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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 28 Nov 2016 16:15:56 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/28/t14803498672mgpmef9zs2t977.htm/, Retrieved Sat, 04 May 2024 16:28:38 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 16:28:38 +0200

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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	1 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 & 1 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]1 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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.116260861139079
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.116260861139079 \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]0.116260861139079[/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	0.116260861139079
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	101.5	101.211539161553	0.288460838447179
14	99	98.5798368088367	0.420163191163311
15	106.2	106.158194186787	0.0418058132132586
16	97.6	97.5985741959501	0.00142580404984471
17	103.7	103.419446131496	0.280553868504001
18	103.4	103.442374577409	-0.042374577408637
19	99.9	94.5463050482759	5.35369495172408
20	105	106.339358887778	-1.33935888777788
21	103.4	111.372061853047	-7.97206185304687
22	117.8	110.803540444009	6.99645955599117
23	110.6	111.286669340043	-0.686669340042727
24	102	109.625465203923	-7.62546520392289
25	105.1	101.647279441298	3.45272055870196
26	98.5	99.4856408562672	-0.985640856267239
27	104.4	106.592974120275	-2.1929741202753
28	103.9	97.7266170942545	6.17338290574548
29	105.8	104.563726601021	1.23627339897942
30	100.3	104.409060303819	-4.10906030381892
31	106.3	99.7563952373567	6.54360476264327
32	101.4	105.803305781248	-4.40330578124849
33	104.3	104.556927883011	-0.256927883011102
34	114.6	118.215608216813	-3.61560821681304
35	105	110.67494048144	-5.67494048144049
36	103.4	102.288090522188	1.11190947781203
37	102.9	105.114742047132	-2.2147420471323
38	96.4	98.3859254334453	-1.98592543344533
39	102.6	104.283976779767	-1.68397677976705
40	104.7	102.834593138193	1.86540686180697
41	100.8	104.792293485608	-3.99229348560787
42	102.1	99.3599059446568	2.74009405534323
43	101.1	104.84203847114	-3.74203847114045
44	98.1	100.079288485198	-1.9792884851984
45	109.2	102.734887002552	6.46511299744786
46	114.4	114.112357134743	0.287642865256615
47	104	105.211236487002	-1.21123648700197
48	107.2	103.338713384585	3.8612866154153
49	101.3	103.53920976453	-2.2392097645301
50	98.1	96.9823754516292	1.11762454837083
51	109.6	103.552187215495	6.04781278450545
52	105.9	106.164528746254	-0.264528746253959
53	99.5	102.634331955495	-3.13433195549453
54	109.9	103.257151716389	6.64284828361114
55	105.3	103.438922474654	1.86107752534593
56	102.5	100.810135662773	1.68986433722716
57	111.9	111.617382446531	0.282617553469294
58	118	116.931490426574	1.06850957342621
59	112.1	106.555816640636	5.54418335936433
60	113.8	110.019432674025	3.78056732597499

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101.5 & 101.211539161553 & 0.288460838447179 \tabularnewline
14 & 99 & 98.5798368088367 & 0.420163191163311 \tabularnewline
15 & 106.2 & 106.158194186787 & 0.0418058132132586 \tabularnewline
16 & 97.6 & 97.5985741959501 & 0.00142580404984471 \tabularnewline
17 & 103.7 & 103.419446131496 & 0.280553868504001 \tabularnewline
18 & 103.4 & 103.442374577409 & -0.042374577408637 \tabularnewline
19 & 99.9 & 94.5463050482759 & 5.35369495172408 \tabularnewline
20 & 105 & 106.339358887778 & -1.33935888777788 \tabularnewline
21 & 103.4 & 111.372061853047 & -7.97206185304687 \tabularnewline
22 & 117.8 & 110.803540444009 & 6.99645955599117 \tabularnewline
23 & 110.6 & 111.286669340043 & -0.686669340042727 \tabularnewline
24 & 102 & 109.625465203923 & -7.62546520392289 \tabularnewline
25 & 105.1 & 101.647279441298 & 3.45272055870196 \tabularnewline
26 & 98.5 & 99.4856408562672 & -0.985640856267239 \tabularnewline
27 & 104.4 & 106.592974120275 & -2.1929741202753 \tabularnewline
28 & 103.9 & 97.7266170942545 & 6.17338290574548 \tabularnewline
29 & 105.8 & 104.563726601021 & 1.23627339897942 \tabularnewline
30 & 100.3 & 104.409060303819 & -4.10906030381892 \tabularnewline
31 & 106.3 & 99.7563952373567 & 6.54360476264327 \tabularnewline
32 & 101.4 & 105.803305781248 & -4.40330578124849 \tabularnewline
33 & 104.3 & 104.556927883011 & -0.256927883011102 \tabularnewline
34 & 114.6 & 118.215608216813 & -3.61560821681304 \tabularnewline
35 & 105 & 110.67494048144 & -5.67494048144049 \tabularnewline
36 & 103.4 & 102.288090522188 & 1.11190947781203 \tabularnewline
37 & 102.9 & 105.114742047132 & -2.2147420471323 \tabularnewline
38 & 96.4 & 98.3859254334453 & -1.98592543344533 \tabularnewline
39 & 102.6 & 104.283976779767 & -1.68397677976705 \tabularnewline
40 & 104.7 & 102.834593138193 & 1.86540686180697 \tabularnewline
41 & 100.8 & 104.792293485608 & -3.99229348560787 \tabularnewline
42 & 102.1 & 99.3599059446568 & 2.74009405534323 \tabularnewline
43 & 101.1 & 104.84203847114 & -3.74203847114045 \tabularnewline
44 & 98.1 & 100.079288485198 & -1.9792884851984 \tabularnewline
45 & 109.2 & 102.734887002552 & 6.46511299744786 \tabularnewline
46 & 114.4 & 114.112357134743 & 0.287642865256615 \tabularnewline
47 & 104 & 105.211236487002 & -1.21123648700197 \tabularnewline
48 & 107.2 & 103.338713384585 & 3.8612866154153 \tabularnewline
49 & 101.3 & 103.53920976453 & -2.2392097645301 \tabularnewline
50 & 98.1 & 96.9823754516292 & 1.11762454837083 \tabularnewline
51 & 109.6 & 103.552187215495 & 6.04781278450545 \tabularnewline
52 & 105.9 & 106.164528746254 & -0.264528746253959 \tabularnewline
53 & 99.5 & 102.634331955495 & -3.13433195549453 \tabularnewline
54 & 109.9 & 103.257151716389 & 6.64284828361114 \tabularnewline
55 & 105.3 & 103.438922474654 & 1.86107752534593 \tabularnewline
56 & 102.5 & 100.810135662773 & 1.68986433722716 \tabularnewline
57 & 111.9 & 111.617382446531 & 0.282617553469294 \tabularnewline
58 & 118 & 116.931490426574 & 1.06850957342621 \tabularnewline
59 & 112.1 & 106.555816640636 & 5.54418335936433 \tabularnewline
60 & 113.8 & 110.019432674025 & 3.78056732597499 \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]101.5[/C][C]101.211539161553[/C][C]0.288460838447179[/C][/ROW]
[ROW][C]14[/C][C]99[/C][C]98.5798368088367[/C][C]0.420163191163311[/C][/ROW]
[ROW][C]15[/C][C]106.2[/C][C]106.158194186787[/C][C]0.0418058132132586[/C][/ROW]
[ROW][C]16[/C][C]97.6[/C][C]97.5985741959501[/C][C]0.00142580404984471[/C][/ROW]
[ROW][C]17[/C][C]103.7[/C][C]103.419446131496[/C][C]0.280553868504001[/C][/ROW]
[ROW][C]18[/C][C]103.4[/C][C]103.442374577409[/C][C]-0.042374577408637[/C][/ROW]
[ROW][C]19[/C][C]99.9[/C][C]94.5463050482759[/C][C]5.35369495172408[/C][/ROW]
[ROW][C]20[/C][C]105[/C][C]106.339358887778[/C][C]-1.33935888777788[/C][/ROW]
[ROW][C]21[/C][C]103.4[/C][C]111.372061853047[/C][C]-7.97206185304687[/C][/ROW]
[ROW][C]22[/C][C]117.8[/C][C]110.803540444009[/C][C]6.99645955599117[/C][/ROW]
[ROW][C]23[/C][C]110.6[/C][C]111.286669340043[/C][C]-0.686669340042727[/C][/ROW]
[ROW][C]24[/C][C]102[/C][C]109.625465203923[/C][C]-7.62546520392289[/C][/ROW]
[ROW][C]25[/C][C]105.1[/C][C]101.647279441298[/C][C]3.45272055870196[/C][/ROW]
[ROW][C]26[/C][C]98.5[/C][C]99.4856408562672[/C][C]-0.985640856267239[/C][/ROW]
[ROW][C]27[/C][C]104.4[/C][C]106.592974120275[/C][C]-2.1929741202753[/C][/ROW]
[ROW][C]28[/C][C]103.9[/C][C]97.7266170942545[/C][C]6.17338290574548[/C][/ROW]
[ROW][C]29[/C][C]105.8[/C][C]104.563726601021[/C][C]1.23627339897942[/C][/ROW]
[ROW][C]30[/C][C]100.3[/C][C]104.409060303819[/C][C]-4.10906030381892[/C][/ROW]
[ROW][C]31[/C][C]106.3[/C][C]99.7563952373567[/C][C]6.54360476264327[/C][/ROW]
[ROW][C]32[/C][C]101.4[/C][C]105.803305781248[/C][C]-4.40330578124849[/C][/ROW]
[ROW][C]33[/C][C]104.3[/C][C]104.556927883011[/C][C]-0.256927883011102[/C][/ROW]
[ROW][C]34[/C][C]114.6[/C][C]118.215608216813[/C][C]-3.61560821681304[/C][/ROW]
[ROW][C]35[/C][C]105[/C][C]110.67494048144[/C][C]-5.67494048144049[/C][/ROW]
[ROW][C]36[/C][C]103.4[/C][C]102.288090522188[/C][C]1.11190947781203[/C][/ROW]
[ROW][C]37[/C][C]102.9[/C][C]105.114742047132[/C][C]-2.2147420471323[/C][/ROW]
[ROW][C]38[/C][C]96.4[/C][C]98.3859254334453[/C][C]-1.98592543344533[/C][/ROW]
[ROW][C]39[/C][C]102.6[/C][C]104.283976779767[/C][C]-1.68397677976705[/C][/ROW]
[ROW][C]40[/C][C]104.7[/C][C]102.834593138193[/C][C]1.86540686180697[/C][/ROW]
[ROW][C]41[/C][C]100.8[/C][C]104.792293485608[/C][C]-3.99229348560787[/C][/ROW]
[ROW][C]42[/C][C]102.1[/C][C]99.3599059446568[/C][C]2.74009405534323[/C][/ROW]
[ROW][C]43[/C][C]101.1[/C][C]104.84203847114[/C][C]-3.74203847114045[/C][/ROW]
[ROW][C]44[/C][C]98.1[/C][C]100.079288485198[/C][C]-1.9792884851984[/C][/ROW]
[ROW][C]45[/C][C]109.2[/C][C]102.734887002552[/C][C]6.46511299744786[/C][/ROW]
[ROW][C]46[/C][C]114.4[/C][C]114.112357134743[/C][C]0.287642865256615[/C][/ROW]
[ROW][C]47[/C][C]104[/C][C]105.211236487002[/C][C]-1.21123648700197[/C][/ROW]
[ROW][C]48[/C][C]107.2[/C][C]103.338713384585[/C][C]3.8612866154153[/C][/ROW]
[ROW][C]49[/C][C]101.3[/C][C]103.53920976453[/C][C]-2.2392097645301[/C][/ROW]
[ROW][C]50[/C][C]98.1[/C][C]96.9823754516292[/C][C]1.11762454837083[/C][/ROW]
[ROW][C]51[/C][C]109.6[/C][C]103.552187215495[/C][C]6.04781278450545[/C][/ROW]
[ROW][C]52[/C][C]105.9[/C][C]106.164528746254[/C][C]-0.264528746253959[/C][/ROW]
[ROW][C]53[/C][C]99.5[/C][C]102.634331955495[/C][C]-3.13433195549453[/C][/ROW]
[ROW][C]54[/C][C]109.9[/C][C]103.257151716389[/C][C]6.64284828361114[/C][/ROW]
[ROW][C]55[/C][C]105.3[/C][C]103.438922474654[/C][C]1.86107752534593[/C][/ROW]
[ROW][C]56[/C][C]102.5[/C][C]100.810135662773[/C][C]1.68986433722716[/C][/ROW]
[ROW][C]57[/C][C]111.9[/C][C]111.617382446531[/C][C]0.282617553469294[/C][/ROW]
[ROW][C]58[/C][C]118[/C][C]116.931490426574[/C][C]1.06850957342621[/C][/ROW]
[ROW][C]59[/C][C]112.1[/C][C]106.555816640636[/C][C]5.54418335936433[/C][/ROW]
[ROW][C]60[/C][C]113.8[/C][C]110.019432674025[/C][C]3.78056732597499[/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	101.5	101.211539161553	0.288460838447179
14	99	98.5798368088367	0.420163191163311
15	106.2	106.158194186787	0.0418058132132586
16	97.6	97.5985741959501	0.00142580404984471
17	103.7	103.419446131496	0.280553868504001
18	103.4	103.442374577409	-0.042374577408637
19	99.9	94.5463050482759	5.35369495172408
20	105	106.339358887778	-1.33935888777788
21	103.4	111.372061853047	-7.97206185304687
22	117.8	110.803540444009	6.99645955599117
23	110.6	111.286669340043	-0.686669340042727
24	102	109.625465203923	-7.62546520392289
25	105.1	101.647279441298	3.45272055870196
26	98.5	99.4856408562672	-0.985640856267239
27	104.4	106.592974120275	-2.1929741202753
28	103.9	97.7266170942545	6.17338290574548
29	105.8	104.563726601021	1.23627339897942
30	100.3	104.409060303819	-4.10906030381892
31	106.3	99.7563952373567	6.54360476264327
32	101.4	105.803305781248	-4.40330578124849
33	104.3	104.556927883011	-0.256927883011102
34	114.6	118.215608216813	-3.61560821681304
35	105	110.67494048144	-5.67494048144049
36	103.4	102.288090522188	1.11190947781203
37	102.9	105.114742047132	-2.2147420471323
38	96.4	98.3859254334453	-1.98592543344533
39	102.6	104.283976779767	-1.68397677976705
40	104.7	102.834593138193	1.86540686180697
41	100.8	104.792293485608	-3.99229348560787
42	102.1	99.3599059446568	2.74009405534323
43	101.1	104.84203847114	-3.74203847114045
44	98.1	100.079288485198	-1.9792884851984
45	109.2	102.734887002552	6.46511299744786
46	114.4	114.112357134743	0.287642865256615
47	104	105.211236487002	-1.21123648700197
48	107.2	103.338713384585	3.8612866154153
49	101.3	103.53920976453	-2.2392097645301
50	98.1	96.9823754516292	1.11762454837083
51	109.6	103.552187215495	6.04781278450545
52	105.9	106.164528746254	-0.264528746253959
53	99.5	102.634331955495	-3.13433195549453
54	109.9	103.257151716389	6.64284828361114
55	105.3	103.438922474654	1.86107752534593
56	102.5	100.810135662773	1.68986433722716
57	111.9	111.617382446531	0.282617553469294
58	118	116.931490426574	1.06850957342621
59	112.1	106.555816640636	5.54418335936433
60	113.8	110.019432674025	3.78056732597499

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	104.64131868937	97.3795641133143	111.903073265426
62	101.198725523715	93.8912538762224	108.506197171208
63	112.297915753325	104.920282524586	119.675548982065
64	108.537113958604	101.122154716392	115.952073200817
65	102.339990372986	94.8993190782762	109.780661667697
66	112.196265971714	104.663149148313	119.729382795115
67	107.274781014859	99.7215559895269	114.828006040192
68	104.218311014674	96.6369356748015	111.799686354546
69	113.74158052216	106.04565781674	121.437503227579
70	119.813824440434	112.021322387461	127.606326493408
71	113.137984939153	105.360689484467	120.915280393839
72	114.396246540096	-47.3694733110359	276.161966391227

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 104.64131868937 & 97.3795641133143 & 111.903073265426 \tabularnewline
62 & 101.198725523715 & 93.8912538762224 & 108.506197171208 \tabularnewline
63 & 112.297915753325 & 104.920282524586 & 119.675548982065 \tabularnewline
64 & 108.537113958604 & 101.122154716392 & 115.952073200817 \tabularnewline
65 & 102.339990372986 & 94.8993190782762 & 109.780661667697 \tabularnewline
66 & 112.196265971714 & 104.663149148313 & 119.729382795115 \tabularnewline
67 & 107.274781014859 & 99.7215559895269 & 114.828006040192 \tabularnewline
68 & 104.218311014674 & 96.6369356748015 & 111.799686354546 \tabularnewline
69 & 113.74158052216 & 106.04565781674 & 121.437503227579 \tabularnewline
70 & 119.813824440434 & 112.021322387461 & 127.606326493408 \tabularnewline
71 & 113.137984939153 & 105.360689484467 & 120.915280393839 \tabularnewline
72 & 114.396246540096 & -47.3694733110359 & 276.161966391227 \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]104.64131868937[/C][C]97.3795641133143[/C][C]111.903073265426[/C][/ROW]
[ROW][C]62[/C][C]101.198725523715[/C][C]93.8912538762224[/C][C]108.506197171208[/C][/ROW]
[ROW][C]63[/C][C]112.297915753325[/C][C]104.920282524586[/C][C]119.675548982065[/C][/ROW]
[ROW][C]64[/C][C]108.537113958604[/C][C]101.122154716392[/C][C]115.952073200817[/C][/ROW]
[ROW][C]65[/C][C]102.339990372986[/C][C]94.8993190782762[/C][C]109.780661667697[/C][/ROW]
[ROW][C]66[/C][C]112.196265971714[/C][C]104.663149148313[/C][C]119.729382795115[/C][/ROW]
[ROW][C]67[/C][C]107.274781014859[/C][C]99.7215559895269[/C][C]114.828006040192[/C][/ROW]
[ROW][C]68[/C][C]104.218311014674[/C][C]96.6369356748015[/C][C]111.799686354546[/C][/ROW]
[ROW][C]69[/C][C]113.74158052216[/C][C]106.04565781674[/C][C]121.437503227579[/C][/ROW]
[ROW][C]70[/C][C]119.813824440434[/C][C]112.021322387461[/C][C]127.606326493408[/C][/ROW]
[ROW][C]71[/C][C]113.137984939153[/C][C]105.360689484467[/C][C]120.915280393839[/C][/ROW]
[ROW][C]72[/C][C]114.396246540096[/C][C]-47.3694733110359[/C][C]276.161966391227[/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	104.64131868937	97.3795641133143	111.903073265426
62	101.198725523715	93.8912538762224	108.506197171208
63	112.297915753325	104.920282524586	119.675548982065
64	108.537113958604	101.122154716392	115.952073200817
65	102.339990372986	94.8993190782762	109.780661667697
66	112.196265971714	104.663149148313	119.729382795115
67	107.274781014859	99.7215559895269	114.828006040192
68	104.218311014674	96.6369356748015	111.799686354546
69	113.74158052216	106.04565781674	121.437503227579
70	119.813824440434	112.021322387461	127.606326493408
71	113.137984939153	105.360689484467	120.915280393839
72	114.396246540096	-47.3694733110359	276.161966391227

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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