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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 24 Nov 2016 18:33:44 +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/2016/Nov/24/t1480015564q0m3d9ejvf9t50s.htm/, Retrieved Tue, 07 May 2024 15:32:01 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 07 May 2024 15:32:01 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
154
156
152
150
152
138
140
138
141
152
158
146
166
167
163
169
168
158
159
161
166
177
186
182
203
213
215
216
219
217
216
222
224
234
237
233
253
257
254
258
253
241
238
240
240
245
249
247
263
265
261
257
252
245
235
240
243
255
252
240




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.65608700669263
beta0.199347512411938
gamma0.778784375543958

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.65608700669263 \tabularnewline
beta & 0.199347512411938 \tabularnewline
gamma & 0.778784375543958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.65608700669263[/C][/ROW]
[ROW][C]beta[/C][C]0.199347512411938[/C][/ROW]
[ROW][C]gamma[/C][C]0.778784375543958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.65608700669263
beta0.199347512411938
gamma0.778784375543958







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13166157.7278311965818.27216880341874
14167165.1488639124511.85113608754861
15163163.349249310514-0.349249310513926
16169169.976979028572-0.976979028571549
17168168.940085019218-0.940085019217804
18158158.34611028314-0.346110283140092
19159161.179900460986-2.17990046098626
20161159.1504570470781.84954295292155
21166165.0482462195460.951753780454453
22177178.148153470689-1.1481534706891
23186184.5118393224471.4881606775526
24182174.7581454779797.2418545220205
25203203.817101184095-0.81710118409535
26213204.421472760078.57852723993014
27215208.1926068776936.80739312230722
28216222.029934612889-6.02993461288895
29219219.709216291758-0.709216291758281
30217211.4774660786785.52253392132152
31216220.489669811131-4.48966981113142
32222220.54116962871.45883037130045
33224228.408188477132-4.40818847713197
34234239.194087044029-5.194087044029
35237244.845224798244-7.84522479824417
36233230.524187771362.47581222863977
37253253.689529328555-0.689529328555068
38257256.3025406830680.697459316932168
39254252.8063512095591.19364879044076
40258257.1657955100410.834204489959347
41253259.314870283401-6.31487028340132
42241246.882489682149-5.88248968214907
43238242.046832549729-4.0468325497292
44240240.356437675536-0.35643767553637
45240241.598032118701-1.59803211870056
46245250.521622655281-5.52162265528051
47249251.709440694276-2.70944069427568
48247240.6555930169586.34440698304167
49263263.150596697325-0.150596697325227
50265264.1984778545050.801522145494744
51261258.6268696983742.37313030162647
52257261.54155924439-4.5415592443901
53252255.423481253515-3.42348125351492
54245242.5566542001472.44334579985298
55235242.316795880531-7.31679588053095
56240237.6834325794672.31656742053286
57243238.9098087101744.09019128982595
58255249.82205540365.17794459639961
59252259.489865562035-7.48986556203522
60240247.806290533727-7.80629053372743

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 166 & 157.727831196581 & 8.27216880341874 \tabularnewline
14 & 167 & 165.148863912451 & 1.85113608754861 \tabularnewline
15 & 163 & 163.349249310514 & -0.349249310513926 \tabularnewline
16 & 169 & 169.976979028572 & -0.976979028571549 \tabularnewline
17 & 168 & 168.940085019218 & -0.940085019217804 \tabularnewline
18 & 158 & 158.34611028314 & -0.346110283140092 \tabularnewline
19 & 159 & 161.179900460986 & -2.17990046098626 \tabularnewline
20 & 161 & 159.150457047078 & 1.84954295292155 \tabularnewline
21 & 166 & 165.048246219546 & 0.951753780454453 \tabularnewline
22 & 177 & 178.148153470689 & -1.1481534706891 \tabularnewline
23 & 186 & 184.511839322447 & 1.4881606775526 \tabularnewline
24 & 182 & 174.758145477979 & 7.2418545220205 \tabularnewline
25 & 203 & 203.817101184095 & -0.81710118409535 \tabularnewline
26 & 213 & 204.42147276007 & 8.57852723993014 \tabularnewline
27 & 215 & 208.192606877693 & 6.80739312230722 \tabularnewline
28 & 216 & 222.029934612889 & -6.02993461288895 \tabularnewline
29 & 219 & 219.709216291758 & -0.709216291758281 \tabularnewline
30 & 217 & 211.477466078678 & 5.52253392132152 \tabularnewline
31 & 216 & 220.489669811131 & -4.48966981113142 \tabularnewline
32 & 222 & 220.5411696287 & 1.45883037130045 \tabularnewline
33 & 224 & 228.408188477132 & -4.40818847713197 \tabularnewline
34 & 234 & 239.194087044029 & -5.194087044029 \tabularnewline
35 & 237 & 244.845224798244 & -7.84522479824417 \tabularnewline
36 & 233 & 230.52418777136 & 2.47581222863977 \tabularnewline
37 & 253 & 253.689529328555 & -0.689529328555068 \tabularnewline
38 & 257 & 256.302540683068 & 0.697459316932168 \tabularnewline
39 & 254 & 252.806351209559 & 1.19364879044076 \tabularnewline
40 & 258 & 257.165795510041 & 0.834204489959347 \tabularnewline
41 & 253 & 259.314870283401 & -6.31487028340132 \tabularnewline
42 & 241 & 246.882489682149 & -5.88248968214907 \tabularnewline
43 & 238 & 242.046832549729 & -4.0468325497292 \tabularnewline
44 & 240 & 240.356437675536 & -0.35643767553637 \tabularnewline
45 & 240 & 241.598032118701 & -1.59803211870056 \tabularnewline
46 & 245 & 250.521622655281 & -5.52162265528051 \tabularnewline
47 & 249 & 251.709440694276 & -2.70944069427568 \tabularnewline
48 & 247 & 240.655593016958 & 6.34440698304167 \tabularnewline
49 & 263 & 263.150596697325 & -0.150596697325227 \tabularnewline
50 & 265 & 264.198477854505 & 0.801522145494744 \tabularnewline
51 & 261 & 258.626869698374 & 2.37313030162647 \tabularnewline
52 & 257 & 261.54155924439 & -4.5415592443901 \tabularnewline
53 & 252 & 255.423481253515 & -3.42348125351492 \tabularnewline
54 & 245 & 242.556654200147 & 2.44334579985298 \tabularnewline
55 & 235 & 242.316795880531 & -7.31679588053095 \tabularnewline
56 & 240 & 237.683432579467 & 2.31656742053286 \tabularnewline
57 & 243 & 238.909808710174 & 4.09019128982595 \tabularnewline
58 & 255 & 249.8220554036 & 5.17794459639961 \tabularnewline
59 & 252 & 259.489865562035 & -7.48986556203522 \tabularnewline
60 & 240 & 247.806290533727 & -7.80629053372743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]166[/C][C]157.727831196581[/C][C]8.27216880341874[/C][/ROW]
[ROW][C]14[/C][C]167[/C][C]165.148863912451[/C][C]1.85113608754861[/C][/ROW]
[ROW][C]15[/C][C]163[/C][C]163.349249310514[/C][C]-0.349249310513926[/C][/ROW]
[ROW][C]16[/C][C]169[/C][C]169.976979028572[/C][C]-0.976979028571549[/C][/ROW]
[ROW][C]17[/C][C]168[/C][C]168.940085019218[/C][C]-0.940085019217804[/C][/ROW]
[ROW][C]18[/C][C]158[/C][C]158.34611028314[/C][C]-0.346110283140092[/C][/ROW]
[ROW][C]19[/C][C]159[/C][C]161.179900460986[/C][C]-2.17990046098626[/C][/ROW]
[ROW][C]20[/C][C]161[/C][C]159.150457047078[/C][C]1.84954295292155[/C][/ROW]
[ROW][C]21[/C][C]166[/C][C]165.048246219546[/C][C]0.951753780454453[/C][/ROW]
[ROW][C]22[/C][C]177[/C][C]178.148153470689[/C][C]-1.1481534706891[/C][/ROW]
[ROW][C]23[/C][C]186[/C][C]184.511839322447[/C][C]1.4881606775526[/C][/ROW]
[ROW][C]24[/C][C]182[/C][C]174.758145477979[/C][C]7.2418545220205[/C][/ROW]
[ROW][C]25[/C][C]203[/C][C]203.817101184095[/C][C]-0.81710118409535[/C][/ROW]
[ROW][C]26[/C][C]213[/C][C]204.42147276007[/C][C]8.57852723993014[/C][/ROW]
[ROW][C]27[/C][C]215[/C][C]208.192606877693[/C][C]6.80739312230722[/C][/ROW]
[ROW][C]28[/C][C]216[/C][C]222.029934612889[/C][C]-6.02993461288895[/C][/ROW]
[ROW][C]29[/C][C]219[/C][C]219.709216291758[/C][C]-0.709216291758281[/C][/ROW]
[ROW][C]30[/C][C]217[/C][C]211.477466078678[/C][C]5.52253392132152[/C][/ROW]
[ROW][C]31[/C][C]216[/C][C]220.489669811131[/C][C]-4.48966981113142[/C][/ROW]
[ROW][C]32[/C][C]222[/C][C]220.5411696287[/C][C]1.45883037130045[/C][/ROW]
[ROW][C]33[/C][C]224[/C][C]228.408188477132[/C][C]-4.40818847713197[/C][/ROW]
[ROW][C]34[/C][C]234[/C][C]239.194087044029[/C][C]-5.194087044029[/C][/ROW]
[ROW][C]35[/C][C]237[/C][C]244.845224798244[/C][C]-7.84522479824417[/C][/ROW]
[ROW][C]36[/C][C]233[/C][C]230.52418777136[/C][C]2.47581222863977[/C][/ROW]
[ROW][C]37[/C][C]253[/C][C]253.689529328555[/C][C]-0.689529328555068[/C][/ROW]
[ROW][C]38[/C][C]257[/C][C]256.302540683068[/C][C]0.697459316932168[/C][/ROW]
[ROW][C]39[/C][C]254[/C][C]252.806351209559[/C][C]1.19364879044076[/C][/ROW]
[ROW][C]40[/C][C]258[/C][C]257.165795510041[/C][C]0.834204489959347[/C][/ROW]
[ROW][C]41[/C][C]253[/C][C]259.314870283401[/C][C]-6.31487028340132[/C][/ROW]
[ROW][C]42[/C][C]241[/C][C]246.882489682149[/C][C]-5.88248968214907[/C][/ROW]
[ROW][C]43[/C][C]238[/C][C]242.046832549729[/C][C]-4.0468325497292[/C][/ROW]
[ROW][C]44[/C][C]240[/C][C]240.356437675536[/C][C]-0.35643767553637[/C][/ROW]
[ROW][C]45[/C][C]240[/C][C]241.598032118701[/C][C]-1.59803211870056[/C][/ROW]
[ROW][C]46[/C][C]245[/C][C]250.521622655281[/C][C]-5.52162265528051[/C][/ROW]
[ROW][C]47[/C][C]249[/C][C]251.709440694276[/C][C]-2.70944069427568[/C][/ROW]
[ROW][C]48[/C][C]247[/C][C]240.655593016958[/C][C]6.34440698304167[/C][/ROW]
[ROW][C]49[/C][C]263[/C][C]263.150596697325[/C][C]-0.150596697325227[/C][/ROW]
[ROW][C]50[/C][C]265[/C][C]264.198477854505[/C][C]0.801522145494744[/C][/ROW]
[ROW][C]51[/C][C]261[/C][C]258.626869698374[/C][C]2.37313030162647[/C][/ROW]
[ROW][C]52[/C][C]257[/C][C]261.54155924439[/C][C]-4.5415592443901[/C][/ROW]
[ROW][C]53[/C][C]252[/C][C]255.423481253515[/C][C]-3.42348125351492[/C][/ROW]
[ROW][C]54[/C][C]245[/C][C]242.556654200147[/C][C]2.44334579985298[/C][/ROW]
[ROW][C]55[/C][C]235[/C][C]242.316795880531[/C][C]-7.31679588053095[/C][/ROW]
[ROW][C]56[/C][C]240[/C][C]237.683432579467[/C][C]2.31656742053286[/C][/ROW]
[ROW][C]57[/C][C]243[/C][C]238.909808710174[/C][C]4.09019128982595[/C][/ROW]
[ROW][C]58[/C][C]255[/C][C]249.8220554036[/C][C]5.17794459639961[/C][/ROW]
[ROW][C]59[/C][C]252[/C][C]259.489865562035[/C][C]-7.48986556203522[/C][/ROW]
[ROW][C]60[/C][C]240[/C][C]247.806290533727[/C][C]-7.80629053372743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
13166157.7278311965818.27216880341874
14167165.1488639124511.85113608754861
15163163.349249310514-0.349249310513926
16169169.976979028572-0.976979028571549
17168168.940085019218-0.940085019217804
18158158.34611028314-0.346110283140092
19159161.179900460986-2.17990046098626
20161159.1504570470781.84954295292155
21166165.0482462195460.951753780454453
22177178.148153470689-1.1481534706891
23186184.5118393224471.4881606775526
24182174.7581454779797.2418545220205
25203203.817101184095-0.81710118409535
26213204.421472760078.57852723993014
27215208.1926068776936.80739312230722
28216222.029934612889-6.02993461288895
29219219.709216291758-0.709216291758281
30217211.4774660786785.52253392132152
31216220.489669811131-4.48966981113142
32222220.54116962871.45883037130045
33224228.408188477132-4.40818847713197
34234239.194087044029-5.194087044029
35237244.845224798244-7.84522479824417
36233230.524187771362.47581222863977
37253253.689529328555-0.689529328555068
38257256.3025406830680.697459316932168
39254252.8063512095591.19364879044076
40258257.1657955100410.834204489959347
41253259.314870283401-6.31487028340132
42241246.882489682149-5.88248968214907
43238242.046832549729-4.0468325497292
44240240.356437675536-0.35643767553637
45240241.598032118701-1.59803211870056
46245250.521622655281-5.52162265528051
47249251.709440694276-2.70944069427568
48247240.6555930169586.34440698304167
49263263.150596697325-0.150596697325227
50265264.1984778545050.801522145494744
51261258.6268696983742.37313030162647
52257261.54155924439-4.5415592443901
53252255.423481253515-3.42348125351492
54245242.5566542001472.44334579985298
55235242.316795880531-7.31679588053095
56240237.6834325794672.31656742053286
57243238.9098087101744.09019128982595
58255249.82205540365.17794459639961
59252259.489865562035-7.48986556203522
60240247.806290533727-7.80629053372743







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61257.508580649709248.963599976447266.053561322971
62257.160931097206246.287718204553268.034143989859
63249.630209240722236.22443201991263.035986461534
64246.971373697817230.847508404831263.095238990804
65242.561844785185223.548236755391261.575452814979
66232.38964189656210.325470434854254.453813358266
67226.49026065252201.223520214668251.757001090372
68228.752076559485200.138149095363257.366004023608
69228.145219177242196.04581568713260.244622667355
70235.341927973286199.62427442108271.059581525492
71236.219111119095196.755303878664275.682918359527
72228.343810807525185.010294347985271.677327267064

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 257.508580649709 & 248.963599976447 & 266.053561322971 \tabularnewline
62 & 257.160931097206 & 246.287718204553 & 268.034143989859 \tabularnewline
63 & 249.630209240722 & 236.22443201991 & 263.035986461534 \tabularnewline
64 & 246.971373697817 & 230.847508404831 & 263.095238990804 \tabularnewline
65 & 242.561844785185 & 223.548236755391 & 261.575452814979 \tabularnewline
66 & 232.38964189656 & 210.325470434854 & 254.453813358266 \tabularnewline
67 & 226.49026065252 & 201.223520214668 & 251.757001090372 \tabularnewline
68 & 228.752076559485 & 200.138149095363 & 257.366004023608 \tabularnewline
69 & 228.145219177242 & 196.04581568713 & 260.244622667355 \tabularnewline
70 & 235.341927973286 & 199.62427442108 & 271.059581525492 \tabularnewline
71 & 236.219111119095 & 196.755303878664 & 275.682918359527 \tabularnewline
72 & 228.343810807525 & 185.010294347985 & 271.677327267064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]257.508580649709[/C][C]248.963599976447[/C][C]266.053561322971[/C][/ROW]
[ROW][C]62[/C][C]257.160931097206[/C][C]246.287718204553[/C][C]268.034143989859[/C][/ROW]
[ROW][C]63[/C][C]249.630209240722[/C][C]236.22443201991[/C][C]263.035986461534[/C][/ROW]
[ROW][C]64[/C][C]246.971373697817[/C][C]230.847508404831[/C][C]263.095238990804[/C][/ROW]
[ROW][C]65[/C][C]242.561844785185[/C][C]223.548236755391[/C][C]261.575452814979[/C][/ROW]
[ROW][C]66[/C][C]232.38964189656[/C][C]210.325470434854[/C][C]254.453813358266[/C][/ROW]
[ROW][C]67[/C][C]226.49026065252[/C][C]201.223520214668[/C][C]251.757001090372[/C][/ROW]
[ROW][C]68[/C][C]228.752076559485[/C][C]200.138149095363[/C][C]257.366004023608[/C][/ROW]
[ROW][C]69[/C][C]228.145219177242[/C][C]196.04581568713[/C][C]260.244622667355[/C][/ROW]
[ROW][C]70[/C][C]235.341927973286[/C][C]199.62427442108[/C][C]271.059581525492[/C][/ROW]
[ROW][C]71[/C][C]236.219111119095[/C][C]196.755303878664[/C][C]275.682918359527[/C][/ROW]
[ROW][C]72[/C][C]228.343810807525[/C][C]185.010294347985[/C][C]271.677327267064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61257.508580649709248.963599976447266.053561322971
62257.160931097206246.287718204553268.034143989859
63249.630209240722236.22443201991263.035986461534
64246.971373697817230.847508404831263.095238990804
65242.561844785185223.548236755391261.575452814979
66232.38964189656210.325470434854254.453813358266
67226.49026065252201.223520214668251.757001090372
68228.752076559485200.138149095363257.366004023608
69228.145219177242196.04581568713260.244622667355
70235.341927973286199.62427442108271.059581525492
71236.219111119095196.755303878664275.682918359527
72228.343810807525185.010294347985271.677327267064



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')