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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 02 May 2017 11:34:05 +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/t1493721262o7sqoskovpfhopx.htm/, Retrieved Fri, 17 May 2024 07:36:03 +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 07:36:03 +0200

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Estimated Impact

Dataseries X:

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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' @ 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 & 3 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]3 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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.9856399763309
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.9856399763309 \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]0.9856399763309[/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	0.9856399763309
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	98.2	95.6450701169092	2.55492988309079
14	99.46	99.3917206459192	0.0682793540808149
15	100.35	100.380479549851	-0.0304795498512505
16	99.72	99.8290111810082	-0.109011181008157
17	99.69	99.8206792529881	-0.13067925298806
18	99.62	99.7272533815783	-0.107253381578275
19	99.77	98.8802921138712	0.889707886128818
20	100.19	100.915400091655	-0.72540009165489
21	100.82	101.548454931901	-0.728454931900814
22	100.36	101.469385923913	-1.10938592391273
23	101.08	100.450914548463	0.629085451537364
24	100.73	100.702895261564	0.0271047384358951
25	101.51	101.579925244173	-0.0699252441731488
26	102.12	102.730685296501	-0.610685296500563
27	102.88	103.062911156517	-0.182911156516838
28	103.47	102.337015178018	1.13298482198165
29	103.53	103.541633821602	-0.0116338216015635
30	103.67	103.552290772279	0.117709227721207
31	103.68	102.896110877064	0.783889122935904
32	103.76	104.832878725764	-1.0728787257636
33	103.67	105.157581716958	-1.48758171695812
34	103.01	104.331525514324	-1.32152551432415
35	103.39	103.121141616667	0.268858383332812
36	103.43	102.99198698895	0.438013011050103
37	103.4	104.284921338969	-0.884921338969107
38	104.8	104.639930683392	0.160069316607789
39	105.53	105.75229093658	-0.222290936580052
40	107.45	104.982628860115	2.46737113988473
41	108.73	107.473898366615	1.25610163338511
42	109.04	108.71769843947	0.322301560530462
43	108.75	108.213299612544	0.536700387455625
44	108.75	109.916246077638	-1.16624607763771
45	108.76	110.190209300316	-1.43020930031648
46	108.41	109.435207311086	-1.0252073110864
47	110.15	108.525231883944	1.62476811605646
48	109.93	109.684140281221	0.245859718779457
49	110.6	110.797019258395	-0.197019258395059
50	112.17	111.904249327808	0.265750672192027
51	113.47	113.154254359683	0.315745640317118
52	113.35	112.88475390134	0.465246098660131
53	114.12	113.365953921862	0.754046078137605
54	115	114.081885977492	0.918114022507524
55	114.01	114.102164034059	-0.0921640340587686
56	113.86	115.197532166471	-1.33753216647094
57	113.83	115.34713885987	-1.51713885987033
58	112.7	114.52472058394	-1.82472058394026
59	111.79	112.854379564488	-1.06437956448841
60	113.77	111.330175392709	2.43982460729069

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 98.2 & 95.6450701169092 & 2.55492988309079 \tabularnewline
14 & 99.46 & 99.3917206459192 & 0.0682793540808149 \tabularnewline
15 & 100.35 & 100.380479549851 & -0.0304795498512505 \tabularnewline
16 & 99.72 & 99.8290111810082 & -0.109011181008157 \tabularnewline
17 & 99.69 & 99.8206792529881 & -0.13067925298806 \tabularnewline
18 & 99.62 & 99.7272533815783 & -0.107253381578275 \tabularnewline
19 & 99.77 & 98.8802921138712 & 0.889707886128818 \tabularnewline
20 & 100.19 & 100.915400091655 & -0.72540009165489 \tabularnewline
21 & 100.82 & 101.548454931901 & -0.728454931900814 \tabularnewline
22 & 100.36 & 101.469385923913 & -1.10938592391273 \tabularnewline
23 & 101.08 & 100.450914548463 & 0.629085451537364 \tabularnewline
24 & 100.73 & 100.702895261564 & 0.0271047384358951 \tabularnewline
25 & 101.51 & 101.579925244173 & -0.0699252441731488 \tabularnewline
26 & 102.12 & 102.730685296501 & -0.610685296500563 \tabularnewline
27 & 102.88 & 103.062911156517 & -0.182911156516838 \tabularnewline
28 & 103.47 & 102.337015178018 & 1.13298482198165 \tabularnewline
29 & 103.53 & 103.541633821602 & -0.0116338216015635 \tabularnewline
30 & 103.67 & 103.552290772279 & 0.117709227721207 \tabularnewline
31 & 103.68 & 102.896110877064 & 0.783889122935904 \tabularnewline
32 & 103.76 & 104.832878725764 & -1.0728787257636 \tabularnewline
33 & 103.67 & 105.157581716958 & -1.48758171695812 \tabularnewline
34 & 103.01 & 104.331525514324 & -1.32152551432415 \tabularnewline
35 & 103.39 & 103.121141616667 & 0.268858383332812 \tabularnewline
36 & 103.43 & 102.99198698895 & 0.438013011050103 \tabularnewline
37 & 103.4 & 104.284921338969 & -0.884921338969107 \tabularnewline
38 & 104.8 & 104.639930683392 & 0.160069316607789 \tabularnewline
39 & 105.53 & 105.75229093658 & -0.222290936580052 \tabularnewline
40 & 107.45 & 104.982628860115 & 2.46737113988473 \tabularnewline
41 & 108.73 & 107.473898366615 & 1.25610163338511 \tabularnewline
42 & 109.04 & 108.71769843947 & 0.322301560530462 \tabularnewline
43 & 108.75 & 108.213299612544 & 0.536700387455625 \tabularnewline
44 & 108.75 & 109.916246077638 & -1.16624607763771 \tabularnewline
45 & 108.76 & 110.190209300316 & -1.43020930031648 \tabularnewline
46 & 108.41 & 109.435207311086 & -1.0252073110864 \tabularnewline
47 & 110.15 & 108.525231883944 & 1.62476811605646 \tabularnewline
48 & 109.93 & 109.684140281221 & 0.245859718779457 \tabularnewline
49 & 110.6 & 110.797019258395 & -0.197019258395059 \tabularnewline
50 & 112.17 & 111.904249327808 & 0.265750672192027 \tabularnewline
51 & 113.47 & 113.154254359683 & 0.315745640317118 \tabularnewline
52 & 113.35 & 112.88475390134 & 0.465246098660131 \tabularnewline
53 & 114.12 & 113.365953921862 & 0.754046078137605 \tabularnewline
54 & 115 & 114.081885977492 & 0.918114022507524 \tabularnewline
55 & 114.01 & 114.102164034059 & -0.0921640340587686 \tabularnewline
56 & 113.86 & 115.197532166471 & -1.33753216647094 \tabularnewline
57 & 113.83 & 115.34713885987 & -1.51713885987033 \tabularnewline
58 & 112.7 & 114.52472058394 & -1.82472058394026 \tabularnewline
59 & 111.79 & 112.854379564488 & -1.06437956448841 \tabularnewline
60 & 113.77 & 111.330175392709 & 2.43982460729069 \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]98.2[/C][C]95.6450701169092[/C][C]2.55492988309079[/C][/ROW]
[ROW][C]14[/C][C]99.46[/C][C]99.3917206459192[/C][C]0.0682793540808149[/C][/ROW]
[ROW][C]15[/C][C]100.35[/C][C]100.380479549851[/C][C]-0.0304795498512505[/C][/ROW]
[ROW][C]16[/C][C]99.72[/C][C]99.8290111810082[/C][C]-0.109011181008157[/C][/ROW]
[ROW][C]17[/C][C]99.69[/C][C]99.8206792529881[/C][C]-0.13067925298806[/C][/ROW]
[ROW][C]18[/C][C]99.62[/C][C]99.7272533815783[/C][C]-0.107253381578275[/C][/ROW]
[ROW][C]19[/C][C]99.77[/C][C]98.8802921138712[/C][C]0.889707886128818[/C][/ROW]
[ROW][C]20[/C][C]100.19[/C][C]100.915400091655[/C][C]-0.72540009165489[/C][/ROW]
[ROW][C]21[/C][C]100.82[/C][C]101.548454931901[/C][C]-0.728454931900814[/C][/ROW]
[ROW][C]22[/C][C]100.36[/C][C]101.469385923913[/C][C]-1.10938592391273[/C][/ROW]
[ROW][C]23[/C][C]101.08[/C][C]100.450914548463[/C][C]0.629085451537364[/C][/ROW]
[ROW][C]24[/C][C]100.73[/C][C]100.702895261564[/C][C]0.0271047384358951[/C][/ROW]
[ROW][C]25[/C][C]101.51[/C][C]101.579925244173[/C][C]-0.0699252441731488[/C][/ROW]
[ROW][C]26[/C][C]102.12[/C][C]102.730685296501[/C][C]-0.610685296500563[/C][/ROW]
[ROW][C]27[/C][C]102.88[/C][C]103.062911156517[/C][C]-0.182911156516838[/C][/ROW]
[ROW][C]28[/C][C]103.47[/C][C]102.337015178018[/C][C]1.13298482198165[/C][/ROW]
[ROW][C]29[/C][C]103.53[/C][C]103.541633821602[/C][C]-0.0116338216015635[/C][/ROW]
[ROW][C]30[/C][C]103.67[/C][C]103.552290772279[/C][C]0.117709227721207[/C][/ROW]
[ROW][C]31[/C][C]103.68[/C][C]102.896110877064[/C][C]0.783889122935904[/C][/ROW]
[ROW][C]32[/C][C]103.76[/C][C]104.832878725764[/C][C]-1.0728787257636[/C][/ROW]
[ROW][C]33[/C][C]103.67[/C][C]105.157581716958[/C][C]-1.48758171695812[/C][/ROW]
[ROW][C]34[/C][C]103.01[/C][C]104.331525514324[/C][C]-1.32152551432415[/C][/ROW]
[ROW][C]35[/C][C]103.39[/C][C]103.121141616667[/C][C]0.268858383332812[/C][/ROW]
[ROW][C]36[/C][C]103.43[/C][C]102.99198698895[/C][C]0.438013011050103[/C][/ROW]
[ROW][C]37[/C][C]103.4[/C][C]104.284921338969[/C][C]-0.884921338969107[/C][/ROW]
[ROW][C]38[/C][C]104.8[/C][C]104.639930683392[/C][C]0.160069316607789[/C][/ROW]
[ROW][C]39[/C][C]105.53[/C][C]105.75229093658[/C][C]-0.222290936580052[/C][/ROW]
[ROW][C]40[/C][C]107.45[/C][C]104.982628860115[/C][C]2.46737113988473[/C][/ROW]
[ROW][C]41[/C][C]108.73[/C][C]107.473898366615[/C][C]1.25610163338511[/C][/ROW]
[ROW][C]42[/C][C]109.04[/C][C]108.71769843947[/C][C]0.322301560530462[/C][/ROW]
[ROW][C]43[/C][C]108.75[/C][C]108.213299612544[/C][C]0.536700387455625[/C][/ROW]
[ROW][C]44[/C][C]108.75[/C][C]109.916246077638[/C][C]-1.16624607763771[/C][/ROW]
[ROW][C]45[/C][C]108.76[/C][C]110.190209300316[/C][C]-1.43020930031648[/C][/ROW]
[ROW][C]46[/C][C]108.41[/C][C]109.435207311086[/C][C]-1.0252073110864[/C][/ROW]
[ROW][C]47[/C][C]110.15[/C][C]108.525231883944[/C][C]1.62476811605646[/C][/ROW]
[ROW][C]48[/C][C]109.93[/C][C]109.684140281221[/C][C]0.245859718779457[/C][/ROW]
[ROW][C]49[/C][C]110.6[/C][C]110.797019258395[/C][C]-0.197019258395059[/C][/ROW]
[ROW][C]50[/C][C]112.17[/C][C]111.904249327808[/C][C]0.265750672192027[/C][/ROW]
[ROW][C]51[/C][C]113.47[/C][C]113.154254359683[/C][C]0.315745640317118[/C][/ROW]
[ROW][C]52[/C][C]113.35[/C][C]112.88475390134[/C][C]0.465246098660131[/C][/ROW]
[ROW][C]53[/C][C]114.12[/C][C]113.365953921862[/C][C]0.754046078137605[/C][/ROW]
[ROW][C]54[/C][C]115[/C][C]114.081885977492[/C][C]0.918114022507524[/C][/ROW]
[ROW][C]55[/C][C]114.01[/C][C]114.102164034059[/C][C]-0.0921640340587686[/C][/ROW]
[ROW][C]56[/C][C]113.86[/C][C]115.197532166471[/C][C]-1.33753216647094[/C][/ROW]
[ROW][C]57[/C][C]113.83[/C][C]115.34713885987[/C][C]-1.51713885987033[/C][/ROW]
[ROW][C]58[/C][C]112.7[/C][C]114.52472058394[/C][C]-1.82472058394026[/C][/ROW]
[ROW][C]59[/C][C]111.79[/C][C]112.854379564488[/C][C]-1.06437956448841[/C][/ROW]
[ROW][C]60[/C][C]113.77[/C][C]111.330175392709[/C][C]2.43982460729069[/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	98.2	95.6450701169092	2.55492988309079
14	99.46	99.3917206459192	0.0682793540808149
15	100.35	100.380479549851	-0.0304795498512505
16	99.72	99.8290111810082	-0.109011181008157
17	99.69	99.8206792529881	-0.13067925298806
18	99.62	99.7272533815783	-0.107253381578275
19	99.77	98.8802921138712	0.889707886128818
20	100.19	100.915400091655	-0.72540009165489
21	100.82	101.548454931901	-0.728454931900814
22	100.36	101.469385923913	-1.10938592391273
23	101.08	100.450914548463	0.629085451537364
24	100.73	100.702895261564	0.0271047384358951
25	101.51	101.579925244173	-0.0699252441731488
26	102.12	102.730685296501	-0.610685296500563
27	102.88	103.062911156517	-0.182911156516838
28	103.47	102.337015178018	1.13298482198165
29	103.53	103.541633821602	-0.0116338216015635
30	103.67	103.552290772279	0.117709227721207
31	103.68	102.896110877064	0.783889122935904
32	103.76	104.832878725764	-1.0728787257636
33	103.67	105.157581716958	-1.48758171695812
34	103.01	104.331525514324	-1.32152551432415
35	103.39	103.121141616667	0.268858383332812
36	103.43	102.99198698895	0.438013011050103
37	103.4	104.284921338969	-0.884921338969107
38	104.8	104.639930683392	0.160069316607789
39	105.53	105.75229093658	-0.222290936580052
40	107.45	104.982628860115	2.46737113988473
41	108.73	107.473898366615	1.25610163338511
42	109.04	108.71769843947	0.322301560530462
43	108.75	108.213299612544	0.536700387455625
44	108.75	109.916246077638	-1.16624607763771
45	108.76	110.190209300316	-1.43020930031648
46	108.41	109.435207311086	-1.0252073110864
47	110.15	108.525231883944	1.62476811605646
48	109.93	109.684140281221	0.245859718779457
49	110.6	110.797019258395	-0.197019258395059
50	112.17	111.904249327808	0.265750672192027
51	113.47	113.154254359683	0.315745640317118
52	113.35	112.88475390134	0.465246098660131
53	114.12	113.365953921862	0.754046078137605
54	115	114.081885977492	0.918114022507524
55	114.01	114.102164034059	-0.0921640340587686
56	113.86	115.197532166471	-1.33753216647094
57	113.83	115.34713885987	-1.51713885987033
58	112.7	114.52472058394	-1.82472058394026
59	111.79	112.854379564488	-1.06437956448841
60	113.77	111.330175392709	2.43982460729069

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	114.615587729231	112.590593383506	116.640582074956
62	115.956886553841	113.101976846939	118.811796260744
63	116.965723597435	113.470079334713	120.461367860156
64	116.357255058783	112.357602556511	120.356907561054
65	116.374330115944	111.915710637821	120.832949594068
66	116.341127170869	111.470809464337	121.211444877401
67	115.427000364806	110.213573924348	120.640426805264
68	116.604813613018	110.989150008571	122.220477217465
69	118.095785501084	112.086192363789	124.105378638379
70	118.774253777464	112.428065816721	125.120441738208
71	118.899645373918	112.260467118372	125.538823629464
72	118.422395985545	110.05369967959	126.791092291501

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 114.615587729231 & 112.590593383506 & 116.640582074956 \tabularnewline
62 & 115.956886553841 & 113.101976846939 & 118.811796260744 \tabularnewline
63 & 116.965723597435 & 113.470079334713 & 120.461367860156 \tabularnewline
64 & 116.357255058783 & 112.357602556511 & 120.356907561054 \tabularnewline
65 & 116.374330115944 & 111.915710637821 & 120.832949594068 \tabularnewline
66 & 116.341127170869 & 111.470809464337 & 121.211444877401 \tabularnewline
67 & 115.427000364806 & 110.213573924348 & 120.640426805264 \tabularnewline
68 & 116.604813613018 & 110.989150008571 & 122.220477217465 \tabularnewline
69 & 118.095785501084 & 112.086192363789 & 124.105378638379 \tabularnewline
70 & 118.774253777464 & 112.428065816721 & 125.120441738208 \tabularnewline
71 & 118.899645373918 & 112.260467118372 & 125.538823629464 \tabularnewline
72 & 118.422395985545 & 110.05369967959 & 126.791092291501 \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]114.615587729231[/C][C]112.590593383506[/C][C]116.640582074956[/C][/ROW]
[ROW][C]62[/C][C]115.956886553841[/C][C]113.101976846939[/C][C]118.811796260744[/C][/ROW]
[ROW][C]63[/C][C]116.965723597435[/C][C]113.470079334713[/C][C]120.461367860156[/C][/ROW]
[ROW][C]64[/C][C]116.357255058783[/C][C]112.357602556511[/C][C]120.356907561054[/C][/ROW]
[ROW][C]65[/C][C]116.374330115944[/C][C]111.915710637821[/C][C]120.832949594068[/C][/ROW]
[ROW][C]66[/C][C]116.341127170869[/C][C]111.470809464337[/C][C]121.211444877401[/C][/ROW]
[ROW][C]67[/C][C]115.427000364806[/C][C]110.213573924348[/C][C]120.640426805264[/C][/ROW]
[ROW][C]68[/C][C]116.604813613018[/C][C]110.989150008571[/C][C]122.220477217465[/C][/ROW]
[ROW][C]69[/C][C]118.095785501084[/C][C]112.086192363789[/C][C]124.105378638379[/C][/ROW]
[ROW][C]70[/C][C]118.774253777464[/C][C]112.428065816721[/C][C]125.120441738208[/C][/ROW]
[ROW][C]71[/C][C]118.899645373918[/C][C]112.260467118372[/C][C]125.538823629464[/C][/ROW]
[ROW][C]72[/C][C]118.422395985545[/C][C]110.05369967959[/C][C]126.791092291501[/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	114.615587729231	112.590593383506	116.640582074956
62	115.956886553841	113.101976846939	118.811796260744
63	116.965723597435	113.470079334713	120.461367860156
64	116.357255058783	112.357602556511	120.356907561054
65	116.374330115944	111.915710637821	120.832949594068
66	116.341127170869	111.470809464337	121.211444877401
67	115.427000364806	110.213573924348	120.640426805264
68	116.604813613018	110.989150008571	122.220477217465
69	118.095785501084	112.086192363789	124.105378638379
70	118.774253777464	112.428065816721	125.120441738208
71	118.899645373918	112.260467118372	125.538823629464
72	118.422395985545	110.05369967959	126.791092291501

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