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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 computationMon, 09 Jan 2017 13:43:28 +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/2017/Jan/09/t1483969430iah8m1d7xgg65ni.htm/, Retrieved Tue, 14 May 2024 23:00:35 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 23:00:35 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
272567
266674
301601
322421
313776
300156
315745
299214
295184
340003
332748
316337
293572
308713
354188
334540
313285
337881
356955
323661
296034
377623
342590
300905
309470
271492
307759
326106
335576
310485
335173
298344
288269
319410
327692
315401
277720
260573
318025
300264
317640
303273
315089
275840
292823
339759
328032
344675
260952
275466
331940
347644
338063
384283
398482
347062
350731
368799
387710
362988




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.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]'Herman Ole Andreas Wold' @ wold.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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.395396172773361
beta0
gamma0.404851033526451

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.395396172773361 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.404851033526451 \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]0.395396172773361[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.404851033526451[/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
alpha0.395396172773361
beta0
gamma0.404851033526451







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13293572281710.91639232711861.0836076727
14308713300556.8090089438156.19099105685
15354188349601.7463708824586.25362911751
16334540332362.4480387162177.55196128384
17313285312101.9673299031183.03267009667
18337881339425.232720009-1544.23272000859
19356955341086.39629408915868.6037059106
20323661328336.711029651-4675.71102965076
21296034319946.030611324-23912.0306113239
22377623356760.39752785320862.6024721466
23342590358797.530114766-16207.530114766
24300905335386.031578242-34481.0315782418
25309470300405.484709739064.51529027015
26271492317790.765055323-46298.7650553226
27307759343545.220808412-35786.2208084115
28326106311177.26813306914928.7318669308
29335576296878.470499738697.5295003004
30310485338314.170644859-27829.1706448595
31335173333631.01436851541.98563149996
32298344311440.380237121-13096.3802371211
33288269295613.159152706-7344.1591527061
34319410347672.502546839-28262.5025468391
35327692322725.4113998184966.58860018209
36315401304475.95578152810925.0442184724
37277720298262.98647332-20542.9864733196
38260573289818.322955382-29245.3229553825
39318025322997.576644947-4972.576644947
40300264315149.093773591-14885.0937735909
41317640295017.7494841122622.2505158905
42303273313166.880915313-9893.88091531268
43315089322363.767255925-7274.76725592487
44275840294332.247853974-18492.2478539741
45292823278349.75346386614473.2465361339
46339759332569.9310085527189.06899144774
47328032329629.333834172-1597.33383417182
48344675310008.53879162634666.4612083737
49260952304544.509723702-43592.5097237021
50275466284523.394880173-9057.39488017315
51331940333381.557369171-1441.55736917147
52347644324008.95203652123635.0479634792
53338063327468.41581080910594.5841891915
54384283332814.758688451468.2413115995
55398482368656.98814121229825.0118587879
56347062346526.426291907535.573708093318
57350731345485.0704022085245.92959779227
58368799403539.949168056-34740.9491680561
59387710380301.9358084377408.06419156323
60362988370681.75031876-7693.75031875953

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 293572 & 281710.916392327 & 11861.0836076727 \tabularnewline
14 & 308713 & 300556.809008943 & 8156.19099105685 \tabularnewline
15 & 354188 & 349601.746370882 & 4586.25362911751 \tabularnewline
16 & 334540 & 332362.448038716 & 2177.55196128384 \tabularnewline
17 & 313285 & 312101.967329903 & 1183.03267009667 \tabularnewline
18 & 337881 & 339425.232720009 & -1544.23272000859 \tabularnewline
19 & 356955 & 341086.396294089 & 15868.6037059106 \tabularnewline
20 & 323661 & 328336.711029651 & -4675.71102965076 \tabularnewline
21 & 296034 & 319946.030611324 & -23912.0306113239 \tabularnewline
22 & 377623 & 356760.397527853 & 20862.6024721466 \tabularnewline
23 & 342590 & 358797.530114766 & -16207.530114766 \tabularnewline
24 & 300905 & 335386.031578242 & -34481.0315782418 \tabularnewline
25 & 309470 & 300405.48470973 & 9064.51529027015 \tabularnewline
26 & 271492 & 317790.765055323 & -46298.7650553226 \tabularnewline
27 & 307759 & 343545.220808412 & -35786.2208084115 \tabularnewline
28 & 326106 & 311177.268133069 & 14928.7318669308 \tabularnewline
29 & 335576 & 296878.4704997 & 38697.5295003004 \tabularnewline
30 & 310485 & 338314.170644859 & -27829.1706448595 \tabularnewline
31 & 335173 & 333631.0143685 & 1541.98563149996 \tabularnewline
32 & 298344 & 311440.380237121 & -13096.3802371211 \tabularnewline
33 & 288269 & 295613.159152706 & -7344.1591527061 \tabularnewline
34 & 319410 & 347672.502546839 & -28262.5025468391 \tabularnewline
35 & 327692 & 322725.411399818 & 4966.58860018209 \tabularnewline
36 & 315401 & 304475.955781528 & 10925.0442184724 \tabularnewline
37 & 277720 & 298262.98647332 & -20542.9864733196 \tabularnewline
38 & 260573 & 289818.322955382 & -29245.3229553825 \tabularnewline
39 & 318025 & 322997.576644947 & -4972.576644947 \tabularnewline
40 & 300264 & 315149.093773591 & -14885.0937735909 \tabularnewline
41 & 317640 & 295017.74948411 & 22622.2505158905 \tabularnewline
42 & 303273 & 313166.880915313 & -9893.88091531268 \tabularnewline
43 & 315089 & 322363.767255925 & -7274.76725592487 \tabularnewline
44 & 275840 & 294332.247853974 & -18492.2478539741 \tabularnewline
45 & 292823 & 278349.753463866 & 14473.2465361339 \tabularnewline
46 & 339759 & 332569.931008552 & 7189.06899144774 \tabularnewline
47 & 328032 & 329629.333834172 & -1597.33383417182 \tabularnewline
48 & 344675 & 310008.538791626 & 34666.4612083737 \tabularnewline
49 & 260952 & 304544.509723702 & -43592.5097237021 \tabularnewline
50 & 275466 & 284523.394880173 & -9057.39488017315 \tabularnewline
51 & 331940 & 333381.557369171 & -1441.55736917147 \tabularnewline
52 & 347644 & 324008.952036521 & 23635.0479634792 \tabularnewline
53 & 338063 & 327468.415810809 & 10594.5841891915 \tabularnewline
54 & 384283 & 332814.7586884 & 51468.2413115995 \tabularnewline
55 & 398482 & 368656.988141212 & 29825.0118587879 \tabularnewline
56 & 347062 & 346526.426291907 & 535.573708093318 \tabularnewline
57 & 350731 & 345485.070402208 & 5245.92959779227 \tabularnewline
58 & 368799 & 403539.949168056 & -34740.9491680561 \tabularnewline
59 & 387710 & 380301.935808437 & 7408.06419156323 \tabularnewline
60 & 362988 & 370681.75031876 & -7693.75031875953 \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]293572[/C][C]281710.916392327[/C][C]11861.0836076727[/C][/ROW]
[ROW][C]14[/C][C]308713[/C][C]300556.809008943[/C][C]8156.19099105685[/C][/ROW]
[ROW][C]15[/C][C]354188[/C][C]349601.746370882[/C][C]4586.25362911751[/C][/ROW]
[ROW][C]16[/C][C]334540[/C][C]332362.448038716[/C][C]2177.55196128384[/C][/ROW]
[ROW][C]17[/C][C]313285[/C][C]312101.967329903[/C][C]1183.03267009667[/C][/ROW]
[ROW][C]18[/C][C]337881[/C][C]339425.232720009[/C][C]-1544.23272000859[/C][/ROW]
[ROW][C]19[/C][C]356955[/C][C]341086.396294089[/C][C]15868.6037059106[/C][/ROW]
[ROW][C]20[/C][C]323661[/C][C]328336.711029651[/C][C]-4675.71102965076[/C][/ROW]
[ROW][C]21[/C][C]296034[/C][C]319946.030611324[/C][C]-23912.0306113239[/C][/ROW]
[ROW][C]22[/C][C]377623[/C][C]356760.397527853[/C][C]20862.6024721466[/C][/ROW]
[ROW][C]23[/C][C]342590[/C][C]358797.530114766[/C][C]-16207.530114766[/C][/ROW]
[ROW][C]24[/C][C]300905[/C][C]335386.031578242[/C][C]-34481.0315782418[/C][/ROW]
[ROW][C]25[/C][C]309470[/C][C]300405.48470973[/C][C]9064.51529027015[/C][/ROW]
[ROW][C]26[/C][C]271492[/C][C]317790.765055323[/C][C]-46298.7650553226[/C][/ROW]
[ROW][C]27[/C][C]307759[/C][C]343545.220808412[/C][C]-35786.2208084115[/C][/ROW]
[ROW][C]28[/C][C]326106[/C][C]311177.268133069[/C][C]14928.7318669308[/C][/ROW]
[ROW][C]29[/C][C]335576[/C][C]296878.4704997[/C][C]38697.5295003004[/C][/ROW]
[ROW][C]30[/C][C]310485[/C][C]338314.170644859[/C][C]-27829.1706448595[/C][/ROW]
[ROW][C]31[/C][C]335173[/C][C]333631.0143685[/C][C]1541.98563149996[/C][/ROW]
[ROW][C]32[/C][C]298344[/C][C]311440.380237121[/C][C]-13096.3802371211[/C][/ROW]
[ROW][C]33[/C][C]288269[/C][C]295613.159152706[/C][C]-7344.1591527061[/C][/ROW]
[ROW][C]34[/C][C]319410[/C][C]347672.502546839[/C][C]-28262.5025468391[/C][/ROW]
[ROW][C]35[/C][C]327692[/C][C]322725.411399818[/C][C]4966.58860018209[/C][/ROW]
[ROW][C]36[/C][C]315401[/C][C]304475.955781528[/C][C]10925.0442184724[/C][/ROW]
[ROW][C]37[/C][C]277720[/C][C]298262.98647332[/C][C]-20542.9864733196[/C][/ROW]
[ROW][C]38[/C][C]260573[/C][C]289818.322955382[/C][C]-29245.3229553825[/C][/ROW]
[ROW][C]39[/C][C]318025[/C][C]322997.576644947[/C][C]-4972.576644947[/C][/ROW]
[ROW][C]40[/C][C]300264[/C][C]315149.093773591[/C][C]-14885.0937735909[/C][/ROW]
[ROW][C]41[/C][C]317640[/C][C]295017.74948411[/C][C]22622.2505158905[/C][/ROW]
[ROW][C]42[/C][C]303273[/C][C]313166.880915313[/C][C]-9893.88091531268[/C][/ROW]
[ROW][C]43[/C][C]315089[/C][C]322363.767255925[/C][C]-7274.76725592487[/C][/ROW]
[ROW][C]44[/C][C]275840[/C][C]294332.247853974[/C][C]-18492.2478539741[/C][/ROW]
[ROW][C]45[/C][C]292823[/C][C]278349.753463866[/C][C]14473.2465361339[/C][/ROW]
[ROW][C]46[/C][C]339759[/C][C]332569.931008552[/C][C]7189.06899144774[/C][/ROW]
[ROW][C]47[/C][C]328032[/C][C]329629.333834172[/C][C]-1597.33383417182[/C][/ROW]
[ROW][C]48[/C][C]344675[/C][C]310008.538791626[/C][C]34666.4612083737[/C][/ROW]
[ROW][C]49[/C][C]260952[/C][C]304544.509723702[/C][C]-43592.5097237021[/C][/ROW]
[ROW][C]50[/C][C]275466[/C][C]284523.394880173[/C][C]-9057.39488017315[/C][/ROW]
[ROW][C]51[/C][C]331940[/C][C]333381.557369171[/C][C]-1441.55736917147[/C][/ROW]
[ROW][C]52[/C][C]347644[/C][C]324008.952036521[/C][C]23635.0479634792[/C][/ROW]
[ROW][C]53[/C][C]338063[/C][C]327468.415810809[/C][C]10594.5841891915[/C][/ROW]
[ROW][C]54[/C][C]384283[/C][C]332814.7586884[/C][C]51468.2413115995[/C][/ROW]
[ROW][C]55[/C][C]398482[/C][C]368656.988141212[/C][C]29825.0118587879[/C][/ROW]
[ROW][C]56[/C][C]347062[/C][C]346526.426291907[/C][C]535.573708093318[/C][/ROW]
[ROW][C]57[/C][C]350731[/C][C]345485.070402208[/C][C]5245.92959779227[/C][/ROW]
[ROW][C]58[/C][C]368799[/C][C]403539.949168056[/C][C]-34740.9491680561[/C][/ROW]
[ROW][C]59[/C][C]387710[/C][C]380301.935808437[/C][C]7408.06419156323[/C][/ROW]
[ROW][C]60[/C][C]362988[/C][C]370681.75031876[/C][C]-7693.75031875953[/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
13293572281710.91639232711861.0836076727
14308713300556.8090089438156.19099105685
15354188349601.7463708824586.25362911751
16334540332362.4480387162177.55196128384
17313285312101.9673299031183.03267009667
18337881339425.232720009-1544.23272000859
19356955341086.39629408915868.6037059106
20323661328336.711029651-4675.71102965076
21296034319946.030611324-23912.0306113239
22377623356760.39752785320862.6024721466
23342590358797.530114766-16207.530114766
24300905335386.031578242-34481.0315782418
25309470300405.484709739064.51529027015
26271492317790.765055323-46298.7650553226
27307759343545.220808412-35786.2208084115
28326106311177.26813306914928.7318669308
29335576296878.470499738697.5295003004
30310485338314.170644859-27829.1706448595
31335173333631.01436851541.98563149996
32298344311440.380237121-13096.3802371211
33288269295613.159152706-7344.1591527061
34319410347672.502546839-28262.5025468391
35327692322725.4113998184966.58860018209
36315401304475.95578152810925.0442184724
37277720298262.98647332-20542.9864733196
38260573289818.322955382-29245.3229553825
39318025322997.576644947-4972.576644947
40300264315149.093773591-14885.0937735909
41317640295017.7494841122622.2505158905
42303273313166.880915313-9893.88091531268
43315089322363.767255925-7274.76725592487
44275840294332.247853974-18492.2478539741
45292823278349.75346386614473.2465361339
46339759332569.9310085527189.06899144774
47328032329629.333834172-1597.33383417182
48344675310008.53879162634666.4612083737
49260952304544.509723702-43592.5097237021
50275466284523.394880173-9057.39488017315
51331940333381.557369171-1441.55736917147
52347644324008.95203652123635.0479634792
53338063327468.41581080910594.5841891915
54384283332814.758688451468.2413115995
55398482368656.98814121229825.0118587879
56347062346526.426291907535.573708093318
57350731345485.0704022085245.92959779227
58368799403539.949168056-34740.9491680561
59387710380301.9358084377408.06419156323
60362988370681.75031876-7693.75031875953







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61324326.33387993297486.210491264351166.457268595
62330628.495143045298960.052537896362296.937748194
63394645.5727952355840.432177638433450.713412762
64390896.251230595349070.093289528432722.409171661
65380084.599323255336039.843441045424129.355205464
66391665.583062555343808.090143966439523.075981143
67402188.370615924350758.391799994453618.349431855
68359495.005632262309904.688427943409085.322836581
69359314.664404071307247.916542356411381.412265787
70406521.797137365346605.747480494466437.846794236
71407236.543557831345243.4893757469229.597739962
72389921.817092964334399.728890742445443.905295187

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 324326.33387993 & 297486.210491264 & 351166.457268595 \tabularnewline
62 & 330628.495143045 & 298960.052537896 & 362296.937748194 \tabularnewline
63 & 394645.5727952 & 355840.432177638 & 433450.713412762 \tabularnewline
64 & 390896.251230595 & 349070.093289528 & 432722.409171661 \tabularnewline
65 & 380084.599323255 & 336039.843441045 & 424129.355205464 \tabularnewline
66 & 391665.583062555 & 343808.090143966 & 439523.075981143 \tabularnewline
67 & 402188.370615924 & 350758.391799994 & 453618.349431855 \tabularnewline
68 & 359495.005632262 & 309904.688427943 & 409085.322836581 \tabularnewline
69 & 359314.664404071 & 307247.916542356 & 411381.412265787 \tabularnewline
70 & 406521.797137365 & 346605.747480494 & 466437.846794236 \tabularnewline
71 & 407236.543557831 & 345243.4893757 & 469229.597739962 \tabularnewline
72 & 389921.817092964 & 334399.728890742 & 445443.905295187 \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]324326.33387993[/C][C]297486.210491264[/C][C]351166.457268595[/C][/ROW]
[ROW][C]62[/C][C]330628.495143045[/C][C]298960.052537896[/C][C]362296.937748194[/C][/ROW]
[ROW][C]63[/C][C]394645.5727952[/C][C]355840.432177638[/C][C]433450.713412762[/C][/ROW]
[ROW][C]64[/C][C]390896.251230595[/C][C]349070.093289528[/C][C]432722.409171661[/C][/ROW]
[ROW][C]65[/C][C]380084.599323255[/C][C]336039.843441045[/C][C]424129.355205464[/C][/ROW]
[ROW][C]66[/C][C]391665.583062555[/C][C]343808.090143966[/C][C]439523.075981143[/C][/ROW]
[ROW][C]67[/C][C]402188.370615924[/C][C]350758.391799994[/C][C]453618.349431855[/C][/ROW]
[ROW][C]68[/C][C]359495.005632262[/C][C]309904.688427943[/C][C]409085.322836581[/C][/ROW]
[ROW][C]69[/C][C]359314.664404071[/C][C]307247.916542356[/C][C]411381.412265787[/C][/ROW]
[ROW][C]70[/C][C]406521.797137365[/C][C]346605.747480494[/C][C]466437.846794236[/C][/ROW]
[ROW][C]71[/C][C]407236.543557831[/C][C]345243.4893757[/C][C]469229.597739962[/C][/ROW]
[ROW][C]72[/C][C]389921.817092964[/C][C]334399.728890742[/C][C]445443.905295187[/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
61324326.33387993297486.210491264351166.457268595
62330628.495143045298960.052537896362296.937748194
63394645.5727952355840.432177638433450.713412762
64390896.251230595349070.093289528432722.409171661
65380084.599323255336039.843441045424129.355205464
66391665.583062555343808.090143966439523.075981143
67402188.370615924350758.391799994453618.349431855
68359495.005632262309904.688427943409085.322836581
69359314.664404071307247.916542356411381.412265787
70406521.797137365346605.747480494466437.846794236
71407236.543557831345243.4893757469229.597739962
72389921.817092964334399.728890742445443.905295187



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=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')