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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 23 May 2016 15:05:33 +0100
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/May/23/t146401252101xatw7zq6tqyd6.htm/, Retrieved Tue, 07 May 2024 08:58:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295517, Retrieved Tue, 07 May 2024 08:58:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-05-23 14:05:33] [dce1b7f6243247e331d0750a8103b593] [Current]
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Dataseries X:
10670.5
11129
13474.5
12317.8
11990.1
13478.3
11762.4
11149.1
13597.2
13367.9
13304.2
12407.2
13008.3
13379.5
15696
13529.6
14857
14375.1
12958.4
12612.8
14405.2
13655.8
13783.1
12336.1
13366.7
14042.4
15412
13566.5
13981.5
14042
13131
12771.2
13600.1
14886.9
13813.1
11551
13750.5
13415.4
15040.9
14349.5
13900.2
13956.6
13951
11802.1
14219.1
14914.5
14098.2
12773.6
14225
13513
14754.4
14447.7
13777.8
14328.6
14106.1
12157
15425.1
15448.8
13604.5
12269.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295517&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295517&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295517&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.426102502459319
beta0.0375246581481332
gamma0.995916262225933

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.426102502459319 \tabularnewline
beta & 0.0375246581481332 \tabularnewline
gamma & 0.995916262225933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295517&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]0.426102502459319[/C][/ROW]
[ROW][C]beta[/C][C]0.0375246581481332[/C][/ROW]
[ROW][C]gamma[/C][C]0.995916262225933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295517&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295517&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
alpha0.426102502459319
beta0.0375246581481332
gamma0.995916262225933







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1313008.312170.2025131009838.097486899065
1413379.512905.3349359338474.165064066232
151569615425.6485523999270.351447600144
1613529.613488.600103956340.9998960437424
171485714947.9194253712-90.9194253712394
1814375.114552.5642904774-177.464290477406
1912958.413144.8431063616-186.44310636159
2012612.812313.8029266911298.997073308907
2114405.215098.8903551801-693.690355180064
2213655.814524.4399728705-868.639972870456
2313783.114020.0684226434-236.96842264336
2412336.112930.3609500118-594.260950011778
2513366.713810.3605742544-443.660574254358
2614042.413753.8701710055288.529828994548
271541216109.5883683535-697.588368353503
2813566.513560.97479930885.52520069118873
2913981.514876.8007366177-895.300736617715
301404214035.90788759436.09211240565128
311313112678.1149731466452.88502685339
3212771.212354.7170899742416.482910025805
3313600.114553.0179281537-952.917928153693
3414886.913712.70883593031174.19116406974
3513813.114423.643459884-610.543459883984
361155112904.6153475253-1353.61534752535
3713750.513503.7671046509246.732895349103
3813415.414137.6699588168-722.269958816825
3915040.915417.9398102516-377.039810251572
4014349.513387.7402589056961.759741094445
4113900.214568.8541351506-668.654135150618
4213956.614316.7736225008-360.173622500848
431395113018.242383809932.757616190969
4411802.112844.1782446261-1042.07824462612
4514219.113545.1547717018673.945228298242
4614914.514581.4899176211333.010082378853
4714098.213884.8913255935213.308674406519
4812773.612218.1314049912555.468595008811
491422514716.8701656873-491.870165687296
501351314470.1046241154-957.104624115351
5114754.415926.4168715845-1172.01687158452
5214447.714262.8917021708184.80829782924
5313777.814147.4465350739-369.646535073904
5414328.614175.9853621488152.614637851242
5514106.113796.3509452929309.749054707103
561215712188.5923017365-31.5923017364676
5715425.114351.61923323161073.48076676842
5815448.815381.747070130867.052929869189
5913604.514466.0752182617-861.575218261702
6012269.312511.6313275249-242.331327524927

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13008.3 & 12170.2025131009 & 838.097486899065 \tabularnewline
14 & 13379.5 & 12905.3349359338 & 474.165064066232 \tabularnewline
15 & 15696 & 15425.6485523999 & 270.351447600144 \tabularnewline
16 & 13529.6 & 13488.6001039563 & 40.9998960437424 \tabularnewline
17 & 14857 & 14947.9194253712 & -90.9194253712394 \tabularnewline
18 & 14375.1 & 14552.5642904774 & -177.464290477406 \tabularnewline
19 & 12958.4 & 13144.8431063616 & -186.44310636159 \tabularnewline
20 & 12612.8 & 12313.8029266911 & 298.997073308907 \tabularnewline
21 & 14405.2 & 15098.8903551801 & -693.690355180064 \tabularnewline
22 & 13655.8 & 14524.4399728705 & -868.639972870456 \tabularnewline
23 & 13783.1 & 14020.0684226434 & -236.96842264336 \tabularnewline
24 & 12336.1 & 12930.3609500118 & -594.260950011778 \tabularnewline
25 & 13366.7 & 13810.3605742544 & -443.660574254358 \tabularnewline
26 & 14042.4 & 13753.8701710055 & 288.529828994548 \tabularnewline
27 & 15412 & 16109.5883683535 & -697.588368353503 \tabularnewline
28 & 13566.5 & 13560.9747993088 & 5.52520069118873 \tabularnewline
29 & 13981.5 & 14876.8007366177 & -895.300736617715 \tabularnewline
30 & 14042 & 14035.9078875943 & 6.09211240565128 \tabularnewline
31 & 13131 & 12678.1149731466 & 452.88502685339 \tabularnewline
32 & 12771.2 & 12354.7170899742 & 416.482910025805 \tabularnewline
33 & 13600.1 & 14553.0179281537 & -952.917928153693 \tabularnewline
34 & 14886.9 & 13712.7088359303 & 1174.19116406974 \tabularnewline
35 & 13813.1 & 14423.643459884 & -610.543459883984 \tabularnewline
36 & 11551 & 12904.6153475253 & -1353.61534752535 \tabularnewline
37 & 13750.5 & 13503.7671046509 & 246.732895349103 \tabularnewline
38 & 13415.4 & 14137.6699588168 & -722.269958816825 \tabularnewline
39 & 15040.9 & 15417.9398102516 & -377.039810251572 \tabularnewline
40 & 14349.5 & 13387.7402589056 & 961.759741094445 \tabularnewline
41 & 13900.2 & 14568.8541351506 & -668.654135150618 \tabularnewline
42 & 13956.6 & 14316.7736225008 & -360.173622500848 \tabularnewline
43 & 13951 & 13018.242383809 & 932.757616190969 \tabularnewline
44 & 11802.1 & 12844.1782446261 & -1042.07824462612 \tabularnewline
45 & 14219.1 & 13545.1547717018 & 673.945228298242 \tabularnewline
46 & 14914.5 & 14581.4899176211 & 333.010082378853 \tabularnewline
47 & 14098.2 & 13884.8913255935 & 213.308674406519 \tabularnewline
48 & 12773.6 & 12218.1314049912 & 555.468595008811 \tabularnewline
49 & 14225 & 14716.8701656873 & -491.870165687296 \tabularnewline
50 & 13513 & 14470.1046241154 & -957.104624115351 \tabularnewline
51 & 14754.4 & 15926.4168715845 & -1172.01687158452 \tabularnewline
52 & 14447.7 & 14262.8917021708 & 184.80829782924 \tabularnewline
53 & 13777.8 & 14147.4465350739 & -369.646535073904 \tabularnewline
54 & 14328.6 & 14175.9853621488 & 152.614637851242 \tabularnewline
55 & 14106.1 & 13796.3509452929 & 309.749054707103 \tabularnewline
56 & 12157 & 12188.5923017365 & -31.5923017364676 \tabularnewline
57 & 15425.1 & 14351.6192332316 & 1073.48076676842 \tabularnewline
58 & 15448.8 & 15381.7470701308 & 67.052929869189 \tabularnewline
59 & 13604.5 & 14466.0752182617 & -861.575218261702 \tabularnewline
60 & 12269.3 & 12511.6313275249 & -242.331327524927 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295517&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]13008.3[/C][C]12170.2025131009[/C][C]838.097486899065[/C][/ROW]
[ROW][C]14[/C][C]13379.5[/C][C]12905.3349359338[/C][C]474.165064066232[/C][/ROW]
[ROW][C]15[/C][C]15696[/C][C]15425.6485523999[/C][C]270.351447600144[/C][/ROW]
[ROW][C]16[/C][C]13529.6[/C][C]13488.6001039563[/C][C]40.9998960437424[/C][/ROW]
[ROW][C]17[/C][C]14857[/C][C]14947.9194253712[/C][C]-90.9194253712394[/C][/ROW]
[ROW][C]18[/C][C]14375.1[/C][C]14552.5642904774[/C][C]-177.464290477406[/C][/ROW]
[ROW][C]19[/C][C]12958.4[/C][C]13144.8431063616[/C][C]-186.44310636159[/C][/ROW]
[ROW][C]20[/C][C]12612.8[/C][C]12313.8029266911[/C][C]298.997073308907[/C][/ROW]
[ROW][C]21[/C][C]14405.2[/C][C]15098.8903551801[/C][C]-693.690355180064[/C][/ROW]
[ROW][C]22[/C][C]13655.8[/C][C]14524.4399728705[/C][C]-868.639972870456[/C][/ROW]
[ROW][C]23[/C][C]13783.1[/C][C]14020.0684226434[/C][C]-236.96842264336[/C][/ROW]
[ROW][C]24[/C][C]12336.1[/C][C]12930.3609500118[/C][C]-594.260950011778[/C][/ROW]
[ROW][C]25[/C][C]13366.7[/C][C]13810.3605742544[/C][C]-443.660574254358[/C][/ROW]
[ROW][C]26[/C][C]14042.4[/C][C]13753.8701710055[/C][C]288.529828994548[/C][/ROW]
[ROW][C]27[/C][C]15412[/C][C]16109.5883683535[/C][C]-697.588368353503[/C][/ROW]
[ROW][C]28[/C][C]13566.5[/C][C]13560.9747993088[/C][C]5.52520069118873[/C][/ROW]
[ROW][C]29[/C][C]13981.5[/C][C]14876.8007366177[/C][C]-895.300736617715[/C][/ROW]
[ROW][C]30[/C][C]14042[/C][C]14035.9078875943[/C][C]6.09211240565128[/C][/ROW]
[ROW][C]31[/C][C]13131[/C][C]12678.1149731466[/C][C]452.88502685339[/C][/ROW]
[ROW][C]32[/C][C]12771.2[/C][C]12354.7170899742[/C][C]416.482910025805[/C][/ROW]
[ROW][C]33[/C][C]13600.1[/C][C]14553.0179281537[/C][C]-952.917928153693[/C][/ROW]
[ROW][C]34[/C][C]14886.9[/C][C]13712.7088359303[/C][C]1174.19116406974[/C][/ROW]
[ROW][C]35[/C][C]13813.1[/C][C]14423.643459884[/C][C]-610.543459883984[/C][/ROW]
[ROW][C]36[/C][C]11551[/C][C]12904.6153475253[/C][C]-1353.61534752535[/C][/ROW]
[ROW][C]37[/C][C]13750.5[/C][C]13503.7671046509[/C][C]246.732895349103[/C][/ROW]
[ROW][C]38[/C][C]13415.4[/C][C]14137.6699588168[/C][C]-722.269958816825[/C][/ROW]
[ROW][C]39[/C][C]15040.9[/C][C]15417.9398102516[/C][C]-377.039810251572[/C][/ROW]
[ROW][C]40[/C][C]14349.5[/C][C]13387.7402589056[/C][C]961.759741094445[/C][/ROW]
[ROW][C]41[/C][C]13900.2[/C][C]14568.8541351506[/C][C]-668.654135150618[/C][/ROW]
[ROW][C]42[/C][C]13956.6[/C][C]14316.7736225008[/C][C]-360.173622500848[/C][/ROW]
[ROW][C]43[/C][C]13951[/C][C]13018.242383809[/C][C]932.757616190969[/C][/ROW]
[ROW][C]44[/C][C]11802.1[/C][C]12844.1782446261[/C][C]-1042.07824462612[/C][/ROW]
[ROW][C]45[/C][C]14219.1[/C][C]13545.1547717018[/C][C]673.945228298242[/C][/ROW]
[ROW][C]46[/C][C]14914.5[/C][C]14581.4899176211[/C][C]333.010082378853[/C][/ROW]
[ROW][C]47[/C][C]14098.2[/C][C]13884.8913255935[/C][C]213.308674406519[/C][/ROW]
[ROW][C]48[/C][C]12773.6[/C][C]12218.1314049912[/C][C]555.468595008811[/C][/ROW]
[ROW][C]49[/C][C]14225[/C][C]14716.8701656873[/C][C]-491.870165687296[/C][/ROW]
[ROW][C]50[/C][C]13513[/C][C]14470.1046241154[/C][C]-957.104624115351[/C][/ROW]
[ROW][C]51[/C][C]14754.4[/C][C]15926.4168715845[/C][C]-1172.01687158452[/C][/ROW]
[ROW][C]52[/C][C]14447.7[/C][C]14262.8917021708[/C][C]184.80829782924[/C][/ROW]
[ROW][C]53[/C][C]13777.8[/C][C]14147.4465350739[/C][C]-369.646535073904[/C][/ROW]
[ROW][C]54[/C][C]14328.6[/C][C]14175.9853621488[/C][C]152.614637851242[/C][/ROW]
[ROW][C]55[/C][C]14106.1[/C][C]13796.3509452929[/C][C]309.749054707103[/C][/ROW]
[ROW][C]56[/C][C]12157[/C][C]12188.5923017365[/C][C]-31.5923017364676[/C][/ROW]
[ROW][C]57[/C][C]15425.1[/C][C]14351.6192332316[/C][C]1073.48076676842[/C][/ROW]
[ROW][C]58[/C][C]15448.8[/C][C]15381.7470701308[/C][C]67.052929869189[/C][/ROW]
[ROW][C]59[/C][C]13604.5[/C][C]14466.0752182617[/C][C]-861.575218261702[/C][/ROW]
[ROW][C]60[/C][C]12269.3[/C][C]12511.6313275249[/C][C]-242.331327524927[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295517&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295517&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
1313008.312170.2025131009838.097486899065
1413379.512905.3349359338474.165064066232
151569615425.6485523999270.351447600144
1613529.613488.600103956340.9998960437424
171485714947.9194253712-90.9194253712394
1814375.114552.5642904774-177.464290477406
1912958.413144.8431063616-186.44310636159
2012612.812313.8029266911298.997073308907
2114405.215098.8903551801-693.690355180064
2213655.814524.4399728705-868.639972870456
2313783.114020.0684226434-236.96842264336
2412336.112930.3609500118-594.260950011778
2513366.713810.3605742544-443.660574254358
2614042.413753.8701710055288.529828994548
271541216109.5883683535-697.588368353503
2813566.513560.97479930885.52520069118873
2913981.514876.8007366177-895.300736617715
301404214035.90788759436.09211240565128
311313112678.1149731466452.88502685339
3212771.212354.7170899742416.482910025805
3313600.114553.0179281537-952.917928153693
3414886.913712.70883593031174.19116406974
3513813.114423.643459884-610.543459883984
361155112904.6153475253-1353.61534752535
3713750.513503.7671046509246.732895349103
3813415.414137.6699588168-722.269958816825
3915040.915417.9398102516-377.039810251572
4014349.513387.7402589056961.759741094445
4113900.214568.8541351506-668.654135150618
4213956.614316.7736225008-360.173622500848
431395113018.242383809932.757616190969
4411802.112844.1782446261-1042.07824462612
4514219.113545.1547717018673.945228298242
4614914.514581.4899176211333.010082378853
4714098.213884.8913255935213.308674406519
4812773.612218.1314049912555.468595008811
491422514716.8701656873-491.870165687296
501351314470.1046241154-957.104624115351
5114754.415926.4168715845-1172.01687158452
5214447.714262.8917021708184.80829782924
5313777.814147.4465350739-369.646535073904
5414328.614175.9853621488152.614637851242
5514106.113796.3509452929309.749054707103
561215712188.5923017365-31.5923017364676
5715425.114351.61923323161073.48076676842
5815448.815381.747070130867.052929869189
5913604.514466.0752182617-861.575218261702
6012269.312511.6313275249-242.331327524927







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6113986.536716270512756.97196938515216.1014631561
6213646.485356439312307.476596425314985.4941164532
6315367.848512559813862.168153067816873.5288720518
6414964.449830084613365.792629032316563.1070311368
6514431.666662422912752.181936155916111.1513886899
6614943.646920155813121.144864770916766.1489755407
6714574.207570681612671.046224589916477.3689167733
6812572.934258070810729.384501059214416.4840150824
6915455.50909609813223.586573536517687.4316186596
7015434.40686868213095.035390786917773.7783465771
7113930.479413463411657.332436569816203.6263903569
7212661.839576706410807.841733306414515.8374201064

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 13986.5367162705 & 12756.971969385 & 15216.1014631561 \tabularnewline
62 & 13646.4853564393 & 12307.4765964253 & 14985.4941164532 \tabularnewline
63 & 15367.8485125598 & 13862.1681530678 & 16873.5288720518 \tabularnewline
64 & 14964.4498300846 & 13365.7926290323 & 16563.1070311368 \tabularnewline
65 & 14431.6666624229 & 12752.1819361559 & 16111.1513886899 \tabularnewline
66 & 14943.6469201558 & 13121.1448647709 & 16766.1489755407 \tabularnewline
67 & 14574.2075706816 & 12671.0462245899 & 16477.3689167733 \tabularnewline
68 & 12572.9342580708 & 10729.3845010592 & 14416.4840150824 \tabularnewline
69 & 15455.509096098 & 13223.5865735365 & 17687.4316186596 \tabularnewline
70 & 15434.406868682 & 13095.0353907869 & 17773.7783465771 \tabularnewline
71 & 13930.4794134634 & 11657.3324365698 & 16203.6263903569 \tabularnewline
72 & 12661.8395767064 & 10807.8417333064 & 14515.8374201064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295517&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]13986.5367162705[/C][C]12756.971969385[/C][C]15216.1014631561[/C][/ROW]
[ROW][C]62[/C][C]13646.4853564393[/C][C]12307.4765964253[/C][C]14985.4941164532[/C][/ROW]
[ROW][C]63[/C][C]15367.8485125598[/C][C]13862.1681530678[/C][C]16873.5288720518[/C][/ROW]
[ROW][C]64[/C][C]14964.4498300846[/C][C]13365.7926290323[/C][C]16563.1070311368[/C][/ROW]
[ROW][C]65[/C][C]14431.6666624229[/C][C]12752.1819361559[/C][C]16111.1513886899[/C][/ROW]
[ROW][C]66[/C][C]14943.6469201558[/C][C]13121.1448647709[/C][C]16766.1489755407[/C][/ROW]
[ROW][C]67[/C][C]14574.2075706816[/C][C]12671.0462245899[/C][C]16477.3689167733[/C][/ROW]
[ROW][C]68[/C][C]12572.9342580708[/C][C]10729.3845010592[/C][C]14416.4840150824[/C][/ROW]
[ROW][C]69[/C][C]15455.509096098[/C][C]13223.5865735365[/C][C]17687.4316186596[/C][/ROW]
[ROW][C]70[/C][C]15434.406868682[/C][C]13095.0353907869[/C][C]17773.7783465771[/C][/ROW]
[ROW][C]71[/C][C]13930.4794134634[/C][C]11657.3324365698[/C][C]16203.6263903569[/C][/ROW]
[ROW][C]72[/C][C]12661.8395767064[/C][C]10807.8417333064[/C][C]14515.8374201064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295517&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295517&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
6113986.536716270512756.97196938515216.1014631561
6213646.485356439312307.476596425314985.4941164532
6315367.848512559813862.168153067816873.5288720518
6414964.449830084613365.792629032316563.1070311368
6514431.666662422912752.181936155916111.1513886899
6614943.646920155813121.144864770916766.1489755407
6714574.207570681612671.046224589916477.3689167733
6812572.934258070810729.384501059214416.4840150824
6915455.50909609813223.586573536517687.4316186596
7015434.40686868213095.035390786917773.7783465771
7113930.479413463411657.332436569816203.6263903569
7212661.839576706410807.841733306414515.8374201064



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')