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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 19 Dec 2016 09:49:31 +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/Dec/19/t1482141069q16wu034racdi6b.htm/, Retrieved Fri, 17 May 2024 02:35:38 +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 02:35:38 +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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.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]'Herman Ole Andreas Wold' @ wold.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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.913939878081109
beta	0.0243895828387854
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.913939878081109 \tabularnewline
beta & 0.0243895828387854 \tabularnewline
gamma & 0 \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]0.913939878081109[/C][/ROW]
[ROW][C]beta[/C][C]0.0243895828387854[/C][/ROW]
[ROW][C]gamma[/C][C]0[/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	0.913939878081109
beta	0.0243895828387854
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	103.85	103.381784188034	0.468215811965763
14	104.78	104.756193972108	0.02380602789205
15	104.76	104.781220583247	-0.0212205832470005
16	104.84	104.860455892429	-0.02045589242924
17	104.85	104.869934108675	-0.019934108675443
18	104.83	104.861528193746	-0.0315281937459844
19	104.83	104.888906532709	-0.0589065327086473
20	103.71	103.772866319878	-0.0628663198779265
21	103.84	103.905139104211	-0.0651391042105303
22	104.37	104.180132709785	0.189867290214536
23	104.44	104.608669086558	-0.168669086558324
24	104.4	104.532431700296	-0.132431700295797
25	99.54	104.416777789386	-4.8767777893864
26	100.42	100.789287095607	-0.369287095606666
27	100.34	100.329390261452	0.0106097385482542
28	100.36	100.31276612449	0.0472338755096047
29	100.37	100.260667118808	0.109332881192174
30	100.42	100.249843301015	0.170156698985366
31	100.41	100.345485026192	0.0645149738083148
32	99.13	99.2289313108798	-0.0989313108797916
33	99.42	99.2141256118989	0.205874388101137
34	99.76	99.6287330624643	0.131266937535742
35	99.92	99.8943298091771	0.0256701908229218
36	99.92	99.8906563490131	0.0293436509868883
37	100.47	99.8214109651997	0.648589034800253
38	100.44	101.265492745397	-0.825492745397369
39	100.47	100.400201664321	0.0697983356790957
40	100.61	100.450541985708	0.159458014291673
41	100.73	100.516380279621	0.213619720379072
42	100.64	100.618564164306	0.0214358356941773
43	99.99	100.59266468409	-0.602664684090186
44	99.74	98.8658577527193	0.874142247280687
45	99.49	99.7615820674752	-0.271582067475208
46	99.41	99.7503795110968	-0.340379511096828
47	99.49	99.5849629597434	-0.0949629597433983
48	99.53	99.4683922655549	0.0616077344451043
49	99.91	99.426707713318	0.483292286681959
50	99.84	100.71410703703	-0.874107037029844
51	99.67	99.7976906071922	-0.127690607192179
52	99.39	99.6564409497437	-0.266440949743725
53	99.38	99.3124426892107	0.0675573107892546
54	99.29	99.2572879853493	0.0327120146507553
55	97.91	99.2180992799549	-1.30809927995486
56	97.62	96.8072479961196	0.812752003880391
57	97.67	97.6061773492626	0.0638226507374355
58	97.64	97.8683029466704	-0.228302946670425
59	97.63	97.7746042987127	-0.144604298712693
60	97.66	97.5808445311626	0.079155468837385

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 103.85 & 103.381784188034 & 0.468215811965763 \tabularnewline
14 & 104.78 & 104.756193972108 & 0.02380602789205 \tabularnewline
15 & 104.76 & 104.781220583247 & -0.0212205832470005 \tabularnewline
16 & 104.84 & 104.860455892429 & -0.02045589242924 \tabularnewline
17 & 104.85 & 104.869934108675 & -0.019934108675443 \tabularnewline
18 & 104.83 & 104.861528193746 & -0.0315281937459844 \tabularnewline
19 & 104.83 & 104.888906532709 & -0.0589065327086473 \tabularnewline
20 & 103.71 & 103.772866319878 & -0.0628663198779265 \tabularnewline
21 & 103.84 & 103.905139104211 & -0.0651391042105303 \tabularnewline
22 & 104.37 & 104.180132709785 & 0.189867290214536 \tabularnewline
23 & 104.44 & 104.608669086558 & -0.168669086558324 \tabularnewline
24 & 104.4 & 104.532431700296 & -0.132431700295797 \tabularnewline
25 & 99.54 & 104.416777789386 & -4.8767777893864 \tabularnewline
26 & 100.42 & 100.789287095607 & -0.369287095606666 \tabularnewline
27 & 100.34 & 100.329390261452 & 0.0106097385482542 \tabularnewline
28 & 100.36 & 100.31276612449 & 0.0472338755096047 \tabularnewline
29 & 100.37 & 100.260667118808 & 0.109332881192174 \tabularnewline
30 & 100.42 & 100.249843301015 & 0.170156698985366 \tabularnewline
31 & 100.41 & 100.345485026192 & 0.0645149738083148 \tabularnewline
32 & 99.13 & 99.2289313108798 & -0.0989313108797916 \tabularnewline
33 & 99.42 & 99.2141256118989 & 0.205874388101137 \tabularnewline
34 & 99.76 & 99.6287330624643 & 0.131266937535742 \tabularnewline
35 & 99.92 & 99.8943298091771 & 0.0256701908229218 \tabularnewline
36 & 99.92 & 99.8906563490131 & 0.0293436509868883 \tabularnewline
37 & 100.47 & 99.8214109651997 & 0.648589034800253 \tabularnewline
38 & 100.44 & 101.265492745397 & -0.825492745397369 \tabularnewline
39 & 100.47 & 100.400201664321 & 0.0697983356790957 \tabularnewline
40 & 100.61 & 100.450541985708 & 0.159458014291673 \tabularnewline
41 & 100.73 & 100.516380279621 & 0.213619720379072 \tabularnewline
42 & 100.64 & 100.618564164306 & 0.0214358356941773 \tabularnewline
43 & 99.99 & 100.59266468409 & -0.602664684090186 \tabularnewline
44 & 99.74 & 98.8658577527193 & 0.874142247280687 \tabularnewline
45 & 99.49 & 99.7615820674752 & -0.271582067475208 \tabularnewline
46 & 99.41 & 99.7503795110968 & -0.340379511096828 \tabularnewline
47 & 99.49 & 99.5849629597434 & -0.0949629597433983 \tabularnewline
48 & 99.53 & 99.4683922655549 & 0.0616077344451043 \tabularnewline
49 & 99.91 & 99.426707713318 & 0.483292286681959 \tabularnewline
50 & 99.84 & 100.71410703703 & -0.874107037029844 \tabularnewline
51 & 99.67 & 99.7976906071922 & -0.127690607192179 \tabularnewline
52 & 99.39 & 99.6564409497437 & -0.266440949743725 \tabularnewline
53 & 99.38 & 99.3124426892107 & 0.0675573107892546 \tabularnewline
54 & 99.29 & 99.2572879853493 & 0.0327120146507553 \tabularnewline
55 & 97.91 & 99.2180992799549 & -1.30809927995486 \tabularnewline
56 & 97.62 & 96.8072479961196 & 0.812752003880391 \tabularnewline
57 & 97.67 & 97.6061773492626 & 0.0638226507374355 \tabularnewline
58 & 97.64 & 97.8683029466704 & -0.228302946670425 \tabularnewline
59 & 97.63 & 97.7746042987127 & -0.144604298712693 \tabularnewline
60 & 97.66 & 97.5808445311626 & 0.079155468837385 \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]103.85[/C][C]103.381784188034[/C][C]0.468215811965763[/C][/ROW]
[ROW][C]14[/C][C]104.78[/C][C]104.756193972108[/C][C]0.02380602789205[/C][/ROW]
[ROW][C]15[/C][C]104.76[/C][C]104.781220583247[/C][C]-0.0212205832470005[/C][/ROW]
[ROW][C]16[/C][C]104.84[/C][C]104.860455892429[/C][C]-0.02045589242924[/C][/ROW]
[ROW][C]17[/C][C]104.85[/C][C]104.869934108675[/C][C]-0.019934108675443[/C][/ROW]
[ROW][C]18[/C][C]104.83[/C][C]104.861528193746[/C][C]-0.0315281937459844[/C][/ROW]
[ROW][C]19[/C][C]104.83[/C][C]104.888906532709[/C][C]-0.0589065327086473[/C][/ROW]
[ROW][C]20[/C][C]103.71[/C][C]103.772866319878[/C][C]-0.0628663198779265[/C][/ROW]
[ROW][C]21[/C][C]103.84[/C][C]103.905139104211[/C][C]-0.0651391042105303[/C][/ROW]
[ROW][C]22[/C][C]104.37[/C][C]104.180132709785[/C][C]0.189867290214536[/C][/ROW]
[ROW][C]23[/C][C]104.44[/C][C]104.608669086558[/C][C]-0.168669086558324[/C][/ROW]
[ROW][C]24[/C][C]104.4[/C][C]104.532431700296[/C][C]-0.132431700295797[/C][/ROW]
[ROW][C]25[/C][C]99.54[/C][C]104.416777789386[/C][C]-4.8767777893864[/C][/ROW]
[ROW][C]26[/C][C]100.42[/C][C]100.789287095607[/C][C]-0.369287095606666[/C][/ROW]
[ROW][C]27[/C][C]100.34[/C][C]100.329390261452[/C][C]0.0106097385482542[/C][/ROW]
[ROW][C]28[/C][C]100.36[/C][C]100.31276612449[/C][C]0.0472338755096047[/C][/ROW]
[ROW][C]29[/C][C]100.37[/C][C]100.260667118808[/C][C]0.109332881192174[/C][/ROW]
[ROW][C]30[/C][C]100.42[/C][C]100.249843301015[/C][C]0.170156698985366[/C][/ROW]
[ROW][C]31[/C][C]100.41[/C][C]100.345485026192[/C][C]0.0645149738083148[/C][/ROW]
[ROW][C]32[/C][C]99.13[/C][C]99.2289313108798[/C][C]-0.0989313108797916[/C][/ROW]
[ROW][C]33[/C][C]99.42[/C][C]99.2141256118989[/C][C]0.205874388101137[/C][/ROW]
[ROW][C]34[/C][C]99.76[/C][C]99.6287330624643[/C][C]0.131266937535742[/C][/ROW]
[ROW][C]35[/C][C]99.92[/C][C]99.8943298091771[/C][C]0.0256701908229218[/C][/ROW]
[ROW][C]36[/C][C]99.92[/C][C]99.8906563490131[/C][C]0.0293436509868883[/C][/ROW]
[ROW][C]37[/C][C]100.47[/C][C]99.8214109651997[/C][C]0.648589034800253[/C][/ROW]
[ROW][C]38[/C][C]100.44[/C][C]101.265492745397[/C][C]-0.825492745397369[/C][/ROW]
[ROW][C]39[/C][C]100.47[/C][C]100.400201664321[/C][C]0.0697983356790957[/C][/ROW]
[ROW][C]40[/C][C]100.61[/C][C]100.450541985708[/C][C]0.159458014291673[/C][/ROW]
[ROW][C]41[/C][C]100.73[/C][C]100.516380279621[/C][C]0.213619720379072[/C][/ROW]
[ROW][C]42[/C][C]100.64[/C][C]100.618564164306[/C][C]0.0214358356941773[/C][/ROW]
[ROW][C]43[/C][C]99.99[/C][C]100.59266468409[/C][C]-0.602664684090186[/C][/ROW]
[ROW][C]44[/C][C]99.74[/C][C]98.8658577527193[/C][C]0.874142247280687[/C][/ROW]
[ROW][C]45[/C][C]99.49[/C][C]99.7615820674752[/C][C]-0.271582067475208[/C][/ROW]
[ROW][C]46[/C][C]99.41[/C][C]99.7503795110968[/C][C]-0.340379511096828[/C][/ROW]
[ROW][C]47[/C][C]99.49[/C][C]99.5849629597434[/C][C]-0.0949629597433983[/C][/ROW]
[ROW][C]48[/C][C]99.53[/C][C]99.4683922655549[/C][C]0.0616077344451043[/C][/ROW]
[ROW][C]49[/C][C]99.91[/C][C]99.426707713318[/C][C]0.483292286681959[/C][/ROW]
[ROW][C]50[/C][C]99.84[/C][C]100.71410703703[/C][C]-0.874107037029844[/C][/ROW]
[ROW][C]51[/C][C]99.67[/C][C]99.7976906071922[/C][C]-0.127690607192179[/C][/ROW]
[ROW][C]52[/C][C]99.39[/C][C]99.6564409497437[/C][C]-0.266440949743725[/C][/ROW]
[ROW][C]53[/C][C]99.38[/C][C]99.3124426892107[/C][C]0.0675573107892546[/C][/ROW]
[ROW][C]54[/C][C]99.29[/C][C]99.2572879853493[/C][C]0.0327120146507553[/C][/ROW]
[ROW][C]55[/C][C]97.91[/C][C]99.2180992799549[/C][C]-1.30809927995486[/C][/ROW]
[ROW][C]56[/C][C]97.62[/C][C]96.8072479961196[/C][C]0.812752003880391[/C][/ROW]
[ROW][C]57[/C][C]97.67[/C][C]97.6061773492626[/C][C]0.0638226507374355[/C][/ROW]
[ROW][C]58[/C][C]97.64[/C][C]97.8683029466704[/C][C]-0.228302946670425[/C][/ROW]
[ROW][C]59[/C][C]97.63[/C][C]97.7746042987127[/C][C]-0.144604298712693[/C][/ROW]
[ROW][C]60[/C][C]97.66[/C][C]97.5808445311626[/C][C]0.079155468837385[/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	103.85	103.381784188034	0.468215811965763
14	104.78	104.756193972108	0.02380602789205
15	104.76	104.781220583247	-0.0212205832470005
16	104.84	104.860455892429	-0.02045589242924
17	104.85	104.869934108675	-0.019934108675443
18	104.83	104.861528193746	-0.0315281937459844
19	104.83	104.888906532709	-0.0589065327086473
20	103.71	103.772866319878	-0.0628663198779265
21	103.84	103.905139104211	-0.0651391042105303
22	104.37	104.180132709785	0.189867290214536
23	104.44	104.608669086558	-0.168669086558324
24	104.4	104.532431700296	-0.132431700295797
25	99.54	104.416777789386	-4.8767777893864
26	100.42	100.789287095607	-0.369287095606666
27	100.34	100.329390261452	0.0106097385482542
28	100.36	100.31276612449	0.0472338755096047
29	100.37	100.260667118808	0.109332881192174
30	100.42	100.249843301015	0.170156698985366
31	100.41	100.345485026192	0.0645149738083148
32	99.13	99.2289313108798	-0.0989313108797916
33	99.42	99.2141256118989	0.205874388101137
34	99.76	99.6287330624643	0.131266937535742
35	99.92	99.8943298091771	0.0256701908229218
36	99.92	99.8906563490131	0.0293436509868883
37	100.47	99.8214109651997	0.648589034800253
38	100.44	101.265492745397	-0.825492745397369
39	100.47	100.400201664321	0.0697983356790957
40	100.61	100.450541985708	0.159458014291673
41	100.73	100.516380279621	0.213619720379072
42	100.64	100.618564164306	0.0214358356941773
43	99.99	100.59266468409	-0.602664684090186
44	99.74	98.8658577527193	0.874142247280687
45	99.49	99.7615820674752	-0.271582067475208
46	99.41	99.7503795110968	-0.340379511096828
47	99.49	99.5849629597434	-0.0949629597433983
48	99.53	99.4683922655549	0.0616077344451043
49	99.91	99.426707713318	0.483292286681959
50	99.84	100.71410703703	-0.874107037029844
51	99.67	99.7976906071922	-0.127690607192179
52	99.39	99.6564409497437	-0.266440949743725
53	99.38	99.3124426892107	0.0675573107892546
54	99.29	99.2572879853493	0.0327120146507553
55	97.91	99.2180992799549	-1.30809927995486
56	97.62	96.8072479961196	0.812752003880391
57	97.67	97.6061773492626	0.0638226507374355
58	97.64	97.8683029466704	-0.228302946670425
59	97.63	97.7746042987127	-0.144604298712693
60	97.66	97.5808445311626	0.079155468837385

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	97.5237688288259	95.966504879275	99.0810327783767
62	98.3272664536171	96.194026543808	100.460506363426
63	98.1870140784083	95.5834055611126	100.790622595704
64	98.1425950365329	95.1240398687381	101.161150204328
65	98.0281759946575	94.6293796814441	101.426972307871
66	97.8958402861154	94.140629181362	101.651051390869
67	97.8105879109066	93.7162665525464	101.904909269267
68	96.6082522023645	92.1878679307938	101.028636473935
69	96.6592498271558	91.9229000188549	101.395599635457
70	96.856497451947	91.812142738299	101.900852165595
71	96.9699950767383	91.6239945233587	102.315995630118
72	96.9101593681962	91.2676385022763	102.552680234116

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 97.5237688288259 & 95.966504879275 & 99.0810327783767 \tabularnewline
62 & 98.3272664536171 & 96.194026543808 & 100.460506363426 \tabularnewline
63 & 98.1870140784083 & 95.5834055611126 & 100.790622595704 \tabularnewline
64 & 98.1425950365329 & 95.1240398687381 & 101.161150204328 \tabularnewline
65 & 98.0281759946575 & 94.6293796814441 & 101.426972307871 \tabularnewline
66 & 97.8958402861154 & 94.140629181362 & 101.651051390869 \tabularnewline
67 & 97.8105879109066 & 93.7162665525464 & 101.904909269267 \tabularnewline
68 & 96.6082522023645 & 92.1878679307938 & 101.028636473935 \tabularnewline
69 & 96.6592498271558 & 91.9229000188549 & 101.395599635457 \tabularnewline
70 & 96.856497451947 & 91.812142738299 & 101.900852165595 \tabularnewline
71 & 96.9699950767383 & 91.6239945233587 & 102.315995630118 \tabularnewline
72 & 96.9101593681962 & 91.2676385022763 & 102.552680234116 \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]97.5237688288259[/C][C]95.966504879275[/C][C]99.0810327783767[/C][/ROW]
[ROW][C]62[/C][C]98.3272664536171[/C][C]96.194026543808[/C][C]100.460506363426[/C][/ROW]
[ROW][C]63[/C][C]98.1870140784083[/C][C]95.5834055611126[/C][C]100.790622595704[/C][/ROW]
[ROW][C]64[/C][C]98.1425950365329[/C][C]95.1240398687381[/C][C]101.161150204328[/C][/ROW]
[ROW][C]65[/C][C]98.0281759946575[/C][C]94.6293796814441[/C][C]101.426972307871[/C][/ROW]
[ROW][C]66[/C][C]97.8958402861154[/C][C]94.140629181362[/C][C]101.651051390869[/C][/ROW]
[ROW][C]67[/C][C]97.8105879109066[/C][C]93.7162665525464[/C][C]101.904909269267[/C][/ROW]
[ROW][C]68[/C][C]96.6082522023645[/C][C]92.1878679307938[/C][C]101.028636473935[/C][/ROW]
[ROW][C]69[/C][C]96.6592498271558[/C][C]91.9229000188549[/C][C]101.395599635457[/C][/ROW]
[ROW][C]70[/C][C]96.856497451947[/C][C]91.812142738299[/C][C]101.900852165595[/C][/ROW]
[ROW][C]71[/C][C]96.9699950767383[/C][C]91.6239945233587[/C][C]102.315995630118[/C][/ROW]
[ROW][C]72[/C][C]96.9101593681962[/C][C]91.2676385022763[/C][C]102.552680234116[/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	97.5237688288259	95.966504879275	99.0810327783767
62	98.3272664536171	96.194026543808	100.460506363426
63	98.1870140784083	95.5834055611126	100.790622595704
64	98.1425950365329	95.1240398687381	101.161150204328
65	98.0281759946575	94.6293796814441	101.426972307871
66	97.8958402861154	94.140629181362	101.651051390869
67	97.8105879109066	93.7162665525464	101.904909269267
68	96.6082522023645	92.1878679307938	101.028636473935
69	96.6592498271558	91.9229000188549	101.395599635457
70	96.856497451947	91.812142738299	101.900852165595
71	96.9699950767383	91.6239945233587	102.315995630118
72	96.9101593681962	91.2676385022763	102.552680234116

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):

par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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