Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 16 Aug 2011 09:54:30 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/16/t1313502916khzbcsjlwb6j31x.htm/, Retrieved Tue, 14 May 2024 06:43:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123869, Retrieved Tue, 14 May 2024 06:43:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmattias debbaut
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks A - exp...] [2011-08-16 13:54:30] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
21571
21493
21422
21272
22747
22676
21571
20831
20909
20909
20980
21130
21051
21643
21864
21643
22455
21935
20759
20467
20467
20610
20026
20467
20097
20467
21051
21272
21792
21571
20246
19726
19506
19726
19363
19506
19064
19805
20168
20246
21643
21643
19805
19363
19363
19584
18622
18180
17668
17817
18480
17960
19363
19584
18180
17668
17375
17668
16855
16563
15388
15680
15751
15830
17226
17076
15388
14647
14355
14725
13322
12367
10601
10750
10750
10601
11854
11926
10451
10159
9568
10380
8905
8022
6333
6697
6255
6404
7509
7730
6996
6917
6917
7879
6184
5079
3163
4709
4488
4566
6333
6112
5300
5671
5671
6996
5450
4566
3163
5008
4859
4930
6476
6333
5813
5892
6255
7067
5813
4787




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=123869&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=123869&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123869&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
alpha0.698947662125972
beta0.80822440145139
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.698947662125972 \tabularnewline
beta & 0.80822440145139 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123869&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]0.698947662125972[/C][/ROW]
[ROW][C]beta[/C][C]0.80822440145139[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123869&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123869&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
alpha0.698947662125972
beta0.80822440145139
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132105121133.4345013116-82.4345013115671
142164321642.34580671330.654193286689406
152186421821.807630801142.1923691988886
162164321609.650351730233.3496482698065
172245522465.1475396801-10.1475396801288
182193521968.2879735418-33.2879735417919
192075921227.8622987743-468.862298774307
202046719886.9831000868580.016899913229
212046720361.933058334105.066941665955
222061020479.3670505921130.632949407878
232002620787.8673306178-761.867330617766
242046720158.6886030205308.311396979527
252009720227.406799872-130.406799872024
262046720587.248564596-120.24856459599
272105120498.504946822552.495053177983
282127220754.206868203517.793131797007
292179222308.2803443426-516.280344342613
302157121566.7568352444.24316475602245
312024620854.7825736696-608.782573669603
321972619775.2718393671-49.2718393670802
331950619354.3246517425151.675348257508
341972619223.4972949951502.502705004874
351936319448.7054959499-85.7054959498892
361950619902.9640949942-396.96409499419
371906419260.8967225655-196.896722565492
381980519411.6357040809393.364295919135
392016820022.9762734691145.023726530897
402024619916.4568404206329.543159579447
412164320811.5662554577831.433744542293
422164321739.7516627592-96.751662759154
431980521250.0847581131-1445.08475811307
441936319764.7045890098-401.704589009812
451936318969.3198835582393.680116441756
461958419057.0755217458526.92447825423
471862219087.866858188-465.866858188001
481818018908.6532588721-728.653258872091
491766817654.133585087513.8664149124961
501781717729.151853217587.8481467825259
511848017490.4401651021989.559834897904
521796017994.4460422194-34.4460422193551
531936318446.0428572969916.957142703126
541958419007.6772280125576.322771987452
551818018860.2068008999-680.206800899941
561766818788.2474570313-1120.24745703134
571737517881.3118966343-506.311896634339
581766817021.9183478102646.08165218982
591685516637.2044398871217.795560112943
601656316938.029278583-375.029278582995
611538816457.4415881257-1069.44158812572
621568015402.8388326921277.161167307948
631575115271.0942906091479.905709390903
641583014680.90386657071149.0961334293
651722616300.9135962726925.086403727375
661707617009.601082543366.3989174567359
671538816222.1913482763-834.191348276274
681464715702.548151523-1055.54815152297
691435514785.6111122175-430.611112217479
701472514102.6610324565622.338967543512
711332213546.9387717159-224.938771715882
721236712934.3483404946-567.3483404946
731060111610.9327615246-1009.93276152459
741075010162.1867515098587.813248490225
75107509749.791136935091000.20886306491
76106019690.74763276685910.252367233148
771185410610.2080433861243.79195661401
781192611490.4538622526435.546137747411
791045111338.4215113504-887.421511350358
801015910835.5204746105-676.520474610519
81956810532.7068418459-964.706841845933
82103809574.91194242195805.088057578054
8389059256.72230878998-351.722308789982
8480228489.40359816036-467.403598160361
8563337250.44788229484-917.447882294837
8666975991.84988679471705.150113205293
8762555750.45813485346504.541865146543
8864045262.75371304781141.2462869522
8975096222.27490910361286.7250908964
9077307217.16607720626512.833922793743
9169967327.23030065576-331.230300655765
9269177630.11053365509-713.110533655087
9369177456.22581959116-539.225819591155
9478797667.18722094134211.81277905866
9561847062.71593775447-878.715937754467
9650795855.89993163633-776.899931636332
9731634140.85202433091-977.852024330914
9847092384.364470228922324.63552977108
9944883684.04525282018803.954747179825
10045664282.46273291236283.537267087642
10163334807.455740643731525.54425935627
10261126203.68425243041-91.6842524304084
10353005863.63439028895-563.634390288949
10456715747.2624626804-76.2624626803981
10556716221.69227906249-550.692279062489
10669966707.05882914707288.941170852933
10754506153.15302787506-703.153027875058
10845665376.3700334526-810.370033452602
10931633776.36293793636-613.362937936362
11050083694.630355741891313.36964425811
11148593623.24625314481235.7537468552
11249304399.95155822865530.048441771345
11364765600.69957778224875.300422217755
11463335872.0576504911460.942349508896
11558135837.92071950959-24.9207195095905
11658926635.61299710353-743.612997103527
11762556502.14289106603-247.142891066034
11870677779.84777054216-712.84777054216
11958135859.38396283056-46.3839628305586
12047875527.05745440011-740.057454400113

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 21051 & 21133.4345013116 & -82.4345013115671 \tabularnewline
14 & 21643 & 21642.3458067133 & 0.654193286689406 \tabularnewline
15 & 21864 & 21821.8076308011 & 42.1923691988886 \tabularnewline
16 & 21643 & 21609.6503517302 & 33.3496482698065 \tabularnewline
17 & 22455 & 22465.1475396801 & -10.1475396801288 \tabularnewline
18 & 21935 & 21968.2879735418 & -33.2879735417919 \tabularnewline
19 & 20759 & 21227.8622987743 & -468.862298774307 \tabularnewline
20 & 20467 & 19886.9831000868 & 580.016899913229 \tabularnewline
21 & 20467 & 20361.933058334 & 105.066941665955 \tabularnewline
22 & 20610 & 20479.3670505921 & 130.632949407878 \tabularnewline
23 & 20026 & 20787.8673306178 & -761.867330617766 \tabularnewline
24 & 20467 & 20158.6886030205 & 308.311396979527 \tabularnewline
25 & 20097 & 20227.406799872 & -130.406799872024 \tabularnewline
26 & 20467 & 20587.248564596 & -120.24856459599 \tabularnewline
27 & 21051 & 20498.504946822 & 552.495053177983 \tabularnewline
28 & 21272 & 20754.206868203 & 517.793131797007 \tabularnewline
29 & 21792 & 22308.2803443426 & -516.280344342613 \tabularnewline
30 & 21571 & 21566.756835244 & 4.24316475602245 \tabularnewline
31 & 20246 & 20854.7825736696 & -608.782573669603 \tabularnewline
32 & 19726 & 19775.2718393671 & -49.2718393670802 \tabularnewline
33 & 19506 & 19354.3246517425 & 151.675348257508 \tabularnewline
34 & 19726 & 19223.4972949951 & 502.502705004874 \tabularnewline
35 & 19363 & 19448.7054959499 & -85.7054959498892 \tabularnewline
36 & 19506 & 19902.9640949942 & -396.96409499419 \tabularnewline
37 & 19064 & 19260.8967225655 & -196.896722565492 \tabularnewline
38 & 19805 & 19411.6357040809 & 393.364295919135 \tabularnewline
39 & 20168 & 20022.9762734691 & 145.023726530897 \tabularnewline
40 & 20246 & 19916.4568404206 & 329.543159579447 \tabularnewline
41 & 21643 & 20811.5662554577 & 831.433744542293 \tabularnewline
42 & 21643 & 21739.7516627592 & -96.751662759154 \tabularnewline
43 & 19805 & 21250.0847581131 & -1445.08475811307 \tabularnewline
44 & 19363 & 19764.7045890098 & -401.704589009812 \tabularnewline
45 & 19363 & 18969.3198835582 & 393.680116441756 \tabularnewline
46 & 19584 & 19057.0755217458 & 526.92447825423 \tabularnewline
47 & 18622 & 19087.866858188 & -465.866858188001 \tabularnewline
48 & 18180 & 18908.6532588721 & -728.653258872091 \tabularnewline
49 & 17668 & 17654.1335850875 & 13.8664149124961 \tabularnewline
50 & 17817 & 17729.1518532175 & 87.8481467825259 \tabularnewline
51 & 18480 & 17490.4401651021 & 989.559834897904 \tabularnewline
52 & 17960 & 17994.4460422194 & -34.4460422193551 \tabularnewline
53 & 19363 & 18446.0428572969 & 916.957142703126 \tabularnewline
54 & 19584 & 19007.6772280125 & 576.322771987452 \tabularnewline
55 & 18180 & 18860.2068008999 & -680.206800899941 \tabularnewline
56 & 17668 & 18788.2474570313 & -1120.24745703134 \tabularnewline
57 & 17375 & 17881.3118966343 & -506.311896634339 \tabularnewline
58 & 17668 & 17021.9183478102 & 646.08165218982 \tabularnewline
59 & 16855 & 16637.2044398871 & 217.795560112943 \tabularnewline
60 & 16563 & 16938.029278583 & -375.029278582995 \tabularnewline
61 & 15388 & 16457.4415881257 & -1069.44158812572 \tabularnewline
62 & 15680 & 15402.8388326921 & 277.161167307948 \tabularnewline
63 & 15751 & 15271.0942906091 & 479.905709390903 \tabularnewline
64 & 15830 & 14680.9038665707 & 1149.0961334293 \tabularnewline
65 & 17226 & 16300.9135962726 & 925.086403727375 \tabularnewline
66 & 17076 & 17009.6010825433 & 66.3989174567359 \tabularnewline
67 & 15388 & 16222.1913482763 & -834.191348276274 \tabularnewline
68 & 14647 & 15702.548151523 & -1055.54815152297 \tabularnewline
69 & 14355 & 14785.6111122175 & -430.611112217479 \tabularnewline
70 & 14725 & 14102.6610324565 & 622.338967543512 \tabularnewline
71 & 13322 & 13546.9387717159 & -224.938771715882 \tabularnewline
72 & 12367 & 12934.3483404946 & -567.3483404946 \tabularnewline
73 & 10601 & 11610.9327615246 & -1009.93276152459 \tabularnewline
74 & 10750 & 10162.1867515098 & 587.813248490225 \tabularnewline
75 & 10750 & 9749.79113693509 & 1000.20886306491 \tabularnewline
76 & 10601 & 9690.74763276685 & 910.252367233148 \tabularnewline
77 & 11854 & 10610.208043386 & 1243.79195661401 \tabularnewline
78 & 11926 & 11490.4538622526 & 435.546137747411 \tabularnewline
79 & 10451 & 11338.4215113504 & -887.421511350358 \tabularnewline
80 & 10159 & 10835.5204746105 & -676.520474610519 \tabularnewline
81 & 9568 & 10532.7068418459 & -964.706841845933 \tabularnewline
82 & 10380 & 9574.91194242195 & 805.088057578054 \tabularnewline
83 & 8905 & 9256.72230878998 & -351.722308789982 \tabularnewline
84 & 8022 & 8489.40359816036 & -467.403598160361 \tabularnewline
85 & 6333 & 7250.44788229484 & -917.447882294837 \tabularnewline
86 & 6697 & 5991.84988679471 & 705.150113205293 \tabularnewline
87 & 6255 & 5750.45813485346 & 504.541865146543 \tabularnewline
88 & 6404 & 5262.7537130478 & 1141.2462869522 \tabularnewline
89 & 7509 & 6222.2749091036 & 1286.7250908964 \tabularnewline
90 & 7730 & 7217.16607720626 & 512.833922793743 \tabularnewline
91 & 6996 & 7327.23030065576 & -331.230300655765 \tabularnewline
92 & 6917 & 7630.11053365509 & -713.110533655087 \tabularnewline
93 & 6917 & 7456.22581959116 & -539.225819591155 \tabularnewline
94 & 7879 & 7667.18722094134 & 211.81277905866 \tabularnewline
95 & 6184 & 7062.71593775447 & -878.715937754467 \tabularnewline
96 & 5079 & 5855.89993163633 & -776.899931636332 \tabularnewline
97 & 3163 & 4140.85202433091 & -977.852024330914 \tabularnewline
98 & 4709 & 2384.36447022892 & 2324.63552977108 \tabularnewline
99 & 4488 & 3684.04525282018 & 803.954747179825 \tabularnewline
100 & 4566 & 4282.46273291236 & 283.537267087642 \tabularnewline
101 & 6333 & 4807.45574064373 & 1525.54425935627 \tabularnewline
102 & 6112 & 6203.68425243041 & -91.6842524304084 \tabularnewline
103 & 5300 & 5863.63439028895 & -563.634390288949 \tabularnewline
104 & 5671 & 5747.2624626804 & -76.2624626803981 \tabularnewline
105 & 5671 & 6221.69227906249 & -550.692279062489 \tabularnewline
106 & 6996 & 6707.05882914707 & 288.941170852933 \tabularnewline
107 & 5450 & 6153.15302787506 & -703.153027875058 \tabularnewline
108 & 4566 & 5376.3700334526 & -810.370033452602 \tabularnewline
109 & 3163 & 3776.36293793636 & -613.362937936362 \tabularnewline
110 & 5008 & 3694.63035574189 & 1313.36964425811 \tabularnewline
111 & 4859 & 3623.2462531448 & 1235.7537468552 \tabularnewline
112 & 4930 & 4399.95155822865 & 530.048441771345 \tabularnewline
113 & 6476 & 5600.69957778224 & 875.300422217755 \tabularnewline
114 & 6333 & 5872.0576504911 & 460.942349508896 \tabularnewline
115 & 5813 & 5837.92071950959 & -24.9207195095905 \tabularnewline
116 & 5892 & 6635.61299710353 & -743.612997103527 \tabularnewline
117 & 6255 & 6502.14289106603 & -247.142891066034 \tabularnewline
118 & 7067 & 7779.84777054216 & -712.84777054216 \tabularnewline
119 & 5813 & 5859.38396283056 & -46.3839628305586 \tabularnewline
120 & 4787 & 5527.05745440011 & -740.057454400113 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123869&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]21051[/C][C]21133.4345013116[/C][C]-82.4345013115671[/C][/ROW]
[ROW][C]14[/C][C]21643[/C][C]21642.3458067133[/C][C]0.654193286689406[/C][/ROW]
[ROW][C]15[/C][C]21864[/C][C]21821.8076308011[/C][C]42.1923691988886[/C][/ROW]
[ROW][C]16[/C][C]21643[/C][C]21609.6503517302[/C][C]33.3496482698065[/C][/ROW]
[ROW][C]17[/C][C]22455[/C][C]22465.1475396801[/C][C]-10.1475396801288[/C][/ROW]
[ROW][C]18[/C][C]21935[/C][C]21968.2879735418[/C][C]-33.2879735417919[/C][/ROW]
[ROW][C]19[/C][C]20759[/C][C]21227.8622987743[/C][C]-468.862298774307[/C][/ROW]
[ROW][C]20[/C][C]20467[/C][C]19886.9831000868[/C][C]580.016899913229[/C][/ROW]
[ROW][C]21[/C][C]20467[/C][C]20361.933058334[/C][C]105.066941665955[/C][/ROW]
[ROW][C]22[/C][C]20610[/C][C]20479.3670505921[/C][C]130.632949407878[/C][/ROW]
[ROW][C]23[/C][C]20026[/C][C]20787.8673306178[/C][C]-761.867330617766[/C][/ROW]
[ROW][C]24[/C][C]20467[/C][C]20158.6886030205[/C][C]308.311396979527[/C][/ROW]
[ROW][C]25[/C][C]20097[/C][C]20227.406799872[/C][C]-130.406799872024[/C][/ROW]
[ROW][C]26[/C][C]20467[/C][C]20587.248564596[/C][C]-120.24856459599[/C][/ROW]
[ROW][C]27[/C][C]21051[/C][C]20498.504946822[/C][C]552.495053177983[/C][/ROW]
[ROW][C]28[/C][C]21272[/C][C]20754.206868203[/C][C]517.793131797007[/C][/ROW]
[ROW][C]29[/C][C]21792[/C][C]22308.2803443426[/C][C]-516.280344342613[/C][/ROW]
[ROW][C]30[/C][C]21571[/C][C]21566.756835244[/C][C]4.24316475602245[/C][/ROW]
[ROW][C]31[/C][C]20246[/C][C]20854.7825736696[/C][C]-608.782573669603[/C][/ROW]
[ROW][C]32[/C][C]19726[/C][C]19775.2718393671[/C][C]-49.2718393670802[/C][/ROW]
[ROW][C]33[/C][C]19506[/C][C]19354.3246517425[/C][C]151.675348257508[/C][/ROW]
[ROW][C]34[/C][C]19726[/C][C]19223.4972949951[/C][C]502.502705004874[/C][/ROW]
[ROW][C]35[/C][C]19363[/C][C]19448.7054959499[/C][C]-85.7054959498892[/C][/ROW]
[ROW][C]36[/C][C]19506[/C][C]19902.9640949942[/C][C]-396.96409499419[/C][/ROW]
[ROW][C]37[/C][C]19064[/C][C]19260.8967225655[/C][C]-196.896722565492[/C][/ROW]
[ROW][C]38[/C][C]19805[/C][C]19411.6357040809[/C][C]393.364295919135[/C][/ROW]
[ROW][C]39[/C][C]20168[/C][C]20022.9762734691[/C][C]145.023726530897[/C][/ROW]
[ROW][C]40[/C][C]20246[/C][C]19916.4568404206[/C][C]329.543159579447[/C][/ROW]
[ROW][C]41[/C][C]21643[/C][C]20811.5662554577[/C][C]831.433744542293[/C][/ROW]
[ROW][C]42[/C][C]21643[/C][C]21739.7516627592[/C][C]-96.751662759154[/C][/ROW]
[ROW][C]43[/C][C]19805[/C][C]21250.0847581131[/C][C]-1445.08475811307[/C][/ROW]
[ROW][C]44[/C][C]19363[/C][C]19764.7045890098[/C][C]-401.704589009812[/C][/ROW]
[ROW][C]45[/C][C]19363[/C][C]18969.3198835582[/C][C]393.680116441756[/C][/ROW]
[ROW][C]46[/C][C]19584[/C][C]19057.0755217458[/C][C]526.92447825423[/C][/ROW]
[ROW][C]47[/C][C]18622[/C][C]19087.866858188[/C][C]-465.866858188001[/C][/ROW]
[ROW][C]48[/C][C]18180[/C][C]18908.6532588721[/C][C]-728.653258872091[/C][/ROW]
[ROW][C]49[/C][C]17668[/C][C]17654.1335850875[/C][C]13.8664149124961[/C][/ROW]
[ROW][C]50[/C][C]17817[/C][C]17729.1518532175[/C][C]87.8481467825259[/C][/ROW]
[ROW][C]51[/C][C]18480[/C][C]17490.4401651021[/C][C]989.559834897904[/C][/ROW]
[ROW][C]52[/C][C]17960[/C][C]17994.4460422194[/C][C]-34.4460422193551[/C][/ROW]
[ROW][C]53[/C][C]19363[/C][C]18446.0428572969[/C][C]916.957142703126[/C][/ROW]
[ROW][C]54[/C][C]19584[/C][C]19007.6772280125[/C][C]576.322771987452[/C][/ROW]
[ROW][C]55[/C][C]18180[/C][C]18860.2068008999[/C][C]-680.206800899941[/C][/ROW]
[ROW][C]56[/C][C]17668[/C][C]18788.2474570313[/C][C]-1120.24745703134[/C][/ROW]
[ROW][C]57[/C][C]17375[/C][C]17881.3118966343[/C][C]-506.311896634339[/C][/ROW]
[ROW][C]58[/C][C]17668[/C][C]17021.9183478102[/C][C]646.08165218982[/C][/ROW]
[ROW][C]59[/C][C]16855[/C][C]16637.2044398871[/C][C]217.795560112943[/C][/ROW]
[ROW][C]60[/C][C]16563[/C][C]16938.029278583[/C][C]-375.029278582995[/C][/ROW]
[ROW][C]61[/C][C]15388[/C][C]16457.4415881257[/C][C]-1069.44158812572[/C][/ROW]
[ROW][C]62[/C][C]15680[/C][C]15402.8388326921[/C][C]277.161167307948[/C][/ROW]
[ROW][C]63[/C][C]15751[/C][C]15271.0942906091[/C][C]479.905709390903[/C][/ROW]
[ROW][C]64[/C][C]15830[/C][C]14680.9038665707[/C][C]1149.0961334293[/C][/ROW]
[ROW][C]65[/C][C]17226[/C][C]16300.9135962726[/C][C]925.086403727375[/C][/ROW]
[ROW][C]66[/C][C]17076[/C][C]17009.6010825433[/C][C]66.3989174567359[/C][/ROW]
[ROW][C]67[/C][C]15388[/C][C]16222.1913482763[/C][C]-834.191348276274[/C][/ROW]
[ROW][C]68[/C][C]14647[/C][C]15702.548151523[/C][C]-1055.54815152297[/C][/ROW]
[ROW][C]69[/C][C]14355[/C][C]14785.6111122175[/C][C]-430.611112217479[/C][/ROW]
[ROW][C]70[/C][C]14725[/C][C]14102.6610324565[/C][C]622.338967543512[/C][/ROW]
[ROW][C]71[/C][C]13322[/C][C]13546.9387717159[/C][C]-224.938771715882[/C][/ROW]
[ROW][C]72[/C][C]12367[/C][C]12934.3483404946[/C][C]-567.3483404946[/C][/ROW]
[ROW][C]73[/C][C]10601[/C][C]11610.9327615246[/C][C]-1009.93276152459[/C][/ROW]
[ROW][C]74[/C][C]10750[/C][C]10162.1867515098[/C][C]587.813248490225[/C][/ROW]
[ROW][C]75[/C][C]10750[/C][C]9749.79113693509[/C][C]1000.20886306491[/C][/ROW]
[ROW][C]76[/C][C]10601[/C][C]9690.74763276685[/C][C]910.252367233148[/C][/ROW]
[ROW][C]77[/C][C]11854[/C][C]10610.208043386[/C][C]1243.79195661401[/C][/ROW]
[ROW][C]78[/C][C]11926[/C][C]11490.4538622526[/C][C]435.546137747411[/C][/ROW]
[ROW][C]79[/C][C]10451[/C][C]11338.4215113504[/C][C]-887.421511350358[/C][/ROW]
[ROW][C]80[/C][C]10159[/C][C]10835.5204746105[/C][C]-676.520474610519[/C][/ROW]
[ROW][C]81[/C][C]9568[/C][C]10532.7068418459[/C][C]-964.706841845933[/C][/ROW]
[ROW][C]82[/C][C]10380[/C][C]9574.91194242195[/C][C]805.088057578054[/C][/ROW]
[ROW][C]83[/C][C]8905[/C][C]9256.72230878998[/C][C]-351.722308789982[/C][/ROW]
[ROW][C]84[/C][C]8022[/C][C]8489.40359816036[/C][C]-467.403598160361[/C][/ROW]
[ROW][C]85[/C][C]6333[/C][C]7250.44788229484[/C][C]-917.447882294837[/C][/ROW]
[ROW][C]86[/C][C]6697[/C][C]5991.84988679471[/C][C]705.150113205293[/C][/ROW]
[ROW][C]87[/C][C]6255[/C][C]5750.45813485346[/C][C]504.541865146543[/C][/ROW]
[ROW][C]88[/C][C]6404[/C][C]5262.7537130478[/C][C]1141.2462869522[/C][/ROW]
[ROW][C]89[/C][C]7509[/C][C]6222.2749091036[/C][C]1286.7250908964[/C][/ROW]
[ROW][C]90[/C][C]7730[/C][C]7217.16607720626[/C][C]512.833922793743[/C][/ROW]
[ROW][C]91[/C][C]6996[/C][C]7327.23030065576[/C][C]-331.230300655765[/C][/ROW]
[ROW][C]92[/C][C]6917[/C][C]7630.11053365509[/C][C]-713.110533655087[/C][/ROW]
[ROW][C]93[/C][C]6917[/C][C]7456.22581959116[/C][C]-539.225819591155[/C][/ROW]
[ROW][C]94[/C][C]7879[/C][C]7667.18722094134[/C][C]211.81277905866[/C][/ROW]
[ROW][C]95[/C][C]6184[/C][C]7062.71593775447[/C][C]-878.715937754467[/C][/ROW]
[ROW][C]96[/C][C]5079[/C][C]5855.89993163633[/C][C]-776.899931636332[/C][/ROW]
[ROW][C]97[/C][C]3163[/C][C]4140.85202433091[/C][C]-977.852024330914[/C][/ROW]
[ROW][C]98[/C][C]4709[/C][C]2384.36447022892[/C][C]2324.63552977108[/C][/ROW]
[ROW][C]99[/C][C]4488[/C][C]3684.04525282018[/C][C]803.954747179825[/C][/ROW]
[ROW][C]100[/C][C]4566[/C][C]4282.46273291236[/C][C]283.537267087642[/C][/ROW]
[ROW][C]101[/C][C]6333[/C][C]4807.45574064373[/C][C]1525.54425935627[/C][/ROW]
[ROW][C]102[/C][C]6112[/C][C]6203.68425243041[/C][C]-91.6842524304084[/C][/ROW]
[ROW][C]103[/C][C]5300[/C][C]5863.63439028895[/C][C]-563.634390288949[/C][/ROW]
[ROW][C]104[/C][C]5671[/C][C]5747.2624626804[/C][C]-76.2624626803981[/C][/ROW]
[ROW][C]105[/C][C]5671[/C][C]6221.69227906249[/C][C]-550.692279062489[/C][/ROW]
[ROW][C]106[/C][C]6996[/C][C]6707.05882914707[/C][C]288.941170852933[/C][/ROW]
[ROW][C]107[/C][C]5450[/C][C]6153.15302787506[/C][C]-703.153027875058[/C][/ROW]
[ROW][C]108[/C][C]4566[/C][C]5376.3700334526[/C][C]-810.370033452602[/C][/ROW]
[ROW][C]109[/C][C]3163[/C][C]3776.36293793636[/C][C]-613.362937936362[/C][/ROW]
[ROW][C]110[/C][C]5008[/C][C]3694.63035574189[/C][C]1313.36964425811[/C][/ROW]
[ROW][C]111[/C][C]4859[/C][C]3623.2462531448[/C][C]1235.7537468552[/C][/ROW]
[ROW][C]112[/C][C]4930[/C][C]4399.95155822865[/C][C]530.048441771345[/C][/ROW]
[ROW][C]113[/C][C]6476[/C][C]5600.69957778224[/C][C]875.300422217755[/C][/ROW]
[ROW][C]114[/C][C]6333[/C][C]5872.0576504911[/C][C]460.942349508896[/C][/ROW]
[ROW][C]115[/C][C]5813[/C][C]5837.92071950959[/C][C]-24.9207195095905[/C][/ROW]
[ROW][C]116[/C][C]5892[/C][C]6635.61299710353[/C][C]-743.612997103527[/C][/ROW]
[ROW][C]117[/C][C]6255[/C][C]6502.14289106603[/C][C]-247.142891066034[/C][/ROW]
[ROW][C]118[/C][C]7067[/C][C]7779.84777054216[/C][C]-712.84777054216[/C][/ROW]
[ROW][C]119[/C][C]5813[/C][C]5859.38396283056[/C][C]-46.3839628305586[/C][/ROW]
[ROW][C]120[/C][C]4787[/C][C]5527.05745440011[/C][C]-740.057454400113[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123869&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123869&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
132105121133.4345013116-82.4345013115671
142164321642.34580671330.654193286689406
152186421821.807630801142.1923691988886
162164321609.650351730233.3496482698065
172245522465.1475396801-10.1475396801288
182193521968.2879735418-33.2879735417919
192075921227.8622987743-468.862298774307
202046719886.9831000868580.016899913229
212046720361.933058334105.066941665955
222061020479.3670505921130.632949407878
232002620787.8673306178-761.867330617766
242046720158.6886030205308.311396979527
252009720227.406799872-130.406799872024
262046720587.248564596-120.24856459599
272105120498.504946822552.495053177983
282127220754.206868203517.793131797007
292179222308.2803443426-516.280344342613
302157121566.7568352444.24316475602245
312024620854.7825736696-608.782573669603
321972619775.2718393671-49.2718393670802
331950619354.3246517425151.675348257508
341972619223.4972949951502.502705004874
351936319448.7054959499-85.7054959498892
361950619902.9640949942-396.96409499419
371906419260.8967225655-196.896722565492
381980519411.6357040809393.364295919135
392016820022.9762734691145.023726530897
402024619916.4568404206329.543159579447
412164320811.5662554577831.433744542293
422164321739.7516627592-96.751662759154
431980521250.0847581131-1445.08475811307
441936319764.7045890098-401.704589009812
451936318969.3198835582393.680116441756
461958419057.0755217458526.92447825423
471862219087.866858188-465.866858188001
481818018908.6532588721-728.653258872091
491766817654.133585087513.8664149124961
501781717729.151853217587.8481467825259
511848017490.4401651021989.559834897904
521796017994.4460422194-34.4460422193551
531936318446.0428572969916.957142703126
541958419007.6772280125576.322771987452
551818018860.2068008999-680.206800899941
561766818788.2474570313-1120.24745703134
571737517881.3118966343-506.311896634339
581766817021.9183478102646.08165218982
591685516637.2044398871217.795560112943
601656316938.029278583-375.029278582995
611538816457.4415881257-1069.44158812572
621568015402.8388326921277.161167307948
631575115271.0942906091479.905709390903
641583014680.90386657071149.0961334293
651722616300.9135962726925.086403727375
661707617009.601082543366.3989174567359
671538816222.1913482763-834.191348276274
681464715702.548151523-1055.54815152297
691435514785.6111122175-430.611112217479
701472514102.6610324565622.338967543512
711332213546.9387717159-224.938771715882
721236712934.3483404946-567.3483404946
731060111610.9327615246-1009.93276152459
741075010162.1867515098587.813248490225
75107509749.791136935091000.20886306491
76106019690.74763276685910.252367233148
771185410610.2080433861243.79195661401
781192611490.4538622526435.546137747411
791045111338.4215113504-887.421511350358
801015910835.5204746105-676.520474610519
81956810532.7068418459-964.706841845933
82103809574.91194242195805.088057578054
8389059256.72230878998-351.722308789982
8480228489.40359816036-467.403598160361
8563337250.44788229484-917.447882294837
8666975991.84988679471705.150113205293
8762555750.45813485346504.541865146543
8864045262.75371304781141.2462869522
8975096222.27490910361286.7250908964
9077307217.16607720626512.833922793743
9169967327.23030065576-331.230300655765
9269177630.11053365509-713.110533655087
9369177456.22581959116-539.225819591155
9478797667.18722094134211.81277905866
9561847062.71593775447-878.715937754467
9650795855.89993163633-776.899931636332
9731634140.85202433091-977.852024330914
9847092384.364470228922324.63552977108
9944883684.04525282018803.954747179825
10045664282.46273291236283.537267087642
10163334807.455740643731525.54425935627
10261126203.68425243041-91.6842524304084
10353005863.63439028895-563.634390288949
10456715747.2624626804-76.2624626803981
10556716221.69227906249-550.692279062489
10669966707.05882914707288.941170852933
10754506153.15302787506-703.153027875058
10845665376.3700334526-810.370033452602
10931633776.36293793636-613.362937936362
11050083694.630355741891313.36964425811
11148593623.24625314481235.7537468552
11249304399.95155822865530.048441771345
11364765600.69957778224875.300422217755
11463335872.0576504911460.942349508896
11558135837.92071950959-24.9207195095905
11658926635.61299710353-743.612997103527
11762556502.14289106603-247.142891066034
11870677779.84777054216-712.84777054216
11958135859.38396283056-46.3839628305586
12047875527.05745440011-740.057454400113







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1214037.433416721422676.876501096395397.99033234645
1226267.710145159442918.641728063989616.7785622549
1235003.14897287531357.2269355415899649.07101020902
1243881.86964312591-2030.764216458639794.50350271045
1253432.23776505043-5013.5189148574511877.9944449583
1262076.44756276271-6504.547073636210657.4421991616
1271072.34672923839-7228.264570024169372.95802850094
128473.159814726201-9112.2705440135410058.5901734659
129-99.939694334223-11675.833798345911475.9544096774
130-804.32431355115-16424.619039413514815.9704123112
131-1260.71864670637-16358.91490647113837.4776130582
132-1718.45378290862-17617.630401026414180.7228352091

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 4037.43341672142 & 2676.87650109639 & 5397.99033234645 \tabularnewline
122 & 6267.71014515944 & 2918.64172806398 & 9616.7785622549 \tabularnewline
123 & 5003.14897287531 & 357.226935541589 & 9649.07101020902 \tabularnewline
124 & 3881.86964312591 & -2030.76421645863 & 9794.50350271045 \tabularnewline
125 & 3432.23776505043 & -5013.51891485745 & 11877.9944449583 \tabularnewline
126 & 2076.44756276271 & -6504.5470736362 & 10657.4421991616 \tabularnewline
127 & 1072.34672923839 & -7228.26457002416 & 9372.95802850094 \tabularnewline
128 & 473.159814726201 & -9112.27054401354 & 10058.5901734659 \tabularnewline
129 & -99.939694334223 & -11675.8337983459 & 11475.9544096774 \tabularnewline
130 & -804.32431355115 & -16424.6190394135 & 14815.9704123112 \tabularnewline
131 & -1260.71864670637 & -16358.914906471 & 13837.4776130582 \tabularnewline
132 & -1718.45378290862 & -17617.6304010264 & 14180.7228352091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123869&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]4037.43341672142[/C][C]2676.87650109639[/C][C]5397.99033234645[/C][/ROW]
[ROW][C]122[/C][C]6267.71014515944[/C][C]2918.64172806398[/C][C]9616.7785622549[/C][/ROW]
[ROW][C]123[/C][C]5003.14897287531[/C][C]357.226935541589[/C][C]9649.07101020902[/C][/ROW]
[ROW][C]124[/C][C]3881.86964312591[/C][C]-2030.76421645863[/C][C]9794.50350271045[/C][/ROW]
[ROW][C]125[/C][C]3432.23776505043[/C][C]-5013.51891485745[/C][C]11877.9944449583[/C][/ROW]
[ROW][C]126[/C][C]2076.44756276271[/C][C]-6504.5470736362[/C][C]10657.4421991616[/C][/ROW]
[ROW][C]127[/C][C]1072.34672923839[/C][C]-7228.26457002416[/C][C]9372.95802850094[/C][/ROW]
[ROW][C]128[/C][C]473.159814726201[/C][C]-9112.27054401354[/C][C]10058.5901734659[/C][/ROW]
[ROW][C]129[/C][C]-99.939694334223[/C][C]-11675.8337983459[/C][C]11475.9544096774[/C][/ROW]
[ROW][C]130[/C][C]-804.32431355115[/C][C]-16424.6190394135[/C][C]14815.9704123112[/C][/ROW]
[ROW][C]131[/C][C]-1260.71864670637[/C][C]-16358.914906471[/C][C]13837.4776130582[/C][/ROW]
[ROW][C]132[/C][C]-1718.45378290862[/C][C]-17617.6304010264[/C][C]14180.7228352091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123869&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123869&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
1214037.433416721422676.876501096395397.99033234645
1226267.710145159442918.641728063989616.7785622549
1235003.14897287531357.2269355415899649.07101020902
1243881.86964312591-2030.764216458639794.50350271045
1253432.23776505043-5013.5189148574511877.9944449583
1262076.44756276271-6504.547073636210657.4421991616
1271072.34672923839-7228.264570024169372.95802850094
128473.159814726201-9112.2705440135410058.5901734659
129-99.939694334223-11675.833798345911475.9544096774
130-804.32431355115-16424.619039413514815.9704123112
131-1260.71864670637-16358.91490647113837.4776130582
132-1718.45378290862-17617.630401026414180.7228352091



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')