Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 17 Aug 2014 20:39:55 +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/2014/Aug/17/t1408304611ht00nn1jybiuqap.htm/, Retrieved Thu, 31 Oct 2024 23:25:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235634, Retrieved Thu, 31 Oct 2024 23:25:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsStefaan Segers
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Tijdreeks A - Sta...] [2014-08-17 17:13:10] [40556739fb744d7815ea48083fb3e63a]
- R P   [(Partial) Autocorrelation Function] [Tijdreeks A - Sta...] [2014-08-17 17:15:53] [40556739fb744d7815ea48083fb3e63a]
- R P     [(Partial) Autocorrelation Function] [Tijdreeks A - Sta...] [2014-08-17 17:34:53] [40556739fb744d7815ea48083fb3e63a]
- RMP         [Exponential Smoothing] [Tijdreeks A - Sta...] [2014-08-17 19:39:55] [92f35a2db74bf110e350beffc19b3da6] [Current]
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Dataseries X:
24514
24442
24364
24222
25689
25618
24514
23780
23851
23851
23922
24072
24514
24735
25105
25397
26722
26573
25468
23851
24143
24442
24364
24735
24442
24955
25176
25247
26872
26573
25468
23851
24143
23922
24293
25105
25027
24884
25247
25468
26722
26793
25468
23559
23409
23851
23481
24663
24663
24222
24806
25176
26430
26793
25247
23409
23409
22818
22376
23338
22968
22084
22676
23189
24735
25326
23702
22526
22526
22084
21792
22376
21643
21493
21864
22376
23922
24222
22305
20909
20246
19584
19213
19947
19506
19584
19947
20246
21714
21935
19584
18480
17375
16635
16122
16855
16492
17076
17297
17518
18480
19064
16122
15388
13543
12367
11997
13030
12439
13179
13179
13251
14134
14725
11854
10821
9126
8022
7437
8905




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235634&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235634&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235634&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.492837057577933
beta0.0918739086539649
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.492837057577933 \tabularnewline
beta & 0.0918739086539649 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235634&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]0.492837057577933[/C][/ROW]
[ROW][C]beta[/C][C]0.0918739086539649[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235634&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235634&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
alpha0.492837057577933
beta0.0918739086539649
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132451424062.1330128205451.866987179477
142473524540.2164077532194.783592246786
152510525077.002492438427.9975075615803
162539725433.1912426516-36.1912426516283
172672226782.8566996245-60.8566996244772
182657326640.6105829623-67.6105829622611
192546825201.2245717278266.775428272205
202385124678.2990007834-827.299000783372
212414324352.8388461841-209.838846184088
222444224214.4346721814227.565327818633
232436424360.73671776853.26328223152086
242473524484.8088275879250.191172412084
252444225266.3663824784-824.366382478351
262495524937.295749694317.7042503056873
272517625246.4091411271-70.4091411271329
282524725461.2758412386-214.275841238559
292687226642.3322826018229.66771739825
302657326584.6637415088-11.6637415087898
312546825289.7935060176178.20649398235
322385124111.6884801155-260.688480115456
332414324347.6279831268-204.627983126844
342392224402.863132407-480.863132406979
352429324023.4268857777269.57311422225
362510524353.1964234193751.803576580722
372502724808.9212279925218.078772007462
382488425439.8037926953-555.803792695344
392524725414.7461015731-167.746101573062
402546825497.4331550127-29.4331550126881
412672226991.8635842611-269.8635842611
422679326540.1198630404252.8801369596
432546825458.40677811079.59322188927399
442355923953.4619755413-394.461975541319
452340924124.6979957069-715.697995706942
462385123737.6152480471113.384751952883
472348124008.1992813516-527.19928135159
482466324130.3417712312532.658228768752
492466324137.9380270773525.061972922704
502422224472.0884241095-250.088424109472
512480624752.809215080553.1907849195231
522517624982.8352653029193.164734697111
532643026443.4176705744-13.4176705744103
542679326373.1727140204419.82728597962
552524725247.90691216-0.906912160047796
562340923529.9456464958-120.945646495809
572340923682.5263686056-273.526368605621
582281823963.3279849528-1145.32798495275
592237623261.1839216475-885.183921647462
602333823700.7022974606-362.702297460633
612296823178.921785943-210.921785943003
622208422639.6426653817-555.642665381678
632267622792.1699381162-116.169938116152
642318922870.6328454749318.367154525073
652473524154.7322234324580.267776567554
662532624490.2681680243835.731831975656
672370223268.8913567776433.10864322244
682252621635.8981870237890.101812976303
692252622187.1047037675338.895296232517
702208422333.042125067-249.042125066961
712179222250.5963709802-458.596370980238
722237623230.691613521-854.691613521005
732164322586.4966627999-943.496662799891
742149321521.2563565254-28.2563565253695
752186422190.3713984163-326.371398416326
762237622409.8906341722-33.8906341722104
772392223661.5310637341260.468936265865
782422223962.8605153807259.139484619343
792230522220.854943548184.14505645186
802090920599.5817877637309.418212236324
812024620510.6938936409-264.693893640913
821958419959.2897927552-375.289792755186
831921319600.9396809984-387.939680998428
841994720310.7649042504-363.764904250449
851950619781.4993776094-275.499377609365
861958419457.9161939876126.083806012375
871994720007.1585726829-60.1585726829253
882024620473.5222612968-227.522261296785
892171421737.5641968496-23.5641968495693
902193521843.918729387791.0812706122597
911958419868.4090503568-284.409050356819
921848018101.1331548282378.866845171782
931737517679.8324763955-304.832476395477
941663516975.2677640107-340.267764010703
951612216552.0593202186-430.059320218625
961685517175.7769146953-320.776914695307
971649216636.7988533732-144.798853373242
981707616511.5521990313564.447800968723
991729717132.4843497663164.515650233716
1001751817584.971138159-66.9711381589877
1011848018999.1241394612-519.124139461233
1021906418864.4994585406199.500541459376
1031612216702.0042975274-580.004297527441
1041538815062.0691067595325.930893240526
1051354314202.1678317582-659.167831758226
1061236713223.1933192263-856.193319226268
1071199712395.0094270415-398.009427041487
1081303012986.228299771943.7717002280733
1091243912628.9511215997-189.951121599717
1101317912751.899197867427.100802132958
1111317913006.8357965317172.164203468292
1121325113250.56177752440.438222475630027
1131413414376.5448055336-242.544805533624
1141472514663.135118552761.8648814472836
1151185411951.6866904978-97.686690497836
1161082110944.9656961076-123.965696107627
11791269279.41578322176-153.415783221764
11880228388.35311721293-366.35311721293
11974377994.7164500822-557.716450082198
12089058684.81137717013220.188622829874

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 24514 & 24062.1330128205 & 451.866987179477 \tabularnewline
14 & 24735 & 24540.2164077532 & 194.783592246786 \tabularnewline
15 & 25105 & 25077.0024924384 & 27.9975075615803 \tabularnewline
16 & 25397 & 25433.1912426516 & -36.1912426516283 \tabularnewline
17 & 26722 & 26782.8566996245 & -60.8566996244772 \tabularnewline
18 & 26573 & 26640.6105829623 & -67.6105829622611 \tabularnewline
19 & 25468 & 25201.2245717278 & 266.775428272205 \tabularnewline
20 & 23851 & 24678.2990007834 & -827.299000783372 \tabularnewline
21 & 24143 & 24352.8388461841 & -209.838846184088 \tabularnewline
22 & 24442 & 24214.4346721814 & 227.565327818633 \tabularnewline
23 & 24364 & 24360.7367177685 & 3.26328223152086 \tabularnewline
24 & 24735 & 24484.8088275879 & 250.191172412084 \tabularnewline
25 & 24442 & 25266.3663824784 & -824.366382478351 \tabularnewline
26 & 24955 & 24937.2957496943 & 17.7042503056873 \tabularnewline
27 & 25176 & 25246.4091411271 & -70.4091411271329 \tabularnewline
28 & 25247 & 25461.2758412386 & -214.275841238559 \tabularnewline
29 & 26872 & 26642.3322826018 & 229.66771739825 \tabularnewline
30 & 26573 & 26584.6637415088 & -11.6637415087898 \tabularnewline
31 & 25468 & 25289.7935060176 & 178.20649398235 \tabularnewline
32 & 23851 & 24111.6884801155 & -260.688480115456 \tabularnewline
33 & 24143 & 24347.6279831268 & -204.627983126844 \tabularnewline
34 & 23922 & 24402.863132407 & -480.863132406979 \tabularnewline
35 & 24293 & 24023.4268857777 & 269.57311422225 \tabularnewline
36 & 25105 & 24353.1964234193 & 751.803576580722 \tabularnewline
37 & 25027 & 24808.9212279925 & 218.078772007462 \tabularnewline
38 & 24884 & 25439.8037926953 & -555.803792695344 \tabularnewline
39 & 25247 & 25414.7461015731 & -167.746101573062 \tabularnewline
40 & 25468 & 25497.4331550127 & -29.4331550126881 \tabularnewline
41 & 26722 & 26991.8635842611 & -269.8635842611 \tabularnewline
42 & 26793 & 26540.1198630404 & 252.8801369596 \tabularnewline
43 & 25468 & 25458.4067781107 & 9.59322188927399 \tabularnewline
44 & 23559 & 23953.4619755413 & -394.461975541319 \tabularnewline
45 & 23409 & 24124.6979957069 & -715.697995706942 \tabularnewline
46 & 23851 & 23737.6152480471 & 113.384751952883 \tabularnewline
47 & 23481 & 24008.1992813516 & -527.19928135159 \tabularnewline
48 & 24663 & 24130.3417712312 & 532.658228768752 \tabularnewline
49 & 24663 & 24137.9380270773 & 525.061972922704 \tabularnewline
50 & 24222 & 24472.0884241095 & -250.088424109472 \tabularnewline
51 & 24806 & 24752.8092150805 & 53.1907849195231 \tabularnewline
52 & 25176 & 24982.8352653029 & 193.164734697111 \tabularnewline
53 & 26430 & 26443.4176705744 & -13.4176705744103 \tabularnewline
54 & 26793 & 26373.1727140204 & 419.82728597962 \tabularnewline
55 & 25247 & 25247.90691216 & -0.906912160047796 \tabularnewline
56 & 23409 & 23529.9456464958 & -120.945646495809 \tabularnewline
57 & 23409 & 23682.5263686056 & -273.526368605621 \tabularnewline
58 & 22818 & 23963.3279849528 & -1145.32798495275 \tabularnewline
59 & 22376 & 23261.1839216475 & -885.183921647462 \tabularnewline
60 & 23338 & 23700.7022974606 & -362.702297460633 \tabularnewline
61 & 22968 & 23178.921785943 & -210.921785943003 \tabularnewline
62 & 22084 & 22639.6426653817 & -555.642665381678 \tabularnewline
63 & 22676 & 22792.1699381162 & -116.169938116152 \tabularnewline
64 & 23189 & 22870.6328454749 & 318.367154525073 \tabularnewline
65 & 24735 & 24154.7322234324 & 580.267776567554 \tabularnewline
66 & 25326 & 24490.2681680243 & 835.731831975656 \tabularnewline
67 & 23702 & 23268.8913567776 & 433.10864322244 \tabularnewline
68 & 22526 & 21635.8981870237 & 890.101812976303 \tabularnewline
69 & 22526 & 22187.1047037675 & 338.895296232517 \tabularnewline
70 & 22084 & 22333.042125067 & -249.042125066961 \tabularnewline
71 & 21792 & 22250.5963709802 & -458.596370980238 \tabularnewline
72 & 22376 & 23230.691613521 & -854.691613521005 \tabularnewline
73 & 21643 & 22586.4966627999 & -943.496662799891 \tabularnewline
74 & 21493 & 21521.2563565254 & -28.2563565253695 \tabularnewline
75 & 21864 & 22190.3713984163 & -326.371398416326 \tabularnewline
76 & 22376 & 22409.8906341722 & -33.8906341722104 \tabularnewline
77 & 23922 & 23661.5310637341 & 260.468936265865 \tabularnewline
78 & 24222 & 23962.8605153807 & 259.139484619343 \tabularnewline
79 & 22305 & 22220.8549435481 & 84.14505645186 \tabularnewline
80 & 20909 & 20599.5817877637 & 309.418212236324 \tabularnewline
81 & 20246 & 20510.6938936409 & -264.693893640913 \tabularnewline
82 & 19584 & 19959.2897927552 & -375.289792755186 \tabularnewline
83 & 19213 & 19600.9396809984 & -387.939680998428 \tabularnewline
84 & 19947 & 20310.7649042504 & -363.764904250449 \tabularnewline
85 & 19506 & 19781.4993776094 & -275.499377609365 \tabularnewline
86 & 19584 & 19457.9161939876 & 126.083806012375 \tabularnewline
87 & 19947 & 20007.1585726829 & -60.1585726829253 \tabularnewline
88 & 20246 & 20473.5222612968 & -227.522261296785 \tabularnewline
89 & 21714 & 21737.5641968496 & -23.5641968495693 \tabularnewline
90 & 21935 & 21843.9187293877 & 91.0812706122597 \tabularnewline
91 & 19584 & 19868.4090503568 & -284.409050356819 \tabularnewline
92 & 18480 & 18101.1331548282 & 378.866845171782 \tabularnewline
93 & 17375 & 17679.8324763955 & -304.832476395477 \tabularnewline
94 & 16635 & 16975.2677640107 & -340.267764010703 \tabularnewline
95 & 16122 & 16552.0593202186 & -430.059320218625 \tabularnewline
96 & 16855 & 17175.7769146953 & -320.776914695307 \tabularnewline
97 & 16492 & 16636.7988533732 & -144.798853373242 \tabularnewline
98 & 17076 & 16511.5521990313 & 564.447800968723 \tabularnewline
99 & 17297 & 17132.4843497663 & 164.515650233716 \tabularnewline
100 & 17518 & 17584.971138159 & -66.9711381589877 \tabularnewline
101 & 18480 & 18999.1241394612 & -519.124139461233 \tabularnewline
102 & 19064 & 18864.4994585406 & 199.500541459376 \tabularnewline
103 & 16122 & 16702.0042975274 & -580.004297527441 \tabularnewline
104 & 15388 & 15062.0691067595 & 325.930893240526 \tabularnewline
105 & 13543 & 14202.1678317582 & -659.167831758226 \tabularnewline
106 & 12367 & 13223.1933192263 & -856.193319226268 \tabularnewline
107 & 11997 & 12395.0094270415 & -398.009427041487 \tabularnewline
108 & 13030 & 12986.2282997719 & 43.7717002280733 \tabularnewline
109 & 12439 & 12628.9511215997 & -189.951121599717 \tabularnewline
110 & 13179 & 12751.899197867 & 427.100802132958 \tabularnewline
111 & 13179 & 13006.8357965317 & 172.164203468292 \tabularnewline
112 & 13251 & 13250.5617775244 & 0.438222475630027 \tabularnewline
113 & 14134 & 14376.5448055336 & -242.544805533624 \tabularnewline
114 & 14725 & 14663.1351185527 & 61.8648814472836 \tabularnewline
115 & 11854 & 11951.6866904978 & -97.686690497836 \tabularnewline
116 & 10821 & 10944.9656961076 & -123.965696107627 \tabularnewline
117 & 9126 & 9279.41578322176 & -153.415783221764 \tabularnewline
118 & 8022 & 8388.35311721293 & -366.35311721293 \tabularnewline
119 & 7437 & 7994.7164500822 & -557.716450082198 \tabularnewline
120 & 8905 & 8684.81137717013 & 220.188622829874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235634&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]24514[/C][C]24062.1330128205[/C][C]451.866987179477[/C][/ROW]
[ROW][C]14[/C][C]24735[/C][C]24540.2164077532[/C][C]194.783592246786[/C][/ROW]
[ROW][C]15[/C][C]25105[/C][C]25077.0024924384[/C][C]27.9975075615803[/C][/ROW]
[ROW][C]16[/C][C]25397[/C][C]25433.1912426516[/C][C]-36.1912426516283[/C][/ROW]
[ROW][C]17[/C][C]26722[/C][C]26782.8566996245[/C][C]-60.8566996244772[/C][/ROW]
[ROW][C]18[/C][C]26573[/C][C]26640.6105829623[/C][C]-67.6105829622611[/C][/ROW]
[ROW][C]19[/C][C]25468[/C][C]25201.2245717278[/C][C]266.775428272205[/C][/ROW]
[ROW][C]20[/C][C]23851[/C][C]24678.2990007834[/C][C]-827.299000783372[/C][/ROW]
[ROW][C]21[/C][C]24143[/C][C]24352.8388461841[/C][C]-209.838846184088[/C][/ROW]
[ROW][C]22[/C][C]24442[/C][C]24214.4346721814[/C][C]227.565327818633[/C][/ROW]
[ROW][C]23[/C][C]24364[/C][C]24360.7367177685[/C][C]3.26328223152086[/C][/ROW]
[ROW][C]24[/C][C]24735[/C][C]24484.8088275879[/C][C]250.191172412084[/C][/ROW]
[ROW][C]25[/C][C]24442[/C][C]25266.3663824784[/C][C]-824.366382478351[/C][/ROW]
[ROW][C]26[/C][C]24955[/C][C]24937.2957496943[/C][C]17.7042503056873[/C][/ROW]
[ROW][C]27[/C][C]25176[/C][C]25246.4091411271[/C][C]-70.4091411271329[/C][/ROW]
[ROW][C]28[/C][C]25247[/C][C]25461.2758412386[/C][C]-214.275841238559[/C][/ROW]
[ROW][C]29[/C][C]26872[/C][C]26642.3322826018[/C][C]229.66771739825[/C][/ROW]
[ROW][C]30[/C][C]26573[/C][C]26584.6637415088[/C][C]-11.6637415087898[/C][/ROW]
[ROW][C]31[/C][C]25468[/C][C]25289.7935060176[/C][C]178.20649398235[/C][/ROW]
[ROW][C]32[/C][C]23851[/C][C]24111.6884801155[/C][C]-260.688480115456[/C][/ROW]
[ROW][C]33[/C][C]24143[/C][C]24347.6279831268[/C][C]-204.627983126844[/C][/ROW]
[ROW][C]34[/C][C]23922[/C][C]24402.863132407[/C][C]-480.863132406979[/C][/ROW]
[ROW][C]35[/C][C]24293[/C][C]24023.4268857777[/C][C]269.57311422225[/C][/ROW]
[ROW][C]36[/C][C]25105[/C][C]24353.1964234193[/C][C]751.803576580722[/C][/ROW]
[ROW][C]37[/C][C]25027[/C][C]24808.9212279925[/C][C]218.078772007462[/C][/ROW]
[ROW][C]38[/C][C]24884[/C][C]25439.8037926953[/C][C]-555.803792695344[/C][/ROW]
[ROW][C]39[/C][C]25247[/C][C]25414.7461015731[/C][C]-167.746101573062[/C][/ROW]
[ROW][C]40[/C][C]25468[/C][C]25497.4331550127[/C][C]-29.4331550126881[/C][/ROW]
[ROW][C]41[/C][C]26722[/C][C]26991.8635842611[/C][C]-269.8635842611[/C][/ROW]
[ROW][C]42[/C][C]26793[/C][C]26540.1198630404[/C][C]252.8801369596[/C][/ROW]
[ROW][C]43[/C][C]25468[/C][C]25458.4067781107[/C][C]9.59322188927399[/C][/ROW]
[ROW][C]44[/C][C]23559[/C][C]23953.4619755413[/C][C]-394.461975541319[/C][/ROW]
[ROW][C]45[/C][C]23409[/C][C]24124.6979957069[/C][C]-715.697995706942[/C][/ROW]
[ROW][C]46[/C][C]23851[/C][C]23737.6152480471[/C][C]113.384751952883[/C][/ROW]
[ROW][C]47[/C][C]23481[/C][C]24008.1992813516[/C][C]-527.19928135159[/C][/ROW]
[ROW][C]48[/C][C]24663[/C][C]24130.3417712312[/C][C]532.658228768752[/C][/ROW]
[ROW][C]49[/C][C]24663[/C][C]24137.9380270773[/C][C]525.061972922704[/C][/ROW]
[ROW][C]50[/C][C]24222[/C][C]24472.0884241095[/C][C]-250.088424109472[/C][/ROW]
[ROW][C]51[/C][C]24806[/C][C]24752.8092150805[/C][C]53.1907849195231[/C][/ROW]
[ROW][C]52[/C][C]25176[/C][C]24982.8352653029[/C][C]193.164734697111[/C][/ROW]
[ROW][C]53[/C][C]26430[/C][C]26443.4176705744[/C][C]-13.4176705744103[/C][/ROW]
[ROW][C]54[/C][C]26793[/C][C]26373.1727140204[/C][C]419.82728597962[/C][/ROW]
[ROW][C]55[/C][C]25247[/C][C]25247.90691216[/C][C]-0.906912160047796[/C][/ROW]
[ROW][C]56[/C][C]23409[/C][C]23529.9456464958[/C][C]-120.945646495809[/C][/ROW]
[ROW][C]57[/C][C]23409[/C][C]23682.5263686056[/C][C]-273.526368605621[/C][/ROW]
[ROW][C]58[/C][C]22818[/C][C]23963.3279849528[/C][C]-1145.32798495275[/C][/ROW]
[ROW][C]59[/C][C]22376[/C][C]23261.1839216475[/C][C]-885.183921647462[/C][/ROW]
[ROW][C]60[/C][C]23338[/C][C]23700.7022974606[/C][C]-362.702297460633[/C][/ROW]
[ROW][C]61[/C][C]22968[/C][C]23178.921785943[/C][C]-210.921785943003[/C][/ROW]
[ROW][C]62[/C][C]22084[/C][C]22639.6426653817[/C][C]-555.642665381678[/C][/ROW]
[ROW][C]63[/C][C]22676[/C][C]22792.1699381162[/C][C]-116.169938116152[/C][/ROW]
[ROW][C]64[/C][C]23189[/C][C]22870.6328454749[/C][C]318.367154525073[/C][/ROW]
[ROW][C]65[/C][C]24735[/C][C]24154.7322234324[/C][C]580.267776567554[/C][/ROW]
[ROW][C]66[/C][C]25326[/C][C]24490.2681680243[/C][C]835.731831975656[/C][/ROW]
[ROW][C]67[/C][C]23702[/C][C]23268.8913567776[/C][C]433.10864322244[/C][/ROW]
[ROW][C]68[/C][C]22526[/C][C]21635.8981870237[/C][C]890.101812976303[/C][/ROW]
[ROW][C]69[/C][C]22526[/C][C]22187.1047037675[/C][C]338.895296232517[/C][/ROW]
[ROW][C]70[/C][C]22084[/C][C]22333.042125067[/C][C]-249.042125066961[/C][/ROW]
[ROW][C]71[/C][C]21792[/C][C]22250.5963709802[/C][C]-458.596370980238[/C][/ROW]
[ROW][C]72[/C][C]22376[/C][C]23230.691613521[/C][C]-854.691613521005[/C][/ROW]
[ROW][C]73[/C][C]21643[/C][C]22586.4966627999[/C][C]-943.496662799891[/C][/ROW]
[ROW][C]74[/C][C]21493[/C][C]21521.2563565254[/C][C]-28.2563565253695[/C][/ROW]
[ROW][C]75[/C][C]21864[/C][C]22190.3713984163[/C][C]-326.371398416326[/C][/ROW]
[ROW][C]76[/C][C]22376[/C][C]22409.8906341722[/C][C]-33.8906341722104[/C][/ROW]
[ROW][C]77[/C][C]23922[/C][C]23661.5310637341[/C][C]260.468936265865[/C][/ROW]
[ROW][C]78[/C][C]24222[/C][C]23962.8605153807[/C][C]259.139484619343[/C][/ROW]
[ROW][C]79[/C][C]22305[/C][C]22220.8549435481[/C][C]84.14505645186[/C][/ROW]
[ROW][C]80[/C][C]20909[/C][C]20599.5817877637[/C][C]309.418212236324[/C][/ROW]
[ROW][C]81[/C][C]20246[/C][C]20510.6938936409[/C][C]-264.693893640913[/C][/ROW]
[ROW][C]82[/C][C]19584[/C][C]19959.2897927552[/C][C]-375.289792755186[/C][/ROW]
[ROW][C]83[/C][C]19213[/C][C]19600.9396809984[/C][C]-387.939680998428[/C][/ROW]
[ROW][C]84[/C][C]19947[/C][C]20310.7649042504[/C][C]-363.764904250449[/C][/ROW]
[ROW][C]85[/C][C]19506[/C][C]19781.4993776094[/C][C]-275.499377609365[/C][/ROW]
[ROW][C]86[/C][C]19584[/C][C]19457.9161939876[/C][C]126.083806012375[/C][/ROW]
[ROW][C]87[/C][C]19947[/C][C]20007.1585726829[/C][C]-60.1585726829253[/C][/ROW]
[ROW][C]88[/C][C]20246[/C][C]20473.5222612968[/C][C]-227.522261296785[/C][/ROW]
[ROW][C]89[/C][C]21714[/C][C]21737.5641968496[/C][C]-23.5641968495693[/C][/ROW]
[ROW][C]90[/C][C]21935[/C][C]21843.9187293877[/C][C]91.0812706122597[/C][/ROW]
[ROW][C]91[/C][C]19584[/C][C]19868.4090503568[/C][C]-284.409050356819[/C][/ROW]
[ROW][C]92[/C][C]18480[/C][C]18101.1331548282[/C][C]378.866845171782[/C][/ROW]
[ROW][C]93[/C][C]17375[/C][C]17679.8324763955[/C][C]-304.832476395477[/C][/ROW]
[ROW][C]94[/C][C]16635[/C][C]16975.2677640107[/C][C]-340.267764010703[/C][/ROW]
[ROW][C]95[/C][C]16122[/C][C]16552.0593202186[/C][C]-430.059320218625[/C][/ROW]
[ROW][C]96[/C][C]16855[/C][C]17175.7769146953[/C][C]-320.776914695307[/C][/ROW]
[ROW][C]97[/C][C]16492[/C][C]16636.7988533732[/C][C]-144.798853373242[/C][/ROW]
[ROW][C]98[/C][C]17076[/C][C]16511.5521990313[/C][C]564.447800968723[/C][/ROW]
[ROW][C]99[/C][C]17297[/C][C]17132.4843497663[/C][C]164.515650233716[/C][/ROW]
[ROW][C]100[/C][C]17518[/C][C]17584.971138159[/C][C]-66.9711381589877[/C][/ROW]
[ROW][C]101[/C][C]18480[/C][C]18999.1241394612[/C][C]-519.124139461233[/C][/ROW]
[ROW][C]102[/C][C]19064[/C][C]18864.4994585406[/C][C]199.500541459376[/C][/ROW]
[ROW][C]103[/C][C]16122[/C][C]16702.0042975274[/C][C]-580.004297527441[/C][/ROW]
[ROW][C]104[/C][C]15388[/C][C]15062.0691067595[/C][C]325.930893240526[/C][/ROW]
[ROW][C]105[/C][C]13543[/C][C]14202.1678317582[/C][C]-659.167831758226[/C][/ROW]
[ROW][C]106[/C][C]12367[/C][C]13223.1933192263[/C][C]-856.193319226268[/C][/ROW]
[ROW][C]107[/C][C]11997[/C][C]12395.0094270415[/C][C]-398.009427041487[/C][/ROW]
[ROW][C]108[/C][C]13030[/C][C]12986.2282997719[/C][C]43.7717002280733[/C][/ROW]
[ROW][C]109[/C][C]12439[/C][C]12628.9511215997[/C][C]-189.951121599717[/C][/ROW]
[ROW][C]110[/C][C]13179[/C][C]12751.899197867[/C][C]427.100802132958[/C][/ROW]
[ROW][C]111[/C][C]13179[/C][C]13006.8357965317[/C][C]172.164203468292[/C][/ROW]
[ROW][C]112[/C][C]13251[/C][C]13250.5617775244[/C][C]0.438222475630027[/C][/ROW]
[ROW][C]113[/C][C]14134[/C][C]14376.5448055336[/C][C]-242.544805533624[/C][/ROW]
[ROW][C]114[/C][C]14725[/C][C]14663.1351185527[/C][C]61.8648814472836[/C][/ROW]
[ROW][C]115[/C][C]11854[/C][C]11951.6866904978[/C][C]-97.686690497836[/C][/ROW]
[ROW][C]116[/C][C]10821[/C][C]10944.9656961076[/C][C]-123.965696107627[/C][/ROW]
[ROW][C]117[/C][C]9126[/C][C]9279.41578322176[/C][C]-153.415783221764[/C][/ROW]
[ROW][C]118[/C][C]8022[/C][C]8388.35311721293[/C][C]-366.35311721293[/C][/ROW]
[ROW][C]119[/C][C]7437[/C][C]7994.7164500822[/C][C]-557.716450082198[/C][/ROW]
[ROW][C]120[/C][C]8905[/C][C]8684.81137717013[/C][C]220.188622829874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235634&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235634&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
132451424062.1330128205451.866987179477
142473524540.2164077532194.783592246786
152510525077.002492438427.9975075615803
162539725433.1912426516-36.1912426516283
172672226782.8566996245-60.8566996244772
182657326640.6105829623-67.6105829622611
192546825201.2245717278266.775428272205
202385124678.2990007834-827.299000783372
212414324352.8388461841-209.838846184088
222444224214.4346721814227.565327818633
232436424360.73671776853.26328223152086
242473524484.8088275879250.191172412084
252444225266.3663824784-824.366382478351
262495524937.295749694317.7042503056873
272517625246.4091411271-70.4091411271329
282524725461.2758412386-214.275841238559
292687226642.3322826018229.66771739825
302657326584.6637415088-11.6637415087898
312546825289.7935060176178.20649398235
322385124111.6884801155-260.688480115456
332414324347.6279831268-204.627983126844
342392224402.863132407-480.863132406979
352429324023.4268857777269.57311422225
362510524353.1964234193751.803576580722
372502724808.9212279925218.078772007462
382488425439.8037926953-555.803792695344
392524725414.7461015731-167.746101573062
402546825497.4331550127-29.4331550126881
412672226991.8635842611-269.8635842611
422679326540.1198630404252.8801369596
432546825458.40677811079.59322188927399
442355923953.4619755413-394.461975541319
452340924124.6979957069-715.697995706942
462385123737.6152480471113.384751952883
472348124008.1992813516-527.19928135159
482466324130.3417712312532.658228768752
492466324137.9380270773525.061972922704
502422224472.0884241095-250.088424109472
512480624752.809215080553.1907849195231
522517624982.8352653029193.164734697111
532643026443.4176705744-13.4176705744103
542679326373.1727140204419.82728597962
552524725247.90691216-0.906912160047796
562340923529.9456464958-120.945646495809
572340923682.5263686056-273.526368605621
582281823963.3279849528-1145.32798495275
592237623261.1839216475-885.183921647462
602333823700.7022974606-362.702297460633
612296823178.921785943-210.921785943003
622208422639.6426653817-555.642665381678
632267622792.1699381162-116.169938116152
642318922870.6328454749318.367154525073
652473524154.7322234324580.267776567554
662532624490.2681680243835.731831975656
672370223268.8913567776433.10864322244
682252621635.8981870237890.101812976303
692252622187.1047037675338.895296232517
702208422333.042125067-249.042125066961
712179222250.5963709802-458.596370980238
722237623230.691613521-854.691613521005
732164322586.4966627999-943.496662799891
742149321521.2563565254-28.2563565253695
752186422190.3713984163-326.371398416326
762237622409.8906341722-33.8906341722104
772392223661.5310637341260.468936265865
782422223962.8605153807259.139484619343
792230522220.854943548184.14505645186
802090920599.5817877637309.418212236324
812024620510.6938936409-264.693893640913
821958419959.2897927552-375.289792755186
831921319600.9396809984-387.939680998428
841994720310.7649042504-363.764904250449
851950619781.4993776094-275.499377609365
861958419457.9161939876126.083806012375
871994720007.1585726829-60.1585726829253
882024620473.5222612968-227.522261296785
892171421737.5641968496-23.5641968495693
902193521843.918729387791.0812706122597
911958419868.4090503568-284.409050356819
921848018101.1331548282378.866845171782
931737517679.8324763955-304.832476395477
941663516975.2677640107-340.267764010703
951612216552.0593202186-430.059320218625
961685517175.7769146953-320.776914695307
971649216636.7988533732-144.798853373242
981707616511.5521990313564.447800968723
991729717132.4843497663164.515650233716
1001751817584.971138159-66.9711381589877
1011848018999.1241394612-519.124139461233
1021906418864.4994585406199.500541459376
1031612216702.0042975274-580.004297527441
1041538815062.0691067595325.930893240526
1051354314202.1678317582-659.167831758226
1061236713223.1933192263-856.193319226268
1071199712395.0094270415-398.009427041487
1081303012986.228299771943.7717002280733
1091243912628.9511215997-189.951121599717
1101317912751.899197867427.100802132958
1111317913006.8357965317172.164203468292
1121325113250.56177752440.438222475630027
1131413414376.5448055336-242.544805533624
1141472514663.135118552761.8648814472836
1151185411951.6866904978-97.686690497836
1161082110944.9656961076-123.965696107627
11791269279.41578322176-153.415783221764
11880228388.35311721293-366.35311721293
11974377994.7164500822-557.716450082198
12089058684.81137717013220.188622829874







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1218257.461977606787491.500516866479023.4234383471
1228757.090182125787887.270624196029626.90974005554
1238623.021949465727645.132349464259600.91154946719
1248637.791243949617547.768931135299727.81355676393
1259583.291736781868377.2098800759410789.3735934878
12610097.75000912928771.8057638801111423.6942543784
1277226.040036998755776.54412616388675.5359478337
1286209.704475317164633.072028955297786.33692167903
1294551.496034157282844.238516533616258.75355178095
1303596.177494945031754.89556623245437.45942365765
1313270.757951631791292.135131770355249.38077149322
1324640.210729970192521.007751939866759.41370800052

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 8257.46197760678 & 7491.50051686647 & 9023.4234383471 \tabularnewline
122 & 8757.09018212578 & 7887.27062419602 & 9626.90974005554 \tabularnewline
123 & 8623.02194946572 & 7645.13234946425 & 9600.91154946719 \tabularnewline
124 & 8637.79124394961 & 7547.76893113529 & 9727.81355676393 \tabularnewline
125 & 9583.29173678186 & 8377.20988007594 & 10789.3735934878 \tabularnewline
126 & 10097.7500091292 & 8771.80576388011 & 11423.6942543784 \tabularnewline
127 & 7226.04003699875 & 5776.5441261638 & 8675.5359478337 \tabularnewline
128 & 6209.70447531716 & 4633.07202895529 & 7786.33692167903 \tabularnewline
129 & 4551.49603415728 & 2844.23851653361 & 6258.75355178095 \tabularnewline
130 & 3596.17749494503 & 1754.8955662324 & 5437.45942365765 \tabularnewline
131 & 3270.75795163179 & 1292.13513177035 & 5249.38077149322 \tabularnewline
132 & 4640.21072997019 & 2521.00775193986 & 6759.41370800052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235634&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]121[/C][C]8257.46197760678[/C][C]7491.50051686647[/C][C]9023.4234383471[/C][/ROW]
[ROW][C]122[/C][C]8757.09018212578[/C][C]7887.27062419602[/C][C]9626.90974005554[/C][/ROW]
[ROW][C]123[/C][C]8623.02194946572[/C][C]7645.13234946425[/C][C]9600.91154946719[/C][/ROW]
[ROW][C]124[/C][C]8637.79124394961[/C][C]7547.76893113529[/C][C]9727.81355676393[/C][/ROW]
[ROW][C]125[/C][C]9583.29173678186[/C][C]8377.20988007594[/C][C]10789.3735934878[/C][/ROW]
[ROW][C]126[/C][C]10097.7500091292[/C][C]8771.80576388011[/C][C]11423.6942543784[/C][/ROW]
[ROW][C]127[/C][C]7226.04003699875[/C][C]5776.5441261638[/C][C]8675.5359478337[/C][/ROW]
[ROW][C]128[/C][C]6209.70447531716[/C][C]4633.07202895529[/C][C]7786.33692167903[/C][/ROW]
[ROW][C]129[/C][C]4551.49603415728[/C][C]2844.23851653361[/C][C]6258.75355178095[/C][/ROW]
[ROW][C]130[/C][C]3596.17749494503[/C][C]1754.8955662324[/C][C]5437.45942365765[/C][/ROW]
[ROW][C]131[/C][C]3270.75795163179[/C][C]1292.13513177035[/C][C]5249.38077149322[/C][/ROW]
[ROW][C]132[/C][C]4640.21072997019[/C][C]2521.00775193986[/C][C]6759.41370800052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235634&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235634&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
1218257.461977606787491.500516866479023.4234383471
1228757.090182125787887.270624196029626.90974005554
1238623.021949465727645.132349464259600.91154946719
1248637.791243949617547.768931135299727.81355676393
1259583.291736781868377.2098800759410789.3735934878
12610097.75000912928771.8057638801111423.6942543784
1277226.040036998755776.54412616388675.5359478337
1286209.704475317164633.072028955297786.33692167903
1294551.496034157282844.238516533616258.75355178095
1303596.177494945031754.89556623245437.45942365765
1313270.757951631791292.135131770355249.38077149322
1324640.210729970192521.007751939866759.41370800052



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):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')