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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Dec 2009 10:47:44 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/02/t1259776143r37t4zkwpvcd990.htm/, Retrieved Sun, 28 Apr 2024 16:12:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62491, Retrieved Sun, 28 Apr 2024 16:12:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [Workshop 9: Expon...] [2009-12-02 17:47:44] [63d6214c2814604a6f6cfa44dba5912e] [Current]
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Dataseries X:
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7.0
7.1
7.2
7.1
6.9
7.0
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
7.9
7.7
7.4
7.5
8.0
8.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62491&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62491&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62491&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.899913987353234
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.899913987353234 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62491&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.899913987353234[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62491&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62491&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
alpha1
beta0.899913987353234
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137.67.480259655679420.119740344320576
147.77.78467255465862-0.0846725546586216
157.77.70842463477782-0.0084246347778194
167.97.92194022754802-0.0219402275480167
178.18.14557182661695-0.0455718266169516
188.28.25328008681465-0.053280086814647
198.27.877898750758270.322101249241725
208.28.128877060827370.0711229391726338
217.98.47725542963737-0.577255429637374
227.37.238006287477940.0619937125220567
236.97.51292475603305-0.61292475603305
246.66.151827895294140.448172104705860
256.76.337590384581120.362409615418879
266.96.7526933538890.147306646110998
2776.995868390528630.00413160947137303
287.17.30222370767404-0.202223707674045
297.27.25567270945402-0.0556727094540204
307.17.25623961196135-0.156239611961346
316.96.647466933630210.252533066369794
3276.655288482262680.34471151773732
336.87.30460093243933-0.504600932439332
346.46.28582328155910.114176718440899
356.76.70563966404874-0.00563966404873995
366.66.63678201396038-0.0367820139603783
376.46.58758138338824-0.18758138338824
386.36.203839842640640.0961601573593631
396.26.108391364010510.0916086359894877
406.56.266967319319870.233032680680133
416.86.81855803213871-0.0185580321387135
426.87.06518701134419-0.265187011344190
436.46.47238707388988-0.0723870738898826
446.16.002435361719570.0975646382804323
455.86.01284942528561-0.212849425285614
466.15.218842052968170.881157947031832
477.26.987082997393940.212917002606056
487.37.9258423645877-0.625842364587703
496.97.55703420929963-0.657034209299631
506.16.54700458599799-0.447004585997989
515.85.264177077742550.535822922257449
526.25.60668098476810.593319015231902
537.16.585329823991150.514670176008847
547.77.93762349963424-0.237623499634238
557.97.91563004175484-0.0156300417548421
567.78.0495831772975-0.349583177297499
577.47.80935188173757-0.409351881737571
587.56.749586080580790.750413919419208
5988.35852704878512-0.358527048785119
608.18.10831121120325-0.00831121120325129

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7.6 & 7.48025965567942 & 0.119740344320576 \tabularnewline
14 & 7.7 & 7.78467255465862 & -0.0846725546586216 \tabularnewline
15 & 7.7 & 7.70842463477782 & -0.0084246347778194 \tabularnewline
16 & 7.9 & 7.92194022754802 & -0.0219402275480167 \tabularnewline
17 & 8.1 & 8.14557182661695 & -0.0455718266169516 \tabularnewline
18 & 8.2 & 8.25328008681465 & -0.053280086814647 \tabularnewline
19 & 8.2 & 7.87789875075827 & 0.322101249241725 \tabularnewline
20 & 8.2 & 8.12887706082737 & 0.0711229391726338 \tabularnewline
21 & 7.9 & 8.47725542963737 & -0.577255429637374 \tabularnewline
22 & 7.3 & 7.23800628747794 & 0.0619937125220567 \tabularnewline
23 & 6.9 & 7.51292475603305 & -0.61292475603305 \tabularnewline
24 & 6.6 & 6.15182789529414 & 0.448172104705860 \tabularnewline
25 & 6.7 & 6.33759038458112 & 0.362409615418879 \tabularnewline
26 & 6.9 & 6.752693353889 & 0.147306646110998 \tabularnewline
27 & 7 & 6.99586839052863 & 0.00413160947137303 \tabularnewline
28 & 7.1 & 7.30222370767404 & -0.202223707674045 \tabularnewline
29 & 7.2 & 7.25567270945402 & -0.0556727094540204 \tabularnewline
30 & 7.1 & 7.25623961196135 & -0.156239611961346 \tabularnewline
31 & 6.9 & 6.64746693363021 & 0.252533066369794 \tabularnewline
32 & 7 & 6.65528848226268 & 0.34471151773732 \tabularnewline
33 & 6.8 & 7.30460093243933 & -0.504600932439332 \tabularnewline
34 & 6.4 & 6.2858232815591 & 0.114176718440899 \tabularnewline
35 & 6.7 & 6.70563966404874 & -0.00563966404873995 \tabularnewline
36 & 6.6 & 6.63678201396038 & -0.0367820139603783 \tabularnewline
37 & 6.4 & 6.58758138338824 & -0.18758138338824 \tabularnewline
38 & 6.3 & 6.20383984264064 & 0.0961601573593631 \tabularnewline
39 & 6.2 & 6.10839136401051 & 0.0916086359894877 \tabularnewline
40 & 6.5 & 6.26696731931987 & 0.233032680680133 \tabularnewline
41 & 6.8 & 6.81855803213871 & -0.0185580321387135 \tabularnewline
42 & 6.8 & 7.06518701134419 & -0.265187011344190 \tabularnewline
43 & 6.4 & 6.47238707388988 & -0.0723870738898826 \tabularnewline
44 & 6.1 & 6.00243536171957 & 0.0975646382804323 \tabularnewline
45 & 5.8 & 6.01284942528561 & -0.212849425285614 \tabularnewline
46 & 6.1 & 5.21884205296817 & 0.881157947031832 \tabularnewline
47 & 7.2 & 6.98708299739394 & 0.212917002606056 \tabularnewline
48 & 7.3 & 7.9258423645877 & -0.625842364587703 \tabularnewline
49 & 6.9 & 7.55703420929963 & -0.657034209299631 \tabularnewline
50 & 6.1 & 6.54700458599799 & -0.447004585997989 \tabularnewline
51 & 5.8 & 5.26417707774255 & 0.535822922257449 \tabularnewline
52 & 6.2 & 5.6066809847681 & 0.593319015231902 \tabularnewline
53 & 7.1 & 6.58532982399115 & 0.514670176008847 \tabularnewline
54 & 7.7 & 7.93762349963424 & -0.237623499634238 \tabularnewline
55 & 7.9 & 7.91563004175484 & -0.0156300417548421 \tabularnewline
56 & 7.7 & 8.0495831772975 & -0.349583177297499 \tabularnewline
57 & 7.4 & 7.80935188173757 & -0.409351881737571 \tabularnewline
58 & 7.5 & 6.74958608058079 & 0.750413919419208 \tabularnewline
59 & 8 & 8.35852704878512 & -0.358527048785119 \tabularnewline
60 & 8.1 & 8.10831121120325 & -0.00831121120325129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62491&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]7.6[/C][C]7.48025965567942[/C][C]0.119740344320576[/C][/ROW]
[ROW][C]14[/C][C]7.7[/C][C]7.78467255465862[/C][C]-0.0846725546586216[/C][/ROW]
[ROW][C]15[/C][C]7.7[/C][C]7.70842463477782[/C][C]-0.0084246347778194[/C][/ROW]
[ROW][C]16[/C][C]7.9[/C][C]7.92194022754802[/C][C]-0.0219402275480167[/C][/ROW]
[ROW][C]17[/C][C]8.1[/C][C]8.14557182661695[/C][C]-0.0455718266169516[/C][/ROW]
[ROW][C]18[/C][C]8.2[/C][C]8.25328008681465[/C][C]-0.053280086814647[/C][/ROW]
[ROW][C]19[/C][C]8.2[/C][C]7.87789875075827[/C][C]0.322101249241725[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]8.12887706082737[/C][C]0.0711229391726338[/C][/ROW]
[ROW][C]21[/C][C]7.9[/C][C]8.47725542963737[/C][C]-0.577255429637374[/C][/ROW]
[ROW][C]22[/C][C]7.3[/C][C]7.23800628747794[/C][C]0.0619937125220567[/C][/ROW]
[ROW][C]23[/C][C]6.9[/C][C]7.51292475603305[/C][C]-0.61292475603305[/C][/ROW]
[ROW][C]24[/C][C]6.6[/C][C]6.15182789529414[/C][C]0.448172104705860[/C][/ROW]
[ROW][C]25[/C][C]6.7[/C][C]6.33759038458112[/C][C]0.362409615418879[/C][/ROW]
[ROW][C]26[/C][C]6.9[/C][C]6.752693353889[/C][C]0.147306646110998[/C][/ROW]
[ROW][C]27[/C][C]7[/C][C]6.99586839052863[/C][C]0.00413160947137303[/C][/ROW]
[ROW][C]28[/C][C]7.1[/C][C]7.30222370767404[/C][C]-0.202223707674045[/C][/ROW]
[ROW][C]29[/C][C]7.2[/C][C]7.25567270945402[/C][C]-0.0556727094540204[/C][/ROW]
[ROW][C]30[/C][C]7.1[/C][C]7.25623961196135[/C][C]-0.156239611961346[/C][/ROW]
[ROW][C]31[/C][C]6.9[/C][C]6.64746693363021[/C][C]0.252533066369794[/C][/ROW]
[ROW][C]32[/C][C]7[/C][C]6.65528848226268[/C][C]0.34471151773732[/C][/ROW]
[ROW][C]33[/C][C]6.8[/C][C]7.30460093243933[/C][C]-0.504600932439332[/C][/ROW]
[ROW][C]34[/C][C]6.4[/C][C]6.2858232815591[/C][C]0.114176718440899[/C][/ROW]
[ROW][C]35[/C][C]6.7[/C][C]6.70563966404874[/C][C]-0.00563966404873995[/C][/ROW]
[ROW][C]36[/C][C]6.6[/C][C]6.63678201396038[/C][C]-0.0367820139603783[/C][/ROW]
[ROW][C]37[/C][C]6.4[/C][C]6.58758138338824[/C][C]-0.18758138338824[/C][/ROW]
[ROW][C]38[/C][C]6.3[/C][C]6.20383984264064[/C][C]0.0961601573593631[/C][/ROW]
[ROW][C]39[/C][C]6.2[/C][C]6.10839136401051[/C][C]0.0916086359894877[/C][/ROW]
[ROW][C]40[/C][C]6.5[/C][C]6.26696731931987[/C][C]0.233032680680133[/C][/ROW]
[ROW][C]41[/C][C]6.8[/C][C]6.81855803213871[/C][C]-0.0185580321387135[/C][/ROW]
[ROW][C]42[/C][C]6.8[/C][C]7.06518701134419[/C][C]-0.265187011344190[/C][/ROW]
[ROW][C]43[/C][C]6.4[/C][C]6.47238707388988[/C][C]-0.0723870738898826[/C][/ROW]
[ROW][C]44[/C][C]6.1[/C][C]6.00243536171957[/C][C]0.0975646382804323[/C][/ROW]
[ROW][C]45[/C][C]5.8[/C][C]6.01284942528561[/C][C]-0.212849425285614[/C][/ROW]
[ROW][C]46[/C][C]6.1[/C][C]5.21884205296817[/C][C]0.881157947031832[/C][/ROW]
[ROW][C]47[/C][C]7.2[/C][C]6.98708299739394[/C][C]0.212917002606056[/C][/ROW]
[ROW][C]48[/C][C]7.3[/C][C]7.9258423645877[/C][C]-0.625842364587703[/C][/ROW]
[ROW][C]49[/C][C]6.9[/C][C]7.55703420929963[/C][C]-0.657034209299631[/C][/ROW]
[ROW][C]50[/C][C]6.1[/C][C]6.54700458599799[/C][C]-0.447004585997989[/C][/ROW]
[ROW][C]51[/C][C]5.8[/C][C]5.26417707774255[/C][C]0.535822922257449[/C][/ROW]
[ROW][C]52[/C][C]6.2[/C][C]5.6066809847681[/C][C]0.593319015231902[/C][/ROW]
[ROW][C]53[/C][C]7.1[/C][C]6.58532982399115[/C][C]0.514670176008847[/C][/ROW]
[ROW][C]54[/C][C]7.7[/C][C]7.93762349963424[/C][C]-0.237623499634238[/C][/ROW]
[ROW][C]55[/C][C]7.9[/C][C]7.91563004175484[/C][C]-0.0156300417548421[/C][/ROW]
[ROW][C]56[/C][C]7.7[/C][C]8.0495831772975[/C][C]-0.349583177297499[/C][/ROW]
[ROW][C]57[/C][C]7.4[/C][C]7.80935188173757[/C][C]-0.409351881737571[/C][/ROW]
[ROW][C]58[/C][C]7.5[/C][C]6.74958608058079[/C][C]0.750413919419208[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]8.35852704878512[/C][C]-0.358527048785119[/C][/ROW]
[ROW][C]60[/C][C]8.1[/C][C]8.10831121120325[/C][C]-0.00831121120325129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62491&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62491&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
137.67.480259655679420.119740344320576
147.77.78467255465862-0.0846725546586216
157.77.70842463477782-0.0084246347778194
167.97.92194022754802-0.0219402275480167
178.18.14557182661695-0.0455718266169516
188.28.25328008681465-0.053280086814647
198.27.877898750758270.322101249241725
208.28.128877060827370.0711229391726338
217.98.47725542963737-0.577255429637374
227.37.238006287477940.0619937125220567
236.97.51292475603305-0.61292475603305
246.66.151827895294140.448172104705860
256.76.337590384581120.362409615418879
266.96.7526933538890.147306646110998
2776.995868390528630.00413160947137303
287.17.30222370767404-0.202223707674045
297.27.25567270945402-0.0556727094540204
307.17.25623961196135-0.156239611961346
316.96.647466933630210.252533066369794
3276.655288482262680.34471151773732
336.87.30460093243933-0.504600932439332
346.46.28582328155910.114176718440899
356.76.70563966404874-0.00563966404873995
366.66.63678201396038-0.0367820139603783
376.46.58758138338824-0.18758138338824
386.36.203839842640640.0961601573593631
396.26.108391364010510.0916086359894877
406.56.266967319319870.233032680680133
416.86.81855803213871-0.0185580321387135
426.87.06518701134419-0.265187011344190
436.46.47238707388988-0.0723870738898826
446.16.002435361719570.0975646382804323
455.86.01284942528561-0.212849425285614
466.15.218842052968170.881157947031832
477.26.987082997393940.212917002606056
487.37.9258423645877-0.625842364587703
496.97.55703420929963-0.657034209299631
506.16.54700458599799-0.447004585997989
515.85.264177077742550.535822922257449
526.25.60668098476810.593319015231902
537.16.585329823991150.514670176008847
547.77.93762349963424-0.237623499634238
557.97.91563004175484-0.0156300417548421
567.78.0495831772975-0.349583177297499
577.47.80935188173757-0.409351881737571
587.56.749586080580790.750413919419208
5988.35852704878512-0.358527048785119
608.18.10831121120325-0.00831121120325129







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
618.304902834999757.619509374242798.9902962957567
628.497758053064287.017955205688989.97756090043958
638.580353884802226.1643492200135910.9963585495909
648.91068044822095.3341843146334212.4871765818084
659.295187239873774.3611308722087614.2292436075388
669.628272603472053.1974398685897116.0591053383544
679.457041414106341.7829822772108117.1311005510019
689.25106233024810.3622519891752418.1398726713210
699.37349463238458-1.0825180722575019.8295073370266
708.97444624167821-2.468655796137720.4175482794941
719.58078539597907-4.2070616434372323.3686324353954
729.6755968305694-6.6484705945609725.9996642556998

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 8.30490283499975 & 7.61950937424279 & 8.9902962957567 \tabularnewline
62 & 8.49775805306428 & 7.01795520568898 & 9.97756090043958 \tabularnewline
63 & 8.58035388480222 & 6.16434922001359 & 10.9963585495909 \tabularnewline
64 & 8.9106804482209 & 5.33418431463342 & 12.4871765818084 \tabularnewline
65 & 9.29518723987377 & 4.36113087220876 & 14.2292436075388 \tabularnewline
66 & 9.62827260347205 & 3.19743986858971 & 16.0591053383544 \tabularnewline
67 & 9.45704141410634 & 1.78298227721081 & 17.1311005510019 \tabularnewline
68 & 9.2510623302481 & 0.36225198917524 & 18.1398726713210 \tabularnewline
69 & 9.37349463238458 & -1.08251807225750 & 19.8295073370266 \tabularnewline
70 & 8.97444624167821 & -2.4686557961377 & 20.4175482794941 \tabularnewline
71 & 9.58078539597907 & -4.20706164343723 & 23.3686324353954 \tabularnewline
72 & 9.6755968305694 & -6.64847059456097 & 25.9996642556998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62491&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]8.30490283499975[/C][C]7.61950937424279[/C][C]8.9902962957567[/C][/ROW]
[ROW][C]62[/C][C]8.49775805306428[/C][C]7.01795520568898[/C][C]9.97756090043958[/C][/ROW]
[ROW][C]63[/C][C]8.58035388480222[/C][C]6.16434922001359[/C][C]10.9963585495909[/C][/ROW]
[ROW][C]64[/C][C]8.9106804482209[/C][C]5.33418431463342[/C][C]12.4871765818084[/C][/ROW]
[ROW][C]65[/C][C]9.29518723987377[/C][C]4.36113087220876[/C][C]14.2292436075388[/C][/ROW]
[ROW][C]66[/C][C]9.62827260347205[/C][C]3.19743986858971[/C][C]16.0591053383544[/C][/ROW]
[ROW][C]67[/C][C]9.45704141410634[/C][C]1.78298227721081[/C][C]17.1311005510019[/C][/ROW]
[ROW][C]68[/C][C]9.2510623302481[/C][C]0.36225198917524[/C][C]18.1398726713210[/C][/ROW]
[ROW][C]69[/C][C]9.37349463238458[/C][C]-1.08251807225750[/C][C]19.8295073370266[/C][/ROW]
[ROW][C]70[/C][C]8.97444624167821[/C][C]-2.4686557961377[/C][C]20.4175482794941[/C][/ROW]
[ROW][C]71[/C][C]9.58078539597907[/C][C]-4.20706164343723[/C][C]23.3686324353954[/C][/ROW]
[ROW][C]72[/C][C]9.6755968305694[/C][C]-6.64847059456097[/C][C]25.9996642556998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62491&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62491&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
618.304902834999757.619509374242798.9902962957567
628.497758053064287.017955205688989.97756090043958
638.580353884802226.1643492200135910.9963585495909
648.91068044822095.3341843146334212.4871765818084
659.295187239873774.3611308722087614.2292436075388
669.628272603472053.1974398685897116.0591053383544
679.457041414106341.7829822772108117.1311005510019
689.25106233024810.3622519891752418.1398726713210
699.37349463238458-1.0825180722575019.8295073370266
708.97444624167821-2.468655796137720.4175482794941
719.58078539597907-4.2070616434372323.3686324353954
729.6755968305694-6.6484705945609725.9996642556998



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')