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 19:56:25 +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/t1480190204v4aii49dcpjrahg.htm/, Retrieved Fri, 03 May 2024 18:32:55 +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 18:32:55 +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 Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.450263840526657
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.450263840526657 \tabularnewline
beta & FALSE \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]0.450263840526657[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/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
alpha0.450263840526657
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2481913772910462
35249842439.660299589910058.3397004101
45731946968.566962418310350.4330375817
54437751628.9926930338-7251.99269303382
64808148363.6826115971-282.682611597149
75259748236.40085324934360.59914675069
85333150199.82097206253131.17902793747
93958751609.6776665582-12022.6776665582
104627846196.300646999681.699353000382
115036546233.08691145014131.91308854989
125717648093.53796742299082.46203257705
133925152183.0422036486-12932.0422036486
144794646360.2112151811585.78878481901
155042747074.23456369773352.7654363023
165431748583.86360543225733.1363945678
174121051165.2876167134-9955.28761671345
185059246682.78158086463909.21841913542
195572848442.9612797227285.03872027797
205909951723.15079229987375.84920770021
214751955044.2289837044-7525.22898370439
225320351655.89048065911547.10951934087
235388252352.49795455291529.50204544711
245516353041.17741962932121.82258037072
254525553996.5574035832-8741.55740358318
265042350060.5501948616362.449805138414
275216150223.74823612131937.25176387865
285456251096.02265539243465.97734460761
294097152656.6269257538-11685.6269257538
304801447395.0116672022618.988332797824
314844047673.7197311689766.280268831091
324496748018.7480279326-3051.7480279326
332721846644.656240556-19426.656240556
343026937897.5353930921-7628.53539309211
353323434462.6817494049-1228.68174940492
363681133909.45078613292901.54921386715
372774535215.9134786458-7470.91347864577
383189131852.031283508438.9687164916395
393239831869.5774874563528.422512543719
403409332107.5070373751985.49296262504
412835833001.5027240652-4643.50272406516
422953230910.7013540316-1378.70135403159
433076930289.921987426479.078012573977
443208030505.63349327951574.36650672054
452395131214.513802992-7263.51380299199
463462827944.01618233846683.98381766157
472297830953.5724060968-7975.57240609676
483570427362.46054412928341.5394558708
492309031118.3541354342-8028.35413543422
502211127503.4765693055-5392.47656930554
512892525075.439359263849.56064073998
523596826808.75731769999159.24268230014
532896330932.833104148-1969.833104148
543407430045.88848547784028.11151452223
553916031859.60144607627300.39855392381
565131435146.706936341216167.2930636588
573452742426.2544021042-7899.25440210418
584072238869.50577771561852.49422228435
595060939703.616940794810905.3830592052
605243544613.91659944697821.08340055311

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 48191 & 37729 & 10462 \tabularnewline
3 & 52498 & 42439.6602995899 & 10058.3397004101 \tabularnewline
4 & 57319 & 46968.5669624183 & 10350.4330375817 \tabularnewline
5 & 44377 & 51628.9926930338 & -7251.99269303382 \tabularnewline
6 & 48081 & 48363.6826115971 & -282.682611597149 \tabularnewline
7 & 52597 & 48236.4008532493 & 4360.59914675069 \tabularnewline
8 & 53331 & 50199.8209720625 & 3131.17902793747 \tabularnewline
9 & 39587 & 51609.6776665582 & -12022.6776665582 \tabularnewline
10 & 46278 & 46196.3006469996 & 81.699353000382 \tabularnewline
11 & 50365 & 46233.0869114501 & 4131.91308854989 \tabularnewline
12 & 57176 & 48093.5379674229 & 9082.46203257705 \tabularnewline
13 & 39251 & 52183.0422036486 & -12932.0422036486 \tabularnewline
14 & 47946 & 46360.211215181 & 1585.78878481901 \tabularnewline
15 & 50427 & 47074.2345636977 & 3352.7654363023 \tabularnewline
16 & 54317 & 48583.8636054322 & 5733.1363945678 \tabularnewline
17 & 41210 & 51165.2876167134 & -9955.28761671345 \tabularnewline
18 & 50592 & 46682.7815808646 & 3909.21841913542 \tabularnewline
19 & 55728 & 48442.961279722 & 7285.03872027797 \tabularnewline
20 & 59099 & 51723.1507922998 & 7375.84920770021 \tabularnewline
21 & 47519 & 55044.2289837044 & -7525.22898370439 \tabularnewline
22 & 53203 & 51655.8904806591 & 1547.10951934087 \tabularnewline
23 & 53882 & 52352.4979545529 & 1529.50204544711 \tabularnewline
24 & 55163 & 53041.1774196293 & 2121.82258037072 \tabularnewline
25 & 45255 & 53996.5574035832 & -8741.55740358318 \tabularnewline
26 & 50423 & 50060.5501948616 & 362.449805138414 \tabularnewline
27 & 52161 & 50223.7482361213 & 1937.25176387865 \tabularnewline
28 & 54562 & 51096.0226553924 & 3465.97734460761 \tabularnewline
29 & 40971 & 52656.6269257538 & -11685.6269257538 \tabularnewline
30 & 48014 & 47395.0116672022 & 618.988332797824 \tabularnewline
31 & 48440 & 47673.7197311689 & 766.280268831091 \tabularnewline
32 & 44967 & 48018.7480279326 & -3051.7480279326 \tabularnewline
33 & 27218 & 46644.656240556 & -19426.656240556 \tabularnewline
34 & 30269 & 37897.5353930921 & -7628.53539309211 \tabularnewline
35 & 33234 & 34462.6817494049 & -1228.68174940492 \tabularnewline
36 & 36811 & 33909.4507861329 & 2901.54921386715 \tabularnewline
37 & 27745 & 35215.9134786458 & -7470.91347864577 \tabularnewline
38 & 31891 & 31852.0312835084 & 38.9687164916395 \tabularnewline
39 & 32398 & 31869.5774874563 & 528.422512543719 \tabularnewline
40 & 34093 & 32107.507037375 & 1985.49296262504 \tabularnewline
41 & 28358 & 33001.5027240652 & -4643.50272406516 \tabularnewline
42 & 29532 & 30910.7013540316 & -1378.70135403159 \tabularnewline
43 & 30769 & 30289.921987426 & 479.078012573977 \tabularnewline
44 & 32080 & 30505.6334932795 & 1574.36650672054 \tabularnewline
45 & 23951 & 31214.513802992 & -7263.51380299199 \tabularnewline
46 & 34628 & 27944.0161823384 & 6683.98381766157 \tabularnewline
47 & 22978 & 30953.5724060968 & -7975.57240609676 \tabularnewline
48 & 35704 & 27362.4605441292 & 8341.5394558708 \tabularnewline
49 & 23090 & 31118.3541354342 & -8028.35413543422 \tabularnewline
50 & 22111 & 27503.4765693055 & -5392.47656930554 \tabularnewline
51 & 28925 & 25075.43935926 & 3849.56064073998 \tabularnewline
52 & 35968 & 26808.7573176999 & 9159.24268230014 \tabularnewline
53 & 28963 & 30932.833104148 & -1969.833104148 \tabularnewline
54 & 34074 & 30045.8884854778 & 4028.11151452223 \tabularnewline
55 & 39160 & 31859.6014460762 & 7300.39855392381 \tabularnewline
56 & 51314 & 35146.7069363412 & 16167.2930636588 \tabularnewline
57 & 34527 & 42426.2544021042 & -7899.25440210418 \tabularnewline
58 & 40722 & 38869.5057777156 & 1852.49422228435 \tabularnewline
59 & 50609 & 39703.6169407948 & 10905.3830592052 \tabularnewline
60 & 52435 & 44613.9165994469 & 7821.08340055311 \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]2[/C][C]48191[/C][C]37729[/C][C]10462[/C][/ROW]
[ROW][C]3[/C][C]52498[/C][C]42439.6602995899[/C][C]10058.3397004101[/C][/ROW]
[ROW][C]4[/C][C]57319[/C][C]46968.5669624183[/C][C]10350.4330375817[/C][/ROW]
[ROW][C]5[/C][C]44377[/C][C]51628.9926930338[/C][C]-7251.99269303382[/C][/ROW]
[ROW][C]6[/C][C]48081[/C][C]48363.6826115971[/C][C]-282.682611597149[/C][/ROW]
[ROW][C]7[/C][C]52597[/C][C]48236.4008532493[/C][C]4360.59914675069[/C][/ROW]
[ROW][C]8[/C][C]53331[/C][C]50199.8209720625[/C][C]3131.17902793747[/C][/ROW]
[ROW][C]9[/C][C]39587[/C][C]51609.6776665582[/C][C]-12022.6776665582[/C][/ROW]
[ROW][C]10[/C][C]46278[/C][C]46196.3006469996[/C][C]81.699353000382[/C][/ROW]
[ROW][C]11[/C][C]50365[/C][C]46233.0869114501[/C][C]4131.91308854989[/C][/ROW]
[ROW][C]12[/C][C]57176[/C][C]48093.5379674229[/C][C]9082.46203257705[/C][/ROW]
[ROW][C]13[/C][C]39251[/C][C]52183.0422036486[/C][C]-12932.0422036486[/C][/ROW]
[ROW][C]14[/C][C]47946[/C][C]46360.211215181[/C][C]1585.78878481901[/C][/ROW]
[ROW][C]15[/C][C]50427[/C][C]47074.2345636977[/C][C]3352.7654363023[/C][/ROW]
[ROW][C]16[/C][C]54317[/C][C]48583.8636054322[/C][C]5733.1363945678[/C][/ROW]
[ROW][C]17[/C][C]41210[/C][C]51165.2876167134[/C][C]-9955.28761671345[/C][/ROW]
[ROW][C]18[/C][C]50592[/C][C]46682.7815808646[/C][C]3909.21841913542[/C][/ROW]
[ROW][C]19[/C][C]55728[/C][C]48442.961279722[/C][C]7285.03872027797[/C][/ROW]
[ROW][C]20[/C][C]59099[/C][C]51723.1507922998[/C][C]7375.84920770021[/C][/ROW]
[ROW][C]21[/C][C]47519[/C][C]55044.2289837044[/C][C]-7525.22898370439[/C][/ROW]
[ROW][C]22[/C][C]53203[/C][C]51655.8904806591[/C][C]1547.10951934087[/C][/ROW]
[ROW][C]23[/C][C]53882[/C][C]52352.4979545529[/C][C]1529.50204544711[/C][/ROW]
[ROW][C]24[/C][C]55163[/C][C]53041.1774196293[/C][C]2121.82258037072[/C][/ROW]
[ROW][C]25[/C][C]45255[/C][C]53996.5574035832[/C][C]-8741.55740358318[/C][/ROW]
[ROW][C]26[/C][C]50423[/C][C]50060.5501948616[/C][C]362.449805138414[/C][/ROW]
[ROW][C]27[/C][C]52161[/C][C]50223.7482361213[/C][C]1937.25176387865[/C][/ROW]
[ROW][C]28[/C][C]54562[/C][C]51096.0226553924[/C][C]3465.97734460761[/C][/ROW]
[ROW][C]29[/C][C]40971[/C][C]52656.6269257538[/C][C]-11685.6269257538[/C][/ROW]
[ROW][C]30[/C][C]48014[/C][C]47395.0116672022[/C][C]618.988332797824[/C][/ROW]
[ROW][C]31[/C][C]48440[/C][C]47673.7197311689[/C][C]766.280268831091[/C][/ROW]
[ROW][C]32[/C][C]44967[/C][C]48018.7480279326[/C][C]-3051.7480279326[/C][/ROW]
[ROW][C]33[/C][C]27218[/C][C]46644.656240556[/C][C]-19426.656240556[/C][/ROW]
[ROW][C]34[/C][C]30269[/C][C]37897.5353930921[/C][C]-7628.53539309211[/C][/ROW]
[ROW][C]35[/C][C]33234[/C][C]34462.6817494049[/C][C]-1228.68174940492[/C][/ROW]
[ROW][C]36[/C][C]36811[/C][C]33909.4507861329[/C][C]2901.54921386715[/C][/ROW]
[ROW][C]37[/C][C]27745[/C][C]35215.9134786458[/C][C]-7470.91347864577[/C][/ROW]
[ROW][C]38[/C][C]31891[/C][C]31852.0312835084[/C][C]38.9687164916395[/C][/ROW]
[ROW][C]39[/C][C]32398[/C][C]31869.5774874563[/C][C]528.422512543719[/C][/ROW]
[ROW][C]40[/C][C]34093[/C][C]32107.507037375[/C][C]1985.49296262504[/C][/ROW]
[ROW][C]41[/C][C]28358[/C][C]33001.5027240652[/C][C]-4643.50272406516[/C][/ROW]
[ROW][C]42[/C][C]29532[/C][C]30910.7013540316[/C][C]-1378.70135403159[/C][/ROW]
[ROW][C]43[/C][C]30769[/C][C]30289.921987426[/C][C]479.078012573977[/C][/ROW]
[ROW][C]44[/C][C]32080[/C][C]30505.6334932795[/C][C]1574.36650672054[/C][/ROW]
[ROW][C]45[/C][C]23951[/C][C]31214.513802992[/C][C]-7263.51380299199[/C][/ROW]
[ROW][C]46[/C][C]34628[/C][C]27944.0161823384[/C][C]6683.98381766157[/C][/ROW]
[ROW][C]47[/C][C]22978[/C][C]30953.5724060968[/C][C]-7975.57240609676[/C][/ROW]
[ROW][C]48[/C][C]35704[/C][C]27362.4605441292[/C][C]8341.5394558708[/C][/ROW]
[ROW][C]49[/C][C]23090[/C][C]31118.3541354342[/C][C]-8028.35413543422[/C][/ROW]
[ROW][C]50[/C][C]22111[/C][C]27503.4765693055[/C][C]-5392.47656930554[/C][/ROW]
[ROW][C]51[/C][C]28925[/C][C]25075.43935926[/C][C]3849.56064073998[/C][/ROW]
[ROW][C]52[/C][C]35968[/C][C]26808.7573176999[/C][C]9159.24268230014[/C][/ROW]
[ROW][C]53[/C][C]28963[/C][C]30932.833104148[/C][C]-1969.833104148[/C][/ROW]
[ROW][C]54[/C][C]34074[/C][C]30045.8884854778[/C][C]4028.11151452223[/C][/ROW]
[ROW][C]55[/C][C]39160[/C][C]31859.6014460762[/C][C]7300.39855392381[/C][/ROW]
[ROW][C]56[/C][C]51314[/C][C]35146.7069363412[/C][C]16167.2930636588[/C][/ROW]
[ROW][C]57[/C][C]34527[/C][C]42426.2544021042[/C][C]-7899.25440210418[/C][/ROW]
[ROW][C]58[/C][C]40722[/C][C]38869.5057777156[/C][C]1852.49422228435[/C][/ROW]
[ROW][C]59[/C][C]50609[/C][C]39703.6169407948[/C][C]10905.3830592052[/C][/ROW]
[ROW][C]60[/C][C]52435[/C][C]44613.9165994469[/C][C]7821.08340055311[/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
2481913772910462
35249842439.660299589910058.3397004101
45731946968.566962418310350.4330375817
54437751628.9926930338-7251.99269303382
64808148363.6826115971-282.682611597149
75259748236.40085324934360.59914675069
85333150199.82097206253131.17902793747
93958751609.6776665582-12022.6776665582
104627846196.300646999681.699353000382
115036546233.08691145014131.91308854989
125717648093.53796742299082.46203257705
133925152183.0422036486-12932.0422036486
144794646360.2112151811585.78878481901
155042747074.23456369773352.7654363023
165431748583.86360543225733.1363945678
174121051165.2876167134-9955.28761671345
185059246682.78158086463909.21841913542
195572848442.9612797227285.03872027797
205909951723.15079229987375.84920770021
214751955044.2289837044-7525.22898370439
225320351655.89048065911547.10951934087
235388252352.49795455291529.50204544711
245516353041.17741962932121.82258037072
254525553996.5574035832-8741.55740358318
265042350060.5501948616362.449805138414
275216150223.74823612131937.25176387865
285456251096.02265539243465.97734460761
294097152656.6269257538-11685.6269257538
304801447395.0116672022618.988332797824
314844047673.7197311689766.280268831091
324496748018.7480279326-3051.7480279326
332721846644.656240556-19426.656240556
343026937897.5353930921-7628.53539309211
353323434462.6817494049-1228.68174940492
363681133909.45078613292901.54921386715
372774535215.9134786458-7470.91347864577
383189131852.031283508438.9687164916395
393239831869.5774874563528.422512543719
403409332107.5070373751985.49296262504
412835833001.5027240652-4643.50272406516
422953230910.7013540316-1378.70135403159
433076930289.921987426479.078012573977
443208030505.63349327951574.36650672054
452395131214.513802992-7263.51380299199
463462827944.01618233846683.98381766157
472297830953.5724060968-7975.57240609676
483570427362.46054412928341.5394558708
492309031118.3541354342-8028.35413543422
502211127503.4765693055-5392.47656930554
512892525075.439359263849.56064073998
523596826808.75731769999159.24268230014
532896330932.833104148-1969.833104148
543407430045.88848547784028.11151452223
553916031859.60144607627300.39855392381
565131435146.706936341216167.2930636588
573452742426.2544021042-7899.25440210418
584072238869.50577771561852.49422228435
595060939703.616940794810905.3830592052
605243544613.91659944697821.08340055311







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6148135.467648459234251.711129713962019.2241672045
6248135.467648459232909.236465326963361.6988315915
6348135.467648459231675.89484074164595.0404561774
6448135.467648459230528.737174490965742.1981224275

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 48135.4676484592 & 34251.7111297139 & 62019.2241672045 \tabularnewline
62 & 48135.4676484592 & 32909.2364653269 & 63361.6988315915 \tabularnewline
63 & 48135.4676484592 & 31675.894840741 & 64595.0404561774 \tabularnewline
64 & 48135.4676484592 & 30528.7371744909 & 65742.1981224275 \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]48135.4676484592[/C][C]34251.7111297139[/C][C]62019.2241672045[/C][/ROW]
[ROW][C]62[/C][C]48135.4676484592[/C][C]32909.2364653269[/C][C]63361.6988315915[/C][/ROW]
[ROW][C]63[/C][C]48135.4676484592[/C][C]31675.894840741[/C][C]64595.0404561774[/C][/ROW]
[ROW][C]64[/C][C]48135.4676484592[/C][C]30528.7371744909[/C][C]65742.1981224275[/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
6148135.467648459234251.711129713962019.2241672045
6248135.467648459232909.236465326963361.6988315915
6348135.467648459231675.89484074164595.0404561774
6448135.467648459230528.737174490965742.1981224275



Parameters (Session):
par1 = 4 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 4 ; par2 = Single ; 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')