Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 03 Dec 2009 11:34:36 -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/03/t1259865474jdpapzy8nst9fid.htm/, Retrieved Fri, 19 Apr 2024 01:04:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63045, Retrieved Fri, 19 Apr 2024 01:04:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
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] [WS9(4)] [2009-12-03 18:34:36] [5edea6bc5a9a9483633d9320282a2734] [Current]
Feedback Forum

Post a new message
Dataseries X:
10.9
10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3
8.1
8.5




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=63045&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=63045&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63045&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
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63045&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[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63045&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63045&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
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310.210.2703960340935-0.0703960340935126
149.69.60658797162383-0.00658797162382996
159.29.190123415613040.00987658438696393
169.39.285930742146690.0140692578533113
179.49.4023172574173-0.00231725741730493
189.49.41477372697338-0.0147737269733774
199.29.34942082450971-0.149420824509715
2098.845294816317870.154705183682125
2198.808104703702980.191895296297023
2299.08752947392429-0.0875294739242864
239.810.0892141703574-0.289214170357392
24109.996184088408060.0038159115919445
259.89.9137272574271-0.113727257427110
269.39.22945487465430.0705451253457081
2798.902623415613040.0973765843869625
2899.08384573583718-0.0838457358371798
299.19.098690888473680.00130911152631796
309.19.11397902498662-0.0139790249866234
319.19.050713245821480.0492867541785227
329.28.749044816317880.450955183682124
338.89.00405166392314-0.20405166392314
348.38.88537079371875-0.585370793718745
358.49.30365861480184-0.903658614801836
368.18.56658437997095-0.466584379970953
377.78.02804220939508-0.32804220939508
387.97.24950611556420.650493884435795
397.97.560956748946370.339043251053631
4087.972378201134870.0276217988651268
417.98.08660299199494-0.186602991994938
427.67.9108002170396-0.310800217039604
437.17.5571753523803-0.457175352380296
446.86.82404481631788-0.0240448163178755
456.56.65268814128116-0.152688141281161
466.96.560545971355010.339454028644987
478.27.732547503690730.467452496309273
488.78.362355850194220.337644149805776
498.38.6235216982473-0.323521698247298
507.97.815205761018520.084794238981484
517.57.56095674894637-0.0609567489463698
527.87.568208188515850.231791811484147
538.37.884185412699190.41581458730081
548.48.311859819688610.0881401803113881
558.28.35372889554893-0.153728895548927
567.77.88279481631788-0.182794816317875
577.27.5344494622719-0.334449462271904
587.37.268101352074410.0318986479255887
598.18.18143639257961-0.0814363925796151
608.58.260241585305860.239758414694140

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 10.2 & 10.2703960340935 & -0.0703960340935126 \tabularnewline
14 & 9.6 & 9.60658797162383 & -0.00658797162382996 \tabularnewline
15 & 9.2 & 9.19012341561304 & 0.00987658438696393 \tabularnewline
16 & 9.3 & 9.28593074214669 & 0.0140692578533113 \tabularnewline
17 & 9.4 & 9.4023172574173 & -0.00231725741730493 \tabularnewline
18 & 9.4 & 9.41477372697338 & -0.0147737269733774 \tabularnewline
19 & 9.2 & 9.34942082450971 & -0.149420824509715 \tabularnewline
20 & 9 & 8.84529481631787 & 0.154705183682125 \tabularnewline
21 & 9 & 8.80810470370298 & 0.191895296297023 \tabularnewline
22 & 9 & 9.08752947392429 & -0.0875294739242864 \tabularnewline
23 & 9.8 & 10.0892141703574 & -0.289214170357392 \tabularnewline
24 & 10 & 9.99618408840806 & 0.0038159115919445 \tabularnewline
25 & 9.8 & 9.9137272574271 & -0.113727257427110 \tabularnewline
26 & 9.3 & 9.2294548746543 & 0.0705451253457081 \tabularnewline
27 & 9 & 8.90262341561304 & 0.0973765843869625 \tabularnewline
28 & 9 & 9.08384573583718 & -0.0838457358371798 \tabularnewline
29 & 9.1 & 9.09869088847368 & 0.00130911152631796 \tabularnewline
30 & 9.1 & 9.11397902498662 & -0.0139790249866234 \tabularnewline
31 & 9.1 & 9.05071324582148 & 0.0492867541785227 \tabularnewline
32 & 9.2 & 8.74904481631788 & 0.450955183682124 \tabularnewline
33 & 8.8 & 9.00405166392314 & -0.20405166392314 \tabularnewline
34 & 8.3 & 8.88537079371875 & -0.585370793718745 \tabularnewline
35 & 8.4 & 9.30365861480184 & -0.903658614801836 \tabularnewline
36 & 8.1 & 8.56658437997095 & -0.466584379970953 \tabularnewline
37 & 7.7 & 8.02804220939508 & -0.32804220939508 \tabularnewline
38 & 7.9 & 7.2495061155642 & 0.650493884435795 \tabularnewline
39 & 7.9 & 7.56095674894637 & 0.339043251053631 \tabularnewline
40 & 8 & 7.97237820113487 & 0.0276217988651268 \tabularnewline
41 & 7.9 & 8.08660299199494 & -0.186602991994938 \tabularnewline
42 & 7.6 & 7.9108002170396 & -0.310800217039604 \tabularnewline
43 & 7.1 & 7.5571753523803 & -0.457175352380296 \tabularnewline
44 & 6.8 & 6.82404481631788 & -0.0240448163178755 \tabularnewline
45 & 6.5 & 6.65268814128116 & -0.152688141281161 \tabularnewline
46 & 6.9 & 6.56054597135501 & 0.339454028644987 \tabularnewline
47 & 8.2 & 7.73254750369073 & 0.467452496309273 \tabularnewline
48 & 8.7 & 8.36235585019422 & 0.337644149805776 \tabularnewline
49 & 8.3 & 8.6235216982473 & -0.323521698247298 \tabularnewline
50 & 7.9 & 7.81520576101852 & 0.084794238981484 \tabularnewline
51 & 7.5 & 7.56095674894637 & -0.0609567489463698 \tabularnewline
52 & 7.8 & 7.56820818851585 & 0.231791811484147 \tabularnewline
53 & 8.3 & 7.88418541269919 & 0.41581458730081 \tabularnewline
54 & 8.4 & 8.31185981968861 & 0.0881401803113881 \tabularnewline
55 & 8.2 & 8.35372889554893 & -0.153728895548927 \tabularnewline
56 & 7.7 & 7.88279481631788 & -0.182794816317875 \tabularnewline
57 & 7.2 & 7.5344494622719 & -0.334449462271904 \tabularnewline
58 & 7.3 & 7.26810135207441 & 0.0318986479255887 \tabularnewline
59 & 8.1 & 8.18143639257961 & -0.0814363925796151 \tabularnewline
60 & 8.5 & 8.26024158530586 & 0.239758414694140 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63045&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]10.2[/C][C]10.2703960340935[/C][C]-0.0703960340935126[/C][/ROW]
[ROW][C]14[/C][C]9.6[/C][C]9.60658797162383[/C][C]-0.00658797162382996[/C][/ROW]
[ROW][C]15[/C][C]9.2[/C][C]9.19012341561304[/C][C]0.00987658438696393[/C][/ROW]
[ROW][C]16[/C][C]9.3[/C][C]9.28593074214669[/C][C]0.0140692578533113[/C][/ROW]
[ROW][C]17[/C][C]9.4[/C][C]9.4023172574173[/C][C]-0.00231725741730493[/C][/ROW]
[ROW][C]18[/C][C]9.4[/C][C]9.41477372697338[/C][C]-0.0147737269733774[/C][/ROW]
[ROW][C]19[/C][C]9.2[/C][C]9.34942082450971[/C][C]-0.149420824509715[/C][/ROW]
[ROW][C]20[/C][C]9[/C][C]8.84529481631787[/C][C]0.154705183682125[/C][/ROW]
[ROW][C]21[/C][C]9[/C][C]8.80810470370298[/C][C]0.191895296297023[/C][/ROW]
[ROW][C]22[/C][C]9[/C][C]9.08752947392429[/C][C]-0.0875294739242864[/C][/ROW]
[ROW][C]23[/C][C]9.8[/C][C]10.0892141703574[/C][C]-0.289214170357392[/C][/ROW]
[ROW][C]24[/C][C]10[/C][C]9.99618408840806[/C][C]0.0038159115919445[/C][/ROW]
[ROW][C]25[/C][C]9.8[/C][C]9.9137272574271[/C][C]-0.113727257427110[/C][/ROW]
[ROW][C]26[/C][C]9.3[/C][C]9.2294548746543[/C][C]0.0705451253457081[/C][/ROW]
[ROW][C]27[/C][C]9[/C][C]8.90262341561304[/C][C]0.0973765843869625[/C][/ROW]
[ROW][C]28[/C][C]9[/C][C]9.08384573583718[/C][C]-0.0838457358371798[/C][/ROW]
[ROW][C]29[/C][C]9.1[/C][C]9.09869088847368[/C][C]0.00130911152631796[/C][/ROW]
[ROW][C]30[/C][C]9.1[/C][C]9.11397902498662[/C][C]-0.0139790249866234[/C][/ROW]
[ROW][C]31[/C][C]9.1[/C][C]9.05071324582148[/C][C]0.0492867541785227[/C][/ROW]
[ROW][C]32[/C][C]9.2[/C][C]8.74904481631788[/C][C]0.450955183682124[/C][/ROW]
[ROW][C]33[/C][C]8.8[/C][C]9.00405166392314[/C][C]-0.20405166392314[/C][/ROW]
[ROW][C]34[/C][C]8.3[/C][C]8.88537079371875[/C][C]-0.585370793718745[/C][/ROW]
[ROW][C]35[/C][C]8.4[/C][C]9.30365861480184[/C][C]-0.903658614801836[/C][/ROW]
[ROW][C]36[/C][C]8.1[/C][C]8.56658437997095[/C][C]-0.466584379970953[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]8.02804220939508[/C][C]-0.32804220939508[/C][/ROW]
[ROW][C]38[/C][C]7.9[/C][C]7.2495061155642[/C][C]0.650493884435795[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.56095674894637[/C][C]0.339043251053631[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]7.97237820113487[/C][C]0.0276217988651268[/C][/ROW]
[ROW][C]41[/C][C]7.9[/C][C]8.08660299199494[/C][C]-0.186602991994938[/C][/ROW]
[ROW][C]42[/C][C]7.6[/C][C]7.9108002170396[/C][C]-0.310800217039604[/C][/ROW]
[ROW][C]43[/C][C]7.1[/C][C]7.5571753523803[/C][C]-0.457175352380296[/C][/ROW]
[ROW][C]44[/C][C]6.8[/C][C]6.82404481631788[/C][C]-0.0240448163178755[/C][/ROW]
[ROW][C]45[/C][C]6.5[/C][C]6.65268814128116[/C][C]-0.152688141281161[/C][/ROW]
[ROW][C]46[/C][C]6.9[/C][C]6.56054597135501[/C][C]0.339454028644987[/C][/ROW]
[ROW][C]47[/C][C]8.2[/C][C]7.73254750369073[/C][C]0.467452496309273[/C][/ROW]
[ROW][C]48[/C][C]8.7[/C][C]8.36235585019422[/C][C]0.337644149805776[/C][/ROW]
[ROW][C]49[/C][C]8.3[/C][C]8.6235216982473[/C][C]-0.323521698247298[/C][/ROW]
[ROW][C]50[/C][C]7.9[/C][C]7.81520576101852[/C][C]0.084794238981484[/C][/ROW]
[ROW][C]51[/C][C]7.5[/C][C]7.56095674894637[/C][C]-0.0609567489463698[/C][/ROW]
[ROW][C]52[/C][C]7.8[/C][C]7.56820818851585[/C][C]0.231791811484147[/C][/ROW]
[ROW][C]53[/C][C]8.3[/C][C]7.88418541269919[/C][C]0.41581458730081[/C][/ROW]
[ROW][C]54[/C][C]8.4[/C][C]8.31185981968861[/C][C]0.0881401803113881[/C][/ROW]
[ROW][C]55[/C][C]8.2[/C][C]8.35372889554893[/C][C]-0.153728895548927[/C][/ROW]
[ROW][C]56[/C][C]7.7[/C][C]7.88279481631788[/C][C]-0.182794816317875[/C][/ROW]
[ROW][C]57[/C][C]7.2[/C][C]7.5344494622719[/C][C]-0.334449462271904[/C][/ROW]
[ROW][C]58[/C][C]7.3[/C][C]7.26810135207441[/C][C]0.0318986479255887[/C][/ROW]
[ROW][C]59[/C][C]8.1[/C][C]8.18143639257961[/C][C]-0.0814363925796151[/C][/ROW]
[ROW][C]60[/C][C]8.5[/C][C]8.26024158530586[/C][C]0.239758414694140[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63045&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63045&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
1310.210.2703960340935-0.0703960340935126
149.69.60658797162383-0.00658797162382996
159.29.190123415613040.00987658438696393
169.39.285930742146690.0140692578533113
179.49.4023172574173-0.00231725741730493
189.49.41477372697338-0.0147737269733774
199.29.34942082450971-0.149420824509715
2098.845294816317870.154705183682125
2198.808104703702980.191895296297023
2299.08752947392429-0.0875294739242864
239.810.0892141703574-0.289214170357392
24109.996184088408060.0038159115919445
259.89.9137272574271-0.113727257427110
269.39.22945487465430.0705451253457081
2798.902623415613040.0973765843869625
2899.08384573583718-0.0838457358371798
299.19.098690888473680.00130911152631796
309.19.11397902498662-0.0139790249866234
319.19.050713245821480.0492867541785227
329.28.749044816317880.450955183682124
338.89.00405166392314-0.20405166392314
348.38.88537079371875-0.585370793718745
358.49.30365861480184-0.903658614801836
368.18.56658437997095-0.466584379970953
377.78.02804220939508-0.32804220939508
387.97.24950611556420.650493884435795
397.97.560956748946370.339043251053631
4087.972378201134870.0276217988651268
417.98.08660299199494-0.186602991994938
427.67.9108002170396-0.310800217039604
437.17.5571753523803-0.457175352380296
446.86.82404481631788-0.0240448163178755
456.56.65268814128116-0.152688141281161
466.96.560545971355010.339454028644987
478.27.732547503690730.467452496309273
488.78.362355850194220.337644149805776
498.38.6235216982473-0.323521698247298
507.97.815205761018520.084794238981484
517.57.56095674894637-0.0609567489463698
527.87.568208188515850.231791811484147
538.37.884185412699190.41581458730081
548.48.311859819688610.0881401803113881
558.28.35372889554893-0.153728895548927
567.77.88279481631788-0.182794816317875
577.27.5344494622719-0.334449462271904
587.37.268101352074410.0318986479255887
598.18.18143639257961-0.0814363925796151
608.58.260241585305860.239758414694140







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
618.425028535296567.864304840455138.98575223013799
627.93308675783347.162436634293588.70373688137324
637.592664891870056.665382867358818.5199469163813
647.6618391148076.569921337580338.75375689203368
657.744354453028576.50512318765798.98358571839924
667.754742363983486.391565157897199.11791957006977
677.711251075266966.242684876123929.17981727441
687.412373976262325.891723101546938.93302485097772
697.252652237113855.660792273259238.84451220096847
707.321321885898445.617377708008849.02526606378803
718.205364286754536.212643713480210.1980848600289
728.36783355218012-51.388580555603468.1242476599636

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 8.42502853529656 & 7.86430484045513 & 8.98575223013799 \tabularnewline
62 & 7.9330867578334 & 7.16243663429358 & 8.70373688137324 \tabularnewline
63 & 7.59266489187005 & 6.66538286735881 & 8.5199469163813 \tabularnewline
64 & 7.661839114807 & 6.56992133758033 & 8.75375689203368 \tabularnewline
65 & 7.74435445302857 & 6.5051231876579 & 8.98358571839924 \tabularnewline
66 & 7.75474236398348 & 6.39156515789719 & 9.11791957006977 \tabularnewline
67 & 7.71125107526696 & 6.24268487612392 & 9.17981727441 \tabularnewline
68 & 7.41237397626232 & 5.89172310154693 & 8.93302485097772 \tabularnewline
69 & 7.25265223711385 & 5.66079227325923 & 8.84451220096847 \tabularnewline
70 & 7.32132188589844 & 5.61737770800884 & 9.02526606378803 \tabularnewline
71 & 8.20536428675453 & 6.2126437134802 & 10.1980848600289 \tabularnewline
72 & 8.36783355218012 & -51.3885805556034 & 68.1242476599636 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63045&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]8.42502853529656[/C][C]7.86430484045513[/C][C]8.98575223013799[/C][/ROW]
[ROW][C]62[/C][C]7.9330867578334[/C][C]7.16243663429358[/C][C]8.70373688137324[/C][/ROW]
[ROW][C]63[/C][C]7.59266489187005[/C][C]6.66538286735881[/C][C]8.5199469163813[/C][/ROW]
[ROW][C]64[/C][C]7.661839114807[/C][C]6.56992133758033[/C][C]8.75375689203368[/C][/ROW]
[ROW][C]65[/C][C]7.74435445302857[/C][C]6.5051231876579[/C][C]8.98358571839924[/C][/ROW]
[ROW][C]66[/C][C]7.75474236398348[/C][C]6.39156515789719[/C][C]9.11791957006977[/C][/ROW]
[ROW][C]67[/C][C]7.71125107526696[/C][C]6.24268487612392[/C][C]9.17981727441[/C][/ROW]
[ROW][C]68[/C][C]7.41237397626232[/C][C]5.89172310154693[/C][C]8.93302485097772[/C][/ROW]
[ROW][C]69[/C][C]7.25265223711385[/C][C]5.66079227325923[/C][C]8.84451220096847[/C][/ROW]
[ROW][C]70[/C][C]7.32132188589844[/C][C]5.61737770800884[/C][C]9.02526606378803[/C][/ROW]
[ROW][C]71[/C][C]8.20536428675453[/C][C]6.2126437134802[/C][C]10.1980848600289[/C][/ROW]
[ROW][C]72[/C][C]8.36783355218012[/C][C]-51.3885805556034[/C][C]68.1242476599636[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63045&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63045&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
618.425028535296567.864304840455138.98575223013799
627.93308675783347.162436634293588.70373688137324
637.592664891870056.665382867358818.5199469163813
647.6618391148076.569921337580338.75375689203368
657.744354453028576.50512318765798.98358571839924
667.754742363983486.391565157897199.11791957006977
677.711251075266966.242684876123929.17981727441
687.412373976262325.891723101546938.93302485097772
697.252652237113855.660792273259238.84451220096847
707.321321885898445.617377708008849.02526606378803
718.205364286754536.212643713480210.1980848600289
728.36783355218012-51.388580555603468.1242476599636



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')