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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 computationSat, 17 Dec 2016 20:41:09 +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/Dec/17/t1482007305k12wx0mwzphzy73.htm/, Retrieved Thu, 02 May 2024 11:43:13 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 02 May 2024 11:43:13 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
203089
198480
192684
187827
182414
182510
211524
211451
200140
191568
186424
191987
203583
201920
195978
191395
188222
189422
214419
224325
216222
210506
207221
210027
215191
215177
211701
210176
205491
206996
235980
241292
236675
229127
225436
229570
239973
236168
230703
224790
217811
219576
245472
248511
242084
235572
229827
229697
239567
237201
233164
227755
220189
221270
245413
247826
237736
230079
225939
228987




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.8084782279961
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.8084782279961 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \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]0.8084782279961[/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=&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
alpha0.8084782279961
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13203583201139.5902777782443.40972222216
14201920201539.086870571380.913129428518
15195978195442.641539442535.358460557967
16191395190577.39522928817.604770720325
17188222187153.8805824821068.1194175175
18189422188343.3182400821078.68175991834
19214419220717.753654882-6298.75365488185
20224325216132.5264917028192.47350829793
21216222211908.4743202324313.52567976786
22210506207282.043948533223.95605147042
23207221205097.9702544632123.02974553732
24210027212591.488278087-2564.48827808737
25215191222917.591196004-7726.59119600378
26215177214699.850465508477.149534492462
27211701208710.7898161092990.21018389147
28210176205884.2939906844291.70600931614
29205491205317.493566213173.506433786824
30206996205785.6790225171210.32097748344
31235980236853.602375182-873.602375181741
32241292239429.8774100281862.1225899721
33236675229344.9713838867330.02861611434
34229127226948.6416549722178.35834502758
35225436223708.3736230461727.6263769542
36229570229984.45487371-414.45487370991
37239973241060.157890424-1087.15789042399
38236168239781.449395486-3613.44939548642
39230703230966.534400462-263.534400461504
40224790225758.721705868-968.721705868258
41217811220150.255123553-2339.25512355263
42219576218785.50012725790.499872750341
43245472249114.890563862-3642.89056386214
44248511249976.207284155-1465.20728415501
45242084238248.4505486983835.54945130248
46235572232040.253477753531.74652225047
47229827229807.84533591119.154664089263
48229697234292.409206673-4595.4092066728
49239567241859.064399147-2292.06439914694
50237201239122.375399488-1921.37539948814
51233164232317.047046296846.952953704225
52227755227871.980477684-116.980477684381
53220189222689.641145497-2500.6411454966
54221270221793.825286979-523.82528697903
55245413250211.521655038-4798.52165503765
56247826250555.609559113-2729.60955911252
57237736238820.82143586-1084.82143585957
58230079228576.4267536631502.57324633683
59225939224030.7383804151908.26161958481
60228987229158.814645498-171.814645497885

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 203583 & 201139.590277778 & 2443.40972222216 \tabularnewline
14 & 201920 & 201539.086870571 & 380.913129428518 \tabularnewline
15 & 195978 & 195442.641539442 & 535.358460557967 \tabularnewline
16 & 191395 & 190577.39522928 & 817.604770720325 \tabularnewline
17 & 188222 & 187153.880582482 & 1068.1194175175 \tabularnewline
18 & 189422 & 188343.318240082 & 1078.68175991834 \tabularnewline
19 & 214419 & 220717.753654882 & -6298.75365488185 \tabularnewline
20 & 224325 & 216132.526491702 & 8192.47350829793 \tabularnewline
21 & 216222 & 211908.474320232 & 4313.52567976786 \tabularnewline
22 & 210506 & 207282.04394853 & 3223.95605147042 \tabularnewline
23 & 207221 & 205097.970254463 & 2123.02974553732 \tabularnewline
24 & 210027 & 212591.488278087 & -2564.48827808737 \tabularnewline
25 & 215191 & 222917.591196004 & -7726.59119600378 \tabularnewline
26 & 215177 & 214699.850465508 & 477.149534492462 \tabularnewline
27 & 211701 & 208710.789816109 & 2990.21018389147 \tabularnewline
28 & 210176 & 205884.293990684 & 4291.70600931614 \tabularnewline
29 & 205491 & 205317.493566213 & 173.506433786824 \tabularnewline
30 & 206996 & 205785.679022517 & 1210.32097748344 \tabularnewline
31 & 235980 & 236853.602375182 & -873.602375181741 \tabularnewline
32 & 241292 & 239429.877410028 & 1862.1225899721 \tabularnewline
33 & 236675 & 229344.971383886 & 7330.02861611434 \tabularnewline
34 & 229127 & 226948.641654972 & 2178.35834502758 \tabularnewline
35 & 225436 & 223708.373623046 & 1727.6263769542 \tabularnewline
36 & 229570 & 229984.45487371 & -414.45487370991 \tabularnewline
37 & 239973 & 241060.157890424 & -1087.15789042399 \tabularnewline
38 & 236168 & 239781.449395486 & -3613.44939548642 \tabularnewline
39 & 230703 & 230966.534400462 & -263.534400461504 \tabularnewline
40 & 224790 & 225758.721705868 & -968.721705868258 \tabularnewline
41 & 217811 & 220150.255123553 & -2339.25512355263 \tabularnewline
42 & 219576 & 218785.50012725 & 790.499872750341 \tabularnewline
43 & 245472 & 249114.890563862 & -3642.89056386214 \tabularnewline
44 & 248511 & 249976.207284155 & -1465.20728415501 \tabularnewline
45 & 242084 & 238248.450548698 & 3835.54945130248 \tabularnewline
46 & 235572 & 232040.25347775 & 3531.74652225047 \tabularnewline
47 & 229827 & 229807.845335911 & 19.154664089263 \tabularnewline
48 & 229697 & 234292.409206673 & -4595.4092066728 \tabularnewline
49 & 239567 & 241859.064399147 & -2292.06439914694 \tabularnewline
50 & 237201 & 239122.375399488 & -1921.37539948814 \tabularnewline
51 & 233164 & 232317.047046296 & 846.952953704225 \tabularnewline
52 & 227755 & 227871.980477684 & -116.980477684381 \tabularnewline
53 & 220189 & 222689.641145497 & -2500.6411454966 \tabularnewline
54 & 221270 & 221793.825286979 & -523.82528697903 \tabularnewline
55 & 245413 & 250211.521655038 & -4798.52165503765 \tabularnewline
56 & 247826 & 250555.609559113 & -2729.60955911252 \tabularnewline
57 & 237736 & 238820.82143586 & -1084.82143585957 \tabularnewline
58 & 230079 & 228576.426753663 & 1502.57324633683 \tabularnewline
59 & 225939 & 224030.738380415 & 1908.26161958481 \tabularnewline
60 & 228987 & 229158.814645498 & -171.814645497885 \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]203583[/C][C]201139.590277778[/C][C]2443.40972222216[/C][/ROW]
[ROW][C]14[/C][C]201920[/C][C]201539.086870571[/C][C]380.913129428518[/C][/ROW]
[ROW][C]15[/C][C]195978[/C][C]195442.641539442[/C][C]535.358460557967[/C][/ROW]
[ROW][C]16[/C][C]191395[/C][C]190577.39522928[/C][C]817.604770720325[/C][/ROW]
[ROW][C]17[/C][C]188222[/C][C]187153.880582482[/C][C]1068.1194175175[/C][/ROW]
[ROW][C]18[/C][C]189422[/C][C]188343.318240082[/C][C]1078.68175991834[/C][/ROW]
[ROW][C]19[/C][C]214419[/C][C]220717.753654882[/C][C]-6298.75365488185[/C][/ROW]
[ROW][C]20[/C][C]224325[/C][C]216132.526491702[/C][C]8192.47350829793[/C][/ROW]
[ROW][C]21[/C][C]216222[/C][C]211908.474320232[/C][C]4313.52567976786[/C][/ROW]
[ROW][C]22[/C][C]210506[/C][C]207282.04394853[/C][C]3223.95605147042[/C][/ROW]
[ROW][C]23[/C][C]207221[/C][C]205097.970254463[/C][C]2123.02974553732[/C][/ROW]
[ROW][C]24[/C][C]210027[/C][C]212591.488278087[/C][C]-2564.48827808737[/C][/ROW]
[ROW][C]25[/C][C]215191[/C][C]222917.591196004[/C][C]-7726.59119600378[/C][/ROW]
[ROW][C]26[/C][C]215177[/C][C]214699.850465508[/C][C]477.149534492462[/C][/ROW]
[ROW][C]27[/C][C]211701[/C][C]208710.789816109[/C][C]2990.21018389147[/C][/ROW]
[ROW][C]28[/C][C]210176[/C][C]205884.293990684[/C][C]4291.70600931614[/C][/ROW]
[ROW][C]29[/C][C]205491[/C][C]205317.493566213[/C][C]173.506433786824[/C][/ROW]
[ROW][C]30[/C][C]206996[/C][C]205785.679022517[/C][C]1210.32097748344[/C][/ROW]
[ROW][C]31[/C][C]235980[/C][C]236853.602375182[/C][C]-873.602375181741[/C][/ROW]
[ROW][C]32[/C][C]241292[/C][C]239429.877410028[/C][C]1862.1225899721[/C][/ROW]
[ROW][C]33[/C][C]236675[/C][C]229344.971383886[/C][C]7330.02861611434[/C][/ROW]
[ROW][C]34[/C][C]229127[/C][C]226948.641654972[/C][C]2178.35834502758[/C][/ROW]
[ROW][C]35[/C][C]225436[/C][C]223708.373623046[/C][C]1727.6263769542[/C][/ROW]
[ROW][C]36[/C][C]229570[/C][C]229984.45487371[/C][C]-414.45487370991[/C][/ROW]
[ROW][C]37[/C][C]239973[/C][C]241060.157890424[/C][C]-1087.15789042399[/C][/ROW]
[ROW][C]38[/C][C]236168[/C][C]239781.449395486[/C][C]-3613.44939548642[/C][/ROW]
[ROW][C]39[/C][C]230703[/C][C]230966.534400462[/C][C]-263.534400461504[/C][/ROW]
[ROW][C]40[/C][C]224790[/C][C]225758.721705868[/C][C]-968.721705868258[/C][/ROW]
[ROW][C]41[/C][C]217811[/C][C]220150.255123553[/C][C]-2339.25512355263[/C][/ROW]
[ROW][C]42[/C][C]219576[/C][C]218785.50012725[/C][C]790.499872750341[/C][/ROW]
[ROW][C]43[/C][C]245472[/C][C]249114.890563862[/C][C]-3642.89056386214[/C][/ROW]
[ROW][C]44[/C][C]248511[/C][C]249976.207284155[/C][C]-1465.20728415501[/C][/ROW]
[ROW][C]45[/C][C]242084[/C][C]238248.450548698[/C][C]3835.54945130248[/C][/ROW]
[ROW][C]46[/C][C]235572[/C][C]232040.25347775[/C][C]3531.74652225047[/C][/ROW]
[ROW][C]47[/C][C]229827[/C][C]229807.845335911[/C][C]19.154664089263[/C][/ROW]
[ROW][C]48[/C][C]229697[/C][C]234292.409206673[/C][C]-4595.4092066728[/C][/ROW]
[ROW][C]49[/C][C]239567[/C][C]241859.064399147[/C][C]-2292.06439914694[/C][/ROW]
[ROW][C]50[/C][C]237201[/C][C]239122.375399488[/C][C]-1921.37539948814[/C][/ROW]
[ROW][C]51[/C][C]233164[/C][C]232317.047046296[/C][C]846.952953704225[/C][/ROW]
[ROW][C]52[/C][C]227755[/C][C]227871.980477684[/C][C]-116.980477684381[/C][/ROW]
[ROW][C]53[/C][C]220189[/C][C]222689.641145497[/C][C]-2500.6411454966[/C][/ROW]
[ROW][C]54[/C][C]221270[/C][C]221793.825286979[/C][C]-523.82528697903[/C][/ROW]
[ROW][C]55[/C][C]245413[/C][C]250211.521655038[/C][C]-4798.52165503765[/C][/ROW]
[ROW][C]56[/C][C]247826[/C][C]250555.609559113[/C][C]-2729.60955911252[/C][/ROW]
[ROW][C]57[/C][C]237736[/C][C]238820.82143586[/C][C]-1084.82143585957[/C][/ROW]
[ROW][C]58[/C][C]230079[/C][C]228576.426753663[/C][C]1502.57324633683[/C][/ROW]
[ROW][C]59[/C][C]225939[/C][C]224030.738380415[/C][C]1908.26161958481[/C][/ROW]
[ROW][C]60[/C][C]228987[/C][C]229158.814645498[/C][C]-171.814645497885[/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
13203583201139.5902777782443.40972222216
14201920201539.086870571380.913129428518
15195978195442.641539442535.358460557967
16191395190577.39522928817.604770720325
17188222187153.8805824821068.1194175175
18189422188343.3182400821078.68175991834
19214419220717.753654882-6298.75365488185
20224325216132.5264917028192.47350829793
21216222211908.4743202324313.52567976786
22210506207282.043948533223.95605147042
23207221205097.9702544632123.02974553732
24210027212591.488278087-2564.48827808737
25215191222917.591196004-7726.59119600378
26215177214699.850465508477.149534492462
27211701208710.7898161092990.21018389147
28210176205884.2939906844291.70600931614
29205491205317.493566213173.506433786824
30206996205785.6790225171210.32097748344
31235980236853.602375182-873.602375181741
32241292239429.8774100281862.1225899721
33236675229344.9713838867330.02861611434
34229127226948.6416549722178.35834502758
35225436223708.3736230461727.6263769542
36229570229984.45487371-414.45487370991
37239973241060.157890424-1087.15789042399
38236168239781.449395486-3613.44939548642
39230703230966.534400462-263.534400461504
40224790225758.721705868-968.721705868258
41217811220150.255123553-2339.25512355263
42219576218785.50012725790.499872750341
43245472249114.890563862-3642.89056386214
44248511249976.207284155-1465.20728415501
45242084238248.4505486983835.54945130248
46235572232040.253477753531.74652225047
47229827229807.84533591119.154664089263
48229697234292.409206673-4595.4092066728
49239567241859.064399147-2292.06439914694
50237201239122.375399488-1921.37539948814
51233164232317.047046296846.952953704225
52227755227871.980477684-116.980477684381
53220189222689.641145497-2500.6411454966
54221270221793.825286979-523.82528697903
55245413250211.521655038-4798.52165503765
56247826250555.609559113-2729.60955911252
57237736238820.82143586-1084.82143585957
58230079228576.4267536631502.57324633683
59225939224030.7383804151908.26161958481
60228987229158.814645498-171.814645497885







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61240742.990409237234686.676102794246799.304715681
62239930.380587531232142.33469104247718.426484022
63235208.637564324226009.269390733244408.005737914
64229894.213733632219472.933068537240315.494398727
65224349.927655797212835.684015501235864.171296094
66225854.428995594213342.333946581238366.524044606
67253876.92928026240440.886766821267312.971793699
68258496.759179732244196.341202262272797.177157203
69249283.813691888234168.368933702264399.258450074
70240412.015936255224523.297103536256300.734768974
71234729.2279635218103.161018711251355.29490829
72237916.136363636220584.061532272255248.211195001

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 240742.990409237 & 234686.676102794 & 246799.304715681 \tabularnewline
62 & 239930.380587531 & 232142.33469104 & 247718.426484022 \tabularnewline
63 & 235208.637564324 & 226009.269390733 & 244408.005737914 \tabularnewline
64 & 229894.213733632 & 219472.933068537 & 240315.494398727 \tabularnewline
65 & 224349.927655797 & 212835.684015501 & 235864.171296094 \tabularnewline
66 & 225854.428995594 & 213342.333946581 & 238366.524044606 \tabularnewline
67 & 253876.92928026 & 240440.886766821 & 267312.971793699 \tabularnewline
68 & 258496.759179732 & 244196.341202262 & 272797.177157203 \tabularnewline
69 & 249283.813691888 & 234168.368933702 & 264399.258450074 \tabularnewline
70 & 240412.015936255 & 224523.297103536 & 256300.734768974 \tabularnewline
71 & 234729.2279635 & 218103.161018711 & 251355.29490829 \tabularnewline
72 & 237916.136363636 & 220584.061532272 & 255248.211195001 \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]240742.990409237[/C][C]234686.676102794[/C][C]246799.304715681[/C][/ROW]
[ROW][C]62[/C][C]239930.380587531[/C][C]232142.33469104[/C][C]247718.426484022[/C][/ROW]
[ROW][C]63[/C][C]235208.637564324[/C][C]226009.269390733[/C][C]244408.005737914[/C][/ROW]
[ROW][C]64[/C][C]229894.213733632[/C][C]219472.933068537[/C][C]240315.494398727[/C][/ROW]
[ROW][C]65[/C][C]224349.927655797[/C][C]212835.684015501[/C][C]235864.171296094[/C][/ROW]
[ROW][C]66[/C][C]225854.428995594[/C][C]213342.333946581[/C][C]238366.524044606[/C][/ROW]
[ROW][C]67[/C][C]253876.92928026[/C][C]240440.886766821[/C][C]267312.971793699[/C][/ROW]
[ROW][C]68[/C][C]258496.759179732[/C][C]244196.341202262[/C][C]272797.177157203[/C][/ROW]
[ROW][C]69[/C][C]249283.813691888[/C][C]234168.368933702[/C][C]264399.258450074[/C][/ROW]
[ROW][C]70[/C][C]240412.015936255[/C][C]224523.297103536[/C][C]256300.734768974[/C][/ROW]
[ROW][C]71[/C][C]234729.2279635[/C][C]218103.161018711[/C][C]251355.29490829[/C][/ROW]
[ROW][C]72[/C][C]237916.136363636[/C][C]220584.061532272[/C][C]255248.211195001[/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
61240742.990409237234686.676102794246799.304715681
62239930.380587531232142.33469104247718.426484022
63235208.637564324226009.269390733244408.005737914
64229894.213733632219472.933068537240315.494398727
65224349.927655797212835.684015501235864.171296094
66225854.428995594213342.333946581238366.524044606
67253876.92928026240440.886766821267312.971793699
68258496.759179732244196.341202262272797.177157203
69249283.813691888234168.368933702264399.258450074
70240412.015936255224523.297103536256300.734768974
71234729.2279635218103.161018711251355.29490829
72237916.136363636220584.061532272255248.211195001



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')