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Description of Statistical Computation

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, 30 Nov 2010 19:51:51 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/30/t1291146639u81jk3ro71ieadw.htm/, Retrieved Mon, 29 Apr 2024 14:44:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103795, Retrieved Mon, 29 Apr 2024 14:44:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact189

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
-  M D    [Exponential Smoothing] [Holt-Winters model] [2010-11-30 19:51:51] [214713b86cef2e1efaaf6d85aa84ff3c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,96
0,95
0,95
0,96
0,96
0,96
0,95
0,96
0,96
0,96
0,95
0,95
0,96
0,96
0,96
0,96
0,96
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,96
0,96
0,96
0,97
0,97
0,97
0,96
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,94
0,94
0,94
0,93
0,93
0,93
0,93
0,92
0,93

Tables (Output of Computation)





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=103795&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=103795&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103795&T=0

As an alternative you can also use a QR Code:  
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
alpha0.839082605513062
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.839082605513062 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103795&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]0.839082605513062[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103795&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103795&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.839082605513062
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.960.960080128205128-8.01282051284824e-05
140.960.96018771919682-0.000187719196819036
150.960.960621699125539-0.00062169912553911
160.960.960691534044928-0.000691534044928499
170.960.960286105031534-0.000286105031534145
180.950.9498041977843830.000195802215617435
190.950.948059983859120.00194001614087991
200.950.959029309498839-0.00902930949883884
210.950.950377798133395-0.00037779813339478
220.950.949402286132760.000597713867240279
230.950.9396619759499940.0103380240500064
240.950.9485112572805550.00148874271944510
250.950.959922366553357-0.00992236655335677
260.950.951754193285682-0.00175419328568227
270.950.95080393713506-0.000803937135060995
280.960.9507096216573250.0092903783426751
290.960.958745082278610.00125491772139119
300.960.9496337676767330.0103662323232674
310.970.9567040591056670.0132959408943334
320.970.97543678837430-0.00543678837430095
330.970.971191877661696-0.00119187766169615
340.960.969690262538792-0.00969026253879213
350.950.9528848756439-0.00288487564390072
360.950.9492150485520650.000784951447935223
370.950.958199372838646-0.0081993728386458
380.950.952791334786346-0.00279133478634563
390.950.951123743986915-0.00112374398691517
400.950.95238543508847-0.00238543508847089
410.950.9493308783677850.000669121632214997
420.950.9411942014631880.00880579853681185
430.950.9474266011147140.00257339888528552
440.950.954147809911136-0.00414780991113584
450.950.951667538577556-0.00166753857755586
460.950.9483992667022620.00160073329773802
470.940.942163063140325-0.00216306314032488
480.940.9396894353785170.000310564621482934
490.940.946829975875315-0.00682997587531498
500.930.94344122238765-0.0134412223876503
510.930.93310584051781-0.0031058405178106
520.930.932501360853135-0.00250136085313446
530.930.9298410641485940.000158935851406139
540.920.92258563207701-0.00258563207700990
550.930.9182567789352440.0117432210647556

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.96 & 0.960080128205128 & -8.01282051284824e-05 \tabularnewline
14 & 0.96 & 0.96018771919682 & -0.000187719196819036 \tabularnewline
15 & 0.96 & 0.960621699125539 & -0.00062169912553911 \tabularnewline
16 & 0.96 & 0.960691534044928 & -0.000691534044928499 \tabularnewline
17 & 0.96 & 0.960286105031534 & -0.000286105031534145 \tabularnewline
18 & 0.95 & 0.949804197784383 & 0.000195802215617435 \tabularnewline
19 & 0.95 & 0.94805998385912 & 0.00194001614087991 \tabularnewline
20 & 0.95 & 0.959029309498839 & -0.00902930949883884 \tabularnewline
21 & 0.95 & 0.950377798133395 & -0.00037779813339478 \tabularnewline
22 & 0.95 & 0.94940228613276 & 0.000597713867240279 \tabularnewline
23 & 0.95 & 0.939661975949994 & 0.0103380240500064 \tabularnewline
24 & 0.95 & 0.948511257280555 & 0.00148874271944510 \tabularnewline
25 & 0.95 & 0.959922366553357 & -0.00992236655335677 \tabularnewline
26 & 0.95 & 0.951754193285682 & -0.00175419328568227 \tabularnewline
27 & 0.95 & 0.95080393713506 & -0.000803937135060995 \tabularnewline
28 & 0.96 & 0.950709621657325 & 0.0092903783426751 \tabularnewline
29 & 0.96 & 0.95874508227861 & 0.00125491772139119 \tabularnewline
30 & 0.96 & 0.949633767676733 & 0.0103662323232674 \tabularnewline
31 & 0.97 & 0.956704059105667 & 0.0132959408943334 \tabularnewline
32 & 0.97 & 0.97543678837430 & -0.00543678837430095 \tabularnewline
33 & 0.97 & 0.971191877661696 & -0.00119187766169615 \tabularnewline
34 & 0.96 & 0.969690262538792 & -0.00969026253879213 \tabularnewline
35 & 0.95 & 0.9528848756439 & -0.00288487564390072 \tabularnewline
36 & 0.95 & 0.949215048552065 & 0.000784951447935223 \tabularnewline
37 & 0.95 & 0.958199372838646 & -0.0081993728386458 \tabularnewline
38 & 0.95 & 0.952791334786346 & -0.00279133478634563 \tabularnewline
39 & 0.95 & 0.951123743986915 & -0.00112374398691517 \tabularnewline
40 & 0.95 & 0.95238543508847 & -0.00238543508847089 \tabularnewline
41 & 0.95 & 0.949330878367785 & 0.000669121632214997 \tabularnewline
42 & 0.95 & 0.941194201463188 & 0.00880579853681185 \tabularnewline
43 & 0.95 & 0.947426601114714 & 0.00257339888528552 \tabularnewline
44 & 0.95 & 0.954147809911136 & -0.00414780991113584 \tabularnewline
45 & 0.95 & 0.951667538577556 & -0.00166753857755586 \tabularnewline
46 & 0.95 & 0.948399266702262 & 0.00160073329773802 \tabularnewline
47 & 0.94 & 0.942163063140325 & -0.00216306314032488 \tabularnewline
48 & 0.94 & 0.939689435378517 & 0.000310564621482934 \tabularnewline
49 & 0.94 & 0.946829975875315 & -0.00682997587531498 \tabularnewline
50 & 0.93 & 0.94344122238765 & -0.0134412223876503 \tabularnewline
51 & 0.93 & 0.93310584051781 & -0.0031058405178106 \tabularnewline
52 & 0.93 & 0.932501360853135 & -0.00250136085313446 \tabularnewline
53 & 0.93 & 0.929841064148594 & 0.000158935851406139 \tabularnewline
54 & 0.92 & 0.92258563207701 & -0.00258563207700990 \tabularnewline
55 & 0.93 & 0.918256778935244 & 0.0117432210647556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103795&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]0.96[/C][C]0.960080128205128[/C][C]-8.01282051284824e-05[/C][/ROW]
[ROW][C]14[/C][C]0.96[/C][C]0.96018771919682[/C][C]-0.000187719196819036[/C][/ROW]
[ROW][C]15[/C][C]0.96[/C][C]0.960621699125539[/C][C]-0.00062169912553911[/C][/ROW]
[ROW][C]16[/C][C]0.96[/C][C]0.960691534044928[/C][C]-0.000691534044928499[/C][/ROW]
[ROW][C]17[/C][C]0.96[/C][C]0.960286105031534[/C][C]-0.000286105031534145[/C][/ROW]
[ROW][C]18[/C][C]0.95[/C][C]0.949804197784383[/C][C]0.000195802215617435[/C][/ROW]
[ROW][C]19[/C][C]0.95[/C][C]0.94805998385912[/C][C]0.00194001614087991[/C][/ROW]
[ROW][C]20[/C][C]0.95[/C][C]0.959029309498839[/C][C]-0.00902930949883884[/C][/ROW]
[ROW][C]21[/C][C]0.95[/C][C]0.950377798133395[/C][C]-0.00037779813339478[/C][/ROW]
[ROW][C]22[/C][C]0.95[/C][C]0.94940228613276[/C][C]0.000597713867240279[/C][/ROW]
[ROW][C]23[/C][C]0.95[/C][C]0.939661975949994[/C][C]0.0103380240500064[/C][/ROW]
[ROW][C]24[/C][C]0.95[/C][C]0.948511257280555[/C][C]0.00148874271944510[/C][/ROW]
[ROW][C]25[/C][C]0.95[/C][C]0.959922366553357[/C][C]-0.00992236655335677[/C][/ROW]
[ROW][C]26[/C][C]0.95[/C][C]0.951754193285682[/C][C]-0.00175419328568227[/C][/ROW]
[ROW][C]27[/C][C]0.95[/C][C]0.95080393713506[/C][C]-0.000803937135060995[/C][/ROW]
[ROW][C]28[/C][C]0.96[/C][C]0.950709621657325[/C][C]0.0092903783426751[/C][/ROW]
[ROW][C]29[/C][C]0.96[/C][C]0.95874508227861[/C][C]0.00125491772139119[/C][/ROW]
[ROW][C]30[/C][C]0.96[/C][C]0.949633767676733[/C][C]0.0103662323232674[/C][/ROW]
[ROW][C]31[/C][C]0.97[/C][C]0.956704059105667[/C][C]0.0132959408943334[/C][/ROW]
[ROW][C]32[/C][C]0.97[/C][C]0.97543678837430[/C][C]-0.00543678837430095[/C][/ROW]
[ROW][C]33[/C][C]0.97[/C][C]0.971191877661696[/C][C]-0.00119187766169615[/C][/ROW]
[ROW][C]34[/C][C]0.96[/C][C]0.969690262538792[/C][C]-0.00969026253879213[/C][/ROW]
[ROW][C]35[/C][C]0.95[/C][C]0.9528848756439[/C][C]-0.00288487564390072[/C][/ROW]
[ROW][C]36[/C][C]0.95[/C][C]0.949215048552065[/C][C]0.000784951447935223[/C][/ROW]
[ROW][C]37[/C][C]0.95[/C][C]0.958199372838646[/C][C]-0.0081993728386458[/C][/ROW]
[ROW][C]38[/C][C]0.95[/C][C]0.952791334786346[/C][C]-0.00279133478634563[/C][/ROW]
[ROW][C]39[/C][C]0.95[/C][C]0.951123743986915[/C][C]-0.00112374398691517[/C][/ROW]
[ROW][C]40[/C][C]0.95[/C][C]0.95238543508847[/C][C]-0.00238543508847089[/C][/ROW]
[ROW][C]41[/C][C]0.95[/C][C]0.949330878367785[/C][C]0.000669121632214997[/C][/ROW]
[ROW][C]42[/C][C]0.95[/C][C]0.941194201463188[/C][C]0.00880579853681185[/C][/ROW]
[ROW][C]43[/C][C]0.95[/C][C]0.947426601114714[/C][C]0.00257339888528552[/C][/ROW]
[ROW][C]44[/C][C]0.95[/C][C]0.954147809911136[/C][C]-0.00414780991113584[/C][/ROW]
[ROW][C]45[/C][C]0.95[/C][C]0.951667538577556[/C][C]-0.00166753857755586[/C][/ROW]
[ROW][C]46[/C][C]0.95[/C][C]0.948399266702262[/C][C]0.00160073329773802[/C][/ROW]
[ROW][C]47[/C][C]0.94[/C][C]0.942163063140325[/C][C]-0.00216306314032488[/C][/ROW]
[ROW][C]48[/C][C]0.94[/C][C]0.939689435378517[/C][C]0.000310564621482934[/C][/ROW]
[ROW][C]49[/C][C]0.94[/C][C]0.946829975875315[/C][C]-0.00682997587531498[/C][/ROW]
[ROW][C]50[/C][C]0.93[/C][C]0.94344122238765[/C][C]-0.0134412223876503[/C][/ROW]
[ROW][C]51[/C][C]0.93[/C][C]0.93310584051781[/C][C]-0.0031058405178106[/C][/ROW]
[ROW][C]52[/C][C]0.93[/C][C]0.932501360853135[/C][C]-0.00250136085313446[/C][/ROW]
[ROW][C]53[/C][C]0.93[/C][C]0.929841064148594[/C][C]0.000158935851406139[/C][/ROW]
[ROW][C]54[/C][C]0.92[/C][C]0.92258563207701[/C][C]-0.00258563207700990[/C][/ROW]
[ROW][C]55[/C][C]0.93[/C][C]0.918256778935244[/C][C]0.0117432210647556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103795&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103795&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.960.960080128205128-8.01282051284824e-05
140.960.96018771919682-0.000187719196819036
150.960.960621699125539-0.00062169912553911
160.960.960691534044928-0.000691534044928499
170.960.960286105031534-0.000286105031534145
180.950.9498041977843830.000195802215617435
190.950.948059983859120.00194001614087991
200.950.959029309498839-0.00902930949883884
210.950.950377798133395-0.00037779813339478
220.950.949402286132760.000597713867240279
230.950.9396619759499940.0103380240500064
240.950.9485112572805550.00148874271944510
250.950.959922366553357-0.00992236655335677
260.950.951754193285682-0.00175419328568227
270.950.95080393713506-0.000803937135060995
280.960.9507096216573250.0092903783426751
290.960.958745082278610.00125491772139119
300.960.9496337676767330.0103662323232674
310.970.9567040591056670.0132959408943334
320.970.97543678837430-0.00543678837430095
330.970.971191877661696-0.00119187766169615
340.960.969690262538792-0.00969026253879213
350.950.9528848756439-0.00288487564390072
360.950.9492150485520650.000784951447935223
370.950.958199372838646-0.0081993728386458
380.950.952791334786346-0.00279133478634563
390.950.951123743986915-0.00112374398691517
400.950.95238543508847-0.00238543508847089
410.950.9493308783677850.000669121632214997
420.950.9411942014631880.00880579853681185
430.950.9474266011147140.00257339888528552
440.950.954147809911136-0.00414780991113584
450.950.951667538577556-0.00166753857755586
460.950.9483992667022620.00160073329773802
470.940.942163063140325-0.00216306314032488
480.940.9396894353785170.000310564621482934
490.940.946829975875315-0.00682997587531498
500.930.94344122238765-0.0134412223876503
510.930.93310584051781-0.0031058405178106
520.930.932501360853135-0.00250136085313446
530.930.9298410641485940.000158935851406139
540.920.92258563207701-0.00258563207700990
550.930.9182567789352440.0117432210647556






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
560.9315906666107840.9203647798924640.942816553329105
570.9329898692252330.9183356377280130.947644100722454
580.9316467217590360.9142262605442540.949067182973817
590.9234617104147090.9036577098820570.94326571094736
600.9232011210429350.9012711323229460.945131109762924
610.9289320349959850.905064685469480.952799384522492
620.9302103308982960.9045514856089610.95586917618763
630.9328163876522880.9054832153200550.960149559984521
640.9349152360342650.9060045411635920.963825930904937
650.9347818757259570.9043753921070530.965188359344862
660.9269514346260330.8951193719497270.958783497302339
670.9270979020979020.8939014236342180.960294380561586

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
56 & 0.931590666610784 & 0.920364779892464 & 0.942816553329105 \tabularnewline
57 & 0.932989869225233 & 0.918335637728013 & 0.947644100722454 \tabularnewline
58 & 0.931646721759036 & 0.914226260544254 & 0.949067182973817 \tabularnewline
59 & 0.923461710414709 & 0.903657709882057 & 0.94326571094736 \tabularnewline
60 & 0.923201121042935 & 0.901271132322946 & 0.945131109762924 \tabularnewline
61 & 0.928932034995985 & 0.90506468546948 & 0.952799384522492 \tabularnewline
62 & 0.930210330898296 & 0.904551485608961 & 0.95586917618763 \tabularnewline
63 & 0.932816387652288 & 0.905483215320055 & 0.960149559984521 \tabularnewline
64 & 0.934915236034265 & 0.906004541163592 & 0.963825930904937 \tabularnewline
65 & 0.934781875725957 & 0.904375392107053 & 0.965188359344862 \tabularnewline
66 & 0.926951434626033 & 0.895119371949727 & 0.958783497302339 \tabularnewline
67 & 0.927097902097902 & 0.893901423634218 & 0.960294380561586 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103795&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]56[/C][C]0.931590666610784[/C][C]0.920364779892464[/C][C]0.942816553329105[/C][/ROW]
[ROW][C]57[/C][C]0.932989869225233[/C][C]0.918335637728013[/C][C]0.947644100722454[/C][/ROW]
[ROW][C]58[/C][C]0.931646721759036[/C][C]0.914226260544254[/C][C]0.949067182973817[/C][/ROW]
[ROW][C]59[/C][C]0.923461710414709[/C][C]0.903657709882057[/C][C]0.94326571094736[/C][/ROW]
[ROW][C]60[/C][C]0.923201121042935[/C][C]0.901271132322946[/C][C]0.945131109762924[/C][/ROW]
[ROW][C]61[/C][C]0.928932034995985[/C][C]0.90506468546948[/C][C]0.952799384522492[/C][/ROW]
[ROW][C]62[/C][C]0.930210330898296[/C][C]0.904551485608961[/C][C]0.95586917618763[/C][/ROW]
[ROW][C]63[/C][C]0.932816387652288[/C][C]0.905483215320055[/C][C]0.960149559984521[/C][/ROW]
[ROW][C]64[/C][C]0.934915236034265[/C][C]0.906004541163592[/C][C]0.963825930904937[/C][/ROW]
[ROW][C]65[/C][C]0.934781875725957[/C][C]0.904375392107053[/C][C]0.965188359344862[/C][/ROW]
[ROW][C]66[/C][C]0.926951434626033[/C][C]0.895119371949727[/C][C]0.958783497302339[/C][/ROW]
[ROW][C]67[/C][C]0.927097902097902[/C][C]0.893901423634218[/C][C]0.960294380561586[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103795&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103795&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
560.9315906666107840.9203647798924640.942816553329105
570.9329898692252330.9183356377280130.947644100722454
580.9316467217590360.9142262605442540.949067182973817
590.9234617104147090.9036577098820570.94326571094736
600.9232011210429350.9012711323229460.945131109762924
610.9289320349959850.905064685469480.952799384522492
620.9302103308982960.9045514856089610.95586917618763
630.9328163876522880.9054832153200550.960149559984521
640.9349152360342650.9060045411635920.963825930904937
650.9347818757259570.9043753921070530.965188359344862
660.9269514346260330.8951193719497270.958783497302339
670.9270979020979020.8939014236342180.960294380561586


Figures (Output of Computation)

Input Parameters & R Code

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=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')