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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 03 Jan 2016 17:41:05 +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/2016/Jan/03/t14518429039kg7vbyj9fh95nc.htm/, Retrieved Fri, 17 May 2024 01:43:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287312, Retrieved Fri, 17 May 2024 01:43:30 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

141

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

-     [Univariate Data Series] [] [2015-09-25 19:44:43] [ba9845715efdcdf5bf90594b26d5ea9c]
- R PD  [Univariate Data Series] [] [2015-10-02 11:08:09] [ba9845715efdcdf5bf90594b26d5ea9c]
- RMP     [Histogram] [] [2015-10-02 11:09:44] [ba9845715efdcdf5bf90594b26d5ea9c]
- RMPD        [Exponential Smoothing] [] [2016-01-03 17:41:05] [eed3b94f44ab74d862a61d666a631b56] [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	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=287312&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=287312&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287312&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	0.91793069062011
beta	0.0567382343305122
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.91793069062011 \tabularnewline
beta & 0.0567382343305122 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287312&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]0.91793069062011[/C][/ROW]
[ROW][C]beta[/C][C]0.0567382343305122[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287312&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287312&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	0.91793069062011
beta	0.0567382343305122
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	100	100	-5.6843418860808e-14
14	100	100	1.4210854715202e-14
15	100	100	1.4210854715202e-14
16	100	100	1.4210854715202e-14
17	100	100	1.4210854715202e-14
18	100	100	0
19	100	100	0
20	100	100	0
21	100	100	0
22	100	100	0
23	100	100	0
24	100	100	0
25	100.4	100	0.400000000000006
26	100.4	100.388004982897	0.0119950171025209
27	100.4	100.420473005561	-0.0204730055612004
28	100.4	100.42207136346	-0.0220713634604266
29	100.4	100.421053023989	-0.0210530239885571
30	100.4	100.419872970889	-0.0198729708892813
31	100.4	100.418741105314	-0.0187411053144189
32	100.4	100.417672144015	-0.0176721440151226
33	100.4	100.416664018619	-0.0166640186192097
34	100.4	100.415713390935	-0.0157133909354599
35	101.4	100.414816992418	0.985183007581583
36	101.4	101.383984187714	0.0160158122863265
37	102	101.464357201903	0.535642798097015
38	102	102.049608997246	-0.0496089972464233
39	102.6	102.095056483687	0.504943516313404
40	102.6	102.675843092259	-0.075843092258566
41	102.6	102.71955780589	-0.119557805890139
42	102.6	102.716918660503	-0.116918660503217
43	102.6	102.710612737274	-0.110612737273698
44	102.6	102.704334307741	-0.104334307740956
45	102.3	102.698385126299	-0.398385126298621
46	102.4	102.401769072726	-0.00176907272606286
47	102.4	102.469126930688	-0.0691269306875313
48	102.4	102.4710546909	-0.0710546909002687
49	102.9	102.467512247021	0.432487752979412
50	102.9	102.948711592626	-0.0487115926261481
51	102.9	102.985666304795	-0.0856663047950263
52	104.9	102.984237500007	1.91576249999277
53	104.9	104.919757915656	-0.0197579156561005
54	105.5	105.077575712307	0.42242428769309
55	105.5	105.663286727426	-0.163286727425699
56	105.5	105.702851364702	-0.202851364702184
57	105.5	105.695533549724	-0.195533549723649
58	105.5	105.684749248998	-0.184749248998401
59	105.5	105.674242121616	-0.174242121615521
60	105.5	105.664304971414	-0.164304971413657

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 100 & 100 & -5.6843418860808e-14 \tabularnewline
14 & 100 & 100 & 1.4210854715202e-14 \tabularnewline
15 & 100 & 100 & 1.4210854715202e-14 \tabularnewline
16 & 100 & 100 & 1.4210854715202e-14 \tabularnewline
17 & 100 & 100 & 1.4210854715202e-14 \tabularnewline
18 & 100 & 100 & 0 \tabularnewline
19 & 100 & 100 & 0 \tabularnewline
20 & 100 & 100 & 0 \tabularnewline
21 & 100 & 100 & 0 \tabularnewline
22 & 100 & 100 & 0 \tabularnewline
23 & 100 & 100 & 0 \tabularnewline
24 & 100 & 100 & 0 \tabularnewline
25 & 100.4 & 100 & 0.400000000000006 \tabularnewline
26 & 100.4 & 100.388004982897 & 0.0119950171025209 \tabularnewline
27 & 100.4 & 100.420473005561 & -0.0204730055612004 \tabularnewline
28 & 100.4 & 100.42207136346 & -0.0220713634604266 \tabularnewline
29 & 100.4 & 100.421053023989 & -0.0210530239885571 \tabularnewline
30 & 100.4 & 100.419872970889 & -0.0198729708892813 \tabularnewline
31 & 100.4 & 100.418741105314 & -0.0187411053144189 \tabularnewline
32 & 100.4 & 100.417672144015 & -0.0176721440151226 \tabularnewline
33 & 100.4 & 100.416664018619 & -0.0166640186192097 \tabularnewline
34 & 100.4 & 100.415713390935 & -0.0157133909354599 \tabularnewline
35 & 101.4 & 100.414816992418 & 0.985183007581583 \tabularnewline
36 & 101.4 & 101.383984187714 & 0.0160158122863265 \tabularnewline
37 & 102 & 101.464357201903 & 0.535642798097015 \tabularnewline
38 & 102 & 102.049608997246 & -0.0496089972464233 \tabularnewline
39 & 102.6 & 102.095056483687 & 0.504943516313404 \tabularnewline
40 & 102.6 & 102.675843092259 & -0.075843092258566 \tabularnewline
41 & 102.6 & 102.71955780589 & -0.119557805890139 \tabularnewline
42 & 102.6 & 102.716918660503 & -0.116918660503217 \tabularnewline
43 & 102.6 & 102.710612737274 & -0.110612737273698 \tabularnewline
44 & 102.6 & 102.704334307741 & -0.104334307740956 \tabularnewline
45 & 102.3 & 102.698385126299 & -0.398385126298621 \tabularnewline
46 & 102.4 & 102.401769072726 & -0.00176907272606286 \tabularnewline
47 & 102.4 & 102.469126930688 & -0.0691269306875313 \tabularnewline
48 & 102.4 & 102.4710546909 & -0.0710546909002687 \tabularnewline
49 & 102.9 & 102.467512247021 & 0.432487752979412 \tabularnewline
50 & 102.9 & 102.948711592626 & -0.0487115926261481 \tabularnewline
51 & 102.9 & 102.985666304795 & -0.0856663047950263 \tabularnewline
52 & 104.9 & 102.984237500007 & 1.91576249999277 \tabularnewline
53 & 104.9 & 104.919757915656 & -0.0197579156561005 \tabularnewline
54 & 105.5 & 105.077575712307 & 0.42242428769309 \tabularnewline
55 & 105.5 & 105.663286727426 & -0.163286727425699 \tabularnewline
56 & 105.5 & 105.702851364702 & -0.202851364702184 \tabularnewline
57 & 105.5 & 105.695533549724 & -0.195533549723649 \tabularnewline
58 & 105.5 & 105.684749248998 & -0.184749248998401 \tabularnewline
59 & 105.5 & 105.674242121616 & -0.174242121615521 \tabularnewline
60 & 105.5 & 105.664304971414 & -0.164304971413657 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287312&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]100[/C][C]100[/C][C]-5.6843418860808e-14[/C][/ROW]
[ROW][C]14[/C][C]100[/C][C]100[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]15[/C][C]100[/C][C]100[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]16[/C][C]100[/C][C]100[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]17[/C][C]100[/C][C]100[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]18[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]100[/C][C]100[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]100.4[/C][C]100[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]26[/C][C]100.4[/C][C]100.388004982897[/C][C]0.0119950171025209[/C][/ROW]
[ROW][C]27[/C][C]100.4[/C][C]100.420473005561[/C][C]-0.0204730055612004[/C][/ROW]
[ROW][C]28[/C][C]100.4[/C][C]100.42207136346[/C][C]-0.0220713634604266[/C][/ROW]
[ROW][C]29[/C][C]100.4[/C][C]100.421053023989[/C][C]-0.0210530239885571[/C][/ROW]
[ROW][C]30[/C][C]100.4[/C][C]100.419872970889[/C][C]-0.0198729708892813[/C][/ROW]
[ROW][C]31[/C][C]100.4[/C][C]100.418741105314[/C][C]-0.0187411053144189[/C][/ROW]
[ROW][C]32[/C][C]100.4[/C][C]100.417672144015[/C][C]-0.0176721440151226[/C][/ROW]
[ROW][C]33[/C][C]100.4[/C][C]100.416664018619[/C][C]-0.0166640186192097[/C][/ROW]
[ROW][C]34[/C][C]100.4[/C][C]100.415713390935[/C][C]-0.0157133909354599[/C][/ROW]
[ROW][C]35[/C][C]101.4[/C][C]100.414816992418[/C][C]0.985183007581583[/C][/ROW]
[ROW][C]36[/C][C]101.4[/C][C]101.383984187714[/C][C]0.0160158122863265[/C][/ROW]
[ROW][C]37[/C][C]102[/C][C]101.464357201903[/C][C]0.535642798097015[/C][/ROW]
[ROW][C]38[/C][C]102[/C][C]102.049608997246[/C][C]-0.0496089972464233[/C][/ROW]
[ROW][C]39[/C][C]102.6[/C][C]102.095056483687[/C][C]0.504943516313404[/C][/ROW]
[ROW][C]40[/C][C]102.6[/C][C]102.675843092259[/C][C]-0.075843092258566[/C][/ROW]
[ROW][C]41[/C][C]102.6[/C][C]102.71955780589[/C][C]-0.119557805890139[/C][/ROW]
[ROW][C]42[/C][C]102.6[/C][C]102.716918660503[/C][C]-0.116918660503217[/C][/ROW]
[ROW][C]43[/C][C]102.6[/C][C]102.710612737274[/C][C]-0.110612737273698[/C][/ROW]
[ROW][C]44[/C][C]102.6[/C][C]102.704334307741[/C][C]-0.104334307740956[/C][/ROW]
[ROW][C]45[/C][C]102.3[/C][C]102.698385126299[/C][C]-0.398385126298621[/C][/ROW]
[ROW][C]46[/C][C]102.4[/C][C]102.401769072726[/C][C]-0.00176907272606286[/C][/ROW]
[ROW][C]47[/C][C]102.4[/C][C]102.469126930688[/C][C]-0.0691269306875313[/C][/ROW]
[ROW][C]48[/C][C]102.4[/C][C]102.4710546909[/C][C]-0.0710546909002687[/C][/ROW]
[ROW][C]49[/C][C]102.9[/C][C]102.467512247021[/C][C]0.432487752979412[/C][/ROW]
[ROW][C]50[/C][C]102.9[/C][C]102.948711592626[/C][C]-0.0487115926261481[/C][/ROW]
[ROW][C]51[/C][C]102.9[/C][C]102.985666304795[/C][C]-0.0856663047950263[/C][/ROW]
[ROW][C]52[/C][C]104.9[/C][C]102.984237500007[/C][C]1.91576249999277[/C][/ROW]
[ROW][C]53[/C][C]104.9[/C][C]104.919757915656[/C][C]-0.0197579156561005[/C][/ROW]
[ROW][C]54[/C][C]105.5[/C][C]105.077575712307[/C][C]0.42242428769309[/C][/ROW]
[ROW][C]55[/C][C]105.5[/C][C]105.663286727426[/C][C]-0.163286727425699[/C][/ROW]
[ROW][C]56[/C][C]105.5[/C][C]105.702851364702[/C][C]-0.202851364702184[/C][/ROW]
[ROW][C]57[/C][C]105.5[/C][C]105.695533549724[/C][C]-0.195533549723649[/C][/ROW]
[ROW][C]58[/C][C]105.5[/C][C]105.684749248998[/C][C]-0.184749248998401[/C][/ROW]
[ROW][C]59[/C][C]105.5[/C][C]105.674242121616[/C][C]-0.174242121615521[/C][/ROW]
[ROW][C]60[/C][C]105.5[/C][C]105.664304971414[/C][C]-0.164304971413657[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287312&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287312&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	100	100	-5.6843418860808e-14
14	100	100	1.4210854715202e-14
15	100	100	1.4210854715202e-14
16	100	100	1.4210854715202e-14
17	100	100	1.4210854715202e-14
18	100	100	0
19	100	100	0
20	100	100	0
21	100	100	0
22	100	100	0
23	100	100	0
24	100	100	0
25	100.4	100	0.400000000000006
26	100.4	100.388004982897	0.0119950171025209
27	100.4	100.420473005561	-0.0204730055612004
28	100.4	100.42207136346	-0.0220713634604266
29	100.4	100.421053023989	-0.0210530239885571
30	100.4	100.419872970889	-0.0198729708892813
31	100.4	100.418741105314	-0.0187411053144189
32	100.4	100.417672144015	-0.0176721440151226
33	100.4	100.416664018619	-0.0166640186192097
34	100.4	100.415713390935	-0.0157133909354599
35	101.4	100.414816992418	0.985183007581583
36	101.4	101.383984187714	0.0160158122863265
37	102	101.464357201903	0.535642798097015
38	102	102.049608997246	-0.0496089972464233
39	102.6	102.095056483687	0.504943516313404
40	102.6	102.675843092259	-0.075843092258566
41	102.6	102.71955780589	-0.119557805890139
42	102.6	102.716918660503	-0.116918660503217
43	102.6	102.710612737274	-0.110612737273698
44	102.6	102.704334307741	-0.104334307740956
45	102.3	102.698385126299	-0.398385126298621
46	102.4	102.401769072726	-0.00176907272606286
47	102.4	102.469126930688	-0.0691269306875313
48	102.4	102.4710546909	-0.0710546909002687
49	102.9	102.467512247021	0.432487752979412
50	102.9	102.948711592626	-0.0487115926261481
51	102.9	102.985666304795	-0.0856663047950263
52	104.9	102.984237500007	1.91576249999277
53	104.9	104.919757915656	-0.0197579156561005
54	105.5	105.077575712307	0.42242428769309
55	105.5	105.663286727426	-0.163286727425699
56	105.5	105.702851364702	-0.202851364702184
57	105.5	105.695533549724	-0.195533549723649
58	105.5	105.684749248998	-0.184749248998401
59	105.5	105.674242121616	-0.174242121615521
60	105.5	105.664304971414	-0.164304971413657

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	105.654932143183	104.955041720979	106.354822565387
62	105.796379890835	104.821313169955	106.771446611715
63	105.937827638486	104.728494601141	107.147160675831
64	106.079275386138	104.655302813979	107.503247958296
65	106.220723133789	104.593133808644	107.848312458934
66	106.362170881441	104.537563746072	108.18677801681
67	106.503618629092	104.485999270635	108.52123798755
68	106.645066376744	104.436787755078	108.85334499841
69	106.786514124395	104.38881347329	109.1842147755
70	106.927961872047	104.341290820703	109.514632923391
71	107.069409619699	104.293648814877	109.84517042452
72	107.21085736735	104.245462183989	110.176252550711

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 105.654932143183 & 104.955041720979 & 106.354822565387 \tabularnewline
62 & 105.796379890835 & 104.821313169955 & 106.771446611715 \tabularnewline
63 & 105.937827638486 & 104.728494601141 & 107.147160675831 \tabularnewline
64 & 106.079275386138 & 104.655302813979 & 107.503247958296 \tabularnewline
65 & 106.220723133789 & 104.593133808644 & 107.848312458934 \tabularnewline
66 & 106.362170881441 & 104.537563746072 & 108.18677801681 \tabularnewline
67 & 106.503618629092 & 104.485999270635 & 108.52123798755 \tabularnewline
68 & 106.645066376744 & 104.436787755078 & 108.85334499841 \tabularnewline
69 & 106.786514124395 & 104.38881347329 & 109.1842147755 \tabularnewline
70 & 106.927961872047 & 104.341290820703 & 109.514632923391 \tabularnewline
71 & 107.069409619699 & 104.293648814877 & 109.84517042452 \tabularnewline
72 & 107.21085736735 & 104.245462183989 & 110.176252550711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287312&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]105.654932143183[/C][C]104.955041720979[/C][C]106.354822565387[/C][/ROW]
[ROW][C]62[/C][C]105.796379890835[/C][C]104.821313169955[/C][C]106.771446611715[/C][/ROW]
[ROW][C]63[/C][C]105.937827638486[/C][C]104.728494601141[/C][C]107.147160675831[/C][/ROW]
[ROW][C]64[/C][C]106.079275386138[/C][C]104.655302813979[/C][C]107.503247958296[/C][/ROW]
[ROW][C]65[/C][C]106.220723133789[/C][C]104.593133808644[/C][C]107.848312458934[/C][/ROW]
[ROW][C]66[/C][C]106.362170881441[/C][C]104.537563746072[/C][C]108.18677801681[/C][/ROW]
[ROW][C]67[/C][C]106.503618629092[/C][C]104.485999270635[/C][C]108.52123798755[/C][/ROW]
[ROW][C]68[/C][C]106.645066376744[/C][C]104.436787755078[/C][C]108.85334499841[/C][/ROW]
[ROW][C]69[/C][C]106.786514124395[/C][C]104.38881347329[/C][C]109.1842147755[/C][/ROW]
[ROW][C]70[/C][C]106.927961872047[/C][C]104.341290820703[/C][C]109.514632923391[/C][/ROW]
[ROW][C]71[/C][C]107.069409619699[/C][C]104.293648814877[/C][C]109.84517042452[/C][/ROW]
[ROW][C]72[/C][C]107.21085736735[/C][C]104.245462183989[/C][C]110.176252550711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287312&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287312&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	105.654932143183	104.955041720979	106.354822565387
62	105.796379890835	104.821313169955	106.771446611715
63	105.937827638486	104.728494601141	107.147160675831
64	106.079275386138	104.655302813979	107.503247958296
65	106.220723133789	104.593133808644	107.848312458934
66	106.362170881441	104.537563746072	108.18677801681
67	106.503618629092	104.485999270635	108.52123798755
68	106.645066376744	104.436787755078	108.85334499841
69	106.786514124395	104.38881347329	109.1842147755
70	106.927961872047	104.341290820703	109.514632923391
71	107.069409619699	104.293648814877	109.84517042452
72	107.21085736735	104.245462183989	110.176252550711

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 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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