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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 13:26:53 -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/t1259699260tgythzvmbd9np8b.htm/, Retrieved Thu, 28 Mar 2024 15:46:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62244, Retrieved Thu, 28 Mar 2024 15:46:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139
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] [Exponential Smoot...] [2009-12-01 20:26:53] [e1f26cfd746b288ac2a466939c6f316e] [Current]
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Dataseries X:
105.7
105.7
111.1
82.4
60
107.3
99.3
113.5
108.9
100.2
103.9
138.7
120.2
100.2
143.2
70.9
85.2
133
136.6
117.9
106.3
122.3
125.5
148.4
126.3
99.6
140.4
80.3
92.6
138.5
110.9
119.6
105
109
129.4
148.6
101.4
134.8
143.7
81.6
90.3
141.5
140.7
140.2
100.2
125.7
119.6
134.7
109
116.3
146.9
97.4
89.4
132.1
139.8
129
112.5
121.9
121.7
123.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62244&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62244&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62244&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.196498523917098
beta0.0899638888814172
gamma0.583891170761644

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.196498523917098 \tabularnewline
beta & 0.0899638888814172 \tabularnewline
gamma & 0.583891170761644 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62244&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]0.196498523917098[/C][/ROW]
[ROW][C]beta[/C][C]0.0899638888814172[/C][/ROW]
[ROW][C]gamma[/C][C]0.583891170761644[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62244&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62244&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
alpha0.196498523917098
beta0.0899638888814172
gamma0.583891170761644







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13120.2110.8362668921289.36373310787225
14100.293.77374253906076.42625746093925
15143.2137.7339689612215.46603103877948
1670.969.26776507211881.63223492788116
1785.283.5638594022481.63614059775202
18133131.4712131396451.52878686035532
19136.6112.80243155107323.7975684489271
20117.9136.202701952687-18.3027019526874
21106.3127.870142486416-21.5701424864163
22122.3114.2921397379558.00786026204501
23125.5121.1508893039464.34911069605408
24148.4161.952468839141-13.5524688391415
25126.3141.820088080406-15.5200880804060
2699.6114.330930031326-14.7309300313257
27140.4158.468316777822-18.0683167778224
2880.376.1036674503364.19633254966406
2992.691.50999977838921.09000022161084
30138.5142.155019193663-3.65501919366267
31110.9130.82261788252-19.9226178825200
32119.6124.011853083112-4.41185308311196
33105115.229242095174-10.2292420951737
34109116.476607663784-7.47660766378387
35129.4116.96648270700712.4335172929932
36148.6148.0503298701250.549670129875324
37101.4128.964019288729-27.5640192887285
38134.899.622020512987235.1779794870128
39143.7152.162179437852-8.46217943785194
4081.680.02128219337261.57871780662735
4190.393.4181970405116-3.11819704051156
42141.5140.7833501772990.716649822701498
43140.7121.84997868118918.8500213188111
44140.2130.475290055279.72470994472985
45100.2121.107034884099-20.9070348840991
46125.7122.1470224539003.55297754609956
47119.6135.697013378742-16.0970133787416
48134.7156.956073049891-22.2560730498909
49109118.415772442545-9.41577244254475
50116.3121.236254667216-4.93625466721626
51146.9143.8494625411213.05053745887881
5297.479.190030718868418.2099692811316
5389.493.7095433342137-4.30954333421366
54132.1143.192577388638-11.0925773886379
55139.8129.76864771940510.031352280595
56129131.705789881828-2.70578988182803
57112.5105.6361870525396.86381294746096
58121.9123.320922692383-1.4209226923831
59121.7126.117611532921-4.41761153292131
60123.1146.348068519575-23.2480685195753

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 120.2 & 110.836266892128 & 9.36373310787225 \tabularnewline
14 & 100.2 & 93.7737425390607 & 6.42625746093925 \tabularnewline
15 & 143.2 & 137.733968961221 & 5.46603103877948 \tabularnewline
16 & 70.9 & 69.2677650721188 & 1.63223492788116 \tabularnewline
17 & 85.2 & 83.563859402248 & 1.63614059775202 \tabularnewline
18 & 133 & 131.471213139645 & 1.52878686035532 \tabularnewline
19 & 136.6 & 112.802431551073 & 23.7975684489271 \tabularnewline
20 & 117.9 & 136.202701952687 & -18.3027019526874 \tabularnewline
21 & 106.3 & 127.870142486416 & -21.5701424864163 \tabularnewline
22 & 122.3 & 114.292139737955 & 8.00786026204501 \tabularnewline
23 & 125.5 & 121.150889303946 & 4.34911069605408 \tabularnewline
24 & 148.4 & 161.952468839141 & -13.5524688391415 \tabularnewline
25 & 126.3 & 141.820088080406 & -15.5200880804060 \tabularnewline
26 & 99.6 & 114.330930031326 & -14.7309300313257 \tabularnewline
27 & 140.4 & 158.468316777822 & -18.0683167778224 \tabularnewline
28 & 80.3 & 76.103667450336 & 4.19633254966406 \tabularnewline
29 & 92.6 & 91.5099997783892 & 1.09000022161084 \tabularnewline
30 & 138.5 & 142.155019193663 & -3.65501919366267 \tabularnewline
31 & 110.9 & 130.82261788252 & -19.9226178825200 \tabularnewline
32 & 119.6 & 124.011853083112 & -4.41185308311196 \tabularnewline
33 & 105 & 115.229242095174 & -10.2292420951737 \tabularnewline
34 & 109 & 116.476607663784 & -7.47660766378387 \tabularnewline
35 & 129.4 & 116.966482707007 & 12.4335172929932 \tabularnewline
36 & 148.6 & 148.050329870125 & 0.549670129875324 \tabularnewline
37 & 101.4 & 128.964019288729 & -27.5640192887285 \tabularnewline
38 & 134.8 & 99.6220205129872 & 35.1779794870128 \tabularnewline
39 & 143.7 & 152.162179437852 & -8.46217943785194 \tabularnewline
40 & 81.6 & 80.0212821933726 & 1.57871780662735 \tabularnewline
41 & 90.3 & 93.4181970405116 & -3.11819704051156 \tabularnewline
42 & 141.5 & 140.783350177299 & 0.716649822701498 \tabularnewline
43 & 140.7 & 121.849978681189 & 18.8500213188111 \tabularnewline
44 & 140.2 & 130.47529005527 & 9.72470994472985 \tabularnewline
45 & 100.2 & 121.107034884099 & -20.9070348840991 \tabularnewline
46 & 125.7 & 122.147022453900 & 3.55297754609956 \tabularnewline
47 & 119.6 & 135.697013378742 & -16.0970133787416 \tabularnewline
48 & 134.7 & 156.956073049891 & -22.2560730498909 \tabularnewline
49 & 109 & 118.415772442545 & -9.41577244254475 \tabularnewline
50 & 116.3 & 121.236254667216 & -4.93625466721626 \tabularnewline
51 & 146.9 & 143.849462541121 & 3.05053745887881 \tabularnewline
52 & 97.4 & 79.1900307188684 & 18.2099692811316 \tabularnewline
53 & 89.4 & 93.7095433342137 & -4.30954333421366 \tabularnewline
54 & 132.1 & 143.192577388638 & -11.0925773886379 \tabularnewline
55 & 139.8 & 129.768647719405 & 10.031352280595 \tabularnewline
56 & 129 & 131.705789881828 & -2.70578988182803 \tabularnewline
57 & 112.5 & 105.636187052539 & 6.86381294746096 \tabularnewline
58 & 121.9 & 123.320922692383 & -1.4209226923831 \tabularnewline
59 & 121.7 & 126.117611532921 & -4.41761153292131 \tabularnewline
60 & 123.1 & 146.348068519575 & -23.2480685195753 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62244&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]120.2[/C][C]110.836266892128[/C][C]9.36373310787225[/C][/ROW]
[ROW][C]14[/C][C]100.2[/C][C]93.7737425390607[/C][C]6.42625746093925[/C][/ROW]
[ROW][C]15[/C][C]143.2[/C][C]137.733968961221[/C][C]5.46603103877948[/C][/ROW]
[ROW][C]16[/C][C]70.9[/C][C]69.2677650721188[/C][C]1.63223492788116[/C][/ROW]
[ROW][C]17[/C][C]85.2[/C][C]83.563859402248[/C][C]1.63614059775202[/C][/ROW]
[ROW][C]18[/C][C]133[/C][C]131.471213139645[/C][C]1.52878686035532[/C][/ROW]
[ROW][C]19[/C][C]136.6[/C][C]112.802431551073[/C][C]23.7975684489271[/C][/ROW]
[ROW][C]20[/C][C]117.9[/C][C]136.202701952687[/C][C]-18.3027019526874[/C][/ROW]
[ROW][C]21[/C][C]106.3[/C][C]127.870142486416[/C][C]-21.5701424864163[/C][/ROW]
[ROW][C]22[/C][C]122.3[/C][C]114.292139737955[/C][C]8.00786026204501[/C][/ROW]
[ROW][C]23[/C][C]125.5[/C][C]121.150889303946[/C][C]4.34911069605408[/C][/ROW]
[ROW][C]24[/C][C]148.4[/C][C]161.952468839141[/C][C]-13.5524688391415[/C][/ROW]
[ROW][C]25[/C][C]126.3[/C][C]141.820088080406[/C][C]-15.5200880804060[/C][/ROW]
[ROW][C]26[/C][C]99.6[/C][C]114.330930031326[/C][C]-14.7309300313257[/C][/ROW]
[ROW][C]27[/C][C]140.4[/C][C]158.468316777822[/C][C]-18.0683167778224[/C][/ROW]
[ROW][C]28[/C][C]80.3[/C][C]76.103667450336[/C][C]4.19633254966406[/C][/ROW]
[ROW][C]29[/C][C]92.6[/C][C]91.5099997783892[/C][C]1.09000022161084[/C][/ROW]
[ROW][C]30[/C][C]138.5[/C][C]142.155019193663[/C][C]-3.65501919366267[/C][/ROW]
[ROW][C]31[/C][C]110.9[/C][C]130.82261788252[/C][C]-19.9226178825200[/C][/ROW]
[ROW][C]32[/C][C]119.6[/C][C]124.011853083112[/C][C]-4.41185308311196[/C][/ROW]
[ROW][C]33[/C][C]105[/C][C]115.229242095174[/C][C]-10.2292420951737[/C][/ROW]
[ROW][C]34[/C][C]109[/C][C]116.476607663784[/C][C]-7.47660766378387[/C][/ROW]
[ROW][C]35[/C][C]129.4[/C][C]116.966482707007[/C][C]12.4335172929932[/C][/ROW]
[ROW][C]36[/C][C]148.6[/C][C]148.050329870125[/C][C]0.549670129875324[/C][/ROW]
[ROW][C]37[/C][C]101.4[/C][C]128.964019288729[/C][C]-27.5640192887285[/C][/ROW]
[ROW][C]38[/C][C]134.8[/C][C]99.6220205129872[/C][C]35.1779794870128[/C][/ROW]
[ROW][C]39[/C][C]143.7[/C][C]152.162179437852[/C][C]-8.46217943785194[/C][/ROW]
[ROW][C]40[/C][C]81.6[/C][C]80.0212821933726[/C][C]1.57871780662735[/C][/ROW]
[ROW][C]41[/C][C]90.3[/C][C]93.4181970405116[/C][C]-3.11819704051156[/C][/ROW]
[ROW][C]42[/C][C]141.5[/C][C]140.783350177299[/C][C]0.716649822701498[/C][/ROW]
[ROW][C]43[/C][C]140.7[/C][C]121.849978681189[/C][C]18.8500213188111[/C][/ROW]
[ROW][C]44[/C][C]140.2[/C][C]130.47529005527[/C][C]9.72470994472985[/C][/ROW]
[ROW][C]45[/C][C]100.2[/C][C]121.107034884099[/C][C]-20.9070348840991[/C][/ROW]
[ROW][C]46[/C][C]125.7[/C][C]122.147022453900[/C][C]3.55297754609956[/C][/ROW]
[ROW][C]47[/C][C]119.6[/C][C]135.697013378742[/C][C]-16.0970133787416[/C][/ROW]
[ROW][C]48[/C][C]134.7[/C][C]156.956073049891[/C][C]-22.2560730498909[/C][/ROW]
[ROW][C]49[/C][C]109[/C][C]118.415772442545[/C][C]-9.41577244254475[/C][/ROW]
[ROW][C]50[/C][C]116.3[/C][C]121.236254667216[/C][C]-4.93625466721626[/C][/ROW]
[ROW][C]51[/C][C]146.9[/C][C]143.849462541121[/C][C]3.05053745887881[/C][/ROW]
[ROW][C]52[/C][C]97.4[/C][C]79.1900307188684[/C][C]18.2099692811316[/C][/ROW]
[ROW][C]53[/C][C]89.4[/C][C]93.7095433342137[/C][C]-4.30954333421366[/C][/ROW]
[ROW][C]54[/C][C]132.1[/C][C]143.192577388638[/C][C]-11.0925773886379[/C][/ROW]
[ROW][C]55[/C][C]139.8[/C][C]129.768647719405[/C][C]10.031352280595[/C][/ROW]
[ROW][C]56[/C][C]129[/C][C]131.705789881828[/C][C]-2.70578988182803[/C][/ROW]
[ROW][C]57[/C][C]112.5[/C][C]105.636187052539[/C][C]6.86381294746096[/C][/ROW]
[ROW][C]58[/C][C]121.9[/C][C]123.320922692383[/C][C]-1.4209226923831[/C][/ROW]
[ROW][C]59[/C][C]121.7[/C][C]126.117611532921[/C][C]-4.41761153292131[/C][/ROW]
[ROW][C]60[/C][C]123.1[/C][C]146.348068519575[/C][C]-23.2480685195753[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62244&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62244&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
13120.2110.8362668921289.36373310787225
14100.293.77374253906076.42625746093925
15143.2137.7339689612215.46603103877948
1670.969.26776507211881.63223492788116
1785.283.5638594022481.63614059775202
18133131.4712131396451.52878686035532
19136.6112.80243155107323.7975684489271
20117.9136.202701952687-18.3027019526874
21106.3127.870142486416-21.5701424864163
22122.3114.2921397379558.00786026204501
23125.5121.1508893039464.34911069605408
24148.4161.952468839141-13.5524688391415
25126.3141.820088080406-15.5200880804060
2699.6114.330930031326-14.7309300313257
27140.4158.468316777822-18.0683167778224
2880.376.1036674503364.19633254966406
2992.691.50999977838921.09000022161084
30138.5142.155019193663-3.65501919366267
31110.9130.82261788252-19.9226178825200
32119.6124.011853083112-4.41185308311196
33105115.229242095174-10.2292420951737
34109116.476607663784-7.47660766378387
35129.4116.96648270700712.4335172929932
36148.6148.0503298701250.549670129875324
37101.4128.964019288729-27.5640192887285
38134.899.622020512987235.1779794870128
39143.7152.162179437852-8.46217943785194
4081.680.02128219337261.57871780662735
4190.393.4181970405116-3.11819704051156
42141.5140.7833501772990.716649822701498
43140.7121.84997868118918.8500213188111
44140.2130.475290055279.72470994472985
45100.2121.107034884099-20.9070348840991
46125.7122.1470224539003.55297754609956
47119.6135.697013378742-16.0970133787416
48134.7156.956073049891-22.2560730498909
49109118.415772442545-9.41577244254475
50116.3121.236254667216-4.93625466721626
51146.9143.8494625411213.05053745887881
5297.479.190030718868418.2099692811316
5389.493.7095433342137-4.30954333421366
54132.1143.192577388638-11.0925773886379
55139.8129.76864771940510.031352280595
56129131.705789881828-2.70578988182803
57112.5105.6361870525396.86381294746096
58121.9123.320922692383-1.4209226923831
59121.7126.117611532921-4.41761153292131
60123.1146.348068519575-23.2480685195753







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61113.45964062888096.3315883874954130.587692870264
62120.273009022562102.174500466326138.371517578797
63148.220115600902128.207138399329168.233092802475
6488.782610826024470.0979528260481107.467268826001
6588.797923102709169.0910776021049108.504768603313
66134.411176744043109.622097010197159.200256477890
67132.811807301196106.660707089634158.962907512757
68126.58818135054599.6337017801938153.542660920897
69105.76753336029780.1108516189914131.424215101604
70117.28399388200288.3337441384241146.234243625581
71118.46075372722787.6312341444537149.290273310000
72129.548212502931-45.6960479819908304.792472987854

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 113.459640628880 & 96.3315883874954 & 130.587692870264 \tabularnewline
62 & 120.273009022562 & 102.174500466326 & 138.371517578797 \tabularnewline
63 & 148.220115600902 & 128.207138399329 & 168.233092802475 \tabularnewline
64 & 88.7826108260244 & 70.0979528260481 & 107.467268826001 \tabularnewline
65 & 88.7979231027091 & 69.0910776021049 & 108.504768603313 \tabularnewline
66 & 134.411176744043 & 109.622097010197 & 159.200256477890 \tabularnewline
67 & 132.811807301196 & 106.660707089634 & 158.962907512757 \tabularnewline
68 & 126.588181350545 & 99.6337017801938 & 153.542660920897 \tabularnewline
69 & 105.767533360297 & 80.1108516189914 & 131.424215101604 \tabularnewline
70 & 117.283993882002 & 88.3337441384241 & 146.234243625581 \tabularnewline
71 & 118.460753727227 & 87.6312341444537 & 149.290273310000 \tabularnewline
72 & 129.548212502931 & -45.6960479819908 & 304.792472987854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62244&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]113.459640628880[/C][C]96.3315883874954[/C][C]130.587692870264[/C][/ROW]
[ROW][C]62[/C][C]120.273009022562[/C][C]102.174500466326[/C][C]138.371517578797[/C][/ROW]
[ROW][C]63[/C][C]148.220115600902[/C][C]128.207138399329[/C][C]168.233092802475[/C][/ROW]
[ROW][C]64[/C][C]88.7826108260244[/C][C]70.0979528260481[/C][C]107.467268826001[/C][/ROW]
[ROW][C]65[/C][C]88.7979231027091[/C][C]69.0910776021049[/C][C]108.504768603313[/C][/ROW]
[ROW][C]66[/C][C]134.411176744043[/C][C]109.622097010197[/C][C]159.200256477890[/C][/ROW]
[ROW][C]67[/C][C]132.811807301196[/C][C]106.660707089634[/C][C]158.962907512757[/C][/ROW]
[ROW][C]68[/C][C]126.588181350545[/C][C]99.6337017801938[/C][C]153.542660920897[/C][/ROW]
[ROW][C]69[/C][C]105.767533360297[/C][C]80.1108516189914[/C][C]131.424215101604[/C][/ROW]
[ROW][C]70[/C][C]117.283993882002[/C][C]88.3337441384241[/C][C]146.234243625581[/C][/ROW]
[ROW][C]71[/C][C]118.460753727227[/C][C]87.6312341444537[/C][C]149.290273310000[/C][/ROW]
[ROW][C]72[/C][C]129.548212502931[/C][C]-45.6960479819908[/C][C]304.792472987854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62244&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62244&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
61113.45964062888096.3315883874954130.587692870264
62120.273009022562102.174500466326138.371517578797
63148.220115600902128.207138399329168.233092802475
6488.782610826024470.0979528260481107.467268826001
6588.797923102709169.0910776021049108.504768603313
66134.411176744043109.622097010197159.200256477890
67132.811807301196106.660707089634158.962907512757
68126.58818135054599.6337017801938153.542660920897
69105.76753336029780.1108516189914131.424215101604
70117.28399388200288.3337441384241146.234243625581
71118.46075372722787.6312341444537149.290273310000
72129.548212502931-45.6960479819908304.792472987854



Parameters (Session):
par1 = 12 ;
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')