Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2016 20:00:48 +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/26/t1480190464fv6efacyeduuppa.htm/, Retrieved Fri, 03 May 2024 17:42:52 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 17:42:52 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
37729
48191
52498
57319
44377
48081
52597
53331
39587
46278
50365
57176
39251
47946
50427
54317
41210
50592
55728
59099
47519
53203
53882
55163
45255
50423
52161
54562
40971
48014
48440
44967
27218
30269
33234
36811
27745
31891
32398
34093
28358
29532
30769
32080
23951
34628
22978
35704
23090
22111
28925
35968
28963
34074
39160
51314
34527
40722
50609
52435




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.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]'Sir Maurice George Kendall' @ kendall.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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.435753548115891
beta0.500897312875327
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.435753548115891 \tabularnewline
beta & 0.500897312875327 \tabularnewline
gamma & FALSE \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]0.435753548115891[/C][/ROW]
[ROW][C]beta[/C][C]0.500897312875327[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/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
alpha0.435753548115891
beta0.500897312875327
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35249858653-6155
45731965089.4987172781-7770.49871727814
54437769125.9886217-24748.9886217
64808160362.1344720711-12281.1344720711
75259754350.6160321352-1753.61603213524
85333152543.743224623787.256775376962
93958752015.8975479918-12428.8975479918
104627843016.23784036293261.76215963711
115036541565.77636241328799.22363758684
125717644448.870391812512727.1296081875
133925151821.4857268087-12570.4857268087
144794645426.84339091432519.1566090857
155042746157.41696656644269.5830334336
165431748582.65748324355734.34251675654
174121052897.7943604172-11687.7943604172
185059247070.10433394573521.89566605431
195572848638.80705534737089.19294465266
205909953309.31463851175789.68536148827
214751958677.258959943-11158.258959943
225320354224.5879833796-1021.58798337958
235388253966.0276083743-84.0276083743374
245516354097.67197370041065.32802629961
254525554962.6789195686-9707.67891956864
265042349014.43632528721408.56367471282
275216148217.57995131843943.42004868157
285456249386.01778113745175.98221886257
294097152221.2991049861-11250.2991049861
304801445443.19223470592570.80776529412
314844045248.80622918853191.19377081148
324496746021.2904109168-1054.29041091682
332721844713.6721681218-17495.6721681218
343026932422.9219417339-2153.92194173393
353323426347.26204742826886.73795257178
363681125714.254792864511096.7452071355
372774529337.8350933846-1592.83509338462
383189127084.22117199854806.7788280015
393239828668.42667354643729.57332645361
403409330597.28175100673495.71824899327
412835833187.2363150714-4829.23631507136
422953231095.4956939462-1563.49569394618
433076930085.5523994703683.447600529682
443208030203.89720939851876.1027906015
452395131251.4385437255-7300.43854372555
463462826706.81890853337921.18109146666
472297830524.0126597716-7546.01265977158
483570425954.2704133979749.72958660304
492309031049.2610635854-7959.26106358541
502211126690.2459510508-4579.24595105083
512892522804.58256260146120.41743739863
523596824917.225394171411050.7746058286
532896331590.3169105239-2627.31691052391
543407431729.67288426862344.32711573139
553916034547.1314606794612.86853932102
565131439359.955593097811954.0444069022
573452749980.9059077385-15453.9059077385
584072245285.65487087-4563.65487086998
595060944339.77053978216269.22946021789
605243549482.72479720732952.27520279268

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 52498 & 58653 & -6155 \tabularnewline
4 & 57319 & 65089.4987172781 & -7770.49871727814 \tabularnewline
5 & 44377 & 69125.9886217 & -24748.9886217 \tabularnewline
6 & 48081 & 60362.1344720711 & -12281.1344720711 \tabularnewline
7 & 52597 & 54350.6160321352 & -1753.61603213524 \tabularnewline
8 & 53331 & 52543.743224623 & 787.256775376962 \tabularnewline
9 & 39587 & 52015.8975479918 & -12428.8975479918 \tabularnewline
10 & 46278 & 43016.2378403629 & 3261.76215963711 \tabularnewline
11 & 50365 & 41565.7763624132 & 8799.22363758684 \tabularnewline
12 & 57176 & 44448.8703918125 & 12727.1296081875 \tabularnewline
13 & 39251 & 51821.4857268087 & -12570.4857268087 \tabularnewline
14 & 47946 & 45426.8433909143 & 2519.1566090857 \tabularnewline
15 & 50427 & 46157.4169665664 & 4269.5830334336 \tabularnewline
16 & 54317 & 48582.6574832435 & 5734.34251675654 \tabularnewline
17 & 41210 & 52897.7943604172 & -11687.7943604172 \tabularnewline
18 & 50592 & 47070.1043339457 & 3521.89566605431 \tabularnewline
19 & 55728 & 48638.8070553473 & 7089.19294465266 \tabularnewline
20 & 59099 & 53309.3146385117 & 5789.68536148827 \tabularnewline
21 & 47519 & 58677.258959943 & -11158.258959943 \tabularnewline
22 & 53203 & 54224.5879833796 & -1021.58798337958 \tabularnewline
23 & 53882 & 53966.0276083743 & -84.0276083743374 \tabularnewline
24 & 55163 & 54097.6719737004 & 1065.32802629961 \tabularnewline
25 & 45255 & 54962.6789195686 & -9707.67891956864 \tabularnewline
26 & 50423 & 49014.4363252872 & 1408.56367471282 \tabularnewline
27 & 52161 & 48217.5799513184 & 3943.42004868157 \tabularnewline
28 & 54562 & 49386.0177811374 & 5175.98221886257 \tabularnewline
29 & 40971 & 52221.2991049861 & -11250.2991049861 \tabularnewline
30 & 48014 & 45443.1922347059 & 2570.80776529412 \tabularnewline
31 & 48440 & 45248.8062291885 & 3191.19377081148 \tabularnewline
32 & 44967 & 46021.2904109168 & -1054.29041091682 \tabularnewline
33 & 27218 & 44713.6721681218 & -17495.6721681218 \tabularnewline
34 & 30269 & 32422.9219417339 & -2153.92194173393 \tabularnewline
35 & 33234 & 26347.2620474282 & 6886.73795257178 \tabularnewline
36 & 36811 & 25714.2547928645 & 11096.7452071355 \tabularnewline
37 & 27745 & 29337.8350933846 & -1592.83509338462 \tabularnewline
38 & 31891 & 27084.2211719985 & 4806.7788280015 \tabularnewline
39 & 32398 & 28668.4266735464 & 3729.57332645361 \tabularnewline
40 & 34093 & 30597.2817510067 & 3495.71824899327 \tabularnewline
41 & 28358 & 33187.2363150714 & -4829.23631507136 \tabularnewline
42 & 29532 & 31095.4956939462 & -1563.49569394618 \tabularnewline
43 & 30769 & 30085.5523994703 & 683.447600529682 \tabularnewline
44 & 32080 & 30203.8972093985 & 1876.1027906015 \tabularnewline
45 & 23951 & 31251.4385437255 & -7300.43854372555 \tabularnewline
46 & 34628 & 26706.8189085333 & 7921.18109146666 \tabularnewline
47 & 22978 & 30524.0126597716 & -7546.01265977158 \tabularnewline
48 & 35704 & 25954.270413397 & 9749.72958660304 \tabularnewline
49 & 23090 & 31049.2610635854 & -7959.26106358541 \tabularnewline
50 & 22111 & 26690.2459510508 & -4579.24595105083 \tabularnewline
51 & 28925 & 22804.5825626014 & 6120.41743739863 \tabularnewline
52 & 35968 & 24917.2253941714 & 11050.7746058286 \tabularnewline
53 & 28963 & 31590.3169105239 & -2627.31691052391 \tabularnewline
54 & 34074 & 31729.6728842686 & 2344.32711573139 \tabularnewline
55 & 39160 & 34547.131460679 & 4612.86853932102 \tabularnewline
56 & 51314 & 39359.9555930978 & 11954.0444069022 \tabularnewline
57 & 34527 & 49980.9059077385 & -15453.9059077385 \tabularnewline
58 & 40722 & 45285.65487087 & -4563.65487086998 \tabularnewline
59 & 50609 & 44339.7705397821 & 6269.22946021789 \tabularnewline
60 & 52435 & 49482.7247972073 & 2952.27520279268 \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]3[/C][C]52498[/C][C]58653[/C][C]-6155[/C][/ROW]
[ROW][C]4[/C][C]57319[/C][C]65089.4987172781[/C][C]-7770.49871727814[/C][/ROW]
[ROW][C]5[/C][C]44377[/C][C]69125.9886217[/C][C]-24748.9886217[/C][/ROW]
[ROW][C]6[/C][C]48081[/C][C]60362.1344720711[/C][C]-12281.1344720711[/C][/ROW]
[ROW][C]7[/C][C]52597[/C][C]54350.6160321352[/C][C]-1753.61603213524[/C][/ROW]
[ROW][C]8[/C][C]53331[/C][C]52543.743224623[/C][C]787.256775376962[/C][/ROW]
[ROW][C]9[/C][C]39587[/C][C]52015.8975479918[/C][C]-12428.8975479918[/C][/ROW]
[ROW][C]10[/C][C]46278[/C][C]43016.2378403629[/C][C]3261.76215963711[/C][/ROW]
[ROW][C]11[/C][C]50365[/C][C]41565.7763624132[/C][C]8799.22363758684[/C][/ROW]
[ROW][C]12[/C][C]57176[/C][C]44448.8703918125[/C][C]12727.1296081875[/C][/ROW]
[ROW][C]13[/C][C]39251[/C][C]51821.4857268087[/C][C]-12570.4857268087[/C][/ROW]
[ROW][C]14[/C][C]47946[/C][C]45426.8433909143[/C][C]2519.1566090857[/C][/ROW]
[ROW][C]15[/C][C]50427[/C][C]46157.4169665664[/C][C]4269.5830334336[/C][/ROW]
[ROW][C]16[/C][C]54317[/C][C]48582.6574832435[/C][C]5734.34251675654[/C][/ROW]
[ROW][C]17[/C][C]41210[/C][C]52897.7943604172[/C][C]-11687.7943604172[/C][/ROW]
[ROW][C]18[/C][C]50592[/C][C]47070.1043339457[/C][C]3521.89566605431[/C][/ROW]
[ROW][C]19[/C][C]55728[/C][C]48638.8070553473[/C][C]7089.19294465266[/C][/ROW]
[ROW][C]20[/C][C]59099[/C][C]53309.3146385117[/C][C]5789.68536148827[/C][/ROW]
[ROW][C]21[/C][C]47519[/C][C]58677.258959943[/C][C]-11158.258959943[/C][/ROW]
[ROW][C]22[/C][C]53203[/C][C]54224.5879833796[/C][C]-1021.58798337958[/C][/ROW]
[ROW][C]23[/C][C]53882[/C][C]53966.0276083743[/C][C]-84.0276083743374[/C][/ROW]
[ROW][C]24[/C][C]55163[/C][C]54097.6719737004[/C][C]1065.32802629961[/C][/ROW]
[ROW][C]25[/C][C]45255[/C][C]54962.6789195686[/C][C]-9707.67891956864[/C][/ROW]
[ROW][C]26[/C][C]50423[/C][C]49014.4363252872[/C][C]1408.56367471282[/C][/ROW]
[ROW][C]27[/C][C]52161[/C][C]48217.5799513184[/C][C]3943.42004868157[/C][/ROW]
[ROW][C]28[/C][C]54562[/C][C]49386.0177811374[/C][C]5175.98221886257[/C][/ROW]
[ROW][C]29[/C][C]40971[/C][C]52221.2991049861[/C][C]-11250.2991049861[/C][/ROW]
[ROW][C]30[/C][C]48014[/C][C]45443.1922347059[/C][C]2570.80776529412[/C][/ROW]
[ROW][C]31[/C][C]48440[/C][C]45248.8062291885[/C][C]3191.19377081148[/C][/ROW]
[ROW][C]32[/C][C]44967[/C][C]46021.2904109168[/C][C]-1054.29041091682[/C][/ROW]
[ROW][C]33[/C][C]27218[/C][C]44713.6721681218[/C][C]-17495.6721681218[/C][/ROW]
[ROW][C]34[/C][C]30269[/C][C]32422.9219417339[/C][C]-2153.92194173393[/C][/ROW]
[ROW][C]35[/C][C]33234[/C][C]26347.2620474282[/C][C]6886.73795257178[/C][/ROW]
[ROW][C]36[/C][C]36811[/C][C]25714.2547928645[/C][C]11096.7452071355[/C][/ROW]
[ROW][C]37[/C][C]27745[/C][C]29337.8350933846[/C][C]-1592.83509338462[/C][/ROW]
[ROW][C]38[/C][C]31891[/C][C]27084.2211719985[/C][C]4806.7788280015[/C][/ROW]
[ROW][C]39[/C][C]32398[/C][C]28668.4266735464[/C][C]3729.57332645361[/C][/ROW]
[ROW][C]40[/C][C]34093[/C][C]30597.2817510067[/C][C]3495.71824899327[/C][/ROW]
[ROW][C]41[/C][C]28358[/C][C]33187.2363150714[/C][C]-4829.23631507136[/C][/ROW]
[ROW][C]42[/C][C]29532[/C][C]31095.4956939462[/C][C]-1563.49569394618[/C][/ROW]
[ROW][C]43[/C][C]30769[/C][C]30085.5523994703[/C][C]683.447600529682[/C][/ROW]
[ROW][C]44[/C][C]32080[/C][C]30203.8972093985[/C][C]1876.1027906015[/C][/ROW]
[ROW][C]45[/C][C]23951[/C][C]31251.4385437255[/C][C]-7300.43854372555[/C][/ROW]
[ROW][C]46[/C][C]34628[/C][C]26706.8189085333[/C][C]7921.18109146666[/C][/ROW]
[ROW][C]47[/C][C]22978[/C][C]30524.0126597716[/C][C]-7546.01265977158[/C][/ROW]
[ROW][C]48[/C][C]35704[/C][C]25954.270413397[/C][C]9749.72958660304[/C][/ROW]
[ROW][C]49[/C][C]23090[/C][C]31049.2610635854[/C][C]-7959.26106358541[/C][/ROW]
[ROW][C]50[/C][C]22111[/C][C]26690.2459510508[/C][C]-4579.24595105083[/C][/ROW]
[ROW][C]51[/C][C]28925[/C][C]22804.5825626014[/C][C]6120.41743739863[/C][/ROW]
[ROW][C]52[/C][C]35968[/C][C]24917.2253941714[/C][C]11050.7746058286[/C][/ROW]
[ROW][C]53[/C][C]28963[/C][C]31590.3169105239[/C][C]-2627.31691052391[/C][/ROW]
[ROW][C]54[/C][C]34074[/C][C]31729.6728842686[/C][C]2344.32711573139[/C][/ROW]
[ROW][C]55[/C][C]39160[/C][C]34547.131460679[/C][C]4612.86853932102[/C][/ROW]
[ROW][C]56[/C][C]51314[/C][C]39359.9555930978[/C][C]11954.0444069022[/C][/ROW]
[ROW][C]57[/C][C]34527[/C][C]49980.9059077385[/C][C]-15453.9059077385[/C][/ROW]
[ROW][C]58[/C][C]40722[/C][C]45285.65487087[/C][C]-4563.65487086998[/C][/ROW]
[ROW][C]59[/C][C]50609[/C][C]44339.7705397821[/C][C]6269.22946021789[/C][/ROW]
[ROW][C]60[/C][C]52435[/C][C]49482.7247972073[/C][C]2952.27520279268[/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
35249858653-6155
45731965089.4987172781-7770.49871727814
54437769125.9886217-24748.9886217
64808160362.1344720711-12281.1344720711
75259754350.6160321352-1753.61603213524
85333152543.743224623787.256775376962
93958752015.8975479918-12428.8975479918
104627843016.23784036293261.76215963711
115036541565.77636241328799.22363758684
125717644448.870391812512727.1296081875
133925151821.4857268087-12570.4857268087
144794645426.84339091432519.1566090857
155042746157.41696656644269.5830334336
165431748582.65748324355734.34251675654
174121052897.7943604172-11687.7943604172
185059247070.10433394573521.89566605431
195572848638.80705534737089.19294465266
205909953309.31463851175789.68536148827
214751958677.258959943-11158.258959943
225320354224.5879833796-1021.58798337958
235388253966.0276083743-84.0276083743374
245516354097.67197370041065.32802629961
254525554962.6789195686-9707.67891956864
265042349014.43632528721408.56367471282
275216148217.57995131843943.42004868157
285456249386.01778113745175.98221886257
294097152221.2991049861-11250.2991049861
304801445443.19223470592570.80776529412
314844045248.80622918853191.19377081148
324496746021.2904109168-1054.29041091682
332721844713.6721681218-17495.6721681218
343026932422.9219417339-2153.92194173393
353323426347.26204742826886.73795257178
363681125714.254792864511096.7452071355
372774529337.8350933846-1592.83509338462
383189127084.22117199854806.7788280015
393239828668.42667354643729.57332645361
403409330597.28175100673495.71824899327
412835833187.2363150714-4829.23631507136
422953231095.4956939462-1563.49569394618
433076930085.5523994703683.447600529682
443208030203.89720939851876.1027906015
452395131251.4385437255-7300.43854372555
463462826706.81890853337921.18109146666
472297830524.0126597716-7546.01265977158
483570425954.2704133979749.72958660304
492309031049.2610635854-7959.26106358541
502211126690.2459510508-4579.24595105083
512892522804.58256260146120.41743739863
523596824917.225394171411050.7746058286
532896331590.3169105239-2627.31691052391
543407431729.67288426862344.32711573139
553916034547.1314606794612.86853932102
565131439359.955593097811954.0444069022
573452749980.9059077385-15453.9059077385
584072245285.65487087-4563.65487086998
595060944339.77053978216269.22946021789
605243549482.72479720732952.27520279268







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6153824.691026402138104.258735446369545.1233173578
6256880.192860965438096.125328070375664.2603938604
6359935.694695528636678.845551326683192.5438397306
6462991.196530091934098.314151933891884.07890825

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 53824.6910264021 & 38104.2587354463 & 69545.1233173578 \tabularnewline
62 & 56880.1928609654 & 38096.1253280703 & 75664.2603938604 \tabularnewline
63 & 59935.6946955286 & 36678.8455513266 & 83192.5438397306 \tabularnewline
64 & 62991.1965300919 & 34098.3141519338 & 91884.07890825 \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]53824.6910264021[/C][C]38104.2587354463[/C][C]69545.1233173578[/C][/ROW]
[ROW][C]62[/C][C]56880.1928609654[/C][C]38096.1253280703[/C][C]75664.2603938604[/C][/ROW]
[ROW][C]63[/C][C]59935.6946955286[/C][C]36678.8455513266[/C][C]83192.5438397306[/C][/ROW]
[ROW][C]64[/C][C]62991.1965300919[/C][C]34098.3141519338[/C][C]91884.07890825[/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
6153824.691026402138104.258735446369545.1233173578
6256880.192860965438096.125328070375664.2603938604
6359935.694695528636678.845551326683192.5438397306
6462991.196530091934098.314151933891884.07890825



Parameters (Session):
par1 = 4 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 4 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '4'
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')