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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 computationFri, 04 Dec 2009 08:23:15 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259940228ndkpmvxj4j61x7d.htm/, Retrieved Sun, 28 Apr 2024 13:29:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63749, Retrieved Sun, 28 Apr 2024 13:29:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [] [2009-12-04 15:23:15] [54e293c1fb7c46e2abc5c1dda68d8adb] [Current]
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Dataseries X:
274412
272433
268361
268586
264768
269974
304744
309365
308347
298427
289231
291975
294912
293488
290555
284736
281818
287854
316263
325412
326011
328282
317480
317539
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63749&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63749&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63749&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.897909443669848
beta0.121731637445269
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.897909443669848 \tabularnewline
beta & 0.121731637445269 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63749&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]0.897909443669848[/C][/ROW]
[ROW][C]beta[/C][C]0.121731637445269[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63749&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63749&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
alpha0.897909443669848
beta0.121731637445269
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13294912285544.4313199819367.56868001918
14293488293971.846090189-483.846090189123
15290555291712.505658404-1157.50565840380
16284736285260.591331686-524.591331686475
17281818281804.89867216613.1013278336031
18287854287956.630200848-102.630200848449
19316263326853.300613778-10590.3006137776
20325412321566.0002735803845.99972641963
21326011323685.5404238182325.45957618172
22328282315493.68583310512788.3141668948
23317480318613.054615749-1133.05461574852
24317539322122.483657163-4583.48365716252
25313737323537.415756767-9800.41575676686
26312276312473.656537743-197.656537743344
27309391309133.074789482257.925210517715
28302950302709.928061431240.071938568552
29300316298952.9647144961363.03528550430
30304035305983.45226617-1948.45226616971
31333476343260.82938262-9784.82938262017
32337698339616.444050717-1918.44405071699
33335932334862.5830223631069.41697763669
34323931324727.874595050-796.874595049536
35313927311523.9165590792403.08344092086
36314485315342.959249098-857.959249098029
37313218317417.124090838-4199.12409083801
38309664310882.84271168-1218.84271168016
39302963305139.268241003-2176.26824100252
40298989294904.711892834084.28810717002
41298423293447.9094179534975.09058204654
42301631302391.836013607-760.836013607448
43329765338698.948976348-8933.94897634757
44335083335721.225426708-638.22542670765
45327616331736.865112247-4120.86511224665
46309119315795.872347194-6676.87234719389
47295916296381.391523783-465.391523782630
48291413295130.355029477-3717.35502947686
49291542291699.734879385-157.734879384516
50284678287281.358562566-2603.35856256558
51276475278458.604235113-1983.6042351129
52272566267629.55750634936.44249369996
53264981265575.522763335-594.522763334506
54263290266025.682297671-2735.68229767052
55296806292139.1599906314666.84000936855
56303598299956.6357847073641.36421529332
57286994298621.921577478-11627.9215774777
58276427275170.9024208061256.09757919359
59266424263712.8100929282711.18990707211
60267153264286.4537353832866.54626461701
61268381267008.2062531531372.79374684725
62262522264147.859129584-1625.85912958387
63255542256921.976843391-1379.97684339058
64253158248171.4876651434986.51233485743
65243803246367.213856235-2564.21385623497
66250741244791.0759285565949.92407144394
67280445279121.0208304411323.97916955902
68285257284429.313356364827.686643635912
69270976279838.082179015-8862.08217901486
70261076261515.848421809-439.848421808711
71255603249880.1524773155722.84752268463
72260376254134.1638545086241.83614549204
73263903261036.7409578242866.25904217645
74264291260761.2553804063529.74461959425
75263276260204.0737125583071.92628744247
76262572258423.5784843204148.4215156796
77256167257220.283077732-1053.28307773196
78264221260550.9513103243670.04868967616
79293860296457.037692250-2597.03769225033

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 294912 & 285544.431319981 & 9367.56868001918 \tabularnewline
14 & 293488 & 293971.846090189 & -483.846090189123 \tabularnewline
15 & 290555 & 291712.505658404 & -1157.50565840380 \tabularnewline
16 & 284736 & 285260.591331686 & -524.591331686475 \tabularnewline
17 & 281818 & 281804.898672166 & 13.1013278336031 \tabularnewline
18 & 287854 & 287956.630200848 & -102.630200848449 \tabularnewline
19 & 316263 & 326853.300613778 & -10590.3006137776 \tabularnewline
20 & 325412 & 321566.000273580 & 3845.99972641963 \tabularnewline
21 & 326011 & 323685.540423818 & 2325.45957618172 \tabularnewline
22 & 328282 & 315493.685833105 & 12788.3141668948 \tabularnewline
23 & 317480 & 318613.054615749 & -1133.05461574852 \tabularnewline
24 & 317539 & 322122.483657163 & -4583.48365716252 \tabularnewline
25 & 313737 & 323537.415756767 & -9800.41575676686 \tabularnewline
26 & 312276 & 312473.656537743 & -197.656537743344 \tabularnewline
27 & 309391 & 309133.074789482 & 257.925210517715 \tabularnewline
28 & 302950 & 302709.928061431 & 240.071938568552 \tabularnewline
29 & 300316 & 298952.964714496 & 1363.03528550430 \tabularnewline
30 & 304035 & 305983.45226617 & -1948.45226616971 \tabularnewline
31 & 333476 & 343260.82938262 & -9784.82938262017 \tabularnewline
32 & 337698 & 339616.444050717 & -1918.44405071699 \tabularnewline
33 & 335932 & 334862.583022363 & 1069.41697763669 \tabularnewline
34 & 323931 & 324727.874595050 & -796.874595049536 \tabularnewline
35 & 313927 & 311523.916559079 & 2403.08344092086 \tabularnewline
36 & 314485 & 315342.959249098 & -857.959249098029 \tabularnewline
37 & 313218 & 317417.124090838 & -4199.12409083801 \tabularnewline
38 & 309664 & 310882.84271168 & -1218.84271168016 \tabularnewline
39 & 302963 & 305139.268241003 & -2176.26824100252 \tabularnewline
40 & 298989 & 294904.71189283 & 4084.28810717002 \tabularnewline
41 & 298423 & 293447.909417953 & 4975.09058204654 \tabularnewline
42 & 301631 & 302391.836013607 & -760.836013607448 \tabularnewline
43 & 329765 & 338698.948976348 & -8933.94897634757 \tabularnewline
44 & 335083 & 335721.225426708 & -638.22542670765 \tabularnewline
45 & 327616 & 331736.865112247 & -4120.86511224665 \tabularnewline
46 & 309119 & 315795.872347194 & -6676.87234719389 \tabularnewline
47 & 295916 & 296381.391523783 & -465.391523782630 \tabularnewline
48 & 291413 & 295130.355029477 & -3717.35502947686 \tabularnewline
49 & 291542 & 291699.734879385 & -157.734879384516 \tabularnewline
50 & 284678 & 287281.358562566 & -2603.35856256558 \tabularnewline
51 & 276475 & 278458.604235113 & -1983.6042351129 \tabularnewline
52 & 272566 & 267629.5575063 & 4936.44249369996 \tabularnewline
53 & 264981 & 265575.522763335 & -594.522763334506 \tabularnewline
54 & 263290 & 266025.682297671 & -2735.68229767052 \tabularnewline
55 & 296806 & 292139.159990631 & 4666.84000936855 \tabularnewline
56 & 303598 & 299956.635784707 & 3641.36421529332 \tabularnewline
57 & 286994 & 298621.921577478 & -11627.9215774777 \tabularnewline
58 & 276427 & 275170.902420806 & 1256.09757919359 \tabularnewline
59 & 266424 & 263712.810092928 & 2711.18990707211 \tabularnewline
60 & 267153 & 264286.453735383 & 2866.54626461701 \tabularnewline
61 & 268381 & 267008.206253153 & 1372.79374684725 \tabularnewline
62 & 262522 & 264147.859129584 & -1625.85912958387 \tabularnewline
63 & 255542 & 256921.976843391 & -1379.97684339058 \tabularnewline
64 & 253158 & 248171.487665143 & 4986.51233485743 \tabularnewline
65 & 243803 & 246367.213856235 & -2564.21385623497 \tabularnewline
66 & 250741 & 244791.075928556 & 5949.92407144394 \tabularnewline
67 & 280445 & 279121.020830441 & 1323.97916955902 \tabularnewline
68 & 285257 & 284429.313356364 & 827.686643635912 \tabularnewline
69 & 270976 & 279838.082179015 & -8862.08217901486 \tabularnewline
70 & 261076 & 261515.848421809 & -439.848421808711 \tabularnewline
71 & 255603 & 249880.152477315 & 5722.84752268463 \tabularnewline
72 & 260376 & 254134.163854508 & 6241.83614549204 \tabularnewline
73 & 263903 & 261036.740957824 & 2866.25904217645 \tabularnewline
74 & 264291 & 260761.255380406 & 3529.74461959425 \tabularnewline
75 & 263276 & 260204.073712558 & 3071.92628744247 \tabularnewline
76 & 262572 & 258423.578484320 & 4148.4215156796 \tabularnewline
77 & 256167 & 257220.283077732 & -1053.28307773196 \tabularnewline
78 & 264221 & 260550.951310324 & 3670.04868967616 \tabularnewline
79 & 293860 & 296457.037692250 & -2597.03769225033 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63749&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]294912[/C][C]285544.431319981[/C][C]9367.56868001918[/C][/ROW]
[ROW][C]14[/C][C]293488[/C][C]293971.846090189[/C][C]-483.846090189123[/C][/ROW]
[ROW][C]15[/C][C]290555[/C][C]291712.505658404[/C][C]-1157.50565840380[/C][/ROW]
[ROW][C]16[/C][C]284736[/C][C]285260.591331686[/C][C]-524.591331686475[/C][/ROW]
[ROW][C]17[/C][C]281818[/C][C]281804.898672166[/C][C]13.1013278336031[/C][/ROW]
[ROW][C]18[/C][C]287854[/C][C]287956.630200848[/C][C]-102.630200848449[/C][/ROW]
[ROW][C]19[/C][C]316263[/C][C]326853.300613778[/C][C]-10590.3006137776[/C][/ROW]
[ROW][C]20[/C][C]325412[/C][C]321566.000273580[/C][C]3845.99972641963[/C][/ROW]
[ROW][C]21[/C][C]326011[/C][C]323685.540423818[/C][C]2325.45957618172[/C][/ROW]
[ROW][C]22[/C][C]328282[/C][C]315493.685833105[/C][C]12788.3141668948[/C][/ROW]
[ROW][C]23[/C][C]317480[/C][C]318613.054615749[/C][C]-1133.05461574852[/C][/ROW]
[ROW][C]24[/C][C]317539[/C][C]322122.483657163[/C][C]-4583.48365716252[/C][/ROW]
[ROW][C]25[/C][C]313737[/C][C]323537.415756767[/C][C]-9800.41575676686[/C][/ROW]
[ROW][C]26[/C][C]312276[/C][C]312473.656537743[/C][C]-197.656537743344[/C][/ROW]
[ROW][C]27[/C][C]309391[/C][C]309133.074789482[/C][C]257.925210517715[/C][/ROW]
[ROW][C]28[/C][C]302950[/C][C]302709.928061431[/C][C]240.071938568552[/C][/ROW]
[ROW][C]29[/C][C]300316[/C][C]298952.964714496[/C][C]1363.03528550430[/C][/ROW]
[ROW][C]30[/C][C]304035[/C][C]305983.45226617[/C][C]-1948.45226616971[/C][/ROW]
[ROW][C]31[/C][C]333476[/C][C]343260.82938262[/C][C]-9784.82938262017[/C][/ROW]
[ROW][C]32[/C][C]337698[/C][C]339616.444050717[/C][C]-1918.44405071699[/C][/ROW]
[ROW][C]33[/C][C]335932[/C][C]334862.583022363[/C][C]1069.41697763669[/C][/ROW]
[ROW][C]34[/C][C]323931[/C][C]324727.874595050[/C][C]-796.874595049536[/C][/ROW]
[ROW][C]35[/C][C]313927[/C][C]311523.916559079[/C][C]2403.08344092086[/C][/ROW]
[ROW][C]36[/C][C]314485[/C][C]315342.959249098[/C][C]-857.959249098029[/C][/ROW]
[ROW][C]37[/C][C]313218[/C][C]317417.124090838[/C][C]-4199.12409083801[/C][/ROW]
[ROW][C]38[/C][C]309664[/C][C]310882.84271168[/C][C]-1218.84271168016[/C][/ROW]
[ROW][C]39[/C][C]302963[/C][C]305139.268241003[/C][C]-2176.26824100252[/C][/ROW]
[ROW][C]40[/C][C]298989[/C][C]294904.71189283[/C][C]4084.28810717002[/C][/ROW]
[ROW][C]41[/C][C]298423[/C][C]293447.909417953[/C][C]4975.09058204654[/C][/ROW]
[ROW][C]42[/C][C]301631[/C][C]302391.836013607[/C][C]-760.836013607448[/C][/ROW]
[ROW][C]43[/C][C]329765[/C][C]338698.948976348[/C][C]-8933.94897634757[/C][/ROW]
[ROW][C]44[/C][C]335083[/C][C]335721.225426708[/C][C]-638.22542670765[/C][/ROW]
[ROW][C]45[/C][C]327616[/C][C]331736.865112247[/C][C]-4120.86511224665[/C][/ROW]
[ROW][C]46[/C][C]309119[/C][C]315795.872347194[/C][C]-6676.87234719389[/C][/ROW]
[ROW][C]47[/C][C]295916[/C][C]296381.391523783[/C][C]-465.391523782630[/C][/ROW]
[ROW][C]48[/C][C]291413[/C][C]295130.355029477[/C][C]-3717.35502947686[/C][/ROW]
[ROW][C]49[/C][C]291542[/C][C]291699.734879385[/C][C]-157.734879384516[/C][/ROW]
[ROW][C]50[/C][C]284678[/C][C]287281.358562566[/C][C]-2603.35856256558[/C][/ROW]
[ROW][C]51[/C][C]276475[/C][C]278458.604235113[/C][C]-1983.6042351129[/C][/ROW]
[ROW][C]52[/C][C]272566[/C][C]267629.5575063[/C][C]4936.44249369996[/C][/ROW]
[ROW][C]53[/C][C]264981[/C][C]265575.522763335[/C][C]-594.522763334506[/C][/ROW]
[ROW][C]54[/C][C]263290[/C][C]266025.682297671[/C][C]-2735.68229767052[/C][/ROW]
[ROW][C]55[/C][C]296806[/C][C]292139.159990631[/C][C]4666.84000936855[/C][/ROW]
[ROW][C]56[/C][C]303598[/C][C]299956.635784707[/C][C]3641.36421529332[/C][/ROW]
[ROW][C]57[/C][C]286994[/C][C]298621.921577478[/C][C]-11627.9215774777[/C][/ROW]
[ROW][C]58[/C][C]276427[/C][C]275170.902420806[/C][C]1256.09757919359[/C][/ROW]
[ROW][C]59[/C][C]266424[/C][C]263712.810092928[/C][C]2711.18990707211[/C][/ROW]
[ROW][C]60[/C][C]267153[/C][C]264286.453735383[/C][C]2866.54626461701[/C][/ROW]
[ROW][C]61[/C][C]268381[/C][C]267008.206253153[/C][C]1372.79374684725[/C][/ROW]
[ROW][C]62[/C][C]262522[/C][C]264147.859129584[/C][C]-1625.85912958387[/C][/ROW]
[ROW][C]63[/C][C]255542[/C][C]256921.976843391[/C][C]-1379.97684339058[/C][/ROW]
[ROW][C]64[/C][C]253158[/C][C]248171.487665143[/C][C]4986.51233485743[/C][/ROW]
[ROW][C]65[/C][C]243803[/C][C]246367.213856235[/C][C]-2564.21385623497[/C][/ROW]
[ROW][C]66[/C][C]250741[/C][C]244791.075928556[/C][C]5949.92407144394[/C][/ROW]
[ROW][C]67[/C][C]280445[/C][C]279121.020830441[/C][C]1323.97916955902[/C][/ROW]
[ROW][C]68[/C][C]285257[/C][C]284429.313356364[/C][C]827.686643635912[/C][/ROW]
[ROW][C]69[/C][C]270976[/C][C]279838.082179015[/C][C]-8862.08217901486[/C][/ROW]
[ROW][C]70[/C][C]261076[/C][C]261515.848421809[/C][C]-439.848421808711[/C][/ROW]
[ROW][C]71[/C][C]255603[/C][C]249880.152477315[/C][C]5722.84752268463[/C][/ROW]
[ROW][C]72[/C][C]260376[/C][C]254134.163854508[/C][C]6241.83614549204[/C][/ROW]
[ROW][C]73[/C][C]263903[/C][C]261036.740957824[/C][C]2866.25904217645[/C][/ROW]
[ROW][C]74[/C][C]264291[/C][C]260761.255380406[/C][C]3529.74461959425[/C][/ROW]
[ROW][C]75[/C][C]263276[/C][C]260204.073712558[/C][C]3071.92628744247[/C][/ROW]
[ROW][C]76[/C][C]262572[/C][C]258423.578484320[/C][C]4148.4215156796[/C][/ROW]
[ROW][C]77[/C][C]256167[/C][C]257220.283077732[/C][C]-1053.28307773196[/C][/ROW]
[ROW][C]78[/C][C]264221[/C][C]260550.951310324[/C][C]3670.04868967616[/C][/ROW]
[ROW][C]79[/C][C]293860[/C][C]296457.037692250[/C][C]-2597.03769225033[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63749&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63749&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
13294912285544.4313199819367.56868001918
14293488293971.846090189-483.846090189123
15290555291712.505658404-1157.50565840380
16284736285260.591331686-524.591331686475
17281818281804.89867216613.1013278336031
18287854287956.630200848-102.630200848449
19316263326853.300613778-10590.3006137776
20325412321566.0002735803845.99972641963
21326011323685.5404238182325.45957618172
22328282315493.68583310512788.3141668948
23317480318613.054615749-1133.05461574852
24317539322122.483657163-4583.48365716252
25313737323537.415756767-9800.41575676686
26312276312473.656537743-197.656537743344
27309391309133.074789482257.925210517715
28302950302709.928061431240.071938568552
29300316298952.9647144961363.03528550430
30304035305983.45226617-1948.45226616971
31333476343260.82938262-9784.82938262017
32337698339616.444050717-1918.44405071699
33335932334862.5830223631069.41697763669
34323931324727.874595050-796.874595049536
35313927311523.9165590792403.08344092086
36314485315342.959249098-857.959249098029
37313218317417.124090838-4199.12409083801
38309664310882.84271168-1218.84271168016
39302963305139.268241003-2176.26824100252
40298989294904.711892834084.28810717002
41298423293447.9094179534975.09058204654
42301631302391.836013607-760.836013607448
43329765338698.948976348-8933.94897634757
44335083335721.225426708-638.22542670765
45327616331736.865112247-4120.86511224665
46309119315795.872347194-6676.87234719389
47295916296381.391523783-465.391523782630
48291413295130.355029477-3717.35502947686
49291542291699.734879385-157.734879384516
50284678287281.358562566-2603.35856256558
51276475278458.604235113-1983.6042351129
52272566267629.55750634936.44249369996
53264981265575.522763335-594.522763334506
54263290266025.682297671-2735.68229767052
55296806292139.1599906314666.84000936855
56303598299956.6357847073641.36421529332
57286994298621.921577478-11627.9215774777
58276427275170.9024208061256.09757919359
59266424263712.8100929282711.18990707211
60267153264286.4537353832866.54626461701
61268381267008.2062531531372.79374684725
62262522264147.859129584-1625.85912958387
63255542256921.976843391-1379.97684339058
64253158248171.4876651434986.51233485743
65243803246367.213856235-2564.21385623497
66250741244791.0759285565949.92407144394
67280445279121.0208304411323.97916955902
68285257284429.313356364827.686643635912
69270976279838.082179015-8862.08217901486
70261076261515.848421809-439.848421808711
71255603249880.1524773155722.84752268463
72260376254134.1638545086241.83614549204
73263903261036.7409578242866.25904217645
74264291260761.2553804063529.74461959425
75263276260204.0737125583071.92628744247
76262572258423.5784843204148.4215156796
77256167257220.283077732-1053.28307773196
78264221260550.9513103243670.04868967616
79293860296457.037692250-2597.03769225033







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
80300597.60195908291690.357497741309504.846420420
81295981.006901015283459.160170707308502.853631322
82288674.578714217273015.343944749304333.813483685
83279975.611404529261459.463553877298491.75925518
84281394.657842215259522.52264454303266.793039889
85284019.163037638258665.327653885309372.998421391
86282266.188694958253754.518724470310777.858665446
87279051.090073625247517.40376877310584.776378479
88274805.233219444240374.146123622309236.320315265
89269077.783282806231963.718660532306191.847905080
90274176.786930806232878.063182934315475.510678677
91307014.564577500257793.98058216356235.148572839

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
80 & 300597.60195908 & 291690.357497741 & 309504.846420420 \tabularnewline
81 & 295981.006901015 & 283459.160170707 & 308502.853631322 \tabularnewline
82 & 288674.578714217 & 273015.343944749 & 304333.813483685 \tabularnewline
83 & 279975.611404529 & 261459.463553877 & 298491.75925518 \tabularnewline
84 & 281394.657842215 & 259522.52264454 & 303266.793039889 \tabularnewline
85 & 284019.163037638 & 258665.327653885 & 309372.998421391 \tabularnewline
86 & 282266.188694958 & 253754.518724470 & 310777.858665446 \tabularnewline
87 & 279051.090073625 & 247517.40376877 & 310584.776378479 \tabularnewline
88 & 274805.233219444 & 240374.146123622 & 309236.320315265 \tabularnewline
89 & 269077.783282806 & 231963.718660532 & 306191.847905080 \tabularnewline
90 & 274176.786930806 & 232878.063182934 & 315475.510678677 \tabularnewline
91 & 307014.564577500 & 257793.98058216 & 356235.148572839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63749&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]80[/C][C]300597.60195908[/C][C]291690.357497741[/C][C]309504.846420420[/C][/ROW]
[ROW][C]81[/C][C]295981.006901015[/C][C]283459.160170707[/C][C]308502.853631322[/C][/ROW]
[ROW][C]82[/C][C]288674.578714217[/C][C]273015.343944749[/C][C]304333.813483685[/C][/ROW]
[ROW][C]83[/C][C]279975.611404529[/C][C]261459.463553877[/C][C]298491.75925518[/C][/ROW]
[ROW][C]84[/C][C]281394.657842215[/C][C]259522.52264454[/C][C]303266.793039889[/C][/ROW]
[ROW][C]85[/C][C]284019.163037638[/C][C]258665.327653885[/C][C]309372.998421391[/C][/ROW]
[ROW][C]86[/C][C]282266.188694958[/C][C]253754.518724470[/C][C]310777.858665446[/C][/ROW]
[ROW][C]87[/C][C]279051.090073625[/C][C]247517.40376877[/C][C]310584.776378479[/C][/ROW]
[ROW][C]88[/C][C]274805.233219444[/C][C]240374.146123622[/C][C]309236.320315265[/C][/ROW]
[ROW][C]89[/C][C]269077.783282806[/C][C]231963.718660532[/C][C]306191.847905080[/C][/ROW]
[ROW][C]90[/C][C]274176.786930806[/C][C]232878.063182934[/C][C]315475.510678677[/C][/ROW]
[ROW][C]91[/C][C]307014.564577500[/C][C]257793.98058216[/C][C]356235.148572839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63749&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63749&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
80300597.60195908291690.357497741309504.846420420
81295981.006901015283459.160170707308502.853631322
82288674.578714217273015.343944749304333.813483685
83279975.611404529261459.463553877298491.75925518
84281394.657842215259522.52264454303266.793039889
85284019.163037638258665.327653885309372.998421391
86282266.188694958253754.518724470310777.858665446
87279051.090073625247517.40376877310584.776378479
88274805.233219444240374.146123622309236.320315265
89269077.783282806231963.718660532306191.847905080
90274176.786930806232878.063182934315475.510678677
91307014.564577500257793.98058216356235.148572839



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=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')