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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 computationTue, 01 Dec 2009 13:49:49 -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/01/t1259700621deuj08qfr65otfk.htm/, Retrieved Fri, 29 Mar 2024 12:44:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62256, Retrieved Fri, 29 Mar 2024 12:44:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
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]
-   PD      [Exponential Smoothing] [BBWS9-exponential...] [2009-12-01 20:49:49] [b32ceebc68d054278e6bda97f3d57f91] [Current]
-   PD        [Exponential Smoothing] [shw-ws9] [2009-12-04 13:41:32] [2663058f2a5dda519058ac6b2228468f]
-   PD          [Exponential Smoothing] [ws 9 theorie 2] [2009-12-04 19:32:15] [134dc66689e3d457a82860db6471d419]
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Dataseries X:
96,8
114,1
110,3
103,9
101,6
94,6
95,9
104,7
102,8
98,1
113,9
80,9
95,7
113,2
105,9
108,8
102,3
99
100,7
115,5
100,7
109,9
114,6
85,4
100,5
114,8
116,5
112,9
102
106
105,3
118,8
106,1
109,3
117,2
92,5
104,2
112,5
122,4
113,3
100
110,7
112,8
109,8
117,3
109,1
115,9
96
99,8
116,8
115,7
99,4
94,3
91
93,2
103,1
94,1
91,8
102,7
82,6




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=62256&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=62256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62256&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
alpha0.0710539545448988
beta1
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0710539545448988 \tabularnewline
beta & 1 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62256&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]0.0710539545448988[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62256&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
alpha0.0710539545448988
beta1
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1395.794.93074086795960.769259132040403
14113.2112.0250593038421.17494069615817
15105.9104.9436905837310.95630941626851
16108.8107.9791654232070.820834576792578
17102.3101.6089299351680.691070064832232
189998.73819093090360.261809069096373
19100.798.79071273300631.90928726699369
20115.5108.8743814006426.62561859935799
21100.7108.827552568900-8.12755256890016
22109.9103.9042661717055.9957338282954
23114.6122.072013488954-7.47201348895449
2485.486.63302976268-1.23302976267991
25100.5103.234098631968-2.73409863196801
26114.8121.704799347454-6.9047993474544
27116.5112.7048006582953.7951993417046
28112.9115.575414354338-2.6754143543384
29102107.804475187270-5.80447518727048
30106102.8562012775333.14379872246657
31105.3103.8543715090381.44562849096170
32118.8117.7177450184801.08225498151964
33106.1102.0139249821024.08607501789824
34109.3110.769289825928-1.46928982592766
35117.2114.8896860855882.31031391441218
3692.585.5714487388446.92855126115603
37104.2101.8523718259632.34762817403677
38112.5117.848943691905-5.3489436919053
39122.4119.8714843763552.52851562364518
40113.3117.349409047939-4.04940904793922
41100106.820060208653-6.82006020865268
42110.7110.868186541988-0.168186541988007
43112.8110.3650351565042.43496484349618
44109.8125.096029511562-15.2960295115624
45117.3109.8134466039747.48655339602567
46109.1113.362930794477-4.26293079447697
47115.9120.403668412532-4.50366841253233
489693.33761891758152.66238108241853
4999.8103.802893517563-4.00289351756275
50116.8110.1738871003286.6261128996722
51115.7119.001102352076-3.30110235207604
5299.4108.732376562866-9.3323765628663
5394.394.18059155356650.119408446433539
5491102.959047167137-11.9590471671372
5593.2101.691910201205-8.49191020120477
56103.196.37224317411366.72775682588636
5794.1101.298479898548-7.19847989854793
5891.891.4869381691510.313061830848923
59102.795.0743107060527.62568929394794
6082.677.70063421953784.89936578046223

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 95.7 & 94.9307408679596 & 0.769259132040403 \tabularnewline
14 & 113.2 & 112.025059303842 & 1.17494069615817 \tabularnewline
15 & 105.9 & 104.943690583731 & 0.95630941626851 \tabularnewline
16 & 108.8 & 107.979165423207 & 0.820834576792578 \tabularnewline
17 & 102.3 & 101.608929935168 & 0.691070064832232 \tabularnewline
18 & 99 & 98.7381909309036 & 0.261809069096373 \tabularnewline
19 & 100.7 & 98.7907127330063 & 1.90928726699369 \tabularnewline
20 & 115.5 & 108.874381400642 & 6.62561859935799 \tabularnewline
21 & 100.7 & 108.827552568900 & -8.12755256890016 \tabularnewline
22 & 109.9 & 103.904266171705 & 5.9957338282954 \tabularnewline
23 & 114.6 & 122.072013488954 & -7.47201348895449 \tabularnewline
24 & 85.4 & 86.63302976268 & -1.23302976267991 \tabularnewline
25 & 100.5 & 103.234098631968 & -2.73409863196801 \tabularnewline
26 & 114.8 & 121.704799347454 & -6.9047993474544 \tabularnewline
27 & 116.5 & 112.704800658295 & 3.7951993417046 \tabularnewline
28 & 112.9 & 115.575414354338 & -2.6754143543384 \tabularnewline
29 & 102 & 107.804475187270 & -5.80447518727048 \tabularnewline
30 & 106 & 102.856201277533 & 3.14379872246657 \tabularnewline
31 & 105.3 & 103.854371509038 & 1.44562849096170 \tabularnewline
32 & 118.8 & 117.717745018480 & 1.08225498151964 \tabularnewline
33 & 106.1 & 102.013924982102 & 4.08607501789824 \tabularnewline
34 & 109.3 & 110.769289825928 & -1.46928982592766 \tabularnewline
35 & 117.2 & 114.889686085588 & 2.31031391441218 \tabularnewline
36 & 92.5 & 85.571448738844 & 6.92855126115603 \tabularnewline
37 & 104.2 & 101.852371825963 & 2.34762817403677 \tabularnewline
38 & 112.5 & 117.848943691905 & -5.3489436919053 \tabularnewline
39 & 122.4 & 119.871484376355 & 2.52851562364518 \tabularnewline
40 & 113.3 & 117.349409047939 & -4.04940904793922 \tabularnewline
41 & 100 & 106.820060208653 & -6.82006020865268 \tabularnewline
42 & 110.7 & 110.868186541988 & -0.168186541988007 \tabularnewline
43 & 112.8 & 110.365035156504 & 2.43496484349618 \tabularnewline
44 & 109.8 & 125.096029511562 & -15.2960295115624 \tabularnewline
45 & 117.3 & 109.813446603974 & 7.48655339602567 \tabularnewline
46 & 109.1 & 113.362930794477 & -4.26293079447697 \tabularnewline
47 & 115.9 & 120.403668412532 & -4.50366841253233 \tabularnewline
48 & 96 & 93.3376189175815 & 2.66238108241853 \tabularnewline
49 & 99.8 & 103.802893517563 & -4.00289351756275 \tabularnewline
50 & 116.8 & 110.173887100328 & 6.6261128996722 \tabularnewline
51 & 115.7 & 119.001102352076 & -3.30110235207604 \tabularnewline
52 & 99.4 & 108.732376562866 & -9.3323765628663 \tabularnewline
53 & 94.3 & 94.1805915535665 & 0.119408446433539 \tabularnewline
54 & 91 & 102.959047167137 & -11.9590471671372 \tabularnewline
55 & 93.2 & 101.691910201205 & -8.49191020120477 \tabularnewline
56 & 103.1 & 96.3722431741136 & 6.72775682588636 \tabularnewline
57 & 94.1 & 101.298479898548 & -7.19847989854793 \tabularnewline
58 & 91.8 & 91.486938169151 & 0.313061830848923 \tabularnewline
59 & 102.7 & 95.074310706052 & 7.62568929394794 \tabularnewline
60 & 82.6 & 77.7006342195378 & 4.89936578046223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62256&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]95.7[/C][C]94.9307408679596[/C][C]0.769259132040403[/C][/ROW]
[ROW][C]14[/C][C]113.2[/C][C]112.025059303842[/C][C]1.17494069615817[/C][/ROW]
[ROW][C]15[/C][C]105.9[/C][C]104.943690583731[/C][C]0.95630941626851[/C][/ROW]
[ROW][C]16[/C][C]108.8[/C][C]107.979165423207[/C][C]0.820834576792578[/C][/ROW]
[ROW][C]17[/C][C]102.3[/C][C]101.608929935168[/C][C]0.691070064832232[/C][/ROW]
[ROW][C]18[/C][C]99[/C][C]98.7381909309036[/C][C]0.261809069096373[/C][/ROW]
[ROW][C]19[/C][C]100.7[/C][C]98.7907127330063[/C][C]1.90928726699369[/C][/ROW]
[ROW][C]20[/C][C]115.5[/C][C]108.874381400642[/C][C]6.62561859935799[/C][/ROW]
[ROW][C]21[/C][C]100.7[/C][C]108.827552568900[/C][C]-8.12755256890016[/C][/ROW]
[ROW][C]22[/C][C]109.9[/C][C]103.904266171705[/C][C]5.9957338282954[/C][/ROW]
[ROW][C]23[/C][C]114.6[/C][C]122.072013488954[/C][C]-7.47201348895449[/C][/ROW]
[ROW][C]24[/C][C]85.4[/C][C]86.63302976268[/C][C]-1.23302976267991[/C][/ROW]
[ROW][C]25[/C][C]100.5[/C][C]103.234098631968[/C][C]-2.73409863196801[/C][/ROW]
[ROW][C]26[/C][C]114.8[/C][C]121.704799347454[/C][C]-6.9047993474544[/C][/ROW]
[ROW][C]27[/C][C]116.5[/C][C]112.704800658295[/C][C]3.7951993417046[/C][/ROW]
[ROW][C]28[/C][C]112.9[/C][C]115.575414354338[/C][C]-2.6754143543384[/C][/ROW]
[ROW][C]29[/C][C]102[/C][C]107.804475187270[/C][C]-5.80447518727048[/C][/ROW]
[ROW][C]30[/C][C]106[/C][C]102.856201277533[/C][C]3.14379872246657[/C][/ROW]
[ROW][C]31[/C][C]105.3[/C][C]103.854371509038[/C][C]1.44562849096170[/C][/ROW]
[ROW][C]32[/C][C]118.8[/C][C]117.717745018480[/C][C]1.08225498151964[/C][/ROW]
[ROW][C]33[/C][C]106.1[/C][C]102.013924982102[/C][C]4.08607501789824[/C][/ROW]
[ROW][C]34[/C][C]109.3[/C][C]110.769289825928[/C][C]-1.46928982592766[/C][/ROW]
[ROW][C]35[/C][C]117.2[/C][C]114.889686085588[/C][C]2.31031391441218[/C][/ROW]
[ROW][C]36[/C][C]92.5[/C][C]85.571448738844[/C][C]6.92855126115603[/C][/ROW]
[ROW][C]37[/C][C]104.2[/C][C]101.852371825963[/C][C]2.34762817403677[/C][/ROW]
[ROW][C]38[/C][C]112.5[/C][C]117.848943691905[/C][C]-5.3489436919053[/C][/ROW]
[ROW][C]39[/C][C]122.4[/C][C]119.871484376355[/C][C]2.52851562364518[/C][/ROW]
[ROW][C]40[/C][C]113.3[/C][C]117.349409047939[/C][C]-4.04940904793922[/C][/ROW]
[ROW][C]41[/C][C]100[/C][C]106.820060208653[/C][C]-6.82006020865268[/C][/ROW]
[ROW][C]42[/C][C]110.7[/C][C]110.868186541988[/C][C]-0.168186541988007[/C][/ROW]
[ROW][C]43[/C][C]112.8[/C][C]110.365035156504[/C][C]2.43496484349618[/C][/ROW]
[ROW][C]44[/C][C]109.8[/C][C]125.096029511562[/C][C]-15.2960295115624[/C][/ROW]
[ROW][C]45[/C][C]117.3[/C][C]109.813446603974[/C][C]7.48655339602567[/C][/ROW]
[ROW][C]46[/C][C]109.1[/C][C]113.362930794477[/C][C]-4.26293079447697[/C][/ROW]
[ROW][C]47[/C][C]115.9[/C][C]120.403668412532[/C][C]-4.50366841253233[/C][/ROW]
[ROW][C]48[/C][C]96[/C][C]93.3376189175815[/C][C]2.66238108241853[/C][/ROW]
[ROW][C]49[/C][C]99.8[/C][C]103.802893517563[/C][C]-4.00289351756275[/C][/ROW]
[ROW][C]50[/C][C]116.8[/C][C]110.173887100328[/C][C]6.6261128996722[/C][/ROW]
[ROW][C]51[/C][C]115.7[/C][C]119.001102352076[/C][C]-3.30110235207604[/C][/ROW]
[ROW][C]52[/C][C]99.4[/C][C]108.732376562866[/C][C]-9.3323765628663[/C][/ROW]
[ROW][C]53[/C][C]94.3[/C][C]94.1805915535665[/C][C]0.119408446433539[/C][/ROW]
[ROW][C]54[/C][C]91[/C][C]102.959047167137[/C][C]-11.9590471671372[/C][/ROW]
[ROW][C]55[/C][C]93.2[/C][C]101.691910201205[/C][C]-8.49191020120477[/C][/ROW]
[ROW][C]56[/C][C]103.1[/C][C]96.3722431741136[/C][C]6.72775682588636[/C][/ROW]
[ROW][C]57[/C][C]94.1[/C][C]101.298479898548[/C][C]-7.19847989854793[/C][/ROW]
[ROW][C]58[/C][C]91.8[/C][C]91.486938169151[/C][C]0.313061830848923[/C][/ROW]
[ROW][C]59[/C][C]102.7[/C][C]95.074310706052[/C][C]7.62568929394794[/C][/ROW]
[ROW][C]60[/C][C]82.6[/C][C]77.7006342195378[/C][C]4.89936578046223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62256&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62256&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
1395.794.93074086795960.769259132040403
14113.2112.0250593038421.17494069615817
15105.9104.9436905837310.95630941626851
16108.8107.9791654232070.820834576792578
17102.3101.6089299351680.691070064832232
189998.73819093090360.261809069096373
19100.798.79071273300631.90928726699369
20115.5108.8743814006426.62561859935799
21100.7108.827552568900-8.12755256890016
22109.9103.9042661717055.9957338282954
23114.6122.072013488954-7.47201348895449
2485.486.63302976268-1.23302976267991
25100.5103.234098631968-2.73409863196801
26114.8121.704799347454-6.9047993474544
27116.5112.7048006582953.7951993417046
28112.9115.575414354338-2.6754143543384
29102107.804475187270-5.80447518727048
30106102.8562012775333.14379872246657
31105.3103.8543715090381.44562849096170
32118.8117.7177450184801.08225498151964
33106.1102.0139249821024.08607501789824
34109.3110.769289825928-1.46928982592766
35117.2114.8896860855882.31031391441218
3692.585.5714487388446.92855126115603
37104.2101.8523718259632.34762817403677
38112.5117.848943691905-5.3489436919053
39122.4119.8714843763552.52851562364518
40113.3117.349409047939-4.04940904793922
41100106.820060208653-6.82006020865268
42110.7110.868186541988-0.168186541988007
43112.8110.3650351565042.43496484349618
44109.8125.096029511562-15.2960295115624
45117.3109.8134466039747.48655339602567
46109.1113.362930794477-4.26293079447697
47115.9120.403668412532-4.50366841253233
489693.33761891758152.66238108241853
4999.8103.802893517563-4.00289351756275
50116.8110.1738871003286.6261128996722
51115.7119.001102352076-3.30110235207604
5299.4108.732376562866-9.3323765628663
5394.394.18059155356650.119408446433539
5491102.959047167137-11.9590471671372
5593.2101.691910201205-8.49191020120477
56103.196.37224317411366.72775682588636
5794.1101.298479898548-7.19847989854793
5891.891.4869381691510.313061830848923
59102.795.0743107060527.62568929394794
6082.677.70063421953784.89936578046223







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6180.15043945616169.53775607340190.763122838921
6292.235331062880581.4758782581014102.994783867660
6389.980125363159378.939930538606101.020320187713
6476.56632334303165.271098735670387.8615479503915
6571.915514021951260.164169491352683.6668585525498
6669.256907971241356.84992806099681.6638878814866
6771.202349059171757.645881027344484.758817090999
6878.691724927338662.988819695960594.3946301587168
6972.115948832997955.433873922189588.7980237438063
7070.639024002707552.22945891588389.048589089532
7178.915234700295256.4714948771408101.358974523450
7263.09382575347643.890054125534282.2975973814179

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 80.150439456161 & 69.537756073401 & 90.763122838921 \tabularnewline
62 & 92.2353310628805 & 81.4758782581014 & 102.994783867660 \tabularnewline
63 & 89.9801253631593 & 78.939930538606 & 101.020320187713 \tabularnewline
64 & 76.566323343031 & 65.2710987356703 & 87.8615479503915 \tabularnewline
65 & 71.9155140219512 & 60.1641694913526 & 83.6668585525498 \tabularnewline
66 & 69.2569079712413 & 56.849928060996 & 81.6638878814866 \tabularnewline
67 & 71.2023490591717 & 57.6458810273444 & 84.758817090999 \tabularnewline
68 & 78.6917249273386 & 62.9888196959605 & 94.3946301587168 \tabularnewline
69 & 72.1159488329979 & 55.4338739221895 & 88.7980237438063 \tabularnewline
70 & 70.6390240027075 & 52.229458915883 & 89.048589089532 \tabularnewline
71 & 78.9152347002952 & 56.4714948771408 & 101.358974523450 \tabularnewline
72 & 63.093825753476 & 43.8900541255342 & 82.2975973814179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62256&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]80.150439456161[/C][C]69.537756073401[/C][C]90.763122838921[/C][/ROW]
[ROW][C]62[/C][C]92.2353310628805[/C][C]81.4758782581014[/C][C]102.994783867660[/C][/ROW]
[ROW][C]63[/C][C]89.9801253631593[/C][C]78.939930538606[/C][C]101.020320187713[/C][/ROW]
[ROW][C]64[/C][C]76.566323343031[/C][C]65.2710987356703[/C][C]87.8615479503915[/C][/ROW]
[ROW][C]65[/C][C]71.9155140219512[/C][C]60.1641694913526[/C][C]83.6668585525498[/C][/ROW]
[ROW][C]66[/C][C]69.2569079712413[/C][C]56.849928060996[/C][C]81.6638878814866[/C][/ROW]
[ROW][C]67[/C][C]71.2023490591717[/C][C]57.6458810273444[/C][C]84.758817090999[/C][/ROW]
[ROW][C]68[/C][C]78.6917249273386[/C][C]62.9888196959605[/C][C]94.3946301587168[/C][/ROW]
[ROW][C]69[/C][C]72.1159488329979[/C][C]55.4338739221895[/C][C]88.7980237438063[/C][/ROW]
[ROW][C]70[/C][C]70.6390240027075[/C][C]52.229458915883[/C][C]89.048589089532[/C][/ROW]
[ROW][C]71[/C][C]78.9152347002952[/C][C]56.4714948771408[/C][C]101.358974523450[/C][/ROW]
[ROW][C]72[/C][C]63.093825753476[/C][C]43.8900541255342[/C][C]82.2975973814179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62256&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62256&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
6180.15043945616169.53775607340190.763122838921
6292.235331062880581.4758782581014102.994783867660
6389.980125363159378.939930538606101.020320187713
6476.56632334303165.271098735670387.8615479503915
6571.915514021951260.164169491352683.6668585525498
6669.256907971241356.84992806099681.6638878814866
6771.202349059171757.645881027344484.758817090999
6878.691724927338662.988819695960594.3946301587168
6972.115948832997955.433873922189588.7980237438063
7070.639024002707552.22945891588389.048589089532
7178.915234700295256.4714948771408101.358974523450
7263.09382575347643.890054125534282.2975973814179



Parameters (Session):
par1 = FALSE ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
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')