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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 27 May 2012 10:23:48 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/27/t133812871525vq6804qfu53t9.htm/, Retrieved Wed, 08 May 2024 21:53:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167716, Retrieved Wed, 08 May 2024 21:53:15 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Kleding en kledin...] [2012-05-27 14:23:48] [675223405f94cd8491f4a89fc80aa26c] [Current]
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Dataseries X:
219,20
232,50
235,60
171,00
165,90
187,60
218,20
249,80
256,50
224,90
200,00
182,50
230,30
252,80
270,60
196,90
184,70
202,50
258,20
283,10
268,50
283,80
231,10
212,10
238,50
262,80
245,50
198,20
167,20
184,20
254,90
246,40
264,50
242,40
186,70
254,70
230,10
253,60
228,00
183,80
150,00
178,50
228,40
228,70
236,70
218,20
173,50
189,10
194,60
213,70
216,30
173,90
156,90
182,90
216,40
234,00
257,30
225,70
201,70
189,20




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167716&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167716&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167716&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.374221376292511
beta0.0593536059183779
gamma0.591507822483036

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.374221376292511 \tabularnewline
beta & 0.0593536059183779 \tabularnewline
gamma & 0.591507822483036 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167716&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]0.374221376292511[/C][/ROW]
[ROW][C]beta[/C][C]0.0593536059183779[/C][/ROW]
[ROW][C]gamma[/C][C]0.591507822483036[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167716&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167716&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
ParameterValue
alpha0.374221376292511
beta0.0593536059183779
gamma0.591507822483036







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13230.3218.06472841699412.2352715830065
14252.8244.0228896409418.77711035905915
15270.6265.8388508931264.7611491068742
16196.9194.6989047508612.2010952491388
17184.7182.7941526485621.9058473514375
18202.5201.6014788429690.89852115703107
19258.2247.20106512912710.9989348708727
20283.1289.756798138329-6.65679813832946
21268.5295.539614943488-27.0396149434878
22283.8250.05165060661633.7483493933837
23231.1234.665285384658-3.56528538465849
24212.1214.252407369546-2.1524073695459
25238.5275.3881699606-36.8881699605996
26262.8284.013510175194-21.2135101751941
27245.5293.569820210487-48.0698202104872
28198.2198.440729926364-0.240729926364224
29167.2183.909797185226-16.7097971852262
30184.2192.825632574492-8.6256325744917
31254.9232.93799966333221.9620003366675
32246.4268.712397515681-22.3123975156807
33264.5257.9377366499666.56226335003424
34242.4245.60280637579-3.20280637578955
35186.7205.01831402146-18.3183140214602
36254.7180.07233097307874.6276690269218
37230.1254.253435961407-24.153435961407
38253.6271.971737231726-18.3717372317261
39228270.50473809149-42.5047380914896
40183.8195.234486040439-11.4344860404392
41150170.173627955861-20.1736279558606
42178.5178.817927181645-0.317927181645388
43228.4229.790309637455-1.39030963745492
44228.7237.713300086193-9.01330008619266
45236.7240.610991193787-3.91099119378708
46218.2220.911012208803-2.71101220880283
47173.5177.81735901251-4.31735901250988
48189.1186.8039043486582.29609565134194
49194.6192.6011854001661.99881459983433
50213.7214.519228318078-0.819228318077904
51216.3208.4800225525967.81997744740357
52173.9168.0798944856965.82010551430412
53156.9147.579729692069.32027030794038
54182.9174.1742172093998.72578279060079
55216.4228.3162990006-11.9162990006002
56234229.5820324609444.41796753905609
57257.3239.99833422004117.3016657799592
58225.7229.051139396847-3.35113939684743
59201.7184.19965830476717.5003416952328
60189.2206.471506498399-17.2715064983994

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 230.3 & 218.064728416994 & 12.2352715830065 \tabularnewline
14 & 252.8 & 244.022889640941 & 8.77711035905915 \tabularnewline
15 & 270.6 & 265.838850893126 & 4.7611491068742 \tabularnewline
16 & 196.9 & 194.698904750861 & 2.2010952491388 \tabularnewline
17 & 184.7 & 182.794152648562 & 1.9058473514375 \tabularnewline
18 & 202.5 & 201.601478842969 & 0.89852115703107 \tabularnewline
19 & 258.2 & 247.201065129127 & 10.9989348708727 \tabularnewline
20 & 283.1 & 289.756798138329 & -6.65679813832946 \tabularnewline
21 & 268.5 & 295.539614943488 & -27.0396149434878 \tabularnewline
22 & 283.8 & 250.051650606616 & 33.7483493933837 \tabularnewline
23 & 231.1 & 234.665285384658 & -3.56528538465849 \tabularnewline
24 & 212.1 & 214.252407369546 & -2.1524073695459 \tabularnewline
25 & 238.5 & 275.3881699606 & -36.8881699605996 \tabularnewline
26 & 262.8 & 284.013510175194 & -21.2135101751941 \tabularnewline
27 & 245.5 & 293.569820210487 & -48.0698202104872 \tabularnewline
28 & 198.2 & 198.440729926364 & -0.240729926364224 \tabularnewline
29 & 167.2 & 183.909797185226 & -16.7097971852262 \tabularnewline
30 & 184.2 & 192.825632574492 & -8.6256325744917 \tabularnewline
31 & 254.9 & 232.937999663332 & 21.9620003366675 \tabularnewline
32 & 246.4 & 268.712397515681 & -22.3123975156807 \tabularnewline
33 & 264.5 & 257.937736649966 & 6.56226335003424 \tabularnewline
34 & 242.4 & 245.60280637579 & -3.20280637578955 \tabularnewline
35 & 186.7 & 205.01831402146 & -18.3183140214602 \tabularnewline
36 & 254.7 & 180.072330973078 & 74.6276690269218 \tabularnewline
37 & 230.1 & 254.253435961407 & -24.153435961407 \tabularnewline
38 & 253.6 & 271.971737231726 & -18.3717372317261 \tabularnewline
39 & 228 & 270.50473809149 & -42.5047380914896 \tabularnewline
40 & 183.8 & 195.234486040439 & -11.4344860404392 \tabularnewline
41 & 150 & 170.173627955861 & -20.1736279558606 \tabularnewline
42 & 178.5 & 178.817927181645 & -0.317927181645388 \tabularnewline
43 & 228.4 & 229.790309637455 & -1.39030963745492 \tabularnewline
44 & 228.7 & 237.713300086193 & -9.01330008619266 \tabularnewline
45 & 236.7 & 240.610991193787 & -3.91099119378708 \tabularnewline
46 & 218.2 & 220.911012208803 & -2.71101220880283 \tabularnewline
47 & 173.5 & 177.81735901251 & -4.31735901250988 \tabularnewline
48 & 189.1 & 186.803904348658 & 2.29609565134194 \tabularnewline
49 & 194.6 & 192.601185400166 & 1.99881459983433 \tabularnewline
50 & 213.7 & 214.519228318078 & -0.819228318077904 \tabularnewline
51 & 216.3 & 208.480022552596 & 7.81997744740357 \tabularnewline
52 & 173.9 & 168.079894485696 & 5.82010551430412 \tabularnewline
53 & 156.9 & 147.57972969206 & 9.32027030794038 \tabularnewline
54 & 182.9 & 174.174217209399 & 8.72578279060079 \tabularnewline
55 & 216.4 & 228.3162990006 & -11.9162990006002 \tabularnewline
56 & 234 & 229.582032460944 & 4.41796753905609 \tabularnewline
57 & 257.3 & 239.998334220041 & 17.3016657799592 \tabularnewline
58 & 225.7 & 229.051139396847 & -3.35113939684743 \tabularnewline
59 & 201.7 & 184.199658304767 & 17.5003416952328 \tabularnewline
60 & 189.2 & 206.471506498399 & -17.2715064983994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167716&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]230.3[/C][C]218.064728416994[/C][C]12.2352715830065[/C][/ROW]
[ROW][C]14[/C][C]252.8[/C][C]244.022889640941[/C][C]8.77711035905915[/C][/ROW]
[ROW][C]15[/C][C]270.6[/C][C]265.838850893126[/C][C]4.7611491068742[/C][/ROW]
[ROW][C]16[/C][C]196.9[/C][C]194.698904750861[/C][C]2.2010952491388[/C][/ROW]
[ROW][C]17[/C][C]184.7[/C][C]182.794152648562[/C][C]1.9058473514375[/C][/ROW]
[ROW][C]18[/C][C]202.5[/C][C]201.601478842969[/C][C]0.89852115703107[/C][/ROW]
[ROW][C]19[/C][C]258.2[/C][C]247.201065129127[/C][C]10.9989348708727[/C][/ROW]
[ROW][C]20[/C][C]283.1[/C][C]289.756798138329[/C][C]-6.65679813832946[/C][/ROW]
[ROW][C]21[/C][C]268.5[/C][C]295.539614943488[/C][C]-27.0396149434878[/C][/ROW]
[ROW][C]22[/C][C]283.8[/C][C]250.051650606616[/C][C]33.7483493933837[/C][/ROW]
[ROW][C]23[/C][C]231.1[/C][C]234.665285384658[/C][C]-3.56528538465849[/C][/ROW]
[ROW][C]24[/C][C]212.1[/C][C]214.252407369546[/C][C]-2.1524073695459[/C][/ROW]
[ROW][C]25[/C][C]238.5[/C][C]275.3881699606[/C][C]-36.8881699605996[/C][/ROW]
[ROW][C]26[/C][C]262.8[/C][C]284.013510175194[/C][C]-21.2135101751941[/C][/ROW]
[ROW][C]27[/C][C]245.5[/C][C]293.569820210487[/C][C]-48.0698202104872[/C][/ROW]
[ROW][C]28[/C][C]198.2[/C][C]198.440729926364[/C][C]-0.240729926364224[/C][/ROW]
[ROW][C]29[/C][C]167.2[/C][C]183.909797185226[/C][C]-16.7097971852262[/C][/ROW]
[ROW][C]30[/C][C]184.2[/C][C]192.825632574492[/C][C]-8.6256325744917[/C][/ROW]
[ROW][C]31[/C][C]254.9[/C][C]232.937999663332[/C][C]21.9620003366675[/C][/ROW]
[ROW][C]32[/C][C]246.4[/C][C]268.712397515681[/C][C]-22.3123975156807[/C][/ROW]
[ROW][C]33[/C][C]264.5[/C][C]257.937736649966[/C][C]6.56226335003424[/C][/ROW]
[ROW][C]34[/C][C]242.4[/C][C]245.60280637579[/C][C]-3.20280637578955[/C][/ROW]
[ROW][C]35[/C][C]186.7[/C][C]205.01831402146[/C][C]-18.3183140214602[/C][/ROW]
[ROW][C]36[/C][C]254.7[/C][C]180.072330973078[/C][C]74.6276690269218[/C][/ROW]
[ROW][C]37[/C][C]230.1[/C][C]254.253435961407[/C][C]-24.153435961407[/C][/ROW]
[ROW][C]38[/C][C]253.6[/C][C]271.971737231726[/C][C]-18.3717372317261[/C][/ROW]
[ROW][C]39[/C][C]228[/C][C]270.50473809149[/C][C]-42.5047380914896[/C][/ROW]
[ROW][C]40[/C][C]183.8[/C][C]195.234486040439[/C][C]-11.4344860404392[/C][/ROW]
[ROW][C]41[/C][C]150[/C][C]170.173627955861[/C][C]-20.1736279558606[/C][/ROW]
[ROW][C]42[/C][C]178.5[/C][C]178.817927181645[/C][C]-0.317927181645388[/C][/ROW]
[ROW][C]43[/C][C]228.4[/C][C]229.790309637455[/C][C]-1.39030963745492[/C][/ROW]
[ROW][C]44[/C][C]228.7[/C][C]237.713300086193[/C][C]-9.01330008619266[/C][/ROW]
[ROW][C]45[/C][C]236.7[/C][C]240.610991193787[/C][C]-3.91099119378708[/C][/ROW]
[ROW][C]46[/C][C]218.2[/C][C]220.911012208803[/C][C]-2.71101220880283[/C][/ROW]
[ROW][C]47[/C][C]173.5[/C][C]177.81735901251[/C][C]-4.31735901250988[/C][/ROW]
[ROW][C]48[/C][C]189.1[/C][C]186.803904348658[/C][C]2.29609565134194[/C][/ROW]
[ROW][C]49[/C][C]194.6[/C][C]192.601185400166[/C][C]1.99881459983433[/C][/ROW]
[ROW][C]50[/C][C]213.7[/C][C]214.519228318078[/C][C]-0.819228318077904[/C][/ROW]
[ROW][C]51[/C][C]216.3[/C][C]208.480022552596[/C][C]7.81997744740357[/C][/ROW]
[ROW][C]52[/C][C]173.9[/C][C]168.079894485696[/C][C]5.82010551430412[/C][/ROW]
[ROW][C]53[/C][C]156.9[/C][C]147.57972969206[/C][C]9.32027030794038[/C][/ROW]
[ROW][C]54[/C][C]182.9[/C][C]174.174217209399[/C][C]8.72578279060079[/C][/ROW]
[ROW][C]55[/C][C]216.4[/C][C]228.3162990006[/C][C]-11.9162990006002[/C][/ROW]
[ROW][C]56[/C][C]234[/C][C]229.582032460944[/C][C]4.41796753905609[/C][/ROW]
[ROW][C]57[/C][C]257.3[/C][C]239.998334220041[/C][C]17.3016657799592[/C][/ROW]
[ROW][C]58[/C][C]225.7[/C][C]229.051139396847[/C][C]-3.35113939684743[/C][/ROW]
[ROW][C]59[/C][C]201.7[/C][C]184.199658304767[/C][C]17.5003416952328[/C][/ROW]
[ROW][C]60[/C][C]189.2[/C][C]206.471506498399[/C][C]-17.2715064983994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167716&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167716&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
tObservedFittedResiduals
13230.3218.06472841699412.2352715830065
14252.8244.0228896409418.77711035905915
15270.6265.8388508931264.7611491068742
16196.9194.6989047508612.2010952491388
17184.7182.7941526485621.9058473514375
18202.5201.6014788429690.89852115703107
19258.2247.20106512912710.9989348708727
20283.1289.756798138329-6.65679813832946
21268.5295.539614943488-27.0396149434878
22283.8250.05165060661633.7483493933837
23231.1234.665285384658-3.56528538465849
24212.1214.252407369546-2.1524073695459
25238.5275.3881699606-36.8881699605996
26262.8284.013510175194-21.2135101751941
27245.5293.569820210487-48.0698202104872
28198.2198.440729926364-0.240729926364224
29167.2183.909797185226-16.7097971852262
30184.2192.825632574492-8.6256325744917
31254.9232.93799966333221.9620003366675
32246.4268.712397515681-22.3123975156807
33264.5257.9377366499666.56226335003424
34242.4245.60280637579-3.20280637578955
35186.7205.01831402146-18.3183140214602
36254.7180.07233097307874.6276690269218
37230.1254.253435961407-24.153435961407
38253.6271.971737231726-18.3717372317261
39228270.50473809149-42.5047380914896
40183.8195.234486040439-11.4344860404392
41150170.173627955861-20.1736279558606
42178.5178.817927181645-0.317927181645388
43228.4229.790309637455-1.39030963745492
44228.7237.713300086193-9.01330008619266
45236.7240.610991193787-3.91099119378708
46218.2220.911012208803-2.71101220880283
47173.5177.81735901251-4.31735901250988
48189.1186.8039043486582.29609565134194
49194.6192.6011854001661.99881459983433
50213.7214.519228318078-0.819228318077904
51216.3208.4800225525967.81997744740357
52173.9168.0798944856965.82010551430412
53156.9147.579729692069.32027030794038
54182.9174.1742172093998.72578279060079
55216.4228.3162990006-11.9162990006002
56234229.5820324609444.41796753905609
57257.3239.99833422004117.3016657799592
58225.7229.051139396847-3.35113939684743
59201.7184.19965830476717.5003416952328
60189.2206.471506498399-17.2715064983994







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61206.160133267262177.53581723912234.784449295404
62228.632125912916195.389665619629261.874586206203
63226.991512411677190.082427993912263.900596829442
64181.015818283869144.26359319998217.768043367758
65158.997467964379120.88208295545197.112852973308
66182.816779292047137.511555033183228.122003550911
67226.633556276193169.460238241737283.806874310649
68239.227970949675175.324152621506303.131789277843
69253.322876401912181.921409754233324.724343049592
70228.172444807787158.836876872989297.508012742586
71191.848083621458128.123999657699255.572167585217
72194.061071273802-442.430784186659830.552926734263

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 206.160133267262 & 177.53581723912 & 234.784449295404 \tabularnewline
62 & 228.632125912916 & 195.389665619629 & 261.874586206203 \tabularnewline
63 & 226.991512411677 & 190.082427993912 & 263.900596829442 \tabularnewline
64 & 181.015818283869 & 144.26359319998 & 217.768043367758 \tabularnewline
65 & 158.997467964379 & 120.88208295545 & 197.112852973308 \tabularnewline
66 & 182.816779292047 & 137.511555033183 & 228.122003550911 \tabularnewline
67 & 226.633556276193 & 169.460238241737 & 283.806874310649 \tabularnewline
68 & 239.227970949675 & 175.324152621506 & 303.131789277843 \tabularnewline
69 & 253.322876401912 & 181.921409754233 & 324.724343049592 \tabularnewline
70 & 228.172444807787 & 158.836876872989 & 297.508012742586 \tabularnewline
71 & 191.848083621458 & 128.123999657699 & 255.572167585217 \tabularnewline
72 & 194.061071273802 & -442.430784186659 & 830.552926734263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167716&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]206.160133267262[/C][C]177.53581723912[/C][C]234.784449295404[/C][/ROW]
[ROW][C]62[/C][C]228.632125912916[/C][C]195.389665619629[/C][C]261.874586206203[/C][/ROW]
[ROW][C]63[/C][C]226.991512411677[/C][C]190.082427993912[/C][C]263.900596829442[/C][/ROW]
[ROW][C]64[/C][C]181.015818283869[/C][C]144.26359319998[/C][C]217.768043367758[/C][/ROW]
[ROW][C]65[/C][C]158.997467964379[/C][C]120.88208295545[/C][C]197.112852973308[/C][/ROW]
[ROW][C]66[/C][C]182.816779292047[/C][C]137.511555033183[/C][C]228.122003550911[/C][/ROW]
[ROW][C]67[/C][C]226.633556276193[/C][C]169.460238241737[/C][C]283.806874310649[/C][/ROW]
[ROW][C]68[/C][C]239.227970949675[/C][C]175.324152621506[/C][C]303.131789277843[/C][/ROW]
[ROW][C]69[/C][C]253.322876401912[/C][C]181.921409754233[/C][C]324.724343049592[/C][/ROW]
[ROW][C]70[/C][C]228.172444807787[/C][C]158.836876872989[/C][C]297.508012742586[/C][/ROW]
[ROW][C]71[/C][C]191.848083621458[/C][C]128.123999657699[/C][C]255.572167585217[/C][/ROW]
[ROW][C]72[/C][C]194.061071273802[/C][C]-442.430784186659[/C][C]830.552926734263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167716&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167716&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
tForecast95% Lower Bound95% Upper Bound
61206.160133267262177.53581723912234.784449295404
62228.632125912916195.389665619629261.874586206203
63226.991512411677190.082427993912263.900596829442
64181.015818283869144.26359319998217.768043367758
65158.997467964379120.88208295545197.112852973308
66182.816779292047137.511555033183228.122003550911
67226.633556276193169.460238241737283.806874310649
68239.227970949675175.324152621506303.131789277843
69253.322876401912181.921409754233324.724343049592
70228.172444807787158.836876872989297.508012742586
71191.848083621458128.123999657699255.572167585217
72194.061071273802-442.430784186659830.552926734263



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')