/C][C]112.888993298368[/C][C]-2.5389932983683[/C][/ROW]
[ROW][C]59[/C][C]109.77[/C][C]110.172326631702[/C][C]-0.402326631701627[/C][/ROW]
[ROW][C]60[/C][C]111.25[/C][C]109.074826631702[/C][C]2.17517336829837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
13	97.75	94.6418563034188	3.10814369658119
14	99.27	99.265659965035	0.00434003496502555
15	100.63	100.708993298368	-0.0789932983682888
16	99.8	99.953159965035	-0.153159965034973
17	99.5	99.674409965035	-0.174409965034968
18	99.72	99.8727432983683	-0.152743298368293
19	99.77	98.940659965035	0.829340034965043
20	100.18	101.427326631702	-1.24732663170163
21	101.11	101.721493298368	-0.611493298368302
22	100.67	101.678993298368	-1.0089932983683
23	101.13	100.492326631702	0.637673368298366
24	100.46	100.434826631702	0.0251733682983684
25	101.6	101.167326631702	0.432673368298381
26	102.3	103.115659965035	-0.815659965034968
27	103.26	103.738993298368	-0.47899329836828
28	104.56	102.583159965035	1.97684003496502
29	104.61	104.434409965035	0.175590034965026
30	104.62	104.982743298368	-0.362743298368287
31	105.03	103.840659965035	1.18934003496504
32	104.93	106.687326631702	-1.75732663170163
33	104.73	106.471493298368	-1.7414932983683
34	104.33	105.298993298368	-0.968993298368304
35	104.6	104.152326631702	0.447673368298368
36	104.41	103.904826631702	0.505173368298372
37	104.63	105.117326631702	-0.48732663170162
38	105.55	106.145659965035	-0.595659965034969
39	106.12	106.988993298368	-0.868993298368281
40	106.62	105.443159965035	1.17684003496502
41	106.72	106.494409965035	0.225590034965023
42	106.52	107.092743298368	-0.572743298368295
43	106.79	105.740659965035	1.04934003496506
44	106.95	108.447326631702	-1.49732663170164
45	106.92	108.491493298368	-1.5714932983683
46	106.74	107.488993298368	-0.748993298368305
47	108.13	106.562326631702	1.56767336829837
48	107.86	107.434826631702	0.425173368298374
49	108.6	108.567326631702	0.0326733682983757
50	110.97	110.115659965035	0.854340034965034
51	111.8	112.408993298368	-0.60899329836829
52	111	111.123159965035	-0.123159965034972
53	113.41	110.874409965035	2.53559003496503
54	114.32	113.782743298368	0.537256701631705
55	111.89	113.540659965035	-1.65065996503495
56	112.48	113.547326631702	-1.06732663170163
57	112.32	114.021493298368	-1.70149329836831
58	110.35	112.888993298368	-2.5389932983683
59	109.77	110.172326631702	-0.402326631701627
60	111.25	109.074826631702	2.17517336829837

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	111.957326631702	109.642145844139	114.272507419265
62	113.472986596737	110.198826527619	116.747146665854
63	114.911979895105	110.901969142338	118.921990647871
64	114.23513986014	109.604778285014	118.865501435266
65	114.109549825175	108.932648203982	119.286451446367
66	114.482293123543	108.811281531719	120.153304715368
67	113.702953088578	107.577560484532	119.828345692625
68	115.36027972028	108.811959582045	121.908599858514
69	116.901773018648	109.956230655959	123.847315381337
70	117.470766317016	110.149521833255	124.792010800778
71	117.293092948718	109.614506954532	124.971678942904
72	116.59791958042	108.577898074886	124.617941085953

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 111.957326631702 & 109.642145844139 & 114.272507419265 \tabularnewline
62 & 113.472986596737 & 110.198826527619 & 116.747146665854 \tabularnewline
63 & 114.911979895105 & 110.901969142338 & 118.921990647871 \tabularnewline
64 & 114.23513986014 & 109.604778285014 & 118.865501435266 \tabularnewline
65 & 114.109549825175 & 108.932648203982 & 119.286451446367 \tabularnewline
66 & 114.482293123543 & 108.811281531719 & 120.153304715368 \tabularnewline
67 & 113.702953088578 & 107.577560484532 & 119.828345692625 \tabularnewline
68 & 115.36027972028 & 108.811959582045 & 121.908599858514 \tabularnewline
69 & 116.901773018648 & 109.956230655959 & 123.847315381337 \tabularnewline
70 & 117.470766317016 & 110.149521833255 & 124.792010800778 \tabularnewline
71 & 117.293092948718 & 109.614506954532 & 124.971678942904 \tabularnewline
72 & 116.59791958042 & 108.577898074886 & 124.617941085953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]111.957326631702[/C][C]109.642145844139[/C][C]114.272507419265[/C][/ROW]
[ROW][C]62[/C][C]113.472986596737[/C][C]110.198826527619[/C][C]116.747146665854[/C][/ROW]
[ROW][C]63[/C][C]114.911979895105[/C][C]110.901969142338[/C][C]118.921990647871[/C][/ROW]
[ROW][C]64[/C][C]114.23513986014[/C][C]109.604778285014[/C][C]118.865501435266[/C][/ROW]
[ROW][C]65[/C][C]114.109549825175[/C][C]108.932648203982[/C][C]119.286451446367[/C][/ROW]
[ROW][C]66[/C][C]114.482293123543[/C][C]108.811281531719[/C][C]120.153304715368[/C][/ROW]
[ROW][C]67[/C][C]113.702953088578[/C][C]107.577560484532[/C][C]119.828345692625[/C][/ROW]
[ROW][C]68[/C][C]115.36027972028[/C][C]108.811959582045[/C][C]121.908599858514[/C][/ROW]
[ROW][C]69[/C][C]116.901773018648[/C][C]109.956230655959[/C][C]123.847315381337[/C][/ROW]
[ROW][C]70[/C][C]117.470766317016[/C][C]110.149521833255[/C][C]124.792010800778[/C][/ROW]
[ROW][C]71[/C][C]117.293092948718[/C][C]109.614506954532[/C][C]124.971678942904[/C][/ROW]
[ROW][C]72[/C][C]116.59791958042[/C][C]108.577898074886[/C][C]124.617941085953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61	111.957326631702	109.642145844139	114.272507419265
62	113.472986596737	110.198826527619	116.747146665854
63	114.911979895105	110.901969142338	118.921990647871
64	114.23513986014	109.604778285014	118.865501435266
65	114.109549825175	108.932648203982	119.286451446367
66	114.482293123543	108.811281531719	120.153304715368
67	113.702953088578	107.577560484532	119.828345692625
68	115.36027972028	108.811959582045	121.908599858514
69	116.901773018648	109.956230655959	123.847315381337
70	117.470766317016	110.149521833255	124.792010800778
71	117.293092948718	109.614506954532	124.971678942904
72	116.59791958042	108.577898074886	124.617941085953

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 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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