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 20:02:42 +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/t1480190578edsa678yh76geci.htm/, Retrieved Fri, 03 May 2024 23:33:43 +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 23:33:43 +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 time2 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 & 2 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]2 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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.595209960822174
beta0.163559722888248
gamma0.246514752199846

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.595209960822174 \tabularnewline
beta & 0.163559722888248 \tabularnewline
gamma & 0.246514752199846 \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]0.595209960822174[/C][/ROW]
[ROW][C]beta[/C][C]0.163559722888248[/C][/ROW]
[ROW][C]gamma[/C][C]0.246514752199846[/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
alpha0.595209960822174
beta0.163559722888248
gamma0.246514752199846







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
54437743686.1619251963690.838074803687
64808148409.4524157648-328.452415764797
75259753141.2689133479-544.268913347878
85333156839.3547211234-3508.3547211234
93958742271.7216373826-2684.72163738259
104627843909.8180541622368.18194583804
115036549511.6168398986853.383160101432
125717653229.90238202283946.09761797717
133925143223.1174255028-3972.1174255028
144794644848.76185523083097.23814476922
155042751146.2148741489-719.214874148944
165431754429.9198723269-112.919872326936
174121041398.3024406481-188.302440648098
185059246279.56170513884312.43829486121
195572853431.30690936812296.69309063185
205909959579.7400634152-480.740063415244
214751945649.33383540261869.66616459741
225320353710.4174515247-507.417451524685
235388258472.1943405044-4590.19434050444
245516359950.5658394128-4787.56583941281
254525543604.7903860511650.20961394903
265042350312.9577315625110.042268437544
275216154124.7947827123-1963.79478271228
285456256513.7494030157-1951.74940301565
294097142645.4090114355-1674.4090114355
304801446321.31797696151692.68202303855
314844050265.401418885-1825.40141888501
324496752082.0966276568-7115.09662765679
332721836110.3257836386-8892.32578363858
343026932823.6992797764-2554.6992797764
353323430765.14229517592468.85770482414
363681131763.59952916055047.40047083945
372774525138.44704546832606.55295453173
383189129515.08330556862375.91669443141
393239832147.8705177368250.129482263201
403409333154.6349402355938.365059764525
412835824746.10465108373611.89534891635
422953230420.6565048838-888.656504883849
433076931259.801975108-490.80197510797
443208032206.7838124048-126.783812404796
452395124022.1670041445-71.1670041444668
463462826461.38011791688166.6198820832
472297833624.3313896242-10646.3313896242
483570428095.28841631197608.71158368807
492309024814.5841887702-1724.58418877019
502211127226.2962927209-5115.29629272085
512892523297.52113832445627.47886167562
523596829817.81251966316150.18748033689
532896325026.05715722613936.9428427739
543407431963.07160009912110.92839990086
553916035565.99098813793594.00901186206
565131444051.73572067757262.26427932253
573452737380.3392200344-2853.33922003445
584072242016.9913128738-1294.99131287375
595060944636.13059281495972.86940718512
605243557117.7469128258-4682.74691282583

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 44377 & 43686.1619251963 & 690.838074803687 \tabularnewline
6 & 48081 & 48409.4524157648 & -328.452415764797 \tabularnewline
7 & 52597 & 53141.2689133479 & -544.268913347878 \tabularnewline
8 & 53331 & 56839.3547211234 & -3508.3547211234 \tabularnewline
9 & 39587 & 42271.7216373826 & -2684.72163738259 \tabularnewline
10 & 46278 & 43909.818054162 & 2368.18194583804 \tabularnewline
11 & 50365 & 49511.6168398986 & 853.383160101432 \tabularnewline
12 & 57176 & 53229.9023820228 & 3946.09761797717 \tabularnewline
13 & 39251 & 43223.1174255028 & -3972.1174255028 \tabularnewline
14 & 47946 & 44848.7618552308 & 3097.23814476922 \tabularnewline
15 & 50427 & 51146.2148741489 & -719.214874148944 \tabularnewline
16 & 54317 & 54429.9198723269 & -112.919872326936 \tabularnewline
17 & 41210 & 41398.3024406481 & -188.302440648098 \tabularnewline
18 & 50592 & 46279.5617051388 & 4312.43829486121 \tabularnewline
19 & 55728 & 53431.3069093681 & 2296.69309063185 \tabularnewline
20 & 59099 & 59579.7400634152 & -480.740063415244 \tabularnewline
21 & 47519 & 45649.3338354026 & 1869.66616459741 \tabularnewline
22 & 53203 & 53710.4174515247 & -507.417451524685 \tabularnewline
23 & 53882 & 58472.1943405044 & -4590.19434050444 \tabularnewline
24 & 55163 & 59950.5658394128 & -4787.56583941281 \tabularnewline
25 & 45255 & 43604.790386051 & 1650.20961394903 \tabularnewline
26 & 50423 & 50312.9577315625 & 110.042268437544 \tabularnewline
27 & 52161 & 54124.7947827123 & -1963.79478271228 \tabularnewline
28 & 54562 & 56513.7494030157 & -1951.74940301565 \tabularnewline
29 & 40971 & 42645.4090114355 & -1674.4090114355 \tabularnewline
30 & 48014 & 46321.3179769615 & 1692.68202303855 \tabularnewline
31 & 48440 & 50265.401418885 & -1825.40141888501 \tabularnewline
32 & 44967 & 52082.0966276568 & -7115.09662765679 \tabularnewline
33 & 27218 & 36110.3257836386 & -8892.32578363858 \tabularnewline
34 & 30269 & 32823.6992797764 & -2554.6992797764 \tabularnewline
35 & 33234 & 30765.1422951759 & 2468.85770482414 \tabularnewline
36 & 36811 & 31763.5995291605 & 5047.40047083945 \tabularnewline
37 & 27745 & 25138.4470454683 & 2606.55295453173 \tabularnewline
38 & 31891 & 29515.0833055686 & 2375.91669443141 \tabularnewline
39 & 32398 & 32147.8705177368 & 250.129482263201 \tabularnewline
40 & 34093 & 33154.6349402355 & 938.365059764525 \tabularnewline
41 & 28358 & 24746.1046510837 & 3611.89534891635 \tabularnewline
42 & 29532 & 30420.6565048838 & -888.656504883849 \tabularnewline
43 & 30769 & 31259.801975108 & -490.80197510797 \tabularnewline
44 & 32080 & 32206.7838124048 & -126.783812404796 \tabularnewline
45 & 23951 & 24022.1670041445 & -71.1670041444668 \tabularnewline
46 & 34628 & 26461.3801179168 & 8166.6198820832 \tabularnewline
47 & 22978 & 33624.3313896242 & -10646.3313896242 \tabularnewline
48 & 35704 & 28095.2884163119 & 7608.71158368807 \tabularnewline
49 & 23090 & 24814.5841887702 & -1724.58418877019 \tabularnewline
50 & 22111 & 27226.2962927209 & -5115.29629272085 \tabularnewline
51 & 28925 & 23297.5211383244 & 5627.47886167562 \tabularnewline
52 & 35968 & 29817.8125196631 & 6150.18748033689 \tabularnewline
53 & 28963 & 25026.0571572261 & 3936.9428427739 \tabularnewline
54 & 34074 & 31963.0716000991 & 2110.92839990086 \tabularnewline
55 & 39160 & 35565.9909881379 & 3594.00901186206 \tabularnewline
56 & 51314 & 44051.7357206775 & 7262.26427932253 \tabularnewline
57 & 34527 & 37380.3392200344 & -2853.33922003445 \tabularnewline
58 & 40722 & 42016.9913128738 & -1294.99131287375 \tabularnewline
59 & 50609 & 44636.1305928149 & 5972.86940718512 \tabularnewline
60 & 52435 & 57117.7469128258 & -4682.74691282583 \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]5[/C][C]44377[/C][C]43686.1619251963[/C][C]690.838074803687[/C][/ROW]
[ROW][C]6[/C][C]48081[/C][C]48409.4524157648[/C][C]-328.452415764797[/C][/ROW]
[ROW][C]7[/C][C]52597[/C][C]53141.2689133479[/C][C]-544.268913347878[/C][/ROW]
[ROW][C]8[/C][C]53331[/C][C]56839.3547211234[/C][C]-3508.3547211234[/C][/ROW]
[ROW][C]9[/C][C]39587[/C][C]42271.7216373826[/C][C]-2684.72163738259[/C][/ROW]
[ROW][C]10[/C][C]46278[/C][C]43909.818054162[/C][C]2368.18194583804[/C][/ROW]
[ROW][C]11[/C][C]50365[/C][C]49511.6168398986[/C][C]853.383160101432[/C][/ROW]
[ROW][C]12[/C][C]57176[/C][C]53229.9023820228[/C][C]3946.09761797717[/C][/ROW]
[ROW][C]13[/C][C]39251[/C][C]43223.1174255028[/C][C]-3972.1174255028[/C][/ROW]
[ROW][C]14[/C][C]47946[/C][C]44848.7618552308[/C][C]3097.23814476922[/C][/ROW]
[ROW][C]15[/C][C]50427[/C][C]51146.2148741489[/C][C]-719.214874148944[/C][/ROW]
[ROW][C]16[/C][C]54317[/C][C]54429.9198723269[/C][C]-112.919872326936[/C][/ROW]
[ROW][C]17[/C][C]41210[/C][C]41398.3024406481[/C][C]-188.302440648098[/C][/ROW]
[ROW][C]18[/C][C]50592[/C][C]46279.5617051388[/C][C]4312.43829486121[/C][/ROW]
[ROW][C]19[/C][C]55728[/C][C]53431.3069093681[/C][C]2296.69309063185[/C][/ROW]
[ROW][C]20[/C][C]59099[/C][C]59579.7400634152[/C][C]-480.740063415244[/C][/ROW]
[ROW][C]21[/C][C]47519[/C][C]45649.3338354026[/C][C]1869.66616459741[/C][/ROW]
[ROW][C]22[/C][C]53203[/C][C]53710.4174515247[/C][C]-507.417451524685[/C][/ROW]
[ROW][C]23[/C][C]53882[/C][C]58472.1943405044[/C][C]-4590.19434050444[/C][/ROW]
[ROW][C]24[/C][C]55163[/C][C]59950.5658394128[/C][C]-4787.56583941281[/C][/ROW]
[ROW][C]25[/C][C]45255[/C][C]43604.790386051[/C][C]1650.20961394903[/C][/ROW]
[ROW][C]26[/C][C]50423[/C][C]50312.9577315625[/C][C]110.042268437544[/C][/ROW]
[ROW][C]27[/C][C]52161[/C][C]54124.7947827123[/C][C]-1963.79478271228[/C][/ROW]
[ROW][C]28[/C][C]54562[/C][C]56513.7494030157[/C][C]-1951.74940301565[/C][/ROW]
[ROW][C]29[/C][C]40971[/C][C]42645.4090114355[/C][C]-1674.4090114355[/C][/ROW]
[ROW][C]30[/C][C]48014[/C][C]46321.3179769615[/C][C]1692.68202303855[/C][/ROW]
[ROW][C]31[/C][C]48440[/C][C]50265.401418885[/C][C]-1825.40141888501[/C][/ROW]
[ROW][C]32[/C][C]44967[/C][C]52082.0966276568[/C][C]-7115.09662765679[/C][/ROW]
[ROW][C]33[/C][C]27218[/C][C]36110.3257836386[/C][C]-8892.32578363858[/C][/ROW]
[ROW][C]34[/C][C]30269[/C][C]32823.6992797764[/C][C]-2554.6992797764[/C][/ROW]
[ROW][C]35[/C][C]33234[/C][C]30765.1422951759[/C][C]2468.85770482414[/C][/ROW]
[ROW][C]36[/C][C]36811[/C][C]31763.5995291605[/C][C]5047.40047083945[/C][/ROW]
[ROW][C]37[/C][C]27745[/C][C]25138.4470454683[/C][C]2606.55295453173[/C][/ROW]
[ROW][C]38[/C][C]31891[/C][C]29515.0833055686[/C][C]2375.91669443141[/C][/ROW]
[ROW][C]39[/C][C]32398[/C][C]32147.8705177368[/C][C]250.129482263201[/C][/ROW]
[ROW][C]40[/C][C]34093[/C][C]33154.6349402355[/C][C]938.365059764525[/C][/ROW]
[ROW][C]41[/C][C]28358[/C][C]24746.1046510837[/C][C]3611.89534891635[/C][/ROW]
[ROW][C]42[/C][C]29532[/C][C]30420.6565048838[/C][C]-888.656504883849[/C][/ROW]
[ROW][C]43[/C][C]30769[/C][C]31259.801975108[/C][C]-490.80197510797[/C][/ROW]
[ROW][C]44[/C][C]32080[/C][C]32206.7838124048[/C][C]-126.783812404796[/C][/ROW]
[ROW][C]45[/C][C]23951[/C][C]24022.1670041445[/C][C]-71.1670041444668[/C][/ROW]
[ROW][C]46[/C][C]34628[/C][C]26461.3801179168[/C][C]8166.6198820832[/C][/ROW]
[ROW][C]47[/C][C]22978[/C][C]33624.3313896242[/C][C]-10646.3313896242[/C][/ROW]
[ROW][C]48[/C][C]35704[/C][C]28095.2884163119[/C][C]7608.71158368807[/C][/ROW]
[ROW][C]49[/C][C]23090[/C][C]24814.5841887702[/C][C]-1724.58418877019[/C][/ROW]
[ROW][C]50[/C][C]22111[/C][C]27226.2962927209[/C][C]-5115.29629272085[/C][/ROW]
[ROW][C]51[/C][C]28925[/C][C]23297.5211383244[/C][C]5627.47886167562[/C][/ROW]
[ROW][C]52[/C][C]35968[/C][C]29817.8125196631[/C][C]6150.18748033689[/C][/ROW]
[ROW][C]53[/C][C]28963[/C][C]25026.0571572261[/C][C]3936.9428427739[/C][/ROW]
[ROW][C]54[/C][C]34074[/C][C]31963.0716000991[/C][C]2110.92839990086[/C][/ROW]
[ROW][C]55[/C][C]39160[/C][C]35565.9909881379[/C][C]3594.00901186206[/C][/ROW]
[ROW][C]56[/C][C]51314[/C][C]44051.7357206775[/C][C]7262.26427932253[/C][/ROW]
[ROW][C]57[/C][C]34527[/C][C]37380.3392200344[/C][C]-2853.33922003445[/C][/ROW]
[ROW][C]58[/C][C]40722[/C][C]42016.9913128738[/C][C]-1294.99131287375[/C][/ROW]
[ROW][C]59[/C][C]50609[/C][C]44636.1305928149[/C][C]5972.86940718512[/C][/ROW]
[ROW][C]60[/C][C]52435[/C][C]57117.7469128258[/C][C]-4682.74691282583[/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
54437743686.1619251963690.838074803687
64808148409.4524157648-328.452415764797
75259753141.2689133479-544.268913347878
85333156839.3547211234-3508.3547211234
93958742271.7216373826-2684.72163738259
104627843909.8180541622368.18194583804
115036549511.6168398986853.383160101432
125717653229.90238202283946.09761797717
133925143223.1174255028-3972.1174255028
144794644848.76185523083097.23814476922
155042751146.2148741489-719.214874148944
165431754429.9198723269-112.919872326936
174121041398.3024406481-188.302440648098
185059246279.56170513884312.43829486121
195572853431.30690936812296.69309063185
205909959579.7400634152-480.740063415244
214751945649.33383540261869.66616459741
225320353710.4174515247-507.417451524685
235388258472.1943405044-4590.19434050444
245516359950.5658394128-4787.56583941281
254525543604.7903860511650.20961394903
265042350312.9577315625110.042268437544
275216154124.7947827123-1963.79478271228
285456256513.7494030157-1951.74940301565
294097142645.4090114355-1674.4090114355
304801446321.31797696151692.68202303855
314844050265.401418885-1825.40141888501
324496752082.0966276568-7115.09662765679
332721836110.3257836386-8892.32578363858
343026932823.6992797764-2554.6992797764
353323430765.14229517592468.85770482414
363681131763.59952916055047.40047083945
372774525138.44704546832606.55295453173
383189129515.08330556862375.91669443141
393239832147.8705177368250.129482263201
403409333154.6349402355938.365059764525
412835824746.10465108373611.89534891635
422953230420.6565048838-888.656504883849
433076931259.801975108-490.80197510797
443208032206.7838124048-126.783812404796
452395124022.1670041445-71.1670041444668
463462826461.38011791688166.6198820832
472297833624.3313896242-10646.3313896242
483570428095.28841631197608.71158368807
492309024814.5841887702-1724.58418877019
502211127226.2962927209-5115.29629272085
512892523297.52113832445627.47886167562
523596829817.81251966316150.18748033689
532896325026.05715722613936.9428427739
543407431963.07160009912110.92839990086
553916035565.99098813793594.00901186206
565131444051.73572067757262.26427932253
573452737380.3392200344-2853.33922003445
584072242016.9913128738-1294.99131287375
595060944636.13059281495972.86940718512
605243557117.7469128258-4682.74691282583







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6140644.185432823935318.555709857945969.8151557899
6247941.669966425139860.39006046156022.9498723892
6352656.982272078841923.512138759763390.4524053979
6460498.641601406847324.829036260873672.4541665527

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 40644.1854328239 & 35318.5557098579 & 45969.8151557899 \tabularnewline
62 & 47941.6699664251 & 39860.390060461 & 56022.9498723892 \tabularnewline
63 & 52656.9822720788 & 41923.5121387597 & 63390.4524053979 \tabularnewline
64 & 60498.6416014068 & 47324.8290362608 & 73672.4541665527 \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]40644.1854328239[/C][C]35318.5557098579[/C][C]45969.8151557899[/C][/ROW]
[ROW][C]62[/C][C]47941.6699664251[/C][C]39860.390060461[/C][C]56022.9498723892[/C][/ROW]
[ROW][C]63[/C][C]52656.9822720788[/C][C]41923.5121387597[/C][C]63390.4524053979[/C][/ROW]
[ROW][C]64[/C][C]60498.6416014068[/C][C]47324.8290362608[/C][C]73672.4541665527[/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
6140644.185432823935318.555709857945969.8151557899
6247941.669966425139860.39006046156022.9498723892
6352656.982272078841923.512138759763390.4524053979
6460498.641601406847324.829036260873672.4541665527



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