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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 28 Apr 2017 10:38:06 +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/Apr/28/t1493372340gsm0r5x3tvvwm7h.htm/, Retrieved Fri, 10 May 2024 03:28:04 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 10 May 2024 03:28:04 +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	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	0.889472739292855
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.889472739292855 \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]0.889472739292855[/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	0.889472739292855
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	99.36	98.6684134083128	0.691586591687184
14	99.58	99.4964020599412	0.0835979400588229
15	99.77	99.7728461515372	-0.00284615153718448
16	99.77	99.7928133308214	-0.0228133308214353
17	100.03	100.059239049778	-0.0292390497776438
18	100.2	100.227047142364	-0.0270471423641823
19	100.24	99.9419003762269	0.298099623773098
20	100.1	100.419482135146	-0.319482135145776
21	100.03	100.184623549256	-0.154623549256357
22	100.18	100.341646644197	-0.16164664419729
23	100.29	100.264159987714	0.0258400122861389
24	100.41	100.355949177163	0.0540508228369987
25	100.6	100.401979516437	0.198020483562885
26	100.75	100.72423660552	0.0257633944801938
27	100.79	100.940699388648	-0.150699388648064
28	100.44	100.826059136724	-0.386059136724214
29	100.29	100.769962360798	-0.479962360797728
30	100.34	100.537381187755	-0.197381187754829
31	100.46	100.136042817997	0.323957182003156
32	100.12	100.56833469334	-0.448334693339973
33	100.06	100.237036577793	-0.17703657779326
34	100.28	100.373415079674	-0.0934150796737185
35	100.28	100.377319450506	-0.0973194505056938
36	100.4	100.362676602047	0.0373233979532728
37	100.61	100.409715533611	0.200284466388766
38	100.89	100.714944055447	0.175055944552938
39	100.73	101.04475399319	-0.314753993189541
40	101.12	100.758060299645	0.361939700354782
41	101.16	101.357771494658	-0.197771494658056
42	101.33	101.408448463789	-0.078448463789087
43	101.37	101.167689437586	0.202310562413729
44	101.61	101.405806798913	0.204193201087193
45	101.85	101.684748084462	0.165251915537837
46	102.27	102.13830766107	0.131692338929938
47	102.28	102.341616802276	-0.0616168022764043
48	102.23	102.373228796341	-0.143228796341376
49	102.42	102.276283448696	0.143716551303655
50	102.53	102.52870671055	0.001293289449535
51	103.47	102.649953405578	0.820046594421825
52	103.53	103.446303553862	0.0836964461380774
53	103.77	103.739234057987	0.0307659420133319
54	103.74	104.009816642358	-0.269816642357625
55	103.93	103.623914437502	0.306085562498438
56	103.97	103.953322853031	0.0166771469694282
57	103.68	104.060847260529	-0.38084726052908
58	103.86	104.028559789978	-0.168559789977635
59	103.97	103.942786783778	0.0272132162217957
60	104.05	104.043900577846	0.00609942215366743

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 99.36 & 98.6684134083128 & 0.691586591687184 \tabularnewline
14 & 99.58 & 99.4964020599412 & 0.0835979400588229 \tabularnewline
15 & 99.77 & 99.7728461515372 & -0.00284615153718448 \tabularnewline
16 & 99.77 & 99.7928133308214 & -0.0228133308214353 \tabularnewline
17 & 100.03 & 100.059239049778 & -0.0292390497776438 \tabularnewline
18 & 100.2 & 100.227047142364 & -0.0270471423641823 \tabularnewline
19 & 100.24 & 99.9419003762269 & 0.298099623773098 \tabularnewline
20 & 100.1 & 100.419482135146 & -0.319482135145776 \tabularnewline
21 & 100.03 & 100.184623549256 & -0.154623549256357 \tabularnewline
22 & 100.18 & 100.341646644197 & -0.16164664419729 \tabularnewline
23 & 100.29 & 100.264159987714 & 0.0258400122861389 \tabularnewline
24 & 100.41 & 100.355949177163 & 0.0540508228369987 \tabularnewline
25 & 100.6 & 100.401979516437 & 0.198020483562885 \tabularnewline
26 & 100.75 & 100.72423660552 & 0.0257633944801938 \tabularnewline
27 & 100.79 & 100.940699388648 & -0.150699388648064 \tabularnewline
28 & 100.44 & 100.826059136724 & -0.386059136724214 \tabularnewline
29 & 100.29 & 100.769962360798 & -0.479962360797728 \tabularnewline
30 & 100.34 & 100.537381187755 & -0.197381187754829 \tabularnewline
31 & 100.46 & 100.136042817997 & 0.323957182003156 \tabularnewline
32 & 100.12 & 100.56833469334 & -0.448334693339973 \tabularnewline
33 & 100.06 & 100.237036577793 & -0.17703657779326 \tabularnewline
34 & 100.28 & 100.373415079674 & -0.0934150796737185 \tabularnewline
35 & 100.28 & 100.377319450506 & -0.0973194505056938 \tabularnewline
36 & 100.4 & 100.362676602047 & 0.0373233979532728 \tabularnewline
37 & 100.61 & 100.409715533611 & 0.200284466388766 \tabularnewline
38 & 100.89 & 100.714944055447 & 0.175055944552938 \tabularnewline
39 & 100.73 & 101.04475399319 & -0.314753993189541 \tabularnewline
40 & 101.12 & 100.758060299645 & 0.361939700354782 \tabularnewline
41 & 101.16 & 101.357771494658 & -0.197771494658056 \tabularnewline
42 & 101.33 & 101.408448463789 & -0.078448463789087 \tabularnewline
43 & 101.37 & 101.167689437586 & 0.202310562413729 \tabularnewline
44 & 101.61 & 101.405806798913 & 0.204193201087193 \tabularnewline
45 & 101.85 & 101.684748084462 & 0.165251915537837 \tabularnewline
46 & 102.27 & 102.13830766107 & 0.131692338929938 \tabularnewline
47 & 102.28 & 102.341616802276 & -0.0616168022764043 \tabularnewline
48 & 102.23 & 102.373228796341 & -0.143228796341376 \tabularnewline
49 & 102.42 & 102.276283448696 & 0.143716551303655 \tabularnewline
50 & 102.53 & 102.52870671055 & 0.001293289449535 \tabularnewline
51 & 103.47 & 102.649953405578 & 0.820046594421825 \tabularnewline
52 & 103.53 & 103.446303553862 & 0.0836964461380774 \tabularnewline
53 & 103.77 & 103.739234057987 & 0.0307659420133319 \tabularnewline
54 & 103.74 & 104.009816642358 & -0.269816642357625 \tabularnewline
55 & 103.93 & 103.623914437502 & 0.306085562498438 \tabularnewline
56 & 103.97 & 103.953322853031 & 0.0166771469694282 \tabularnewline
57 & 103.68 & 104.060847260529 & -0.38084726052908 \tabularnewline
58 & 103.86 & 104.028559789978 & -0.168559789977635 \tabularnewline
59 & 103.97 & 103.942786783778 & 0.0272132162217957 \tabularnewline
60 & 104.05 & 104.043900577846 & 0.00609942215366743 \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]99.36[/C][C]98.6684134083128[/C][C]0.691586591687184[/C][/ROW]
[ROW][C]14[/C][C]99.58[/C][C]99.4964020599412[/C][C]0.0835979400588229[/C][/ROW]
[ROW][C]15[/C][C]99.77[/C][C]99.7728461515372[/C][C]-0.00284615153718448[/C][/ROW]
[ROW][C]16[/C][C]99.77[/C][C]99.7928133308214[/C][C]-0.0228133308214353[/C][/ROW]
[ROW][C]17[/C][C]100.03[/C][C]100.059239049778[/C][C]-0.0292390497776438[/C][/ROW]
[ROW][C]18[/C][C]100.2[/C][C]100.227047142364[/C][C]-0.0270471423641823[/C][/ROW]
[ROW][C]19[/C][C]100.24[/C][C]99.9419003762269[/C][C]0.298099623773098[/C][/ROW]
[ROW][C]20[/C][C]100.1[/C][C]100.419482135146[/C][C]-0.319482135145776[/C][/ROW]
[ROW][C]21[/C][C]100.03[/C][C]100.184623549256[/C][C]-0.154623549256357[/C][/ROW]
[ROW][C]22[/C][C]100.18[/C][C]100.341646644197[/C][C]-0.16164664419729[/C][/ROW]
[ROW][C]23[/C][C]100.29[/C][C]100.264159987714[/C][C]0.0258400122861389[/C][/ROW]
[ROW][C]24[/C][C]100.41[/C][C]100.355949177163[/C][C]0.0540508228369987[/C][/ROW]
[ROW][C]25[/C][C]100.6[/C][C]100.401979516437[/C][C]0.198020483562885[/C][/ROW]
[ROW][C]26[/C][C]100.75[/C][C]100.72423660552[/C][C]0.0257633944801938[/C][/ROW]
[ROW][C]27[/C][C]100.79[/C][C]100.940699388648[/C][C]-0.150699388648064[/C][/ROW]
[ROW][C]28[/C][C]100.44[/C][C]100.826059136724[/C][C]-0.386059136724214[/C][/ROW]
[ROW][C]29[/C][C]100.29[/C][C]100.769962360798[/C][C]-0.479962360797728[/C][/ROW]
[ROW][C]30[/C][C]100.34[/C][C]100.537381187755[/C][C]-0.197381187754829[/C][/ROW]
[ROW][C]31[/C][C]100.46[/C][C]100.136042817997[/C][C]0.323957182003156[/C][/ROW]
[ROW][C]32[/C][C]100.12[/C][C]100.56833469334[/C][C]-0.448334693339973[/C][/ROW]
[ROW][C]33[/C][C]100.06[/C][C]100.237036577793[/C][C]-0.17703657779326[/C][/ROW]
[ROW][C]34[/C][C]100.28[/C][C]100.373415079674[/C][C]-0.0934150796737185[/C][/ROW]
[ROW][C]35[/C][C]100.28[/C][C]100.377319450506[/C][C]-0.0973194505056938[/C][/ROW]
[ROW][C]36[/C][C]100.4[/C][C]100.362676602047[/C][C]0.0373233979532728[/C][/ROW]
[ROW][C]37[/C][C]100.61[/C][C]100.409715533611[/C][C]0.200284466388766[/C][/ROW]
[ROW][C]38[/C][C]100.89[/C][C]100.714944055447[/C][C]0.175055944552938[/C][/ROW]
[ROW][C]39[/C][C]100.73[/C][C]101.04475399319[/C][C]-0.314753993189541[/C][/ROW]
[ROW][C]40[/C][C]101.12[/C][C]100.758060299645[/C][C]0.361939700354782[/C][/ROW]
[ROW][C]41[/C][C]101.16[/C][C]101.357771494658[/C][C]-0.197771494658056[/C][/ROW]
[ROW][C]42[/C][C]101.33[/C][C]101.408448463789[/C][C]-0.078448463789087[/C][/ROW]
[ROW][C]43[/C][C]101.37[/C][C]101.167689437586[/C][C]0.202310562413729[/C][/ROW]
[ROW][C]44[/C][C]101.61[/C][C]101.405806798913[/C][C]0.204193201087193[/C][/ROW]
[ROW][C]45[/C][C]101.85[/C][C]101.684748084462[/C][C]0.165251915537837[/C][/ROW]
[ROW][C]46[/C][C]102.27[/C][C]102.13830766107[/C][C]0.131692338929938[/C][/ROW]
[ROW][C]47[/C][C]102.28[/C][C]102.341616802276[/C][C]-0.0616168022764043[/C][/ROW]
[ROW][C]48[/C][C]102.23[/C][C]102.373228796341[/C][C]-0.143228796341376[/C][/ROW]
[ROW][C]49[/C][C]102.42[/C][C]102.276283448696[/C][C]0.143716551303655[/C][/ROW]
[ROW][C]50[/C][C]102.53[/C][C]102.52870671055[/C][C]0.001293289449535[/C][/ROW]
[ROW][C]51[/C][C]103.47[/C][C]102.649953405578[/C][C]0.820046594421825[/C][/ROW]
[ROW][C]52[/C][C]103.53[/C][C]103.446303553862[/C][C]0.0836964461380774[/C][/ROW]
[ROW][C]53[/C][C]103.77[/C][C]103.739234057987[/C][C]0.0307659420133319[/C][/ROW]
[ROW][C]54[/C][C]103.74[/C][C]104.009816642358[/C][C]-0.269816642357625[/C][/ROW]
[ROW][C]55[/C][C]103.93[/C][C]103.623914437502[/C][C]0.306085562498438[/C][/ROW]
[ROW][C]56[/C][C]103.97[/C][C]103.953322853031[/C][C]0.0166771469694282[/C][/ROW]
[ROW][C]57[/C][C]103.68[/C][C]104.060847260529[/C][C]-0.38084726052908[/C][/ROW]
[ROW][C]58[/C][C]103.86[/C][C]104.028559789978[/C][C]-0.168559789977635[/C][/ROW]
[ROW][C]59[/C][C]103.97[/C][C]103.942786783778[/C][C]0.0272132162217957[/C][/ROW]
[ROW][C]60[/C][C]104.05[/C][C]104.043900577846[/C][C]0.00609942215366743[/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	99.36	98.6684134083128	0.691586591687184
14	99.58	99.4964020599412	0.0835979400588229
15	99.77	99.7728461515372	-0.00284615153718448
16	99.77	99.7928133308214	-0.0228133308214353
17	100.03	100.059239049778	-0.0292390497776438
18	100.2	100.227047142364	-0.0270471423641823
19	100.24	99.9419003762269	0.298099623773098
20	100.1	100.419482135146	-0.319482135145776
21	100.03	100.184623549256	-0.154623549256357
22	100.18	100.341646644197	-0.16164664419729
23	100.29	100.264159987714	0.0258400122861389
24	100.41	100.355949177163	0.0540508228369987
25	100.6	100.401979516437	0.198020483562885
26	100.75	100.72423660552	0.0257633944801938
27	100.79	100.940699388648	-0.150699388648064
28	100.44	100.826059136724	-0.386059136724214
29	100.29	100.769962360798	-0.479962360797728
30	100.34	100.537381187755	-0.197381187754829
31	100.46	100.136042817997	0.323957182003156
32	100.12	100.56833469334	-0.448334693339973
33	100.06	100.237036577793	-0.17703657779326
34	100.28	100.373415079674	-0.0934150796737185
35	100.28	100.377319450506	-0.0973194505056938
36	100.4	100.362676602047	0.0373233979532728
37	100.61	100.409715533611	0.200284466388766
38	100.89	100.714944055447	0.175055944552938
39	100.73	101.04475399319	-0.314753993189541
40	101.12	100.758060299645	0.361939700354782
41	101.16	101.357771494658	-0.197771494658056
42	101.33	101.408448463789	-0.078448463789087
43	101.37	101.167689437586	0.202310562413729
44	101.61	101.405806798913	0.204193201087193
45	101.85	101.684748084462	0.165251915537837
46	102.27	102.13830766107	0.131692338929938
47	102.28	102.341616802276	-0.0616168022764043
48	102.23	102.373228796341	-0.143228796341376
49	102.42	102.276283448696	0.143716551303655
50	102.53	102.52870671055	0.001293289449535
51	103.47	102.649953405578	0.820046594421825
52	103.53	103.446303553862	0.0836964461380774
53	103.77	103.739234057987	0.0307659420133319
54	103.74	104.009816642358	-0.269816642357625
55	103.93	103.623914437502	0.306085562498438
56	103.97	103.953322853031	0.0166771469694282
57	103.68	104.060847260529	-0.38084726052908
58	103.86	104.028559789978	-0.168559789977635
59	103.97	103.942786783778	0.0272132162217957
60	104.05	104.043900577846	0.00609942215366743

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	104.110696705569	103.606666517023	104.614726894115
62	104.219596172098	103.545022162154	104.894170182042
63	104.431261593241	103.620793863526	105.241729322956
64	104.415691908925	103.490247738639	105.341136079211
65	104.62923842788	103.600114675249	105.658362180511
66	104.840024271688	103.716590687681	105.963457855695
67	104.755685432591	103.547913751499	105.963457113682
68	104.780211035808	103.492761967502	106.067660104113
69	104.828381980538	103.46575378891	106.191010172166
70	105.160765227094	103.7235635244	106.597966929787
71	105.246307215713	103.741062658035	106.751551773392
72	105.320497679244	100.331962354945	110.309033003542

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 104.110696705569 & 103.606666517023 & 104.614726894115 \tabularnewline
62 & 104.219596172098 & 103.545022162154 & 104.894170182042 \tabularnewline
63 & 104.431261593241 & 103.620793863526 & 105.241729322956 \tabularnewline
64 & 104.415691908925 & 103.490247738639 & 105.341136079211 \tabularnewline
65 & 104.62923842788 & 103.600114675249 & 105.658362180511 \tabularnewline
66 & 104.840024271688 & 103.716590687681 & 105.963457855695 \tabularnewline
67 & 104.755685432591 & 103.547913751499 & 105.963457113682 \tabularnewline
68 & 104.780211035808 & 103.492761967502 & 106.067660104113 \tabularnewline
69 & 104.828381980538 & 103.46575378891 & 106.191010172166 \tabularnewline
70 & 105.160765227094 & 103.7235635244 & 106.597966929787 \tabularnewline
71 & 105.246307215713 & 103.741062658035 & 106.751551773392 \tabularnewline
72 & 105.320497679244 & 100.331962354945 & 110.309033003542 \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]104.110696705569[/C][C]103.606666517023[/C][C]104.614726894115[/C][/ROW]
[ROW][C]62[/C][C]104.219596172098[/C][C]103.545022162154[/C][C]104.894170182042[/C][/ROW]
[ROW][C]63[/C][C]104.431261593241[/C][C]103.620793863526[/C][C]105.241729322956[/C][/ROW]
[ROW][C]64[/C][C]104.415691908925[/C][C]103.490247738639[/C][C]105.341136079211[/C][/ROW]
[ROW][C]65[/C][C]104.62923842788[/C][C]103.600114675249[/C][C]105.658362180511[/C][/ROW]
[ROW][C]66[/C][C]104.840024271688[/C][C]103.716590687681[/C][C]105.963457855695[/C][/ROW]
[ROW][C]67[/C][C]104.755685432591[/C][C]103.547913751499[/C][C]105.963457113682[/C][/ROW]
[ROW][C]68[/C][C]104.780211035808[/C][C]103.492761967502[/C][C]106.067660104113[/C][/ROW]
[ROW][C]69[/C][C]104.828381980538[/C][C]103.46575378891[/C][C]106.191010172166[/C][/ROW]
[ROW][C]70[/C][C]105.160765227094[/C][C]103.7235635244[/C][C]106.597966929787[/C][/ROW]
[ROW][C]71[/C][C]105.246307215713[/C][C]103.741062658035[/C][C]106.751551773392[/C][/ROW]
[ROW][C]72[/C][C]105.320497679244[/C][C]100.331962354945[/C][C]110.309033003542[/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	104.110696705569	103.606666517023	104.614726894115
62	104.219596172098	103.545022162154	104.894170182042
63	104.431261593241	103.620793863526	105.241729322956
64	104.415691908925	103.490247738639	105.341136079211
65	104.62923842788	103.600114675249	105.658362180511
66	104.840024271688	103.716590687681	105.963457855695
67	104.755685432591	103.547913751499	105.963457113682
68	104.780211035808	103.492761967502	106.067660104113
69	104.828381980538	103.46575378891	106.191010172166
70	105.160765227094	103.7235635244	106.597966929787
71	105.246307215713	103.741062658035	106.751551773392
72	105.320497679244	100.331962354945	110.309033003542

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