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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 27 Dec 2010 06:47:49 +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/2010/Dec/27/t1293432453cmufimf03wl7pmo.htm/, Retrieved Mon, 06 May 2024 19:17:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115854, Retrieved Mon, 06 May 2024 19:17:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact258
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
-  M D  [Exponential Smoothing] [] [2010-12-09 19:54:22] [897115520fe7b6114489bc0eeed64548]
-    D      [Exponential Smoothing] [] [2010-12-27 06:47:49] [09751a0677eea0d04db8ae90045d6548] [Current]
- RM          [Exponential Smoothing] [] [2012-08-21 21:50:05] [897115520fe7b6114489bc0eeed64548]
Feedback Forum

Post a new message
Dataseries X:
313737
312276
309391
302950
300316
304035
333476
337698
335932
323931
313927
314485
313218
309664
302963
298989
298423
301631
329765
335083
327616
309119
295916
291413
291542
284678
276475
272566
264981
263290
296806
303598
286994
276427
266424
267153
268381
262522
255542
253158
243803
250741
280445
285257
270976
261076
255603
260376
263903
264291
263276
262572
256167
264221
293860
300713
287224
275902
271115
277509
279681





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=115854&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=115854&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115854&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'Gwilym Jenkins' @ 72.249.127.135
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.519991743636534
beta0.543769083912884
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.519991743636534 \tabularnewline
beta & 0.543769083912884 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115854&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]0.519991743636534[/C][/ROW]
[ROW][C]beta[/C][C]0.543769083912884[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115854&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115854&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
alpha0.519991743636534
beta0.543769083912884
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13313218314937.831730769-1719.83173076925
14309664309777.65862079-113.658620789764
15302963302465.419674192497.580325807736
16298989298846.921807561142.078192438872
17298423298895.697481043-472.697481042531
18301631302609.303765351-978.303765351186
19329765326328.7115837893436.28841621149
20335083332202.6334442422880.36655575765
21327616332860.128156268-5244.1281562678
22309119317631.355296961-8512.35529696062
23295916300104.2582578-4188.25825779984
24291413294138.528195965-2725.52819596475
25291542285587.9643509825954.03564901819
26284678282552.539429152125.46057084994
27276475274694.5709901461780.42900985375
28272566269931.7795988432634.22040115687
29264981270045.297708218-5064.29770821839
30263290268894.261140499-5604.2611404988
31296806288784.8819745508021.11802545033
32303598294530.0477426959067.95225730474
33286994294008.802320778-7014.8023207782
34276427275293.4406908151133.55930918502
35266424266588.099845105-164.099845105084
36267153266285.232056573867.767943427025
37268381267653.649470515727.350529485324
38262522262469.00479931452.9952006864478
39255542255188.113642516353.886357483512
40253158251510.3562418181647.64375818230
41243803248553.547955925-4750.54795592546
42250741248533.2237785472207.77622145310
43280445282461.982068065-2016.98206806486
44285257284087.2284213781169.77157862228
45270976270103.206449268872.793550731905
46261076259994.9381773611081.06182263902
47255603251218.8957839964384.10421600423
48260376255641.8748470824734.12515291807
49263903261912.1113144521990.88868554833
50264291260376.8189509933914.18104900717
51263276259655.9331004683620.06689953234
52262572263628.897450846-1056.89745084598
53256167260761.16209574-4594.16209574009
54264221268773.026160229-4552.02616022911
55293860299858.269135979-5998.26913597935
56300713302516.661566683-1803.66156668309
57287224287576.887044053-352.887044053408
58275902277317.637664595-1415.63766459492
59271115268509.25661622605.74338380009
60277509271353.1113246326155.88867536822
61279681276625.4839492133055.51605078712

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 313218 & 314937.831730769 & -1719.83173076925 \tabularnewline
14 & 309664 & 309777.65862079 & -113.658620789764 \tabularnewline
15 & 302963 & 302465.419674192 & 497.580325807736 \tabularnewline
16 & 298989 & 298846.921807561 & 142.078192438872 \tabularnewline
17 & 298423 & 298895.697481043 & -472.697481042531 \tabularnewline
18 & 301631 & 302609.303765351 & -978.303765351186 \tabularnewline
19 & 329765 & 326328.711583789 & 3436.28841621149 \tabularnewline
20 & 335083 & 332202.633444242 & 2880.36655575765 \tabularnewline
21 & 327616 & 332860.128156268 & -5244.1281562678 \tabularnewline
22 & 309119 & 317631.355296961 & -8512.35529696062 \tabularnewline
23 & 295916 & 300104.2582578 & -4188.25825779984 \tabularnewline
24 & 291413 & 294138.528195965 & -2725.52819596475 \tabularnewline
25 & 291542 & 285587.964350982 & 5954.03564901819 \tabularnewline
26 & 284678 & 282552.53942915 & 2125.46057084994 \tabularnewline
27 & 276475 & 274694.570990146 & 1780.42900985375 \tabularnewline
28 & 272566 & 269931.779598843 & 2634.22040115687 \tabularnewline
29 & 264981 & 270045.297708218 & -5064.29770821839 \tabularnewline
30 & 263290 & 268894.261140499 & -5604.2611404988 \tabularnewline
31 & 296806 & 288784.881974550 & 8021.11802545033 \tabularnewline
32 & 303598 & 294530.047742695 & 9067.95225730474 \tabularnewline
33 & 286994 & 294008.802320778 & -7014.8023207782 \tabularnewline
34 & 276427 & 275293.440690815 & 1133.55930918502 \tabularnewline
35 & 266424 & 266588.099845105 & -164.099845105084 \tabularnewline
36 & 267153 & 266285.232056573 & 867.767943427025 \tabularnewline
37 & 268381 & 267653.649470515 & 727.350529485324 \tabularnewline
38 & 262522 & 262469.004799314 & 52.9952006864478 \tabularnewline
39 & 255542 & 255188.113642516 & 353.886357483512 \tabularnewline
40 & 253158 & 251510.356241818 & 1647.64375818230 \tabularnewline
41 & 243803 & 248553.547955925 & -4750.54795592546 \tabularnewline
42 & 250741 & 248533.223778547 & 2207.77622145310 \tabularnewline
43 & 280445 & 282461.982068065 & -2016.98206806486 \tabularnewline
44 & 285257 & 284087.228421378 & 1169.77157862228 \tabularnewline
45 & 270976 & 270103.206449268 & 872.793550731905 \tabularnewline
46 & 261076 & 259994.938177361 & 1081.06182263902 \tabularnewline
47 & 255603 & 251218.895783996 & 4384.10421600423 \tabularnewline
48 & 260376 & 255641.874847082 & 4734.12515291807 \tabularnewline
49 & 263903 & 261912.111314452 & 1990.88868554833 \tabularnewline
50 & 264291 & 260376.818950993 & 3914.18104900717 \tabularnewline
51 & 263276 & 259655.933100468 & 3620.06689953234 \tabularnewline
52 & 262572 & 263628.897450846 & -1056.89745084598 \tabularnewline
53 & 256167 & 260761.16209574 & -4594.16209574009 \tabularnewline
54 & 264221 & 268773.026160229 & -4552.02616022911 \tabularnewline
55 & 293860 & 299858.269135979 & -5998.26913597935 \tabularnewline
56 & 300713 & 302516.661566683 & -1803.66156668309 \tabularnewline
57 & 287224 & 287576.887044053 & -352.887044053408 \tabularnewline
58 & 275902 & 277317.637664595 & -1415.63766459492 \tabularnewline
59 & 271115 & 268509.2566162 & 2605.74338380009 \tabularnewline
60 & 277509 & 271353.111324632 & 6155.88867536822 \tabularnewline
61 & 279681 & 276625.483949213 & 3055.51605078712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115854&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]313218[/C][C]314937.831730769[/C][C]-1719.83173076925[/C][/ROW]
[ROW][C]14[/C][C]309664[/C][C]309777.65862079[/C][C]-113.658620789764[/C][/ROW]
[ROW][C]15[/C][C]302963[/C][C]302465.419674192[/C][C]497.580325807736[/C][/ROW]
[ROW][C]16[/C][C]298989[/C][C]298846.921807561[/C][C]142.078192438872[/C][/ROW]
[ROW][C]17[/C][C]298423[/C][C]298895.697481043[/C][C]-472.697481042531[/C][/ROW]
[ROW][C]18[/C][C]301631[/C][C]302609.303765351[/C][C]-978.303765351186[/C][/ROW]
[ROW][C]19[/C][C]329765[/C][C]326328.711583789[/C][C]3436.28841621149[/C][/ROW]
[ROW][C]20[/C][C]335083[/C][C]332202.633444242[/C][C]2880.36655575765[/C][/ROW]
[ROW][C]21[/C][C]327616[/C][C]332860.128156268[/C][C]-5244.1281562678[/C][/ROW]
[ROW][C]22[/C][C]309119[/C][C]317631.355296961[/C][C]-8512.35529696062[/C][/ROW]
[ROW][C]23[/C][C]295916[/C][C]300104.2582578[/C][C]-4188.25825779984[/C][/ROW]
[ROW][C]24[/C][C]291413[/C][C]294138.528195965[/C][C]-2725.52819596475[/C][/ROW]
[ROW][C]25[/C][C]291542[/C][C]285587.964350982[/C][C]5954.03564901819[/C][/ROW]
[ROW][C]26[/C][C]284678[/C][C]282552.53942915[/C][C]2125.46057084994[/C][/ROW]
[ROW][C]27[/C][C]276475[/C][C]274694.570990146[/C][C]1780.42900985375[/C][/ROW]
[ROW][C]28[/C][C]272566[/C][C]269931.779598843[/C][C]2634.22040115687[/C][/ROW]
[ROW][C]29[/C][C]264981[/C][C]270045.297708218[/C][C]-5064.29770821839[/C][/ROW]
[ROW][C]30[/C][C]263290[/C][C]268894.261140499[/C][C]-5604.2611404988[/C][/ROW]
[ROW][C]31[/C][C]296806[/C][C]288784.881974550[/C][C]8021.11802545033[/C][/ROW]
[ROW][C]32[/C][C]303598[/C][C]294530.047742695[/C][C]9067.95225730474[/C][/ROW]
[ROW][C]33[/C][C]286994[/C][C]294008.802320778[/C][C]-7014.8023207782[/C][/ROW]
[ROW][C]34[/C][C]276427[/C][C]275293.440690815[/C][C]1133.55930918502[/C][/ROW]
[ROW][C]35[/C][C]266424[/C][C]266588.099845105[/C][C]-164.099845105084[/C][/ROW]
[ROW][C]36[/C][C]267153[/C][C]266285.232056573[/C][C]867.767943427025[/C][/ROW]
[ROW][C]37[/C][C]268381[/C][C]267653.649470515[/C][C]727.350529485324[/C][/ROW]
[ROW][C]38[/C][C]262522[/C][C]262469.004799314[/C][C]52.9952006864478[/C][/ROW]
[ROW][C]39[/C][C]255542[/C][C]255188.113642516[/C][C]353.886357483512[/C][/ROW]
[ROW][C]40[/C][C]253158[/C][C]251510.356241818[/C][C]1647.64375818230[/C][/ROW]
[ROW][C]41[/C][C]243803[/C][C]248553.547955925[/C][C]-4750.54795592546[/C][/ROW]
[ROW][C]42[/C][C]250741[/C][C]248533.223778547[/C][C]2207.77622145310[/C][/ROW]
[ROW][C]43[/C][C]280445[/C][C]282461.982068065[/C][C]-2016.98206806486[/C][/ROW]
[ROW][C]44[/C][C]285257[/C][C]284087.228421378[/C][C]1169.77157862228[/C][/ROW]
[ROW][C]45[/C][C]270976[/C][C]270103.206449268[/C][C]872.793550731905[/C][/ROW]
[ROW][C]46[/C][C]261076[/C][C]259994.938177361[/C][C]1081.06182263902[/C][/ROW]
[ROW][C]47[/C][C]255603[/C][C]251218.895783996[/C][C]4384.10421600423[/C][/ROW]
[ROW][C]48[/C][C]260376[/C][C]255641.874847082[/C][C]4734.12515291807[/C][/ROW]
[ROW][C]49[/C][C]263903[/C][C]261912.111314452[/C][C]1990.88868554833[/C][/ROW]
[ROW][C]50[/C][C]264291[/C][C]260376.818950993[/C][C]3914.18104900717[/C][/ROW]
[ROW][C]51[/C][C]263276[/C][C]259655.933100468[/C][C]3620.06689953234[/C][/ROW]
[ROW][C]52[/C][C]262572[/C][C]263628.897450846[/C][C]-1056.89745084598[/C][/ROW]
[ROW][C]53[/C][C]256167[/C][C]260761.16209574[/C][C]-4594.16209574009[/C][/ROW]
[ROW][C]54[/C][C]264221[/C][C]268773.026160229[/C][C]-4552.02616022911[/C][/ROW]
[ROW][C]55[/C][C]293860[/C][C]299858.269135979[/C][C]-5998.26913597935[/C][/ROW]
[ROW][C]56[/C][C]300713[/C][C]302516.661566683[/C][C]-1803.66156668309[/C][/ROW]
[ROW][C]57[/C][C]287224[/C][C]287576.887044053[/C][C]-352.887044053408[/C][/ROW]
[ROW][C]58[/C][C]275902[/C][C]277317.637664595[/C][C]-1415.63766459492[/C][/ROW]
[ROW][C]59[/C][C]271115[/C][C]268509.2566162[/C][C]2605.74338380009[/C][/ROW]
[ROW][C]60[/C][C]277509[/C][C]271353.111324632[/C][C]6155.88867536822[/C][/ROW]
[ROW][C]61[/C][C]279681[/C][C]276625.483949213[/C][C]3055.51605078712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115854&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115854&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
13313218314937.831730769-1719.83173076925
14309664309777.65862079-113.658620789764
15302963302465.419674192497.580325807736
16298989298846.921807561142.078192438872
17298423298895.697481043-472.697481042531
18301631302609.303765351-978.303765351186
19329765326328.7115837893436.28841621149
20335083332202.6334442422880.36655575765
21327616332860.128156268-5244.1281562678
22309119317631.355296961-8512.35529696062
23295916300104.2582578-4188.25825779984
24291413294138.528195965-2725.52819596475
25291542285587.9643509825954.03564901819
26284678282552.539429152125.46057084994
27276475274694.5709901461780.42900985375
28272566269931.7795988432634.22040115687
29264981270045.297708218-5064.29770821839
30263290268894.261140499-5604.2611404988
31296806288784.8819745508021.11802545033
32303598294530.0477426959067.95225730474
33286994294008.802320778-7014.8023207782
34276427275293.4406908151133.55930918502
35266424266588.099845105-164.099845105084
36267153266285.232056573867.767943427025
37268381267653.649470515727.350529485324
38262522262469.00479931452.9952006864478
39255542255188.113642516353.886357483512
40253158251510.3562418181647.64375818230
41243803248553.547955925-4750.54795592546
42250741248533.2237785472207.77622145310
43280445282461.982068065-2016.98206806486
44285257284087.2284213781169.77157862228
45270976270103.206449268872.793550731905
46261076259994.9381773611081.06182263902
47255603251218.8957839964384.10421600423
48260376255641.8748470824734.12515291807
49263903261912.1113144521990.88868554833
50264291260376.8189509933914.18104900717
51263276259655.9331004683620.06689953234
52262572263628.897450846-1056.89745084598
53256167260761.16209574-4594.16209574009
54264221268773.026160229-4552.02616022911
55293860299858.269135979-5998.26913597935
56300713302516.661566683-1803.66156668309
57287224287576.887044053-352.887044053408
58275902277317.637664595-1415.63766459492
59271115268509.25661622605.74338380009
60277509271353.1113246326155.88867536822
61279681276625.4839492133055.51605078712







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
62276447.621430008268944.816224921283950.426635096
63272324.096759681262702.928599385281945.264919978
64269919.961349259257314.536413130282525.386285388
65263953.017846731247696.239408473280209.796284989
66273722.188303240253283.832817304294160.543789175
67307115.503299307282051.016405556332179.990193059
68317237.700184815287157.966041817347317.434327813
69306773.501405897271327.581194132342219.421617662
70299128.704904528257993.583171717340263.826637338
71296328.102702328249202.244374373343453.961030284
72302125.666158217248724.736528957355526.595787477
73303572.786806536243626.663475406363518.910137667

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 276447.621430008 & 268944.816224921 & 283950.426635096 \tabularnewline
63 & 272324.096759681 & 262702.928599385 & 281945.264919978 \tabularnewline
64 & 269919.961349259 & 257314.536413130 & 282525.386285388 \tabularnewline
65 & 263953.017846731 & 247696.239408473 & 280209.796284989 \tabularnewline
66 & 273722.188303240 & 253283.832817304 & 294160.543789175 \tabularnewline
67 & 307115.503299307 & 282051.016405556 & 332179.990193059 \tabularnewline
68 & 317237.700184815 & 287157.966041817 & 347317.434327813 \tabularnewline
69 & 306773.501405897 & 271327.581194132 & 342219.421617662 \tabularnewline
70 & 299128.704904528 & 257993.583171717 & 340263.826637338 \tabularnewline
71 & 296328.102702328 & 249202.244374373 & 343453.961030284 \tabularnewline
72 & 302125.666158217 & 248724.736528957 & 355526.595787477 \tabularnewline
73 & 303572.786806536 & 243626.663475406 & 363518.910137667 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115854&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]62[/C][C]276447.621430008[/C][C]268944.816224921[/C][C]283950.426635096[/C][/ROW]
[ROW][C]63[/C][C]272324.096759681[/C][C]262702.928599385[/C][C]281945.264919978[/C][/ROW]
[ROW][C]64[/C][C]269919.961349259[/C][C]257314.536413130[/C][C]282525.386285388[/C][/ROW]
[ROW][C]65[/C][C]263953.017846731[/C][C]247696.239408473[/C][C]280209.796284989[/C][/ROW]
[ROW][C]66[/C][C]273722.188303240[/C][C]253283.832817304[/C][C]294160.543789175[/C][/ROW]
[ROW][C]67[/C][C]307115.503299307[/C][C]282051.016405556[/C][C]332179.990193059[/C][/ROW]
[ROW][C]68[/C][C]317237.700184815[/C][C]287157.966041817[/C][C]347317.434327813[/C][/ROW]
[ROW][C]69[/C][C]306773.501405897[/C][C]271327.581194132[/C][C]342219.421617662[/C][/ROW]
[ROW][C]70[/C][C]299128.704904528[/C][C]257993.583171717[/C][C]340263.826637338[/C][/ROW]
[ROW][C]71[/C][C]296328.102702328[/C][C]249202.244374373[/C][C]343453.961030284[/C][/ROW]
[ROW][C]72[/C][C]302125.666158217[/C][C]248724.736528957[/C][C]355526.595787477[/C][/ROW]
[ROW][C]73[/C][C]303572.786806536[/C][C]243626.663475406[/C][C]363518.910137667[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115854&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115854&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
62276447.621430008268944.816224921283950.426635096
63272324.096759681262702.928599385281945.264919978
64269919.961349259257314.536413130282525.386285388
65263953.017846731247696.239408473280209.796284989
66273722.188303240253283.832817304294160.543789175
67307115.503299307282051.016405556332179.990193059
68317237.700184815287157.966041817347317.434327813
69306773.501405897271327.581194132342219.421617662
70299128.704904528257993.583171717340263.826637338
71296328.102702328249202.244374373343453.961030284
72302125.666158217248724.736528957355526.595787477
73303572.786806536243626.663475406363518.910137667



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')