Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 01 Apr 2015 14:57:15 +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/2015/Apr/01/t1427896734hbuhvawv9ild7p2.htm/, Retrieved Fri, 01 Nov 2024 00:14:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278512, Retrieved Fri, 01 Nov 2024 00:14:23 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-01 13:57:15] [aed7930eb470b174eb4d45bdfa14c6e0] [Current]
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Dataseries X:
2341
2115
2402
2180
2453
2507
2679
2622
2618
2648
2523
2473
2513
2466
2544
2537
2564
2582
2716
2904
2851
2932
2772
2811
2935
2783
3003
2995
3127
2985
3287
3236
3252
3228
2856
3176
3362
3036
3330
3251
3318
3238
3597
3708
3902
3745
3426
3526
3483
3458
3824
3696
3518
3814
3996
4136
4037
3915
3760
3955
4160
4115
4202
4018
4233
4029
4401
4645
4491
4379
4394
4472
4614
4160
4328
4202
4635
4542
4920
4774
4698
4916
4703
4616
4873
4375
4801
4427
4684
4648
5225
5174
5181
5266
4839
5032
5221
4658
5014
4980
4952
4946
5365
5456
5397
5436
4995
5019
5249
4799
5137
4979
4951
5265
5612
5572
5403
5373
5252
5437
5296
5011
5294
5335
5398
5396
5724
5898
5718
5625
5380
5488
5678
5224
5596
5184
5620
5531
5816
6086
6175
6112
5813
5740
5821
5294
5881
5589
5845
5706
6355
6404
6426
6375
5869
5994
6105
5792
6011
5968
6255
6208
6897
6814
6897
6596
6188
6406
6548
5842
6555
6424
6596
6645
7203
7128
7133
6778
6593
6591
6120
5612
6070
5983
6145
6303
6588
6640
6719
6575
6487
6510
6365
5844
5974
5880
6279
6342
6598
6801
6529
6369
6028
6187
6164
5866
6198
5898
6462
6063
6496
6678
6554
6513
6210
5928
6268
5582
5869
5764
6082
6062
6810
6727
6537
6175
6014
6109




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278512&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278512&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278512&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.397744939363288
beta0.0238591415702091
gamma0.272304466403946

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.397744939363288 \tabularnewline
beta & 0.0238591415702091 \tabularnewline
gamma & 0.272304466403946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278512&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]0.397744939363288[/C][/ROW]
[ROW][C]beta[/C][C]0.0238591415702091[/C][/ROW]
[ROW][C]gamma[/C][C]0.272304466403946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278512&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278512&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
alpha0.397744939363288
beta0.0238591415702091
gamma0.272304466403946







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325132426.1539803082786.8460196917304
1424662418.8265939397947.1734060602107
1525442511.3783753059432.6216246940608
1625372514.2785126481322.721487351871
1725642546.55895126817.4410487320001
1825822565.7881891578616.2118108421414
1927162903.03193362023-187.031933620229
2029042762.19593594007141.804064059928
2128512810.3958056233340.6041943766718
2229322855.0253052129376.9746947870658
2327722747.6007054361624.3992945638415
2428112713.4482259306997.5517740693144
2529352828.12933360847106.870666391532
2627832815.89168461258-32.8916846125844
2730032885.47260614347117.527393856526
2829952920.0111715154874.9888284845197
2931272977.63613955838149.363860441618
3029853053.9328130428-68.9328130428021
3132873377.3348608544-90.3348608544038
3232363328.85965602057-92.8596560205665
3332523264.29202413751-12.2920241375082
3432283299.60588636155-71.6058863615472
3528563105.24953591629-249.249535916285
3631762969.0434675386206.956532461396
3733623134.90884541064227.091154589363
3830363137.73271454327-101.732714543272
3933303214.56332601358115.43667398642
4032513237.8724067264313.1275932735707
4133183284.6298019048633.3701980951414
4232383274.90474284606-36.9047428460631
4335973633.08783101289-36.0878310128896
4437083602.39448388034105.605516119665
4539023627.68900138282274.310998617177
4637453772.89586312448-27.8958631244823
4734263536.68112372207-110.681123722069
4835263538.76134270811-12.7613427081128
4934833632.9209258201-149.920925820104
5034583416.4517350330841.548264966917
5138243602.3918610673221.6081389327
5236963646.1419534531549.8580465468526
5335183716.78591413501-198.785914135014
5438143598.28673569387215.713264306126
5539964106.71291994136-110.712919941361
5641364070.1159135004365.8840864995668
5740374106.66065858751-69.6606585875134
5839154061.52663469624-146.526634696239
5937603745.2951225631914.7048774368118
6039553815.747538424139.252461576001
6141603953.3222983632206.677701636795
6241153893.8538174567221.146182543303
6342024213.39993698089-11.399936980888
6440184127.33770916606-109.337709166065
6542334093.57943097285139.420569027149
6640294182.74743694785-153.747436947851
6744014529.39323079242-128.393230792417
6846454517.53171844363127.468281556374
6944914554.27987768886-63.2798776888567
7043794494.74621688756-115.746216887565
7143944189.6841016767204.315898323295
7244724368.45337189896103.546628101039
7346144515.198648246498.801351753601
7441604397.52193848647-237.521938486474
7543284506.6922753823-178.692275382303
7642024328.06194728928-126.061947289282
7746354326.22911399546308.770886004543
7845424429.93306478157112.066935218428
7949204922.58070034819-2.58070034819411
8047745010.21551573882-236.215515738822
8146984864.52837529273-166.528375292732
8249164748.64846879785167.351531202154
8347034588.33209615424114.667903845762
8446164718.50491514975-102.504915149751
8548734784.3683283049788.6316716950287
8643754591.22450330516-216.224503305158
8748014726.3587226533874.6412773466236
8844274647.20946948351-220.209469483511
8946844683.794632682360.205367317642413
9046484625.5465406761622.4534593238395
9152255071.5167869921153.483213007898
9251745179.64106174088-5.64106174088101
9351815131.3122575545849.687742445416
9452665154.92362605327111.07637394673
9548394944.39141794217-105.39141794217
9650324950.6201944525181.3798055474908
9752215128.4346838834292.5653161165756
9846584865.23354630024-207.233546300245
9950145068.63470057676-54.6347005767557
10049804877.18219408425102.817805915747
10149525092.23390353819-140.233903538192
10249464976.4922916841-30.4922916841033
10353655453.12020389934-88.1202038993433
10454565436.5827721814119.4172278185897
10553975402.06494854283-5.06494854283028
10654365410.7832381188525.2167618811454
10749955115.08029324659-120.080293246593
10850195144.79480857164-125.79480857164
10952495239.043222324119.95677767589132
11047994883.10405617411-84.1040561741138
11151375161.81068215016-24.8106821501606
11249794999.81196876191-20.8119687619055
11349515121.25502722972-170.255027229724
11452655005.25853265457259.741467345434
11556125598.0944460910113.9055539089895
11655725637.80355307504-65.8035530750358
11754035560.09880709269-157.098807092688
11853735508.59150521651-135.591505216514
11952525117.32121457344134.678785426559
12054375245.23365101096191.766348989042
12152965494.76178333773-198.761783337728
12250115025.25172504168-14.2517250416768
12352945351.33571289622-57.3357128962152
12453355169.23416497921165.765835020789
12553985344.1540548345753.8459451654344
12653965389.191157364446.80884263555618
12757245860.66178905235-136.661789052349
12858985825.5092470335372.4907529664652
12957185783.05053931487-65.0505393148696
13056255771.520655151-146.520655150995
13153805404.16124200936-24.161242009357
13254885479.022168799768.97783120023905
13356785590.3997934166787.6002065833318
13452245247.68557014407-23.6855701440709
13555965575.9152760404920.0847239595114
13651845454.09030441304-270.090304413045
13756205434.51139387097185.488606129032
13855315521.438156985379.56184301463327
13958165977.8134894893-161.813489489298
14060865964.54972627131121.450273728689
14161755913.51736047099261.482639529011
14261126017.8214745538194.1785254461929
14358135749.0960705473163.903929452692
14457405873.00132840477-133.001328404767
14558215949.14353302212-128.143533022121
14652945483.52960871041-189.529608710411
14758815762.28585130314118.714148696859
14855895622.83017835836-33.8301783583647
14958455781.6590222820763.3409777179286
15057065790.04647187597-84.0464718759695
15163556197.24965405008157.750345949918
15264046365.0619918907438.9380081092622
15364266299.73988643233126.260113567669
15463756320.9613959324354.0386040675721
15558696016.55576751575-147.555767515752
15659946023.34890557996-29.3489055799637
15761056144.45340783418-39.453407834184
15857925684.5866098555107.413390144497
15960116159.975367519-148.975367518998
16059685878.7010128791189.2989871208938
16162556113.40530385795141.594696142047
16262086127.358014384780.6419856153025
16368976677.04743433618219.952565663822
16468146859.8085464679-45.8085464678952
16568976772.62896349728124.371036502717
16665966780.64333805522-184.643338055224
16761886328.22089699377-140.22089699377
16864066362.6213494259443.37865057406
16965486520.2096894712827.7903105287232
17058426084.5050173328-242.5050173328
17165556393.50751014317161.492489856834
17264246264.31859343547159.681406564527
17365966551.0189165885944.9810834114105
17466456514.09313508171130.906864918288
17572037141.8315273628161.1684726371896
17671287220.48123749582-92.4812374958155
17771337139.91583614324-6.91583614323918
17867787039.1865542068-261.186554206796
17965936547.0496896746545.9503103253473
18065916691.24807806008-100.248078060078
18161206793.22968082843-673.229680828427
18256126027.8303865355-415.830386535496
18360706318.38103323749-248.381033237492
18459836021.9539285815-38.9539285815017
18561456186.19845451933-41.1984545193282
18663036117.52431626522185.475683734781
18765886707.0920541054-119.092054105399
18866406670.87587646113-30.8758764611293
18967196615.778456379103.221543621003
19065756512.0190702231862.9809297768234
19164876205.78716503087281.212834969135
19265106406.57984946486103.420150535137
19363656482.52768051927-117.527680519265
19458445974.32617547945-130.326175479447
19559746415.74049090333-441.74049090333
19658806073.29916901872-193.299169018723
19762796172.38624913211106.613750867892
19863426197.24040202899144.759597971013
19965986720.51389375184-122.51389375184
20068016694.99632761664106.003672383362
20165296714.67190611774-185.671906117738
20263696486.35498578622-117.354985786224
20360286143.15714468573-115.157144685727
20461876145.9960803207541.0039196792522
20561646151.8223351882812.1776648117184
20658665704.38667834887161.61332165113
20761986193.773433272674.22656672732592
20858986067.22475901804-169.224759018041
20964626225.20677854992236.793221450082
21060636307.80866494699-244.808664946985
21164966623.94176589846-127.941765898465
21266786629.1902252965148.8097747034872
21365546574.87850450631-20.878504506305
21465136421.4712695815791.5287304184267
21562106159.1281170534250.8718829465788
21659286255.64818273071-327.648182730709
21762686107.66674354819160.333256451807
21855825741.36940883944-159.369408839439
21958696064.90032878286-195.900328782857
22057645829.3492755742-65.3492755742009
22160826081.129662944610.870337055393065
22260625987.0029720068174.9970279931913
22368106433.85136208081376.148637919195
22467276668.8594628772458.1405371227593
22565376606.34630939124-69.3463093912396
22661756451.24607835682-276.246078356821
22760146038.48023861495-24.4802386149495
22861096037.1397629051971.8602370948083

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2513 & 2426.15398030827 & 86.8460196917304 \tabularnewline
14 & 2466 & 2418.82659393979 & 47.1734060602107 \tabularnewline
15 & 2544 & 2511.37837530594 & 32.6216246940608 \tabularnewline
16 & 2537 & 2514.27851264813 & 22.721487351871 \tabularnewline
17 & 2564 & 2546.558951268 & 17.4410487320001 \tabularnewline
18 & 2582 & 2565.78818915786 & 16.2118108421414 \tabularnewline
19 & 2716 & 2903.03193362023 & -187.031933620229 \tabularnewline
20 & 2904 & 2762.19593594007 & 141.804064059928 \tabularnewline
21 & 2851 & 2810.39580562333 & 40.6041943766718 \tabularnewline
22 & 2932 & 2855.02530521293 & 76.9746947870658 \tabularnewline
23 & 2772 & 2747.60070543616 & 24.3992945638415 \tabularnewline
24 & 2811 & 2713.44822593069 & 97.5517740693144 \tabularnewline
25 & 2935 & 2828.12933360847 & 106.870666391532 \tabularnewline
26 & 2783 & 2815.89168461258 & -32.8916846125844 \tabularnewline
27 & 3003 & 2885.47260614347 & 117.527393856526 \tabularnewline
28 & 2995 & 2920.01117151548 & 74.9888284845197 \tabularnewline
29 & 3127 & 2977.63613955838 & 149.363860441618 \tabularnewline
30 & 2985 & 3053.9328130428 & -68.9328130428021 \tabularnewline
31 & 3287 & 3377.3348608544 & -90.3348608544038 \tabularnewline
32 & 3236 & 3328.85965602057 & -92.8596560205665 \tabularnewline
33 & 3252 & 3264.29202413751 & -12.2920241375082 \tabularnewline
34 & 3228 & 3299.60588636155 & -71.6058863615472 \tabularnewline
35 & 2856 & 3105.24953591629 & -249.249535916285 \tabularnewline
36 & 3176 & 2969.0434675386 & 206.956532461396 \tabularnewline
37 & 3362 & 3134.90884541064 & 227.091154589363 \tabularnewline
38 & 3036 & 3137.73271454327 & -101.732714543272 \tabularnewline
39 & 3330 & 3214.56332601358 & 115.43667398642 \tabularnewline
40 & 3251 & 3237.87240672643 & 13.1275932735707 \tabularnewline
41 & 3318 & 3284.62980190486 & 33.3701980951414 \tabularnewline
42 & 3238 & 3274.90474284606 & -36.9047428460631 \tabularnewline
43 & 3597 & 3633.08783101289 & -36.0878310128896 \tabularnewline
44 & 3708 & 3602.39448388034 & 105.605516119665 \tabularnewline
45 & 3902 & 3627.68900138282 & 274.310998617177 \tabularnewline
46 & 3745 & 3772.89586312448 & -27.8958631244823 \tabularnewline
47 & 3426 & 3536.68112372207 & -110.681123722069 \tabularnewline
48 & 3526 & 3538.76134270811 & -12.7613427081128 \tabularnewline
49 & 3483 & 3632.9209258201 & -149.920925820104 \tabularnewline
50 & 3458 & 3416.45173503308 & 41.548264966917 \tabularnewline
51 & 3824 & 3602.3918610673 & 221.6081389327 \tabularnewline
52 & 3696 & 3646.14195345315 & 49.8580465468526 \tabularnewline
53 & 3518 & 3716.78591413501 & -198.785914135014 \tabularnewline
54 & 3814 & 3598.28673569387 & 215.713264306126 \tabularnewline
55 & 3996 & 4106.71291994136 & -110.712919941361 \tabularnewline
56 & 4136 & 4070.11591350043 & 65.8840864995668 \tabularnewline
57 & 4037 & 4106.66065858751 & -69.6606585875134 \tabularnewline
58 & 3915 & 4061.52663469624 & -146.526634696239 \tabularnewline
59 & 3760 & 3745.29512256319 & 14.7048774368118 \tabularnewline
60 & 3955 & 3815.747538424 & 139.252461576001 \tabularnewline
61 & 4160 & 3953.3222983632 & 206.677701636795 \tabularnewline
62 & 4115 & 3893.8538174567 & 221.146182543303 \tabularnewline
63 & 4202 & 4213.39993698089 & -11.399936980888 \tabularnewline
64 & 4018 & 4127.33770916606 & -109.337709166065 \tabularnewline
65 & 4233 & 4093.57943097285 & 139.420569027149 \tabularnewline
66 & 4029 & 4182.74743694785 & -153.747436947851 \tabularnewline
67 & 4401 & 4529.39323079242 & -128.393230792417 \tabularnewline
68 & 4645 & 4517.53171844363 & 127.468281556374 \tabularnewline
69 & 4491 & 4554.27987768886 & -63.2798776888567 \tabularnewline
70 & 4379 & 4494.74621688756 & -115.746216887565 \tabularnewline
71 & 4394 & 4189.6841016767 & 204.315898323295 \tabularnewline
72 & 4472 & 4368.45337189896 & 103.546628101039 \tabularnewline
73 & 4614 & 4515.1986482464 & 98.801351753601 \tabularnewline
74 & 4160 & 4397.52193848647 & -237.521938486474 \tabularnewline
75 & 4328 & 4506.6922753823 & -178.692275382303 \tabularnewline
76 & 4202 & 4328.06194728928 & -126.061947289282 \tabularnewline
77 & 4635 & 4326.22911399546 & 308.770886004543 \tabularnewline
78 & 4542 & 4429.93306478157 & 112.066935218428 \tabularnewline
79 & 4920 & 4922.58070034819 & -2.58070034819411 \tabularnewline
80 & 4774 & 5010.21551573882 & -236.215515738822 \tabularnewline
81 & 4698 & 4864.52837529273 & -166.528375292732 \tabularnewline
82 & 4916 & 4748.64846879785 & 167.351531202154 \tabularnewline
83 & 4703 & 4588.33209615424 & 114.667903845762 \tabularnewline
84 & 4616 & 4718.50491514975 & -102.504915149751 \tabularnewline
85 & 4873 & 4784.36832830497 & 88.6316716950287 \tabularnewline
86 & 4375 & 4591.22450330516 & -216.224503305158 \tabularnewline
87 & 4801 & 4726.35872265338 & 74.6412773466236 \tabularnewline
88 & 4427 & 4647.20946948351 & -220.209469483511 \tabularnewline
89 & 4684 & 4683.79463268236 & 0.205367317642413 \tabularnewline
90 & 4648 & 4625.54654067616 & 22.4534593238395 \tabularnewline
91 & 5225 & 5071.5167869921 & 153.483213007898 \tabularnewline
92 & 5174 & 5179.64106174088 & -5.64106174088101 \tabularnewline
93 & 5181 & 5131.31225755458 & 49.687742445416 \tabularnewline
94 & 5266 & 5154.92362605327 & 111.07637394673 \tabularnewline
95 & 4839 & 4944.39141794217 & -105.39141794217 \tabularnewline
96 & 5032 & 4950.62019445251 & 81.3798055474908 \tabularnewline
97 & 5221 & 5128.43468388342 & 92.5653161165756 \tabularnewline
98 & 4658 & 4865.23354630024 & -207.233546300245 \tabularnewline
99 & 5014 & 5068.63470057676 & -54.6347005767557 \tabularnewline
100 & 4980 & 4877.18219408425 & 102.817805915747 \tabularnewline
101 & 4952 & 5092.23390353819 & -140.233903538192 \tabularnewline
102 & 4946 & 4976.4922916841 & -30.4922916841033 \tabularnewline
103 & 5365 & 5453.12020389934 & -88.1202038993433 \tabularnewline
104 & 5456 & 5436.58277218141 & 19.4172278185897 \tabularnewline
105 & 5397 & 5402.06494854283 & -5.06494854283028 \tabularnewline
106 & 5436 & 5410.78323811885 & 25.2167618811454 \tabularnewline
107 & 4995 & 5115.08029324659 & -120.080293246593 \tabularnewline
108 & 5019 & 5144.79480857164 & -125.79480857164 \tabularnewline
109 & 5249 & 5239.04322232411 & 9.95677767589132 \tabularnewline
110 & 4799 & 4883.10405617411 & -84.1040561741138 \tabularnewline
111 & 5137 & 5161.81068215016 & -24.8106821501606 \tabularnewline
112 & 4979 & 4999.81196876191 & -20.8119687619055 \tabularnewline
113 & 4951 & 5121.25502722972 & -170.255027229724 \tabularnewline
114 & 5265 & 5005.25853265457 & 259.741467345434 \tabularnewline
115 & 5612 & 5598.09444609101 & 13.9055539089895 \tabularnewline
116 & 5572 & 5637.80355307504 & -65.8035530750358 \tabularnewline
117 & 5403 & 5560.09880709269 & -157.098807092688 \tabularnewline
118 & 5373 & 5508.59150521651 & -135.591505216514 \tabularnewline
119 & 5252 & 5117.32121457344 & 134.678785426559 \tabularnewline
120 & 5437 & 5245.23365101096 & 191.766348989042 \tabularnewline
121 & 5296 & 5494.76178333773 & -198.761783337728 \tabularnewline
122 & 5011 & 5025.25172504168 & -14.2517250416768 \tabularnewline
123 & 5294 & 5351.33571289622 & -57.3357128962152 \tabularnewline
124 & 5335 & 5169.23416497921 & 165.765835020789 \tabularnewline
125 & 5398 & 5344.15405483457 & 53.8459451654344 \tabularnewline
126 & 5396 & 5389.19115736444 & 6.80884263555618 \tabularnewline
127 & 5724 & 5860.66178905235 & -136.661789052349 \tabularnewline
128 & 5898 & 5825.50924703353 & 72.4907529664652 \tabularnewline
129 & 5718 & 5783.05053931487 & -65.0505393148696 \tabularnewline
130 & 5625 & 5771.520655151 & -146.520655150995 \tabularnewline
131 & 5380 & 5404.16124200936 & -24.161242009357 \tabularnewline
132 & 5488 & 5479.02216879976 & 8.97783120023905 \tabularnewline
133 & 5678 & 5590.39979341667 & 87.6002065833318 \tabularnewline
134 & 5224 & 5247.68557014407 & -23.6855701440709 \tabularnewline
135 & 5596 & 5575.91527604049 & 20.0847239595114 \tabularnewline
136 & 5184 & 5454.09030441304 & -270.090304413045 \tabularnewline
137 & 5620 & 5434.51139387097 & 185.488606129032 \tabularnewline
138 & 5531 & 5521.43815698537 & 9.56184301463327 \tabularnewline
139 & 5816 & 5977.8134894893 & -161.813489489298 \tabularnewline
140 & 6086 & 5964.54972627131 & 121.450273728689 \tabularnewline
141 & 6175 & 5913.51736047099 & 261.482639529011 \tabularnewline
142 & 6112 & 6017.82147455381 & 94.1785254461929 \tabularnewline
143 & 5813 & 5749.09607054731 & 63.903929452692 \tabularnewline
144 & 5740 & 5873.00132840477 & -133.001328404767 \tabularnewline
145 & 5821 & 5949.14353302212 & -128.143533022121 \tabularnewline
146 & 5294 & 5483.52960871041 & -189.529608710411 \tabularnewline
147 & 5881 & 5762.28585130314 & 118.714148696859 \tabularnewline
148 & 5589 & 5622.83017835836 & -33.8301783583647 \tabularnewline
149 & 5845 & 5781.65902228207 & 63.3409777179286 \tabularnewline
150 & 5706 & 5790.04647187597 & -84.0464718759695 \tabularnewline
151 & 6355 & 6197.24965405008 & 157.750345949918 \tabularnewline
152 & 6404 & 6365.06199189074 & 38.9380081092622 \tabularnewline
153 & 6426 & 6299.73988643233 & 126.260113567669 \tabularnewline
154 & 6375 & 6320.96139593243 & 54.0386040675721 \tabularnewline
155 & 5869 & 6016.55576751575 & -147.555767515752 \tabularnewline
156 & 5994 & 6023.34890557996 & -29.3489055799637 \tabularnewline
157 & 6105 & 6144.45340783418 & -39.453407834184 \tabularnewline
158 & 5792 & 5684.5866098555 & 107.413390144497 \tabularnewline
159 & 6011 & 6159.975367519 & -148.975367518998 \tabularnewline
160 & 5968 & 5878.70101287911 & 89.2989871208938 \tabularnewline
161 & 6255 & 6113.40530385795 & 141.594696142047 \tabularnewline
162 & 6208 & 6127.3580143847 & 80.6419856153025 \tabularnewline
163 & 6897 & 6677.04743433618 & 219.952565663822 \tabularnewline
164 & 6814 & 6859.8085464679 & -45.8085464678952 \tabularnewline
165 & 6897 & 6772.62896349728 & 124.371036502717 \tabularnewline
166 & 6596 & 6780.64333805522 & -184.643338055224 \tabularnewline
167 & 6188 & 6328.22089699377 & -140.22089699377 \tabularnewline
168 & 6406 & 6362.62134942594 & 43.37865057406 \tabularnewline
169 & 6548 & 6520.20968947128 & 27.7903105287232 \tabularnewline
170 & 5842 & 6084.5050173328 & -242.5050173328 \tabularnewline
171 & 6555 & 6393.50751014317 & 161.492489856834 \tabularnewline
172 & 6424 & 6264.31859343547 & 159.681406564527 \tabularnewline
173 & 6596 & 6551.01891658859 & 44.9810834114105 \tabularnewline
174 & 6645 & 6514.09313508171 & 130.906864918288 \tabularnewline
175 & 7203 & 7141.83152736281 & 61.1684726371896 \tabularnewline
176 & 7128 & 7220.48123749582 & -92.4812374958155 \tabularnewline
177 & 7133 & 7139.91583614324 & -6.91583614323918 \tabularnewline
178 & 6778 & 7039.1865542068 & -261.186554206796 \tabularnewline
179 & 6593 & 6547.04968967465 & 45.9503103253473 \tabularnewline
180 & 6591 & 6691.24807806008 & -100.248078060078 \tabularnewline
181 & 6120 & 6793.22968082843 & -673.229680828427 \tabularnewline
182 & 5612 & 6027.8303865355 & -415.830386535496 \tabularnewline
183 & 6070 & 6318.38103323749 & -248.381033237492 \tabularnewline
184 & 5983 & 6021.9539285815 & -38.9539285815017 \tabularnewline
185 & 6145 & 6186.19845451933 & -41.1984545193282 \tabularnewline
186 & 6303 & 6117.52431626522 & 185.475683734781 \tabularnewline
187 & 6588 & 6707.0920541054 & -119.092054105399 \tabularnewline
188 & 6640 & 6670.87587646113 & -30.8758764611293 \tabularnewline
189 & 6719 & 6615.778456379 & 103.221543621003 \tabularnewline
190 & 6575 & 6512.01907022318 & 62.9809297768234 \tabularnewline
191 & 6487 & 6205.78716503087 & 281.212834969135 \tabularnewline
192 & 6510 & 6406.57984946486 & 103.420150535137 \tabularnewline
193 & 6365 & 6482.52768051927 & -117.527680519265 \tabularnewline
194 & 5844 & 5974.32617547945 & -130.326175479447 \tabularnewline
195 & 5974 & 6415.74049090333 & -441.74049090333 \tabularnewline
196 & 5880 & 6073.29916901872 & -193.299169018723 \tabularnewline
197 & 6279 & 6172.38624913211 & 106.613750867892 \tabularnewline
198 & 6342 & 6197.24040202899 & 144.759597971013 \tabularnewline
199 & 6598 & 6720.51389375184 & -122.51389375184 \tabularnewline
200 & 6801 & 6694.99632761664 & 106.003672383362 \tabularnewline
201 & 6529 & 6714.67190611774 & -185.671906117738 \tabularnewline
202 & 6369 & 6486.35498578622 & -117.354985786224 \tabularnewline
203 & 6028 & 6143.15714468573 & -115.157144685727 \tabularnewline
204 & 6187 & 6145.99608032075 & 41.0039196792522 \tabularnewline
205 & 6164 & 6151.82233518828 & 12.1776648117184 \tabularnewline
206 & 5866 & 5704.38667834887 & 161.61332165113 \tabularnewline
207 & 6198 & 6193.77343327267 & 4.22656672732592 \tabularnewline
208 & 5898 & 6067.22475901804 & -169.224759018041 \tabularnewline
209 & 6462 & 6225.20677854992 & 236.793221450082 \tabularnewline
210 & 6063 & 6307.80866494699 & -244.808664946985 \tabularnewline
211 & 6496 & 6623.94176589846 & -127.941765898465 \tabularnewline
212 & 6678 & 6629.19022529651 & 48.8097747034872 \tabularnewline
213 & 6554 & 6574.87850450631 & -20.878504506305 \tabularnewline
214 & 6513 & 6421.47126958157 & 91.5287304184267 \tabularnewline
215 & 6210 & 6159.12811705342 & 50.8718829465788 \tabularnewline
216 & 5928 & 6255.64818273071 & -327.648182730709 \tabularnewline
217 & 6268 & 6107.66674354819 & 160.333256451807 \tabularnewline
218 & 5582 & 5741.36940883944 & -159.369408839439 \tabularnewline
219 & 5869 & 6064.90032878286 & -195.900328782857 \tabularnewline
220 & 5764 & 5829.3492755742 & -65.3492755742009 \tabularnewline
221 & 6082 & 6081.12966294461 & 0.870337055393065 \tabularnewline
222 & 6062 & 5987.00297200681 & 74.9970279931913 \tabularnewline
223 & 6810 & 6433.85136208081 & 376.148637919195 \tabularnewline
224 & 6727 & 6668.85946287724 & 58.1405371227593 \tabularnewline
225 & 6537 & 6606.34630939124 & -69.3463093912396 \tabularnewline
226 & 6175 & 6451.24607835682 & -276.246078356821 \tabularnewline
227 & 6014 & 6038.48023861495 & -24.4802386149495 \tabularnewline
228 & 6109 & 6037.13976290519 & 71.8602370948083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278512&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]2513[/C][C]2426.15398030827[/C][C]86.8460196917304[/C][/ROW]
[ROW][C]14[/C][C]2466[/C][C]2418.82659393979[/C][C]47.1734060602107[/C][/ROW]
[ROW][C]15[/C][C]2544[/C][C]2511.37837530594[/C][C]32.6216246940608[/C][/ROW]
[ROW][C]16[/C][C]2537[/C][C]2514.27851264813[/C][C]22.721487351871[/C][/ROW]
[ROW][C]17[/C][C]2564[/C][C]2546.558951268[/C][C]17.4410487320001[/C][/ROW]
[ROW][C]18[/C][C]2582[/C][C]2565.78818915786[/C][C]16.2118108421414[/C][/ROW]
[ROW][C]19[/C][C]2716[/C][C]2903.03193362023[/C][C]-187.031933620229[/C][/ROW]
[ROW][C]20[/C][C]2904[/C][C]2762.19593594007[/C][C]141.804064059928[/C][/ROW]
[ROW][C]21[/C][C]2851[/C][C]2810.39580562333[/C][C]40.6041943766718[/C][/ROW]
[ROW][C]22[/C][C]2932[/C][C]2855.02530521293[/C][C]76.9746947870658[/C][/ROW]
[ROW][C]23[/C][C]2772[/C][C]2747.60070543616[/C][C]24.3992945638415[/C][/ROW]
[ROW][C]24[/C][C]2811[/C][C]2713.44822593069[/C][C]97.5517740693144[/C][/ROW]
[ROW][C]25[/C][C]2935[/C][C]2828.12933360847[/C][C]106.870666391532[/C][/ROW]
[ROW][C]26[/C][C]2783[/C][C]2815.89168461258[/C][C]-32.8916846125844[/C][/ROW]
[ROW][C]27[/C][C]3003[/C][C]2885.47260614347[/C][C]117.527393856526[/C][/ROW]
[ROW][C]28[/C][C]2995[/C][C]2920.01117151548[/C][C]74.9888284845197[/C][/ROW]
[ROW][C]29[/C][C]3127[/C][C]2977.63613955838[/C][C]149.363860441618[/C][/ROW]
[ROW][C]30[/C][C]2985[/C][C]3053.9328130428[/C][C]-68.9328130428021[/C][/ROW]
[ROW][C]31[/C][C]3287[/C][C]3377.3348608544[/C][C]-90.3348608544038[/C][/ROW]
[ROW][C]32[/C][C]3236[/C][C]3328.85965602057[/C][C]-92.8596560205665[/C][/ROW]
[ROW][C]33[/C][C]3252[/C][C]3264.29202413751[/C][C]-12.2920241375082[/C][/ROW]
[ROW][C]34[/C][C]3228[/C][C]3299.60588636155[/C][C]-71.6058863615472[/C][/ROW]
[ROW][C]35[/C][C]2856[/C][C]3105.24953591629[/C][C]-249.249535916285[/C][/ROW]
[ROW][C]36[/C][C]3176[/C][C]2969.0434675386[/C][C]206.956532461396[/C][/ROW]
[ROW][C]37[/C][C]3362[/C][C]3134.90884541064[/C][C]227.091154589363[/C][/ROW]
[ROW][C]38[/C][C]3036[/C][C]3137.73271454327[/C][C]-101.732714543272[/C][/ROW]
[ROW][C]39[/C][C]3330[/C][C]3214.56332601358[/C][C]115.43667398642[/C][/ROW]
[ROW][C]40[/C][C]3251[/C][C]3237.87240672643[/C][C]13.1275932735707[/C][/ROW]
[ROW][C]41[/C][C]3318[/C][C]3284.62980190486[/C][C]33.3701980951414[/C][/ROW]
[ROW][C]42[/C][C]3238[/C][C]3274.90474284606[/C][C]-36.9047428460631[/C][/ROW]
[ROW][C]43[/C][C]3597[/C][C]3633.08783101289[/C][C]-36.0878310128896[/C][/ROW]
[ROW][C]44[/C][C]3708[/C][C]3602.39448388034[/C][C]105.605516119665[/C][/ROW]
[ROW][C]45[/C][C]3902[/C][C]3627.68900138282[/C][C]274.310998617177[/C][/ROW]
[ROW][C]46[/C][C]3745[/C][C]3772.89586312448[/C][C]-27.8958631244823[/C][/ROW]
[ROW][C]47[/C][C]3426[/C][C]3536.68112372207[/C][C]-110.681123722069[/C][/ROW]
[ROW][C]48[/C][C]3526[/C][C]3538.76134270811[/C][C]-12.7613427081128[/C][/ROW]
[ROW][C]49[/C][C]3483[/C][C]3632.9209258201[/C][C]-149.920925820104[/C][/ROW]
[ROW][C]50[/C][C]3458[/C][C]3416.45173503308[/C][C]41.548264966917[/C][/ROW]
[ROW][C]51[/C][C]3824[/C][C]3602.3918610673[/C][C]221.6081389327[/C][/ROW]
[ROW][C]52[/C][C]3696[/C][C]3646.14195345315[/C][C]49.8580465468526[/C][/ROW]
[ROW][C]53[/C][C]3518[/C][C]3716.78591413501[/C][C]-198.785914135014[/C][/ROW]
[ROW][C]54[/C][C]3814[/C][C]3598.28673569387[/C][C]215.713264306126[/C][/ROW]
[ROW][C]55[/C][C]3996[/C][C]4106.71291994136[/C][C]-110.712919941361[/C][/ROW]
[ROW][C]56[/C][C]4136[/C][C]4070.11591350043[/C][C]65.8840864995668[/C][/ROW]
[ROW][C]57[/C][C]4037[/C][C]4106.66065858751[/C][C]-69.6606585875134[/C][/ROW]
[ROW][C]58[/C][C]3915[/C][C]4061.52663469624[/C][C]-146.526634696239[/C][/ROW]
[ROW][C]59[/C][C]3760[/C][C]3745.29512256319[/C][C]14.7048774368118[/C][/ROW]
[ROW][C]60[/C][C]3955[/C][C]3815.747538424[/C][C]139.252461576001[/C][/ROW]
[ROW][C]61[/C][C]4160[/C][C]3953.3222983632[/C][C]206.677701636795[/C][/ROW]
[ROW][C]62[/C][C]4115[/C][C]3893.8538174567[/C][C]221.146182543303[/C][/ROW]
[ROW][C]63[/C][C]4202[/C][C]4213.39993698089[/C][C]-11.399936980888[/C][/ROW]
[ROW][C]64[/C][C]4018[/C][C]4127.33770916606[/C][C]-109.337709166065[/C][/ROW]
[ROW][C]65[/C][C]4233[/C][C]4093.57943097285[/C][C]139.420569027149[/C][/ROW]
[ROW][C]66[/C][C]4029[/C][C]4182.74743694785[/C][C]-153.747436947851[/C][/ROW]
[ROW][C]67[/C][C]4401[/C][C]4529.39323079242[/C][C]-128.393230792417[/C][/ROW]
[ROW][C]68[/C][C]4645[/C][C]4517.53171844363[/C][C]127.468281556374[/C][/ROW]
[ROW][C]69[/C][C]4491[/C][C]4554.27987768886[/C][C]-63.2798776888567[/C][/ROW]
[ROW][C]70[/C][C]4379[/C][C]4494.74621688756[/C][C]-115.746216887565[/C][/ROW]
[ROW][C]71[/C][C]4394[/C][C]4189.6841016767[/C][C]204.315898323295[/C][/ROW]
[ROW][C]72[/C][C]4472[/C][C]4368.45337189896[/C][C]103.546628101039[/C][/ROW]
[ROW][C]73[/C][C]4614[/C][C]4515.1986482464[/C][C]98.801351753601[/C][/ROW]
[ROW][C]74[/C][C]4160[/C][C]4397.52193848647[/C][C]-237.521938486474[/C][/ROW]
[ROW][C]75[/C][C]4328[/C][C]4506.6922753823[/C][C]-178.692275382303[/C][/ROW]
[ROW][C]76[/C][C]4202[/C][C]4328.06194728928[/C][C]-126.061947289282[/C][/ROW]
[ROW][C]77[/C][C]4635[/C][C]4326.22911399546[/C][C]308.770886004543[/C][/ROW]
[ROW][C]78[/C][C]4542[/C][C]4429.93306478157[/C][C]112.066935218428[/C][/ROW]
[ROW][C]79[/C][C]4920[/C][C]4922.58070034819[/C][C]-2.58070034819411[/C][/ROW]
[ROW][C]80[/C][C]4774[/C][C]5010.21551573882[/C][C]-236.215515738822[/C][/ROW]
[ROW][C]81[/C][C]4698[/C][C]4864.52837529273[/C][C]-166.528375292732[/C][/ROW]
[ROW][C]82[/C][C]4916[/C][C]4748.64846879785[/C][C]167.351531202154[/C][/ROW]
[ROW][C]83[/C][C]4703[/C][C]4588.33209615424[/C][C]114.667903845762[/C][/ROW]
[ROW][C]84[/C][C]4616[/C][C]4718.50491514975[/C][C]-102.504915149751[/C][/ROW]
[ROW][C]85[/C][C]4873[/C][C]4784.36832830497[/C][C]88.6316716950287[/C][/ROW]
[ROW][C]86[/C][C]4375[/C][C]4591.22450330516[/C][C]-216.224503305158[/C][/ROW]
[ROW][C]87[/C][C]4801[/C][C]4726.35872265338[/C][C]74.6412773466236[/C][/ROW]
[ROW][C]88[/C][C]4427[/C][C]4647.20946948351[/C][C]-220.209469483511[/C][/ROW]
[ROW][C]89[/C][C]4684[/C][C]4683.79463268236[/C][C]0.205367317642413[/C][/ROW]
[ROW][C]90[/C][C]4648[/C][C]4625.54654067616[/C][C]22.4534593238395[/C][/ROW]
[ROW][C]91[/C][C]5225[/C][C]5071.5167869921[/C][C]153.483213007898[/C][/ROW]
[ROW][C]92[/C][C]5174[/C][C]5179.64106174088[/C][C]-5.64106174088101[/C][/ROW]
[ROW][C]93[/C][C]5181[/C][C]5131.31225755458[/C][C]49.687742445416[/C][/ROW]
[ROW][C]94[/C][C]5266[/C][C]5154.92362605327[/C][C]111.07637394673[/C][/ROW]
[ROW][C]95[/C][C]4839[/C][C]4944.39141794217[/C][C]-105.39141794217[/C][/ROW]
[ROW][C]96[/C][C]5032[/C][C]4950.62019445251[/C][C]81.3798055474908[/C][/ROW]
[ROW][C]97[/C][C]5221[/C][C]5128.43468388342[/C][C]92.5653161165756[/C][/ROW]
[ROW][C]98[/C][C]4658[/C][C]4865.23354630024[/C][C]-207.233546300245[/C][/ROW]
[ROW][C]99[/C][C]5014[/C][C]5068.63470057676[/C][C]-54.6347005767557[/C][/ROW]
[ROW][C]100[/C][C]4980[/C][C]4877.18219408425[/C][C]102.817805915747[/C][/ROW]
[ROW][C]101[/C][C]4952[/C][C]5092.23390353819[/C][C]-140.233903538192[/C][/ROW]
[ROW][C]102[/C][C]4946[/C][C]4976.4922916841[/C][C]-30.4922916841033[/C][/ROW]
[ROW][C]103[/C][C]5365[/C][C]5453.12020389934[/C][C]-88.1202038993433[/C][/ROW]
[ROW][C]104[/C][C]5456[/C][C]5436.58277218141[/C][C]19.4172278185897[/C][/ROW]
[ROW][C]105[/C][C]5397[/C][C]5402.06494854283[/C][C]-5.06494854283028[/C][/ROW]
[ROW][C]106[/C][C]5436[/C][C]5410.78323811885[/C][C]25.2167618811454[/C][/ROW]
[ROW][C]107[/C][C]4995[/C][C]5115.08029324659[/C][C]-120.080293246593[/C][/ROW]
[ROW][C]108[/C][C]5019[/C][C]5144.79480857164[/C][C]-125.79480857164[/C][/ROW]
[ROW][C]109[/C][C]5249[/C][C]5239.04322232411[/C][C]9.95677767589132[/C][/ROW]
[ROW][C]110[/C][C]4799[/C][C]4883.10405617411[/C][C]-84.1040561741138[/C][/ROW]
[ROW][C]111[/C][C]5137[/C][C]5161.81068215016[/C][C]-24.8106821501606[/C][/ROW]
[ROW][C]112[/C][C]4979[/C][C]4999.81196876191[/C][C]-20.8119687619055[/C][/ROW]
[ROW][C]113[/C][C]4951[/C][C]5121.25502722972[/C][C]-170.255027229724[/C][/ROW]
[ROW][C]114[/C][C]5265[/C][C]5005.25853265457[/C][C]259.741467345434[/C][/ROW]
[ROW][C]115[/C][C]5612[/C][C]5598.09444609101[/C][C]13.9055539089895[/C][/ROW]
[ROW][C]116[/C][C]5572[/C][C]5637.80355307504[/C][C]-65.8035530750358[/C][/ROW]
[ROW][C]117[/C][C]5403[/C][C]5560.09880709269[/C][C]-157.098807092688[/C][/ROW]
[ROW][C]118[/C][C]5373[/C][C]5508.59150521651[/C][C]-135.591505216514[/C][/ROW]
[ROW][C]119[/C][C]5252[/C][C]5117.32121457344[/C][C]134.678785426559[/C][/ROW]
[ROW][C]120[/C][C]5437[/C][C]5245.23365101096[/C][C]191.766348989042[/C][/ROW]
[ROW][C]121[/C][C]5296[/C][C]5494.76178333773[/C][C]-198.761783337728[/C][/ROW]
[ROW][C]122[/C][C]5011[/C][C]5025.25172504168[/C][C]-14.2517250416768[/C][/ROW]
[ROW][C]123[/C][C]5294[/C][C]5351.33571289622[/C][C]-57.3357128962152[/C][/ROW]
[ROW][C]124[/C][C]5335[/C][C]5169.23416497921[/C][C]165.765835020789[/C][/ROW]
[ROW][C]125[/C][C]5398[/C][C]5344.15405483457[/C][C]53.8459451654344[/C][/ROW]
[ROW][C]126[/C][C]5396[/C][C]5389.19115736444[/C][C]6.80884263555618[/C][/ROW]
[ROW][C]127[/C][C]5724[/C][C]5860.66178905235[/C][C]-136.661789052349[/C][/ROW]
[ROW][C]128[/C][C]5898[/C][C]5825.50924703353[/C][C]72.4907529664652[/C][/ROW]
[ROW][C]129[/C][C]5718[/C][C]5783.05053931487[/C][C]-65.0505393148696[/C][/ROW]
[ROW][C]130[/C][C]5625[/C][C]5771.520655151[/C][C]-146.520655150995[/C][/ROW]
[ROW][C]131[/C][C]5380[/C][C]5404.16124200936[/C][C]-24.161242009357[/C][/ROW]
[ROW][C]132[/C][C]5488[/C][C]5479.02216879976[/C][C]8.97783120023905[/C][/ROW]
[ROW][C]133[/C][C]5678[/C][C]5590.39979341667[/C][C]87.6002065833318[/C][/ROW]
[ROW][C]134[/C][C]5224[/C][C]5247.68557014407[/C][C]-23.6855701440709[/C][/ROW]
[ROW][C]135[/C][C]5596[/C][C]5575.91527604049[/C][C]20.0847239595114[/C][/ROW]
[ROW][C]136[/C][C]5184[/C][C]5454.09030441304[/C][C]-270.090304413045[/C][/ROW]
[ROW][C]137[/C][C]5620[/C][C]5434.51139387097[/C][C]185.488606129032[/C][/ROW]
[ROW][C]138[/C][C]5531[/C][C]5521.43815698537[/C][C]9.56184301463327[/C][/ROW]
[ROW][C]139[/C][C]5816[/C][C]5977.8134894893[/C][C]-161.813489489298[/C][/ROW]
[ROW][C]140[/C][C]6086[/C][C]5964.54972627131[/C][C]121.450273728689[/C][/ROW]
[ROW][C]141[/C][C]6175[/C][C]5913.51736047099[/C][C]261.482639529011[/C][/ROW]
[ROW][C]142[/C][C]6112[/C][C]6017.82147455381[/C][C]94.1785254461929[/C][/ROW]
[ROW][C]143[/C][C]5813[/C][C]5749.09607054731[/C][C]63.903929452692[/C][/ROW]
[ROW][C]144[/C][C]5740[/C][C]5873.00132840477[/C][C]-133.001328404767[/C][/ROW]
[ROW][C]145[/C][C]5821[/C][C]5949.14353302212[/C][C]-128.143533022121[/C][/ROW]
[ROW][C]146[/C][C]5294[/C][C]5483.52960871041[/C][C]-189.529608710411[/C][/ROW]
[ROW][C]147[/C][C]5881[/C][C]5762.28585130314[/C][C]118.714148696859[/C][/ROW]
[ROW][C]148[/C][C]5589[/C][C]5622.83017835836[/C][C]-33.8301783583647[/C][/ROW]
[ROW][C]149[/C][C]5845[/C][C]5781.65902228207[/C][C]63.3409777179286[/C][/ROW]
[ROW][C]150[/C][C]5706[/C][C]5790.04647187597[/C][C]-84.0464718759695[/C][/ROW]
[ROW][C]151[/C][C]6355[/C][C]6197.24965405008[/C][C]157.750345949918[/C][/ROW]
[ROW][C]152[/C][C]6404[/C][C]6365.06199189074[/C][C]38.9380081092622[/C][/ROW]
[ROW][C]153[/C][C]6426[/C][C]6299.73988643233[/C][C]126.260113567669[/C][/ROW]
[ROW][C]154[/C][C]6375[/C][C]6320.96139593243[/C][C]54.0386040675721[/C][/ROW]
[ROW][C]155[/C][C]5869[/C][C]6016.55576751575[/C][C]-147.555767515752[/C][/ROW]
[ROW][C]156[/C][C]5994[/C][C]6023.34890557996[/C][C]-29.3489055799637[/C][/ROW]
[ROW][C]157[/C][C]6105[/C][C]6144.45340783418[/C][C]-39.453407834184[/C][/ROW]
[ROW][C]158[/C][C]5792[/C][C]5684.5866098555[/C][C]107.413390144497[/C][/ROW]
[ROW][C]159[/C][C]6011[/C][C]6159.975367519[/C][C]-148.975367518998[/C][/ROW]
[ROW][C]160[/C][C]5968[/C][C]5878.70101287911[/C][C]89.2989871208938[/C][/ROW]
[ROW][C]161[/C][C]6255[/C][C]6113.40530385795[/C][C]141.594696142047[/C][/ROW]
[ROW][C]162[/C][C]6208[/C][C]6127.3580143847[/C][C]80.6419856153025[/C][/ROW]
[ROW][C]163[/C][C]6897[/C][C]6677.04743433618[/C][C]219.952565663822[/C][/ROW]
[ROW][C]164[/C][C]6814[/C][C]6859.8085464679[/C][C]-45.8085464678952[/C][/ROW]
[ROW][C]165[/C][C]6897[/C][C]6772.62896349728[/C][C]124.371036502717[/C][/ROW]
[ROW][C]166[/C][C]6596[/C][C]6780.64333805522[/C][C]-184.643338055224[/C][/ROW]
[ROW][C]167[/C][C]6188[/C][C]6328.22089699377[/C][C]-140.22089699377[/C][/ROW]
[ROW][C]168[/C][C]6406[/C][C]6362.62134942594[/C][C]43.37865057406[/C][/ROW]
[ROW][C]169[/C][C]6548[/C][C]6520.20968947128[/C][C]27.7903105287232[/C][/ROW]
[ROW][C]170[/C][C]5842[/C][C]6084.5050173328[/C][C]-242.5050173328[/C][/ROW]
[ROW][C]171[/C][C]6555[/C][C]6393.50751014317[/C][C]161.492489856834[/C][/ROW]
[ROW][C]172[/C][C]6424[/C][C]6264.31859343547[/C][C]159.681406564527[/C][/ROW]
[ROW][C]173[/C][C]6596[/C][C]6551.01891658859[/C][C]44.9810834114105[/C][/ROW]
[ROW][C]174[/C][C]6645[/C][C]6514.09313508171[/C][C]130.906864918288[/C][/ROW]
[ROW][C]175[/C][C]7203[/C][C]7141.83152736281[/C][C]61.1684726371896[/C][/ROW]
[ROW][C]176[/C][C]7128[/C][C]7220.48123749582[/C][C]-92.4812374958155[/C][/ROW]
[ROW][C]177[/C][C]7133[/C][C]7139.91583614324[/C][C]-6.91583614323918[/C][/ROW]
[ROW][C]178[/C][C]6778[/C][C]7039.1865542068[/C][C]-261.186554206796[/C][/ROW]
[ROW][C]179[/C][C]6593[/C][C]6547.04968967465[/C][C]45.9503103253473[/C][/ROW]
[ROW][C]180[/C][C]6591[/C][C]6691.24807806008[/C][C]-100.248078060078[/C][/ROW]
[ROW][C]181[/C][C]6120[/C][C]6793.22968082843[/C][C]-673.229680828427[/C][/ROW]
[ROW][C]182[/C][C]5612[/C][C]6027.8303865355[/C][C]-415.830386535496[/C][/ROW]
[ROW][C]183[/C][C]6070[/C][C]6318.38103323749[/C][C]-248.381033237492[/C][/ROW]
[ROW][C]184[/C][C]5983[/C][C]6021.9539285815[/C][C]-38.9539285815017[/C][/ROW]
[ROW][C]185[/C][C]6145[/C][C]6186.19845451933[/C][C]-41.1984545193282[/C][/ROW]
[ROW][C]186[/C][C]6303[/C][C]6117.52431626522[/C][C]185.475683734781[/C][/ROW]
[ROW][C]187[/C][C]6588[/C][C]6707.0920541054[/C][C]-119.092054105399[/C][/ROW]
[ROW][C]188[/C][C]6640[/C][C]6670.87587646113[/C][C]-30.8758764611293[/C][/ROW]
[ROW][C]189[/C][C]6719[/C][C]6615.778456379[/C][C]103.221543621003[/C][/ROW]
[ROW][C]190[/C][C]6575[/C][C]6512.01907022318[/C][C]62.9809297768234[/C][/ROW]
[ROW][C]191[/C][C]6487[/C][C]6205.78716503087[/C][C]281.212834969135[/C][/ROW]
[ROW][C]192[/C][C]6510[/C][C]6406.57984946486[/C][C]103.420150535137[/C][/ROW]
[ROW][C]193[/C][C]6365[/C][C]6482.52768051927[/C][C]-117.527680519265[/C][/ROW]
[ROW][C]194[/C][C]5844[/C][C]5974.32617547945[/C][C]-130.326175479447[/C][/ROW]
[ROW][C]195[/C][C]5974[/C][C]6415.74049090333[/C][C]-441.74049090333[/C][/ROW]
[ROW][C]196[/C][C]5880[/C][C]6073.29916901872[/C][C]-193.299169018723[/C][/ROW]
[ROW][C]197[/C][C]6279[/C][C]6172.38624913211[/C][C]106.613750867892[/C][/ROW]
[ROW][C]198[/C][C]6342[/C][C]6197.24040202899[/C][C]144.759597971013[/C][/ROW]
[ROW][C]199[/C][C]6598[/C][C]6720.51389375184[/C][C]-122.51389375184[/C][/ROW]
[ROW][C]200[/C][C]6801[/C][C]6694.99632761664[/C][C]106.003672383362[/C][/ROW]
[ROW][C]201[/C][C]6529[/C][C]6714.67190611774[/C][C]-185.671906117738[/C][/ROW]
[ROW][C]202[/C][C]6369[/C][C]6486.35498578622[/C][C]-117.354985786224[/C][/ROW]
[ROW][C]203[/C][C]6028[/C][C]6143.15714468573[/C][C]-115.157144685727[/C][/ROW]
[ROW][C]204[/C][C]6187[/C][C]6145.99608032075[/C][C]41.0039196792522[/C][/ROW]
[ROW][C]205[/C][C]6164[/C][C]6151.82233518828[/C][C]12.1776648117184[/C][/ROW]
[ROW][C]206[/C][C]5866[/C][C]5704.38667834887[/C][C]161.61332165113[/C][/ROW]
[ROW][C]207[/C][C]6198[/C][C]6193.77343327267[/C][C]4.22656672732592[/C][/ROW]
[ROW][C]208[/C][C]5898[/C][C]6067.22475901804[/C][C]-169.224759018041[/C][/ROW]
[ROW][C]209[/C][C]6462[/C][C]6225.20677854992[/C][C]236.793221450082[/C][/ROW]
[ROW][C]210[/C][C]6063[/C][C]6307.80866494699[/C][C]-244.808664946985[/C][/ROW]
[ROW][C]211[/C][C]6496[/C][C]6623.94176589846[/C][C]-127.941765898465[/C][/ROW]
[ROW][C]212[/C][C]6678[/C][C]6629.19022529651[/C][C]48.8097747034872[/C][/ROW]
[ROW][C]213[/C][C]6554[/C][C]6574.87850450631[/C][C]-20.878504506305[/C][/ROW]
[ROW][C]214[/C][C]6513[/C][C]6421.47126958157[/C][C]91.5287304184267[/C][/ROW]
[ROW][C]215[/C][C]6210[/C][C]6159.12811705342[/C][C]50.8718829465788[/C][/ROW]
[ROW][C]216[/C][C]5928[/C][C]6255.64818273071[/C][C]-327.648182730709[/C][/ROW]
[ROW][C]217[/C][C]6268[/C][C]6107.66674354819[/C][C]160.333256451807[/C][/ROW]
[ROW][C]218[/C][C]5582[/C][C]5741.36940883944[/C][C]-159.369408839439[/C][/ROW]
[ROW][C]219[/C][C]5869[/C][C]6064.90032878286[/C][C]-195.900328782857[/C][/ROW]
[ROW][C]220[/C][C]5764[/C][C]5829.3492755742[/C][C]-65.3492755742009[/C][/ROW]
[ROW][C]221[/C][C]6082[/C][C]6081.12966294461[/C][C]0.870337055393065[/C][/ROW]
[ROW][C]222[/C][C]6062[/C][C]5987.00297200681[/C][C]74.9970279931913[/C][/ROW]
[ROW][C]223[/C][C]6810[/C][C]6433.85136208081[/C][C]376.148637919195[/C][/ROW]
[ROW][C]224[/C][C]6727[/C][C]6668.85946287724[/C][C]58.1405371227593[/C][/ROW]
[ROW][C]225[/C][C]6537[/C][C]6606.34630939124[/C][C]-69.3463093912396[/C][/ROW]
[ROW][C]226[/C][C]6175[/C][C]6451.24607835682[/C][C]-276.246078356821[/C][/ROW]
[ROW][C]227[/C][C]6014[/C][C]6038.48023861495[/C][C]-24.4802386149495[/C][/ROW]
[ROW][C]228[/C][C]6109[/C][C]6037.13976290519[/C][C]71.8602370948083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278512&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278512&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
1325132426.1539803082786.8460196917304
1424662418.8265939397947.1734060602107
1525442511.3783753059432.6216246940608
1625372514.2785126481322.721487351871
1725642546.55895126817.4410487320001
1825822565.7881891578616.2118108421414
1927162903.03193362023-187.031933620229
2029042762.19593594007141.804064059928
2128512810.3958056233340.6041943766718
2229322855.0253052129376.9746947870658
2327722747.6007054361624.3992945638415
2428112713.4482259306997.5517740693144
2529352828.12933360847106.870666391532
2627832815.89168461258-32.8916846125844
2730032885.47260614347117.527393856526
2829952920.0111715154874.9888284845197
2931272977.63613955838149.363860441618
3029853053.9328130428-68.9328130428021
3132873377.3348608544-90.3348608544038
3232363328.85965602057-92.8596560205665
3332523264.29202413751-12.2920241375082
3432283299.60588636155-71.6058863615472
3528563105.24953591629-249.249535916285
3631762969.0434675386206.956532461396
3733623134.90884541064227.091154589363
3830363137.73271454327-101.732714543272
3933303214.56332601358115.43667398642
4032513237.8724067264313.1275932735707
4133183284.6298019048633.3701980951414
4232383274.90474284606-36.9047428460631
4335973633.08783101289-36.0878310128896
4437083602.39448388034105.605516119665
4539023627.68900138282274.310998617177
4637453772.89586312448-27.8958631244823
4734263536.68112372207-110.681123722069
4835263538.76134270811-12.7613427081128
4934833632.9209258201-149.920925820104
5034583416.4517350330841.548264966917
5138243602.3918610673221.6081389327
5236963646.1419534531549.8580465468526
5335183716.78591413501-198.785914135014
5438143598.28673569387215.713264306126
5539964106.71291994136-110.712919941361
5641364070.1159135004365.8840864995668
5740374106.66065858751-69.6606585875134
5839154061.52663469624-146.526634696239
5937603745.2951225631914.7048774368118
6039553815.747538424139.252461576001
6141603953.3222983632206.677701636795
6241153893.8538174567221.146182543303
6342024213.39993698089-11.399936980888
6440184127.33770916606-109.337709166065
6542334093.57943097285139.420569027149
6640294182.74743694785-153.747436947851
6744014529.39323079242-128.393230792417
6846454517.53171844363127.468281556374
6944914554.27987768886-63.2798776888567
7043794494.74621688756-115.746216887565
7143944189.6841016767204.315898323295
7244724368.45337189896103.546628101039
7346144515.198648246498.801351753601
7441604397.52193848647-237.521938486474
7543284506.6922753823-178.692275382303
7642024328.06194728928-126.061947289282
7746354326.22911399546308.770886004543
7845424429.93306478157112.066935218428
7949204922.58070034819-2.58070034819411
8047745010.21551573882-236.215515738822
8146984864.52837529273-166.528375292732
8249164748.64846879785167.351531202154
8347034588.33209615424114.667903845762
8446164718.50491514975-102.504915149751
8548734784.3683283049788.6316716950287
8643754591.22450330516-216.224503305158
8748014726.3587226533874.6412773466236
8844274647.20946948351-220.209469483511
8946844683.794632682360.205367317642413
9046484625.5465406761622.4534593238395
9152255071.5167869921153.483213007898
9251745179.64106174088-5.64106174088101
9351815131.3122575545849.687742445416
9452665154.92362605327111.07637394673
9548394944.39141794217-105.39141794217
9650324950.6201944525181.3798055474908
9752215128.4346838834292.5653161165756
9846584865.23354630024-207.233546300245
9950145068.63470057676-54.6347005767557
10049804877.18219408425102.817805915747
10149525092.23390353819-140.233903538192
10249464976.4922916841-30.4922916841033
10353655453.12020389934-88.1202038993433
10454565436.5827721814119.4172278185897
10553975402.06494854283-5.06494854283028
10654365410.7832381188525.2167618811454
10749955115.08029324659-120.080293246593
10850195144.79480857164-125.79480857164
10952495239.043222324119.95677767589132
11047994883.10405617411-84.1040561741138
11151375161.81068215016-24.8106821501606
11249794999.81196876191-20.8119687619055
11349515121.25502722972-170.255027229724
11452655005.25853265457259.741467345434
11556125598.0944460910113.9055539089895
11655725637.80355307504-65.8035530750358
11754035560.09880709269-157.098807092688
11853735508.59150521651-135.591505216514
11952525117.32121457344134.678785426559
12054375245.23365101096191.766348989042
12152965494.76178333773-198.761783337728
12250115025.25172504168-14.2517250416768
12352945351.33571289622-57.3357128962152
12453355169.23416497921165.765835020789
12553985344.1540548345753.8459451654344
12653965389.191157364446.80884263555618
12757245860.66178905235-136.661789052349
12858985825.5092470335372.4907529664652
12957185783.05053931487-65.0505393148696
13056255771.520655151-146.520655150995
13153805404.16124200936-24.161242009357
13254885479.022168799768.97783120023905
13356785590.3997934166787.6002065833318
13452245247.68557014407-23.6855701440709
13555965575.9152760404920.0847239595114
13651845454.09030441304-270.090304413045
13756205434.51139387097185.488606129032
13855315521.438156985379.56184301463327
13958165977.8134894893-161.813489489298
14060865964.54972627131121.450273728689
14161755913.51736047099261.482639529011
14261126017.8214745538194.1785254461929
14358135749.0960705473163.903929452692
14457405873.00132840477-133.001328404767
14558215949.14353302212-128.143533022121
14652945483.52960871041-189.529608710411
14758815762.28585130314118.714148696859
14855895622.83017835836-33.8301783583647
14958455781.6590222820763.3409777179286
15057065790.04647187597-84.0464718759695
15163556197.24965405008157.750345949918
15264046365.0619918907438.9380081092622
15364266299.73988643233126.260113567669
15463756320.9613959324354.0386040675721
15558696016.55576751575-147.555767515752
15659946023.34890557996-29.3489055799637
15761056144.45340783418-39.453407834184
15857925684.5866098555107.413390144497
15960116159.975367519-148.975367518998
16059685878.7010128791189.2989871208938
16162556113.40530385795141.594696142047
16262086127.358014384780.6419856153025
16368976677.04743433618219.952565663822
16468146859.8085464679-45.8085464678952
16568976772.62896349728124.371036502717
16665966780.64333805522-184.643338055224
16761886328.22089699377-140.22089699377
16864066362.6213494259443.37865057406
16965486520.2096894712827.7903105287232
17058426084.5050173328-242.5050173328
17165556393.50751014317161.492489856834
17264246264.31859343547159.681406564527
17365966551.0189165885944.9810834114105
17466456514.09313508171130.906864918288
17572037141.8315273628161.1684726371896
17671287220.48123749582-92.4812374958155
17771337139.91583614324-6.91583614323918
17867787039.1865542068-261.186554206796
17965936547.0496896746545.9503103253473
18065916691.24807806008-100.248078060078
18161206793.22968082843-673.229680828427
18256126027.8303865355-415.830386535496
18360706318.38103323749-248.381033237492
18459836021.9539285815-38.9539285815017
18561456186.19845451933-41.1984545193282
18663036117.52431626522185.475683734781
18765886707.0920541054-119.092054105399
18866406670.87587646113-30.8758764611293
18967196615.778456379103.221543621003
19065756512.0190702231862.9809297768234
19164876205.78716503087281.212834969135
19265106406.57984946486103.420150535137
19363656482.52768051927-117.527680519265
19458445974.32617547945-130.326175479447
19559746415.74049090333-441.74049090333
19658806073.29916901872-193.299169018723
19762796172.38624913211106.613750867892
19863426197.24040202899144.759597971013
19965986720.51389375184-122.51389375184
20068016694.99632761664106.003672383362
20165296714.67190611774-185.671906117738
20263696486.35498578622-117.354985786224
20360286143.15714468573-115.157144685727
20461876145.9960803207541.0039196792522
20561646151.8223351882812.1776648117184
20658665704.38667834887161.61332165113
20761986193.773433272674.22656672732592
20858986067.22475901804-169.224759018041
20964626225.20677854992236.793221450082
21060636307.80866494699-244.808664946985
21164966623.94176589846-127.941765898465
21266786629.1902252965148.8097747034872
21365546574.87850450631-20.878504506305
21465136421.4712695815791.5287304184267
21562106159.1281170534250.8718829465788
21659286255.64818273071-327.648182730709
21762686107.66674354819160.333256451807
21855825741.36940883944-159.369408839439
21958696064.90032878286-195.900328782857
22057645829.3492755742-65.3492755742009
22160826081.129662944610.870337055393065
22260625987.0029720068174.9970279931913
22368106433.85136208081376.148637919195
22467276668.8594628772458.1405371227593
22565376606.34630939124-69.3463093912396
22661756451.24607835682-276.246078356821
22760146038.48023861495-24.4802386149495
22861096037.1397629051971.8602370948083







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
2296127.038812183745966.401813807366287.67581056013
2305647.72527675575454.540641913615840.90991159779
2316027.355864872375792.903077838356261.8086519064
2325890.636746347065630.082978993036151.19051370109
2336186.081794404865887.296283948686484.86730486104
2346104.184753389435782.351142887826426.01836389104
2356576.240878651426207.722138967076944.75961833576
2366606.809383434446212.630390188067000.98837668082
2376498.941907792326086.973151754076910.91066383058
2386336.305302096675910.475816041696762.13478815165
2396073.465541606715640.828086941736506.10299627169
2406098.47589284055661.369140067546535.58264561345

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
229 & 6127.03881218374 & 5966.40181380736 & 6287.67581056013 \tabularnewline
230 & 5647.7252767557 & 5454.54064191361 & 5840.90991159779 \tabularnewline
231 & 6027.35586487237 & 5792.90307783835 & 6261.8086519064 \tabularnewline
232 & 5890.63674634706 & 5630.08297899303 & 6151.19051370109 \tabularnewline
233 & 6186.08179440486 & 5887.29628394868 & 6484.86730486104 \tabularnewline
234 & 6104.18475338943 & 5782.35114288782 & 6426.01836389104 \tabularnewline
235 & 6576.24087865142 & 6207.72213896707 & 6944.75961833576 \tabularnewline
236 & 6606.80938343444 & 6212.63039018806 & 7000.98837668082 \tabularnewline
237 & 6498.94190779232 & 6086.97315175407 & 6910.91066383058 \tabularnewline
238 & 6336.30530209667 & 5910.47581604169 & 6762.13478815165 \tabularnewline
239 & 6073.46554160671 & 5640.82808694173 & 6506.10299627169 \tabularnewline
240 & 6098.4758928405 & 5661.36914006754 & 6535.58264561345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278512&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]229[/C][C]6127.03881218374[/C][C]5966.40181380736[/C][C]6287.67581056013[/C][/ROW]
[ROW][C]230[/C][C]5647.7252767557[/C][C]5454.54064191361[/C][C]5840.90991159779[/C][/ROW]
[ROW][C]231[/C][C]6027.35586487237[/C][C]5792.90307783835[/C][C]6261.8086519064[/C][/ROW]
[ROW][C]232[/C][C]5890.63674634706[/C][C]5630.08297899303[/C][C]6151.19051370109[/C][/ROW]
[ROW][C]233[/C][C]6186.08179440486[/C][C]5887.29628394868[/C][C]6484.86730486104[/C][/ROW]
[ROW][C]234[/C][C]6104.18475338943[/C][C]5782.35114288782[/C][C]6426.01836389104[/C][/ROW]
[ROW][C]235[/C][C]6576.24087865142[/C][C]6207.72213896707[/C][C]6944.75961833576[/C][/ROW]
[ROW][C]236[/C][C]6606.80938343444[/C][C]6212.63039018806[/C][C]7000.98837668082[/C][/ROW]
[ROW][C]237[/C][C]6498.94190779232[/C][C]6086.97315175407[/C][C]6910.91066383058[/C][/ROW]
[ROW][C]238[/C][C]6336.30530209667[/C][C]5910.47581604169[/C][C]6762.13478815165[/C][/ROW]
[ROW][C]239[/C][C]6073.46554160671[/C][C]5640.82808694173[/C][C]6506.10299627169[/C][/ROW]
[ROW][C]240[/C][C]6098.4758928405[/C][C]5661.36914006754[/C][C]6535.58264561345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278512&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278512&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
2296127.038812183745966.401813807366287.67581056013
2305647.72527675575454.540641913615840.90991159779
2316027.355864872375792.903077838356261.8086519064
2325890.636746347065630.082978993036151.19051370109
2336186.081794404865887.296283948686484.86730486104
2346104.184753389435782.351142887826426.01836389104
2356576.240878651426207.722138967076944.75961833576
2366606.809383434446212.630390188067000.98837668082
2376498.941907792326086.973151754076910.91066383058
2386336.305302096675910.475816041696762.13478815165
2396073.465541606715640.828086941736506.10299627169
2406098.47589284055661.369140067546535.58264561345



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')