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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 21:45:39 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/25/t1461617203y1e6q3ekd0mzh28.htm/, Retrieved Mon, 06 May 2024 10:15:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294791, Retrieved Mon, 06 May 2024 10:15:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2016-04-25 20:45:39] [b54f462b245e496e54620f8b97639ccc] [Current]
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Dataseries X:
92,49
92,46
92,55
92,24
92,41
92,83
92,85
93,04
93,04
92,83
92,96
92,83
93,01
93,21
93,58
94,07
94,57
95,03
95,21
95,89
96,43
96,35
96,71
96,32
97,23
97,88
98,2
98,56
99,31
99,69
99,77
101,06
101,77
101,91
102,52
102,09
102,22
102,74
103,56
104,4
104,76
104,86
104,84
104,96
104,83
104,58
104,8
104,17
104,63
105,32
106,16
107,22
107,51
107,87
107,79
108,04
107,74
107,71
111,19
110,82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294791&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294791&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294791&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.958205043210276
beta0.0373725776280312
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.958205043210276 \tabularnewline
beta & 0.0373725776280312 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294791&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]0.958205043210276[/C][/ROW]
[ROW][C]beta[/C][C]0.0373725776280312[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294791&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294791&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
alpha0.958205043210276
beta0.0373725776280312
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1393.0192.11878472222220.891215277777789
1493.2193.18642800662970.0235719933703393
1593.5893.55061858058940.0293814194105977
1694.0794.01351127524590.0564887247541037
1794.5794.49940122128560.0705987787144409
1895.0394.96258967627570.0674103237243173
1995.2195.2405536079047-0.0305536079047073
2095.8995.58688719672960.303112803270395
2196.4396.05254627252970.377453727470339
2296.3596.34795603838460.00204396161541354
2396.7196.57663613546980.133363864530182
2496.3296.6605067981235-0.340506798123556
2597.2396.61703342254110.612966577458948
2697.8897.42853898930560.451461010694359
2798.298.265045445335-0.0650454453350306
2898.5698.6972769716971-0.137276971697091
2999.3199.04983669598640.260163304013631
3099.6999.7530693084297-0.0630693084297036
3199.7799.9557757819209-0.185775781920952
32101.06100.2156248577410.844375142258585
33101.77101.2707188208750.49928117912502
34101.91101.7392242522750.170775747725315
35102.52102.2131651145490.306834885450897
36102.09102.527755887568-0.437755887567874
37102.22102.511770482203-0.291770482202779
38102.74102.4980253070370.241974692963424
39103.56103.1531347123920.406865287607644
40104.4104.0923551328410.307644867158785
41104.76104.961605684069-0.201605684069406
42104.86105.266076687229-0.406076687229202
43104.84105.179917208286-0.339917208285883
44104.96105.37453636912-0.414536369120185
45104.83105.203243482626-0.373243482626435
46104.58104.785047584322-0.205047584322031
47104.8104.854186835933-0.0541868359330095
48104.17104.728423849609-0.558423849609341
49104.63104.5352932709520.0947067290478998
50105.32104.8603983658750.459601634125463
51106.16105.6849419493950.47505805060527
52107.22106.6418114796370.578188520362957
53107.51107.715155921035-0.205155921035001
54107.87107.973693778444-0.103693778443926
55107.79108.156887337282-0.366887337282336
56108.04108.298422140637-0.258422140637421
57107.74108.259912333341-0.519912333341395
58107.71107.6844228482190.0255771517811638
59111.19107.9653274172433.22467258275704
60110.82111.062201709469-0.242201709468659

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 93.01 & 92.1187847222222 & 0.891215277777789 \tabularnewline
14 & 93.21 & 93.1864280066297 & 0.0235719933703393 \tabularnewline
15 & 93.58 & 93.5506185805894 & 0.0293814194105977 \tabularnewline
16 & 94.07 & 94.0135112752459 & 0.0564887247541037 \tabularnewline
17 & 94.57 & 94.4994012212856 & 0.0705987787144409 \tabularnewline
18 & 95.03 & 94.9625896762757 & 0.0674103237243173 \tabularnewline
19 & 95.21 & 95.2405536079047 & -0.0305536079047073 \tabularnewline
20 & 95.89 & 95.5868871967296 & 0.303112803270395 \tabularnewline
21 & 96.43 & 96.0525462725297 & 0.377453727470339 \tabularnewline
22 & 96.35 & 96.3479560383846 & 0.00204396161541354 \tabularnewline
23 & 96.71 & 96.5766361354698 & 0.133363864530182 \tabularnewline
24 & 96.32 & 96.6605067981235 & -0.340506798123556 \tabularnewline
25 & 97.23 & 96.6170334225411 & 0.612966577458948 \tabularnewline
26 & 97.88 & 97.4285389893056 & 0.451461010694359 \tabularnewline
27 & 98.2 & 98.265045445335 & -0.0650454453350306 \tabularnewline
28 & 98.56 & 98.6972769716971 & -0.137276971697091 \tabularnewline
29 & 99.31 & 99.0498366959864 & 0.260163304013631 \tabularnewline
30 & 99.69 & 99.7530693084297 & -0.0630693084297036 \tabularnewline
31 & 99.77 & 99.9557757819209 & -0.185775781920952 \tabularnewline
32 & 101.06 & 100.215624857741 & 0.844375142258585 \tabularnewline
33 & 101.77 & 101.270718820875 & 0.49928117912502 \tabularnewline
34 & 101.91 & 101.739224252275 & 0.170775747725315 \tabularnewline
35 & 102.52 & 102.213165114549 & 0.306834885450897 \tabularnewline
36 & 102.09 & 102.527755887568 & -0.437755887567874 \tabularnewline
37 & 102.22 & 102.511770482203 & -0.291770482202779 \tabularnewline
38 & 102.74 & 102.498025307037 & 0.241974692963424 \tabularnewline
39 & 103.56 & 103.153134712392 & 0.406865287607644 \tabularnewline
40 & 104.4 & 104.092355132841 & 0.307644867158785 \tabularnewline
41 & 104.76 & 104.961605684069 & -0.201605684069406 \tabularnewline
42 & 104.86 & 105.266076687229 & -0.406076687229202 \tabularnewline
43 & 104.84 & 105.179917208286 & -0.339917208285883 \tabularnewline
44 & 104.96 & 105.37453636912 & -0.414536369120185 \tabularnewline
45 & 104.83 & 105.203243482626 & -0.373243482626435 \tabularnewline
46 & 104.58 & 104.785047584322 & -0.205047584322031 \tabularnewline
47 & 104.8 & 104.854186835933 & -0.0541868359330095 \tabularnewline
48 & 104.17 & 104.728423849609 & -0.558423849609341 \tabularnewline
49 & 104.63 & 104.535293270952 & 0.0947067290478998 \tabularnewline
50 & 105.32 & 104.860398365875 & 0.459601634125463 \tabularnewline
51 & 106.16 & 105.684941949395 & 0.47505805060527 \tabularnewline
52 & 107.22 & 106.641811479637 & 0.578188520362957 \tabularnewline
53 & 107.51 & 107.715155921035 & -0.205155921035001 \tabularnewline
54 & 107.87 & 107.973693778444 & -0.103693778443926 \tabularnewline
55 & 107.79 & 108.156887337282 & -0.366887337282336 \tabularnewline
56 & 108.04 & 108.298422140637 & -0.258422140637421 \tabularnewline
57 & 107.74 & 108.259912333341 & -0.519912333341395 \tabularnewline
58 & 107.71 & 107.684422848219 & 0.0255771517811638 \tabularnewline
59 & 111.19 & 107.965327417243 & 3.22467258275704 \tabularnewline
60 & 110.82 & 111.062201709469 & -0.242201709468659 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294791&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]93.01[/C][C]92.1187847222222[/C][C]0.891215277777789[/C][/ROW]
[ROW][C]14[/C][C]93.21[/C][C]93.1864280066297[/C][C]0.0235719933703393[/C][/ROW]
[ROW][C]15[/C][C]93.58[/C][C]93.5506185805894[/C][C]0.0293814194105977[/C][/ROW]
[ROW][C]16[/C][C]94.07[/C][C]94.0135112752459[/C][C]0.0564887247541037[/C][/ROW]
[ROW][C]17[/C][C]94.57[/C][C]94.4994012212856[/C][C]0.0705987787144409[/C][/ROW]
[ROW][C]18[/C][C]95.03[/C][C]94.9625896762757[/C][C]0.0674103237243173[/C][/ROW]
[ROW][C]19[/C][C]95.21[/C][C]95.2405536079047[/C][C]-0.0305536079047073[/C][/ROW]
[ROW][C]20[/C][C]95.89[/C][C]95.5868871967296[/C][C]0.303112803270395[/C][/ROW]
[ROW][C]21[/C][C]96.43[/C][C]96.0525462725297[/C][C]0.377453727470339[/C][/ROW]
[ROW][C]22[/C][C]96.35[/C][C]96.3479560383846[/C][C]0.00204396161541354[/C][/ROW]
[ROW][C]23[/C][C]96.71[/C][C]96.5766361354698[/C][C]0.133363864530182[/C][/ROW]
[ROW][C]24[/C][C]96.32[/C][C]96.6605067981235[/C][C]-0.340506798123556[/C][/ROW]
[ROW][C]25[/C][C]97.23[/C][C]96.6170334225411[/C][C]0.612966577458948[/C][/ROW]
[ROW][C]26[/C][C]97.88[/C][C]97.4285389893056[/C][C]0.451461010694359[/C][/ROW]
[ROW][C]27[/C][C]98.2[/C][C]98.265045445335[/C][C]-0.0650454453350306[/C][/ROW]
[ROW][C]28[/C][C]98.56[/C][C]98.6972769716971[/C][C]-0.137276971697091[/C][/ROW]
[ROW][C]29[/C][C]99.31[/C][C]99.0498366959864[/C][C]0.260163304013631[/C][/ROW]
[ROW][C]30[/C][C]99.69[/C][C]99.7530693084297[/C][C]-0.0630693084297036[/C][/ROW]
[ROW][C]31[/C][C]99.77[/C][C]99.9557757819209[/C][C]-0.185775781920952[/C][/ROW]
[ROW][C]32[/C][C]101.06[/C][C]100.215624857741[/C][C]0.844375142258585[/C][/ROW]
[ROW][C]33[/C][C]101.77[/C][C]101.270718820875[/C][C]0.49928117912502[/C][/ROW]
[ROW][C]34[/C][C]101.91[/C][C]101.739224252275[/C][C]0.170775747725315[/C][/ROW]
[ROW][C]35[/C][C]102.52[/C][C]102.213165114549[/C][C]0.306834885450897[/C][/ROW]
[ROW][C]36[/C][C]102.09[/C][C]102.527755887568[/C][C]-0.437755887567874[/C][/ROW]
[ROW][C]37[/C][C]102.22[/C][C]102.511770482203[/C][C]-0.291770482202779[/C][/ROW]
[ROW][C]38[/C][C]102.74[/C][C]102.498025307037[/C][C]0.241974692963424[/C][/ROW]
[ROW][C]39[/C][C]103.56[/C][C]103.153134712392[/C][C]0.406865287607644[/C][/ROW]
[ROW][C]40[/C][C]104.4[/C][C]104.092355132841[/C][C]0.307644867158785[/C][/ROW]
[ROW][C]41[/C][C]104.76[/C][C]104.961605684069[/C][C]-0.201605684069406[/C][/ROW]
[ROW][C]42[/C][C]104.86[/C][C]105.266076687229[/C][C]-0.406076687229202[/C][/ROW]
[ROW][C]43[/C][C]104.84[/C][C]105.179917208286[/C][C]-0.339917208285883[/C][/ROW]
[ROW][C]44[/C][C]104.96[/C][C]105.37453636912[/C][C]-0.414536369120185[/C][/ROW]
[ROW][C]45[/C][C]104.83[/C][C]105.203243482626[/C][C]-0.373243482626435[/C][/ROW]
[ROW][C]46[/C][C]104.58[/C][C]104.785047584322[/C][C]-0.205047584322031[/C][/ROW]
[ROW][C]47[/C][C]104.8[/C][C]104.854186835933[/C][C]-0.0541868359330095[/C][/ROW]
[ROW][C]48[/C][C]104.17[/C][C]104.728423849609[/C][C]-0.558423849609341[/C][/ROW]
[ROW][C]49[/C][C]104.63[/C][C]104.535293270952[/C][C]0.0947067290478998[/C][/ROW]
[ROW][C]50[/C][C]105.32[/C][C]104.860398365875[/C][C]0.459601634125463[/C][/ROW]
[ROW][C]51[/C][C]106.16[/C][C]105.684941949395[/C][C]0.47505805060527[/C][/ROW]
[ROW][C]52[/C][C]107.22[/C][C]106.641811479637[/C][C]0.578188520362957[/C][/ROW]
[ROW][C]53[/C][C]107.51[/C][C]107.715155921035[/C][C]-0.205155921035001[/C][/ROW]
[ROW][C]54[/C][C]107.87[/C][C]107.973693778444[/C][C]-0.103693778443926[/C][/ROW]
[ROW][C]55[/C][C]107.79[/C][C]108.156887337282[/C][C]-0.366887337282336[/C][/ROW]
[ROW][C]56[/C][C]108.04[/C][C]108.298422140637[/C][C]-0.258422140637421[/C][/ROW]
[ROW][C]57[/C][C]107.74[/C][C]108.259912333341[/C][C]-0.519912333341395[/C][/ROW]
[ROW][C]58[/C][C]107.71[/C][C]107.684422848219[/C][C]0.0255771517811638[/C][/ROW]
[ROW][C]59[/C][C]111.19[/C][C]107.965327417243[/C][C]3.22467258275704[/C][/ROW]
[ROW][C]60[/C][C]110.82[/C][C]111.062201709469[/C][C]-0.242201709468659[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294791&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294791&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
1393.0192.11878472222220.891215277777789
1493.2193.18642800662970.0235719933703393
1593.5893.55061858058940.0293814194105977
1694.0794.01351127524590.0564887247541037
1794.5794.49940122128560.0705987787144409
1895.0394.96258967627570.0674103237243173
1995.2195.2405536079047-0.0305536079047073
2095.8995.58688719672960.303112803270395
2196.4396.05254627252970.377453727470339
2296.3596.34795603838460.00204396161541354
2396.7196.57663613546980.133363864530182
2496.3296.6605067981235-0.340506798123556
2597.2396.61703342254110.612966577458948
2697.8897.42853898930560.451461010694359
2798.298.265045445335-0.0650454453350306
2898.5698.6972769716971-0.137276971697091
2999.3199.04983669598640.260163304013631
3099.6999.7530693084297-0.0630693084297036
3199.7799.9557757819209-0.185775781920952
32101.06100.2156248577410.844375142258585
33101.77101.2707188208750.49928117912502
34101.91101.7392242522750.170775747725315
35102.52102.2131651145490.306834885450897
36102.09102.527755887568-0.437755887567874
37102.22102.511770482203-0.291770482202779
38102.74102.4980253070370.241974692963424
39103.56103.1531347123920.406865287607644
40104.4104.0923551328410.307644867158785
41104.76104.961605684069-0.201605684069406
42104.86105.266076687229-0.406076687229202
43104.84105.179917208286-0.339917208285883
44104.96105.37453636912-0.414536369120185
45104.83105.203243482626-0.373243482626435
46104.58104.785047584322-0.205047584322031
47104.8104.854186835933-0.0541868359330095
48104.17104.728423849609-0.558423849609341
49104.63104.5352932709520.0947067290478998
50105.32104.8603983658750.459601634125463
51106.16105.6849419493950.47505805060527
52107.22106.6418114796370.578188520362957
53107.51107.715155921035-0.205155921035001
54107.87107.973693778444-0.103693778443926
55107.79108.156887337282-0.366887337282336
56108.04108.298422140637-0.258422140637421
57107.74108.259912333341-0.519912333341395
58107.71107.6844228482190.0255771517811638
59111.19107.9653274172433.22467258275704
60110.82111.062201709469-0.242201709468659







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61111.312590658519110.177132029354112.448049287685
62111.672022864703110.07103945119113.273006278215
63112.150186047897110.167644995067114.132727100726
64112.732516984662110.409902851325115.055131118
65113.274747242335110.636820640737115.912673843934
66113.797102718342110.860074158441116.734131278243
67114.135364925398110.910417927764117.360311923031
68114.712833686893111.207922476973118.217744896814
69115.000117919724111.220990795145118.779245044302
70115.053329745524111.004158528245119.102500962802
71115.550236262696111.234026529011119.866445996381
72115.403641775496110.822512516776119.984771034216

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 111.312590658519 & 110.177132029354 & 112.448049287685 \tabularnewline
62 & 111.672022864703 & 110.07103945119 & 113.273006278215 \tabularnewline
63 & 112.150186047897 & 110.167644995067 & 114.132727100726 \tabularnewline
64 & 112.732516984662 & 110.409902851325 & 115.055131118 \tabularnewline
65 & 113.274747242335 & 110.636820640737 & 115.912673843934 \tabularnewline
66 & 113.797102718342 & 110.860074158441 & 116.734131278243 \tabularnewline
67 & 114.135364925398 & 110.910417927764 & 117.360311923031 \tabularnewline
68 & 114.712833686893 & 111.207922476973 & 118.217744896814 \tabularnewline
69 & 115.000117919724 & 111.220990795145 & 118.779245044302 \tabularnewline
70 & 115.053329745524 & 111.004158528245 & 119.102500962802 \tabularnewline
71 & 115.550236262696 & 111.234026529011 & 119.866445996381 \tabularnewline
72 & 115.403641775496 & 110.822512516776 & 119.984771034216 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294791&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]111.312590658519[/C][C]110.177132029354[/C][C]112.448049287685[/C][/ROW]
[ROW][C]62[/C][C]111.672022864703[/C][C]110.07103945119[/C][C]113.273006278215[/C][/ROW]
[ROW][C]63[/C][C]112.150186047897[/C][C]110.167644995067[/C][C]114.132727100726[/C][/ROW]
[ROW][C]64[/C][C]112.732516984662[/C][C]110.409902851325[/C][C]115.055131118[/C][/ROW]
[ROW][C]65[/C][C]113.274747242335[/C][C]110.636820640737[/C][C]115.912673843934[/C][/ROW]
[ROW][C]66[/C][C]113.797102718342[/C][C]110.860074158441[/C][C]116.734131278243[/C][/ROW]
[ROW][C]67[/C][C]114.135364925398[/C][C]110.910417927764[/C][C]117.360311923031[/C][/ROW]
[ROW][C]68[/C][C]114.712833686893[/C][C]111.207922476973[/C][C]118.217744896814[/C][/ROW]
[ROW][C]69[/C][C]115.000117919724[/C][C]111.220990795145[/C][C]118.779245044302[/C][/ROW]
[ROW][C]70[/C][C]115.053329745524[/C][C]111.004158528245[/C][C]119.102500962802[/C][/ROW]
[ROW][C]71[/C][C]115.550236262696[/C][C]111.234026529011[/C][C]119.866445996381[/C][/ROW]
[ROW][C]72[/C][C]115.403641775496[/C][C]110.822512516776[/C][C]119.984771034216[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294791&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294791&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
61111.312590658519110.177132029354112.448049287685
62111.672022864703110.07103945119113.273006278215
63112.150186047897110.167644995067114.132727100726
64112.732516984662110.409902851325115.055131118
65113.274747242335110.636820640737115.912673843934
66113.797102718342110.860074158441116.734131278243
67114.135364925398110.910417927764117.360311923031
68114.712833686893111.207922476973118.217744896814
69115.000117919724111.220990795145118.779245044302
70115.053329745524111.004158528245119.102500962802
71115.550236262696111.234026529011119.866445996381
72115.403641775496110.822512516776119.984771034216



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')