Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 31 May 2016 11:34:35 +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/2016/May/31/t1464690906r3xb8g9guibi1su.htm/, Retrieved Mon, 06 May 2024 14:30:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295746, Retrieved Mon, 06 May 2024 14:30:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10.1 - lev...] [2016-05-31 10:34:35] [d36d23fecd6ad6dfd447f1d2ea855cae] [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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295746&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295746&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.397976136235358
beta0.0245968898593094
gamma0.274548590672376

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.397976136235358 \tabularnewline
beta & 0.0245968898593094 \tabularnewline
gamma & 0.274548590672376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295746&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]0.397976136235358[/C][/ROW]
[ROW][C]beta[/C][C]0.0245968898593094[/C][/ROW]
[ROW][C]gamma[/C][C]0.274548590672376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295746&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
alpha0.397976136235358
beta0.0245968898593094
gamma0.274548590672376







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325132426.1539803082786.8460196917304
1424662418.8715557470647.1284442529359
1525442511.4571607152232.5428392847839
1625372514.3812680163522.6187319836481
1725642546.6805018072917.3194981927149
1825822565.9234171800316.0765828199742
1927162903.19653865057-187.196538650573
2029042762.26138736027141.738612639727
2128512810.5198193580440.4801806419623
2229322855.1732747172376.8267252827718
2327722747.7823498407924.2176501592098
2428112713.6447493912497.3552506087599
2529352828.51440288086106.485597119136
2627832816.21461311075-33.2146131107465
2730032885.7619791768117.238020823199
2829952920.3495070782474.6504929217613
2931272978.02370693601148.976293063988
3029853054.41360637161-69.4136063716064
3132873377.53033110378-90.5303311037833
3232363329.65436541663-93.6543654166258
3332523264.72768708578-12.7276870857772
3432283300.05204562167-72.05204562167
3528563105.5148279563-249.514827956303
3631762969.26897726121206.731022738793
3733623135.301529376226.698470623995
3830363137.90199160562-101.901991605622
3933303214.95072918377115.049270816233
4032513238.1874724263112.8125275736857
4133183285.0518856002532.9481143997514
4232383274.99549479158-36.9954947915758
4335973632.98809528392-35.9880952839162
4437083602.91661192252105.083388077483
4539023628.19241126853273.807588731469
4637453773.47465793808-28.4746579380781
4734263536.87356041602-110.873560416022
4835263539.8435398954-13.8435398953998
4934833633.87440299178-150.87440299178
5034583416.3868966898541.6131033101542
5138243602.97779575899221.022204241005
5236963646.4943454806349.5056545193725
5335183717.31033915846-199.310339158465
5438143598.29358949956215.706410500438
5539964106.68913651519-110.689136515185
5641364070.8516945405565.1483054594455
5740374107.54819074036-70.5481907403637
5839154061.74164289702-146.741642897023
5937603745.0734604029414.9265395970615
6039553816.58599150221138.414008497795
6141603953.98117536004206.018824639958
6241153894.14597613083220.854023869168
6342024214.61493560334-12.6149356033438
6440184127.84409067052-109.84409067052
6542334093.79114404108139.208855958917
6640294183.41166699764-154.411666997637
6744014529.19061579571-128.190615795713
6846454518.33422553574126.665774464262
6944914555.0412236549-64.0412236549046
7043794494.86238369967-115.862383699669
7143944189.68948397888204.310516021123
7244724369.66159029704102.338409702965
7346144516.2716742943697.7283257056361
7441604398.113780788-238.113780787996
7543284507.42798669214-179.427986692135
7642024328.05481648302-126.05481648302
7746354326.34642649875308.653573501249
7845424430.00877293521111.991227064789
7949204922.18773341951-2.18773341950782
8047745011.21789460591-237.217894605906
8146984864.98482549915-166.984825499148
8249164748.45306697256167.546933027438
8347034588.63583585208114.364164147923
8446164719.53767475634-103.537674756341
8548734785.1939638589187.8060361410908
8643754591.15995281967-216.159952819666
8748014726.6639580447974.3360419552082
8844274647.13781791477-220.137817914774
8946844684.37432731938-0.374327319377699
9046484625.4188596934722.5811403065263
9152255070.67619896187154.323801038131
9251745179.74986254931-5.74986254931173
9351815131.3981535325849.6018464674216
9452665155.10027277311110.899727226885
9548394944.75562175031-105.755621750308
9650324951.1701640272680.8298359727432
9752215129.3031250602591.6968749397474
9846584864.86184104109-206.861841041089
9950145069.10940524168-55.1094052416847
10049804876.76958328232103.230416717675
10149525092.98788133182-140.98788133182
10249464976.56117087254-30.5611708725437
10353655452.62434839262-87.62434839262
10454565436.4010463496319.5989536503721
10553975401.98332234346-4.98332234346071
10654365410.8233453338125.1766546661884
10749955114.92834732154-119.928347321542
10850195145.14852526803-126.148525268029
10952495239.537589747189.46241025281779
11047994882.12646943242-83.1264694324209
11151375161.86723814019-24.8672381401893
11249794999.36825730398-20.3682573039769
11349515121.28078843785-170.280788437847
11452655004.9684070524260.0315929476
11556125597.3589547487514.6410452512455
11655725637.54338670744-65.5433867074416
11754035559.82663572657-156.826635726567
11853735508.38288489001-135.382884890008
11952525116.68331060745135.316689392546
12054375245.1941690498191.805830950198
12152965495.29694800208-199.29694800208
12250115024.30095814418-13.3009581441775
12352945351.33965060026-57.3396506002637
12453355168.80543744446166.194562555538
12553985343.9976366246354.0023633753735
12653965389.573915924156.42608407585067
12757245860.00852750824-136.008527508238
12858985825.0586225978572.9413774021459
12957185782.58972938018-64.5897293801772
13056255771.28844668693-146.28844668693
13153805403.9582944637-23.9582944637004
13254885479.180849637548.81915036246119
13356785590.3331404485987.6668595514111
13452245246.90942096546-22.9094209654577
13555965575.8440445112920.1559554887108
13651845454.02839623972-270.028396239716
13756205434.18505013048185.814949869517
13855315521.552351700619.44764829939413
13958165976.9000465735-160.900046573496
14060865964.11542741521121.884572584791
14161755912.85080987747262.149190122531
14261126017.4497113394294.5502886605809
14358135749.1445487049163.8554512950923
14457405873.49016838516-133.490168385157
14558215949.49098319247-128.490983192465
14652945482.92059154852-188.920591548517
14758815762.2073189084118.792681091598
14855895622.39915135456-33.399151354557
14958455781.9117079214563.0882920785452
15057065790.22511343835-84.2251134383505
15163556196.27884136198158.721158638023
15264046365.0994742375838.9005257624167
15364266299.61903145977126.380968540229
15463756320.6417662108754.3582337891303
15558696016.55102398436-147.55102398436
15659946023.38416565748-29.3841656574787
15761056144.57414408384-39.5741440838356
15857925683.92121179677108.078788203235
15960116160.41866491474-149.418664914742
16059685878.3872198188689.6127801811444
16162556113.87178152102141.128218478977
16262086127.5840741272580.4159258727532
16368976676.76800075162220.231999248379
16468146860.14020339454-46.1402033945351
16568976772.93112970146124.068870298538
16665966780.61480909149-184.614809091486
16761886328.05866999653-140.058669996534
16864066362.7731732424543.2268267575491
16965486520.4705055748227.5294944251818
17058426084.30210755662-242.30210755662
17165556393.61356894278161.386431057215
17264246264.36140285158159.638597148416
17365966551.7824214970844.2175785029222
17466456514.48112999067130.518870009329
17572037141.9798666003961.0201333996138
17671287220.60405025475-92.6040502547503
17771337140.32594467915-7.32594467915169
17867787038.78601804642-260.786018046419
17965936546.6721337946746.3278662053317
18065916691.53108919322-100.531089193219
18161206793.46664057831-673.466640578313
18256126026.9648153711-414.964815371103
18360706318.19919471719-248.19919471719
18459836021.3537722308-38.3537722307992
18561456185.75930605852-40.7593060585241
18663036116.87106250872186.128937491285
18765886706.05164711712-118.05164711712
18866406669.54279193069-29.5427919306867
18967196614.88189962841104.118100371589
19065756510.3069090641864.6930909358225
19164876204.78932124865282.210678751353
19265106406.00037095128103.99962904872
19363656481.37572706052-116.375727060523
19458445973.25442356329-129.254423563293
19559746415.75188630406-441.75188630406
19658806073.14609168585-193.146091685849
19762796172.14896627977106.851033720225
19863426197.10155138895144.898448611053
19965986719.45833088263-121.458330882633
20068016693.8330266688107.166973331202
20165296714.06885067956-185.068850679557
20263696484.80958194382-115.809581943824
20360286142.29189553415-114.291895534149
20461876144.9010634742.0989365300011
20561646149.9809664348614.0190335651405
20658665702.78455830863163.215441691365
20761986192.837011326145.16298867386013
20858986067.01662146601-169.016621466008
20964626225.42958626592236.570413734081
21060636308.12398159432-245.12398159432
21164966622.87584866627-126.875848666266
21266786628.3141175068149.6858824931924
21365546573.93792450893-19.9379245089294
21465136420.0318887678792.9681112321259
21562106158.3461057594151.6538942405896
21659286255.01095610729-327.010956107295
21762686106.12071826393161.879281736067
21855825740.18276516698-158.182765166985
21958696063.75460054164-194.754600541636
22057645828.51539564603-64.5153956460317
22160826081.331117846360.668882153639061
22260625986.4810629536675.5189370463404
22368106432.69967074362377.300329256375
22467276668.356387481158.6436125189039
22565376605.66064915672-68.6606491567245
22661756450.26095149715-275.260951497151
22760146037.70471874967-23.7047187496737

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2513 & 2426.15398030827 & 86.8460196917304 \tabularnewline
14 & 2466 & 2418.87155574706 & 47.1284442529359 \tabularnewline
15 & 2544 & 2511.45716071522 & 32.5428392847839 \tabularnewline
16 & 2537 & 2514.38126801635 & 22.6187319836481 \tabularnewline
17 & 2564 & 2546.68050180729 & 17.3194981927149 \tabularnewline
18 & 2582 & 2565.92341718003 & 16.0765828199742 \tabularnewline
19 & 2716 & 2903.19653865057 & -187.196538650573 \tabularnewline
20 & 2904 & 2762.26138736027 & 141.738612639727 \tabularnewline
21 & 2851 & 2810.51981935804 & 40.4801806419623 \tabularnewline
22 & 2932 & 2855.17327471723 & 76.8267252827718 \tabularnewline
23 & 2772 & 2747.78234984079 & 24.2176501592098 \tabularnewline
24 & 2811 & 2713.64474939124 & 97.3552506087599 \tabularnewline
25 & 2935 & 2828.51440288086 & 106.485597119136 \tabularnewline
26 & 2783 & 2816.21461311075 & -33.2146131107465 \tabularnewline
27 & 3003 & 2885.7619791768 & 117.238020823199 \tabularnewline
28 & 2995 & 2920.34950707824 & 74.6504929217613 \tabularnewline
29 & 3127 & 2978.02370693601 & 148.976293063988 \tabularnewline
30 & 2985 & 3054.41360637161 & -69.4136063716064 \tabularnewline
31 & 3287 & 3377.53033110378 & -90.5303311037833 \tabularnewline
32 & 3236 & 3329.65436541663 & -93.6543654166258 \tabularnewline
33 & 3252 & 3264.72768708578 & -12.7276870857772 \tabularnewline
34 & 3228 & 3300.05204562167 & -72.05204562167 \tabularnewline
35 & 2856 & 3105.5148279563 & -249.514827956303 \tabularnewline
36 & 3176 & 2969.26897726121 & 206.731022738793 \tabularnewline
37 & 3362 & 3135.301529376 & 226.698470623995 \tabularnewline
38 & 3036 & 3137.90199160562 & -101.901991605622 \tabularnewline
39 & 3330 & 3214.95072918377 & 115.049270816233 \tabularnewline
40 & 3251 & 3238.18747242631 & 12.8125275736857 \tabularnewline
41 & 3318 & 3285.05188560025 & 32.9481143997514 \tabularnewline
42 & 3238 & 3274.99549479158 & -36.9954947915758 \tabularnewline
43 & 3597 & 3632.98809528392 & -35.9880952839162 \tabularnewline
44 & 3708 & 3602.91661192252 & 105.083388077483 \tabularnewline
45 & 3902 & 3628.19241126853 & 273.807588731469 \tabularnewline
46 & 3745 & 3773.47465793808 & -28.4746579380781 \tabularnewline
47 & 3426 & 3536.87356041602 & -110.873560416022 \tabularnewline
48 & 3526 & 3539.8435398954 & -13.8435398953998 \tabularnewline
49 & 3483 & 3633.87440299178 & -150.87440299178 \tabularnewline
50 & 3458 & 3416.38689668985 & 41.6131033101542 \tabularnewline
51 & 3824 & 3602.97779575899 & 221.022204241005 \tabularnewline
52 & 3696 & 3646.49434548063 & 49.5056545193725 \tabularnewline
53 & 3518 & 3717.31033915846 & -199.310339158465 \tabularnewline
54 & 3814 & 3598.29358949956 & 215.706410500438 \tabularnewline
55 & 3996 & 4106.68913651519 & -110.689136515185 \tabularnewline
56 & 4136 & 4070.85169454055 & 65.1483054594455 \tabularnewline
57 & 4037 & 4107.54819074036 & -70.5481907403637 \tabularnewline
58 & 3915 & 4061.74164289702 & -146.741642897023 \tabularnewline
59 & 3760 & 3745.07346040294 & 14.9265395970615 \tabularnewline
60 & 3955 & 3816.58599150221 & 138.414008497795 \tabularnewline
61 & 4160 & 3953.98117536004 & 206.018824639958 \tabularnewline
62 & 4115 & 3894.14597613083 & 220.854023869168 \tabularnewline
63 & 4202 & 4214.61493560334 & -12.6149356033438 \tabularnewline
64 & 4018 & 4127.84409067052 & -109.84409067052 \tabularnewline
65 & 4233 & 4093.79114404108 & 139.208855958917 \tabularnewline
66 & 4029 & 4183.41166699764 & -154.411666997637 \tabularnewline
67 & 4401 & 4529.19061579571 & -128.190615795713 \tabularnewline
68 & 4645 & 4518.33422553574 & 126.665774464262 \tabularnewline
69 & 4491 & 4555.0412236549 & -64.0412236549046 \tabularnewline
70 & 4379 & 4494.86238369967 & -115.862383699669 \tabularnewline
71 & 4394 & 4189.68948397888 & 204.310516021123 \tabularnewline
72 & 4472 & 4369.66159029704 & 102.338409702965 \tabularnewline
73 & 4614 & 4516.27167429436 & 97.7283257056361 \tabularnewline
74 & 4160 & 4398.113780788 & -238.113780787996 \tabularnewline
75 & 4328 & 4507.42798669214 & -179.427986692135 \tabularnewline
76 & 4202 & 4328.05481648302 & -126.05481648302 \tabularnewline
77 & 4635 & 4326.34642649875 & 308.653573501249 \tabularnewline
78 & 4542 & 4430.00877293521 & 111.991227064789 \tabularnewline
79 & 4920 & 4922.18773341951 & -2.18773341950782 \tabularnewline
80 & 4774 & 5011.21789460591 & -237.217894605906 \tabularnewline
81 & 4698 & 4864.98482549915 & -166.984825499148 \tabularnewline
82 & 4916 & 4748.45306697256 & 167.546933027438 \tabularnewline
83 & 4703 & 4588.63583585208 & 114.364164147923 \tabularnewline
84 & 4616 & 4719.53767475634 & -103.537674756341 \tabularnewline
85 & 4873 & 4785.19396385891 & 87.8060361410908 \tabularnewline
86 & 4375 & 4591.15995281967 & -216.159952819666 \tabularnewline
87 & 4801 & 4726.66395804479 & 74.3360419552082 \tabularnewline
88 & 4427 & 4647.13781791477 & -220.137817914774 \tabularnewline
89 & 4684 & 4684.37432731938 & -0.374327319377699 \tabularnewline
90 & 4648 & 4625.41885969347 & 22.5811403065263 \tabularnewline
91 & 5225 & 5070.67619896187 & 154.323801038131 \tabularnewline
92 & 5174 & 5179.74986254931 & -5.74986254931173 \tabularnewline
93 & 5181 & 5131.39815353258 & 49.6018464674216 \tabularnewline
94 & 5266 & 5155.10027277311 & 110.899727226885 \tabularnewline
95 & 4839 & 4944.75562175031 & -105.755621750308 \tabularnewline
96 & 5032 & 4951.17016402726 & 80.8298359727432 \tabularnewline
97 & 5221 & 5129.30312506025 & 91.6968749397474 \tabularnewline
98 & 4658 & 4864.86184104109 & -206.861841041089 \tabularnewline
99 & 5014 & 5069.10940524168 & -55.1094052416847 \tabularnewline
100 & 4980 & 4876.76958328232 & 103.230416717675 \tabularnewline
101 & 4952 & 5092.98788133182 & -140.98788133182 \tabularnewline
102 & 4946 & 4976.56117087254 & -30.5611708725437 \tabularnewline
103 & 5365 & 5452.62434839262 & -87.62434839262 \tabularnewline
104 & 5456 & 5436.40104634963 & 19.5989536503721 \tabularnewline
105 & 5397 & 5401.98332234346 & -4.98332234346071 \tabularnewline
106 & 5436 & 5410.82334533381 & 25.1766546661884 \tabularnewline
107 & 4995 & 5114.92834732154 & -119.928347321542 \tabularnewline
108 & 5019 & 5145.14852526803 & -126.148525268029 \tabularnewline
109 & 5249 & 5239.53758974718 & 9.46241025281779 \tabularnewline
110 & 4799 & 4882.12646943242 & -83.1264694324209 \tabularnewline
111 & 5137 & 5161.86723814019 & -24.8672381401893 \tabularnewline
112 & 4979 & 4999.36825730398 & -20.3682573039769 \tabularnewline
113 & 4951 & 5121.28078843785 & -170.280788437847 \tabularnewline
114 & 5265 & 5004.9684070524 & 260.0315929476 \tabularnewline
115 & 5612 & 5597.35895474875 & 14.6410452512455 \tabularnewline
116 & 5572 & 5637.54338670744 & -65.5433867074416 \tabularnewline
117 & 5403 & 5559.82663572657 & -156.826635726567 \tabularnewline
118 & 5373 & 5508.38288489001 & -135.382884890008 \tabularnewline
119 & 5252 & 5116.68331060745 & 135.316689392546 \tabularnewline
120 & 5437 & 5245.1941690498 & 191.805830950198 \tabularnewline
121 & 5296 & 5495.29694800208 & -199.29694800208 \tabularnewline
122 & 5011 & 5024.30095814418 & -13.3009581441775 \tabularnewline
123 & 5294 & 5351.33965060026 & -57.3396506002637 \tabularnewline
124 & 5335 & 5168.80543744446 & 166.194562555538 \tabularnewline
125 & 5398 & 5343.99763662463 & 54.0023633753735 \tabularnewline
126 & 5396 & 5389.57391592415 & 6.42608407585067 \tabularnewline
127 & 5724 & 5860.00852750824 & -136.008527508238 \tabularnewline
128 & 5898 & 5825.05862259785 & 72.9413774021459 \tabularnewline
129 & 5718 & 5782.58972938018 & -64.5897293801772 \tabularnewline
130 & 5625 & 5771.28844668693 & -146.28844668693 \tabularnewline
131 & 5380 & 5403.9582944637 & -23.9582944637004 \tabularnewline
132 & 5488 & 5479.18084963754 & 8.81915036246119 \tabularnewline
133 & 5678 & 5590.33314044859 & 87.6668595514111 \tabularnewline
134 & 5224 & 5246.90942096546 & -22.9094209654577 \tabularnewline
135 & 5596 & 5575.84404451129 & 20.1559554887108 \tabularnewline
136 & 5184 & 5454.02839623972 & -270.028396239716 \tabularnewline
137 & 5620 & 5434.18505013048 & 185.814949869517 \tabularnewline
138 & 5531 & 5521.55235170061 & 9.44764829939413 \tabularnewline
139 & 5816 & 5976.9000465735 & -160.900046573496 \tabularnewline
140 & 6086 & 5964.11542741521 & 121.884572584791 \tabularnewline
141 & 6175 & 5912.85080987747 & 262.149190122531 \tabularnewline
142 & 6112 & 6017.44971133942 & 94.5502886605809 \tabularnewline
143 & 5813 & 5749.14454870491 & 63.8554512950923 \tabularnewline
144 & 5740 & 5873.49016838516 & -133.490168385157 \tabularnewline
145 & 5821 & 5949.49098319247 & -128.490983192465 \tabularnewline
146 & 5294 & 5482.92059154852 & -188.920591548517 \tabularnewline
147 & 5881 & 5762.2073189084 & 118.792681091598 \tabularnewline
148 & 5589 & 5622.39915135456 & -33.399151354557 \tabularnewline
149 & 5845 & 5781.91170792145 & 63.0882920785452 \tabularnewline
150 & 5706 & 5790.22511343835 & -84.2251134383505 \tabularnewline
151 & 6355 & 6196.27884136198 & 158.721158638023 \tabularnewline
152 & 6404 & 6365.09947423758 & 38.9005257624167 \tabularnewline
153 & 6426 & 6299.61903145977 & 126.380968540229 \tabularnewline
154 & 6375 & 6320.64176621087 & 54.3582337891303 \tabularnewline
155 & 5869 & 6016.55102398436 & -147.55102398436 \tabularnewline
156 & 5994 & 6023.38416565748 & -29.3841656574787 \tabularnewline
157 & 6105 & 6144.57414408384 & -39.5741440838356 \tabularnewline
158 & 5792 & 5683.92121179677 & 108.078788203235 \tabularnewline
159 & 6011 & 6160.41866491474 & -149.418664914742 \tabularnewline
160 & 5968 & 5878.38721981886 & 89.6127801811444 \tabularnewline
161 & 6255 & 6113.87178152102 & 141.128218478977 \tabularnewline
162 & 6208 & 6127.58407412725 & 80.4159258727532 \tabularnewline
163 & 6897 & 6676.76800075162 & 220.231999248379 \tabularnewline
164 & 6814 & 6860.14020339454 & -46.1402033945351 \tabularnewline
165 & 6897 & 6772.93112970146 & 124.068870298538 \tabularnewline
166 & 6596 & 6780.61480909149 & -184.614809091486 \tabularnewline
167 & 6188 & 6328.05866999653 & -140.058669996534 \tabularnewline
168 & 6406 & 6362.77317324245 & 43.2268267575491 \tabularnewline
169 & 6548 & 6520.47050557482 & 27.5294944251818 \tabularnewline
170 & 5842 & 6084.30210755662 & -242.30210755662 \tabularnewline
171 & 6555 & 6393.61356894278 & 161.386431057215 \tabularnewline
172 & 6424 & 6264.36140285158 & 159.638597148416 \tabularnewline
173 & 6596 & 6551.78242149708 & 44.2175785029222 \tabularnewline
174 & 6645 & 6514.48112999067 & 130.518870009329 \tabularnewline
175 & 7203 & 7141.97986660039 & 61.0201333996138 \tabularnewline
176 & 7128 & 7220.60405025475 & -92.6040502547503 \tabularnewline
177 & 7133 & 7140.32594467915 & -7.32594467915169 \tabularnewline
178 & 6778 & 7038.78601804642 & -260.786018046419 \tabularnewline
179 & 6593 & 6546.67213379467 & 46.3278662053317 \tabularnewline
180 & 6591 & 6691.53108919322 & -100.531089193219 \tabularnewline
181 & 6120 & 6793.46664057831 & -673.466640578313 \tabularnewline
182 & 5612 & 6026.9648153711 & -414.964815371103 \tabularnewline
183 & 6070 & 6318.19919471719 & -248.19919471719 \tabularnewline
184 & 5983 & 6021.3537722308 & -38.3537722307992 \tabularnewline
185 & 6145 & 6185.75930605852 & -40.7593060585241 \tabularnewline
186 & 6303 & 6116.87106250872 & 186.128937491285 \tabularnewline
187 & 6588 & 6706.05164711712 & -118.05164711712 \tabularnewline
188 & 6640 & 6669.54279193069 & -29.5427919306867 \tabularnewline
189 & 6719 & 6614.88189962841 & 104.118100371589 \tabularnewline
190 & 6575 & 6510.30690906418 & 64.6930909358225 \tabularnewline
191 & 6487 & 6204.78932124865 & 282.210678751353 \tabularnewline
192 & 6510 & 6406.00037095128 & 103.99962904872 \tabularnewline
193 & 6365 & 6481.37572706052 & -116.375727060523 \tabularnewline
194 & 5844 & 5973.25442356329 & -129.254423563293 \tabularnewline
195 & 5974 & 6415.75188630406 & -441.75188630406 \tabularnewline
196 & 5880 & 6073.14609168585 & -193.146091685849 \tabularnewline
197 & 6279 & 6172.14896627977 & 106.851033720225 \tabularnewline
198 & 6342 & 6197.10155138895 & 144.898448611053 \tabularnewline
199 & 6598 & 6719.45833088263 & -121.458330882633 \tabularnewline
200 & 6801 & 6693.8330266688 & 107.166973331202 \tabularnewline
201 & 6529 & 6714.06885067956 & -185.068850679557 \tabularnewline
202 & 6369 & 6484.80958194382 & -115.809581943824 \tabularnewline
203 & 6028 & 6142.29189553415 & -114.291895534149 \tabularnewline
204 & 6187 & 6144.90106347 & 42.0989365300011 \tabularnewline
205 & 6164 & 6149.98096643486 & 14.0190335651405 \tabularnewline
206 & 5866 & 5702.78455830863 & 163.215441691365 \tabularnewline
207 & 6198 & 6192.83701132614 & 5.16298867386013 \tabularnewline
208 & 5898 & 6067.01662146601 & -169.016621466008 \tabularnewline
209 & 6462 & 6225.42958626592 & 236.570413734081 \tabularnewline
210 & 6063 & 6308.12398159432 & -245.12398159432 \tabularnewline
211 & 6496 & 6622.87584866627 & -126.875848666266 \tabularnewline
212 & 6678 & 6628.31411750681 & 49.6858824931924 \tabularnewline
213 & 6554 & 6573.93792450893 & -19.9379245089294 \tabularnewline
214 & 6513 & 6420.03188876787 & 92.9681112321259 \tabularnewline
215 & 6210 & 6158.34610575941 & 51.6538942405896 \tabularnewline
216 & 5928 & 6255.01095610729 & -327.010956107295 \tabularnewline
217 & 6268 & 6106.12071826393 & 161.879281736067 \tabularnewline
218 & 5582 & 5740.18276516698 & -158.182765166985 \tabularnewline
219 & 5869 & 6063.75460054164 & -194.754600541636 \tabularnewline
220 & 5764 & 5828.51539564603 & -64.5153956460317 \tabularnewline
221 & 6082 & 6081.33111784636 & 0.668882153639061 \tabularnewline
222 & 6062 & 5986.48106295366 & 75.5189370463404 \tabularnewline
223 & 6810 & 6432.69967074362 & 377.300329256375 \tabularnewline
224 & 6727 & 6668.3563874811 & 58.6436125189039 \tabularnewline
225 & 6537 & 6605.66064915672 & -68.6606491567245 \tabularnewline
226 & 6175 & 6450.26095149715 & -275.260951497151 \tabularnewline
227 & 6014 & 6037.70471874967 & -23.7047187496737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295746&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]2418.87155574706[/C][C]47.1284442529359[/C][/ROW]
[ROW][C]15[/C][C]2544[/C][C]2511.45716071522[/C][C]32.5428392847839[/C][/ROW]
[ROW][C]16[/C][C]2537[/C][C]2514.38126801635[/C][C]22.6187319836481[/C][/ROW]
[ROW][C]17[/C][C]2564[/C][C]2546.68050180729[/C][C]17.3194981927149[/C][/ROW]
[ROW][C]18[/C][C]2582[/C][C]2565.92341718003[/C][C]16.0765828199742[/C][/ROW]
[ROW][C]19[/C][C]2716[/C][C]2903.19653865057[/C][C]-187.196538650573[/C][/ROW]
[ROW][C]20[/C][C]2904[/C][C]2762.26138736027[/C][C]141.738612639727[/C][/ROW]
[ROW][C]21[/C][C]2851[/C][C]2810.51981935804[/C][C]40.4801806419623[/C][/ROW]
[ROW][C]22[/C][C]2932[/C][C]2855.17327471723[/C][C]76.8267252827718[/C][/ROW]
[ROW][C]23[/C][C]2772[/C][C]2747.78234984079[/C][C]24.2176501592098[/C][/ROW]
[ROW][C]24[/C][C]2811[/C][C]2713.64474939124[/C][C]97.3552506087599[/C][/ROW]
[ROW][C]25[/C][C]2935[/C][C]2828.51440288086[/C][C]106.485597119136[/C][/ROW]
[ROW][C]26[/C][C]2783[/C][C]2816.21461311075[/C][C]-33.2146131107465[/C][/ROW]
[ROW][C]27[/C][C]3003[/C][C]2885.7619791768[/C][C]117.238020823199[/C][/ROW]
[ROW][C]28[/C][C]2995[/C][C]2920.34950707824[/C][C]74.6504929217613[/C][/ROW]
[ROW][C]29[/C][C]3127[/C][C]2978.02370693601[/C][C]148.976293063988[/C][/ROW]
[ROW][C]30[/C][C]2985[/C][C]3054.41360637161[/C][C]-69.4136063716064[/C][/ROW]
[ROW][C]31[/C][C]3287[/C][C]3377.53033110378[/C][C]-90.5303311037833[/C][/ROW]
[ROW][C]32[/C][C]3236[/C][C]3329.65436541663[/C][C]-93.6543654166258[/C][/ROW]
[ROW][C]33[/C][C]3252[/C][C]3264.72768708578[/C][C]-12.7276870857772[/C][/ROW]
[ROW][C]34[/C][C]3228[/C][C]3300.05204562167[/C][C]-72.05204562167[/C][/ROW]
[ROW][C]35[/C][C]2856[/C][C]3105.5148279563[/C][C]-249.514827956303[/C][/ROW]
[ROW][C]36[/C][C]3176[/C][C]2969.26897726121[/C][C]206.731022738793[/C][/ROW]
[ROW][C]37[/C][C]3362[/C][C]3135.301529376[/C][C]226.698470623995[/C][/ROW]
[ROW][C]38[/C][C]3036[/C][C]3137.90199160562[/C][C]-101.901991605622[/C][/ROW]
[ROW][C]39[/C][C]3330[/C][C]3214.95072918377[/C][C]115.049270816233[/C][/ROW]
[ROW][C]40[/C][C]3251[/C][C]3238.18747242631[/C][C]12.8125275736857[/C][/ROW]
[ROW][C]41[/C][C]3318[/C][C]3285.05188560025[/C][C]32.9481143997514[/C][/ROW]
[ROW][C]42[/C][C]3238[/C][C]3274.99549479158[/C][C]-36.9954947915758[/C][/ROW]
[ROW][C]43[/C][C]3597[/C][C]3632.98809528392[/C][C]-35.9880952839162[/C][/ROW]
[ROW][C]44[/C][C]3708[/C][C]3602.91661192252[/C][C]105.083388077483[/C][/ROW]
[ROW][C]45[/C][C]3902[/C][C]3628.19241126853[/C][C]273.807588731469[/C][/ROW]
[ROW][C]46[/C][C]3745[/C][C]3773.47465793808[/C][C]-28.4746579380781[/C][/ROW]
[ROW][C]47[/C][C]3426[/C][C]3536.87356041602[/C][C]-110.873560416022[/C][/ROW]
[ROW][C]48[/C][C]3526[/C][C]3539.8435398954[/C][C]-13.8435398953998[/C][/ROW]
[ROW][C]49[/C][C]3483[/C][C]3633.87440299178[/C][C]-150.87440299178[/C][/ROW]
[ROW][C]50[/C][C]3458[/C][C]3416.38689668985[/C][C]41.6131033101542[/C][/ROW]
[ROW][C]51[/C][C]3824[/C][C]3602.97779575899[/C][C]221.022204241005[/C][/ROW]
[ROW][C]52[/C][C]3696[/C][C]3646.49434548063[/C][C]49.5056545193725[/C][/ROW]
[ROW][C]53[/C][C]3518[/C][C]3717.31033915846[/C][C]-199.310339158465[/C][/ROW]
[ROW][C]54[/C][C]3814[/C][C]3598.29358949956[/C][C]215.706410500438[/C][/ROW]
[ROW][C]55[/C][C]3996[/C][C]4106.68913651519[/C][C]-110.689136515185[/C][/ROW]
[ROW][C]56[/C][C]4136[/C][C]4070.85169454055[/C][C]65.1483054594455[/C][/ROW]
[ROW][C]57[/C][C]4037[/C][C]4107.54819074036[/C][C]-70.5481907403637[/C][/ROW]
[ROW][C]58[/C][C]3915[/C][C]4061.74164289702[/C][C]-146.741642897023[/C][/ROW]
[ROW][C]59[/C][C]3760[/C][C]3745.07346040294[/C][C]14.9265395970615[/C][/ROW]
[ROW][C]60[/C][C]3955[/C][C]3816.58599150221[/C][C]138.414008497795[/C][/ROW]
[ROW][C]61[/C][C]4160[/C][C]3953.98117536004[/C][C]206.018824639958[/C][/ROW]
[ROW][C]62[/C][C]4115[/C][C]3894.14597613083[/C][C]220.854023869168[/C][/ROW]
[ROW][C]63[/C][C]4202[/C][C]4214.61493560334[/C][C]-12.6149356033438[/C][/ROW]
[ROW][C]64[/C][C]4018[/C][C]4127.84409067052[/C][C]-109.84409067052[/C][/ROW]
[ROW][C]65[/C][C]4233[/C][C]4093.79114404108[/C][C]139.208855958917[/C][/ROW]
[ROW][C]66[/C][C]4029[/C][C]4183.41166699764[/C][C]-154.411666997637[/C][/ROW]
[ROW][C]67[/C][C]4401[/C][C]4529.19061579571[/C][C]-128.190615795713[/C][/ROW]
[ROW][C]68[/C][C]4645[/C][C]4518.33422553574[/C][C]126.665774464262[/C][/ROW]
[ROW][C]69[/C][C]4491[/C][C]4555.0412236549[/C][C]-64.0412236549046[/C][/ROW]
[ROW][C]70[/C][C]4379[/C][C]4494.86238369967[/C][C]-115.862383699669[/C][/ROW]
[ROW][C]71[/C][C]4394[/C][C]4189.68948397888[/C][C]204.310516021123[/C][/ROW]
[ROW][C]72[/C][C]4472[/C][C]4369.66159029704[/C][C]102.338409702965[/C][/ROW]
[ROW][C]73[/C][C]4614[/C][C]4516.27167429436[/C][C]97.7283257056361[/C][/ROW]
[ROW][C]74[/C][C]4160[/C][C]4398.113780788[/C][C]-238.113780787996[/C][/ROW]
[ROW][C]75[/C][C]4328[/C][C]4507.42798669214[/C][C]-179.427986692135[/C][/ROW]
[ROW][C]76[/C][C]4202[/C][C]4328.05481648302[/C][C]-126.05481648302[/C][/ROW]
[ROW][C]77[/C][C]4635[/C][C]4326.34642649875[/C][C]308.653573501249[/C][/ROW]
[ROW][C]78[/C][C]4542[/C][C]4430.00877293521[/C][C]111.991227064789[/C][/ROW]
[ROW][C]79[/C][C]4920[/C][C]4922.18773341951[/C][C]-2.18773341950782[/C][/ROW]
[ROW][C]80[/C][C]4774[/C][C]5011.21789460591[/C][C]-237.217894605906[/C][/ROW]
[ROW][C]81[/C][C]4698[/C][C]4864.98482549915[/C][C]-166.984825499148[/C][/ROW]
[ROW][C]82[/C][C]4916[/C][C]4748.45306697256[/C][C]167.546933027438[/C][/ROW]
[ROW][C]83[/C][C]4703[/C][C]4588.63583585208[/C][C]114.364164147923[/C][/ROW]
[ROW][C]84[/C][C]4616[/C][C]4719.53767475634[/C][C]-103.537674756341[/C][/ROW]
[ROW][C]85[/C][C]4873[/C][C]4785.19396385891[/C][C]87.8060361410908[/C][/ROW]
[ROW][C]86[/C][C]4375[/C][C]4591.15995281967[/C][C]-216.159952819666[/C][/ROW]
[ROW][C]87[/C][C]4801[/C][C]4726.66395804479[/C][C]74.3360419552082[/C][/ROW]
[ROW][C]88[/C][C]4427[/C][C]4647.13781791477[/C][C]-220.137817914774[/C][/ROW]
[ROW][C]89[/C][C]4684[/C][C]4684.37432731938[/C][C]-0.374327319377699[/C][/ROW]
[ROW][C]90[/C][C]4648[/C][C]4625.41885969347[/C][C]22.5811403065263[/C][/ROW]
[ROW][C]91[/C][C]5225[/C][C]5070.67619896187[/C][C]154.323801038131[/C][/ROW]
[ROW][C]92[/C][C]5174[/C][C]5179.74986254931[/C][C]-5.74986254931173[/C][/ROW]
[ROW][C]93[/C][C]5181[/C][C]5131.39815353258[/C][C]49.6018464674216[/C][/ROW]
[ROW][C]94[/C][C]5266[/C][C]5155.10027277311[/C][C]110.899727226885[/C][/ROW]
[ROW][C]95[/C][C]4839[/C][C]4944.75562175031[/C][C]-105.755621750308[/C][/ROW]
[ROW][C]96[/C][C]5032[/C][C]4951.17016402726[/C][C]80.8298359727432[/C][/ROW]
[ROW][C]97[/C][C]5221[/C][C]5129.30312506025[/C][C]91.6968749397474[/C][/ROW]
[ROW][C]98[/C][C]4658[/C][C]4864.86184104109[/C][C]-206.861841041089[/C][/ROW]
[ROW][C]99[/C][C]5014[/C][C]5069.10940524168[/C][C]-55.1094052416847[/C][/ROW]
[ROW][C]100[/C][C]4980[/C][C]4876.76958328232[/C][C]103.230416717675[/C][/ROW]
[ROW][C]101[/C][C]4952[/C][C]5092.98788133182[/C][C]-140.98788133182[/C][/ROW]
[ROW][C]102[/C][C]4946[/C][C]4976.56117087254[/C][C]-30.5611708725437[/C][/ROW]
[ROW][C]103[/C][C]5365[/C][C]5452.62434839262[/C][C]-87.62434839262[/C][/ROW]
[ROW][C]104[/C][C]5456[/C][C]5436.40104634963[/C][C]19.5989536503721[/C][/ROW]
[ROW][C]105[/C][C]5397[/C][C]5401.98332234346[/C][C]-4.98332234346071[/C][/ROW]
[ROW][C]106[/C][C]5436[/C][C]5410.82334533381[/C][C]25.1766546661884[/C][/ROW]
[ROW][C]107[/C][C]4995[/C][C]5114.92834732154[/C][C]-119.928347321542[/C][/ROW]
[ROW][C]108[/C][C]5019[/C][C]5145.14852526803[/C][C]-126.148525268029[/C][/ROW]
[ROW][C]109[/C][C]5249[/C][C]5239.53758974718[/C][C]9.46241025281779[/C][/ROW]
[ROW][C]110[/C][C]4799[/C][C]4882.12646943242[/C][C]-83.1264694324209[/C][/ROW]
[ROW][C]111[/C][C]5137[/C][C]5161.86723814019[/C][C]-24.8672381401893[/C][/ROW]
[ROW][C]112[/C][C]4979[/C][C]4999.36825730398[/C][C]-20.3682573039769[/C][/ROW]
[ROW][C]113[/C][C]4951[/C][C]5121.28078843785[/C][C]-170.280788437847[/C][/ROW]
[ROW][C]114[/C][C]5265[/C][C]5004.9684070524[/C][C]260.0315929476[/C][/ROW]
[ROW][C]115[/C][C]5612[/C][C]5597.35895474875[/C][C]14.6410452512455[/C][/ROW]
[ROW][C]116[/C][C]5572[/C][C]5637.54338670744[/C][C]-65.5433867074416[/C][/ROW]
[ROW][C]117[/C][C]5403[/C][C]5559.82663572657[/C][C]-156.826635726567[/C][/ROW]
[ROW][C]118[/C][C]5373[/C][C]5508.38288489001[/C][C]-135.382884890008[/C][/ROW]
[ROW][C]119[/C][C]5252[/C][C]5116.68331060745[/C][C]135.316689392546[/C][/ROW]
[ROW][C]120[/C][C]5437[/C][C]5245.1941690498[/C][C]191.805830950198[/C][/ROW]
[ROW][C]121[/C][C]5296[/C][C]5495.29694800208[/C][C]-199.29694800208[/C][/ROW]
[ROW][C]122[/C][C]5011[/C][C]5024.30095814418[/C][C]-13.3009581441775[/C][/ROW]
[ROW][C]123[/C][C]5294[/C][C]5351.33965060026[/C][C]-57.3396506002637[/C][/ROW]
[ROW][C]124[/C][C]5335[/C][C]5168.80543744446[/C][C]166.194562555538[/C][/ROW]
[ROW][C]125[/C][C]5398[/C][C]5343.99763662463[/C][C]54.0023633753735[/C][/ROW]
[ROW][C]126[/C][C]5396[/C][C]5389.57391592415[/C][C]6.42608407585067[/C][/ROW]
[ROW][C]127[/C][C]5724[/C][C]5860.00852750824[/C][C]-136.008527508238[/C][/ROW]
[ROW][C]128[/C][C]5898[/C][C]5825.05862259785[/C][C]72.9413774021459[/C][/ROW]
[ROW][C]129[/C][C]5718[/C][C]5782.58972938018[/C][C]-64.5897293801772[/C][/ROW]
[ROW][C]130[/C][C]5625[/C][C]5771.28844668693[/C][C]-146.28844668693[/C][/ROW]
[ROW][C]131[/C][C]5380[/C][C]5403.9582944637[/C][C]-23.9582944637004[/C][/ROW]
[ROW][C]132[/C][C]5488[/C][C]5479.18084963754[/C][C]8.81915036246119[/C][/ROW]
[ROW][C]133[/C][C]5678[/C][C]5590.33314044859[/C][C]87.6668595514111[/C][/ROW]
[ROW][C]134[/C][C]5224[/C][C]5246.90942096546[/C][C]-22.9094209654577[/C][/ROW]
[ROW][C]135[/C][C]5596[/C][C]5575.84404451129[/C][C]20.1559554887108[/C][/ROW]
[ROW][C]136[/C][C]5184[/C][C]5454.02839623972[/C][C]-270.028396239716[/C][/ROW]
[ROW][C]137[/C][C]5620[/C][C]5434.18505013048[/C][C]185.814949869517[/C][/ROW]
[ROW][C]138[/C][C]5531[/C][C]5521.55235170061[/C][C]9.44764829939413[/C][/ROW]
[ROW][C]139[/C][C]5816[/C][C]5976.9000465735[/C][C]-160.900046573496[/C][/ROW]
[ROW][C]140[/C][C]6086[/C][C]5964.11542741521[/C][C]121.884572584791[/C][/ROW]
[ROW][C]141[/C][C]6175[/C][C]5912.85080987747[/C][C]262.149190122531[/C][/ROW]
[ROW][C]142[/C][C]6112[/C][C]6017.44971133942[/C][C]94.5502886605809[/C][/ROW]
[ROW][C]143[/C][C]5813[/C][C]5749.14454870491[/C][C]63.8554512950923[/C][/ROW]
[ROW][C]144[/C][C]5740[/C][C]5873.49016838516[/C][C]-133.490168385157[/C][/ROW]
[ROW][C]145[/C][C]5821[/C][C]5949.49098319247[/C][C]-128.490983192465[/C][/ROW]
[ROW][C]146[/C][C]5294[/C][C]5482.92059154852[/C][C]-188.920591548517[/C][/ROW]
[ROW][C]147[/C][C]5881[/C][C]5762.2073189084[/C][C]118.792681091598[/C][/ROW]
[ROW][C]148[/C][C]5589[/C][C]5622.39915135456[/C][C]-33.399151354557[/C][/ROW]
[ROW][C]149[/C][C]5845[/C][C]5781.91170792145[/C][C]63.0882920785452[/C][/ROW]
[ROW][C]150[/C][C]5706[/C][C]5790.22511343835[/C][C]-84.2251134383505[/C][/ROW]
[ROW][C]151[/C][C]6355[/C][C]6196.27884136198[/C][C]158.721158638023[/C][/ROW]
[ROW][C]152[/C][C]6404[/C][C]6365.09947423758[/C][C]38.9005257624167[/C][/ROW]
[ROW][C]153[/C][C]6426[/C][C]6299.61903145977[/C][C]126.380968540229[/C][/ROW]
[ROW][C]154[/C][C]6375[/C][C]6320.64176621087[/C][C]54.3582337891303[/C][/ROW]
[ROW][C]155[/C][C]5869[/C][C]6016.55102398436[/C][C]-147.55102398436[/C][/ROW]
[ROW][C]156[/C][C]5994[/C][C]6023.38416565748[/C][C]-29.3841656574787[/C][/ROW]
[ROW][C]157[/C][C]6105[/C][C]6144.57414408384[/C][C]-39.5741440838356[/C][/ROW]
[ROW][C]158[/C][C]5792[/C][C]5683.92121179677[/C][C]108.078788203235[/C][/ROW]
[ROW][C]159[/C][C]6011[/C][C]6160.41866491474[/C][C]-149.418664914742[/C][/ROW]
[ROW][C]160[/C][C]5968[/C][C]5878.38721981886[/C][C]89.6127801811444[/C][/ROW]
[ROW][C]161[/C][C]6255[/C][C]6113.87178152102[/C][C]141.128218478977[/C][/ROW]
[ROW][C]162[/C][C]6208[/C][C]6127.58407412725[/C][C]80.4159258727532[/C][/ROW]
[ROW][C]163[/C][C]6897[/C][C]6676.76800075162[/C][C]220.231999248379[/C][/ROW]
[ROW][C]164[/C][C]6814[/C][C]6860.14020339454[/C][C]-46.1402033945351[/C][/ROW]
[ROW][C]165[/C][C]6897[/C][C]6772.93112970146[/C][C]124.068870298538[/C][/ROW]
[ROW][C]166[/C][C]6596[/C][C]6780.61480909149[/C][C]-184.614809091486[/C][/ROW]
[ROW][C]167[/C][C]6188[/C][C]6328.05866999653[/C][C]-140.058669996534[/C][/ROW]
[ROW][C]168[/C][C]6406[/C][C]6362.77317324245[/C][C]43.2268267575491[/C][/ROW]
[ROW][C]169[/C][C]6548[/C][C]6520.47050557482[/C][C]27.5294944251818[/C][/ROW]
[ROW][C]170[/C][C]5842[/C][C]6084.30210755662[/C][C]-242.30210755662[/C][/ROW]
[ROW][C]171[/C][C]6555[/C][C]6393.61356894278[/C][C]161.386431057215[/C][/ROW]
[ROW][C]172[/C][C]6424[/C][C]6264.36140285158[/C][C]159.638597148416[/C][/ROW]
[ROW][C]173[/C][C]6596[/C][C]6551.78242149708[/C][C]44.2175785029222[/C][/ROW]
[ROW][C]174[/C][C]6645[/C][C]6514.48112999067[/C][C]130.518870009329[/C][/ROW]
[ROW][C]175[/C][C]7203[/C][C]7141.97986660039[/C][C]61.0201333996138[/C][/ROW]
[ROW][C]176[/C][C]7128[/C][C]7220.60405025475[/C][C]-92.6040502547503[/C][/ROW]
[ROW][C]177[/C][C]7133[/C][C]7140.32594467915[/C][C]-7.32594467915169[/C][/ROW]
[ROW][C]178[/C][C]6778[/C][C]7038.78601804642[/C][C]-260.786018046419[/C][/ROW]
[ROW][C]179[/C][C]6593[/C][C]6546.67213379467[/C][C]46.3278662053317[/C][/ROW]
[ROW][C]180[/C][C]6591[/C][C]6691.53108919322[/C][C]-100.531089193219[/C][/ROW]
[ROW][C]181[/C][C]6120[/C][C]6793.46664057831[/C][C]-673.466640578313[/C][/ROW]
[ROW][C]182[/C][C]5612[/C][C]6026.9648153711[/C][C]-414.964815371103[/C][/ROW]
[ROW][C]183[/C][C]6070[/C][C]6318.19919471719[/C][C]-248.19919471719[/C][/ROW]
[ROW][C]184[/C][C]5983[/C][C]6021.3537722308[/C][C]-38.3537722307992[/C][/ROW]
[ROW][C]185[/C][C]6145[/C][C]6185.75930605852[/C][C]-40.7593060585241[/C][/ROW]
[ROW][C]186[/C][C]6303[/C][C]6116.87106250872[/C][C]186.128937491285[/C][/ROW]
[ROW][C]187[/C][C]6588[/C][C]6706.05164711712[/C][C]-118.05164711712[/C][/ROW]
[ROW][C]188[/C][C]6640[/C][C]6669.54279193069[/C][C]-29.5427919306867[/C][/ROW]
[ROW][C]189[/C][C]6719[/C][C]6614.88189962841[/C][C]104.118100371589[/C][/ROW]
[ROW][C]190[/C][C]6575[/C][C]6510.30690906418[/C][C]64.6930909358225[/C][/ROW]
[ROW][C]191[/C][C]6487[/C][C]6204.78932124865[/C][C]282.210678751353[/C][/ROW]
[ROW][C]192[/C][C]6510[/C][C]6406.00037095128[/C][C]103.99962904872[/C][/ROW]
[ROW][C]193[/C][C]6365[/C][C]6481.37572706052[/C][C]-116.375727060523[/C][/ROW]
[ROW][C]194[/C][C]5844[/C][C]5973.25442356329[/C][C]-129.254423563293[/C][/ROW]
[ROW][C]195[/C][C]5974[/C][C]6415.75188630406[/C][C]-441.75188630406[/C][/ROW]
[ROW][C]196[/C][C]5880[/C][C]6073.14609168585[/C][C]-193.146091685849[/C][/ROW]
[ROW][C]197[/C][C]6279[/C][C]6172.14896627977[/C][C]106.851033720225[/C][/ROW]
[ROW][C]198[/C][C]6342[/C][C]6197.10155138895[/C][C]144.898448611053[/C][/ROW]
[ROW][C]199[/C][C]6598[/C][C]6719.45833088263[/C][C]-121.458330882633[/C][/ROW]
[ROW][C]200[/C][C]6801[/C][C]6693.8330266688[/C][C]107.166973331202[/C][/ROW]
[ROW][C]201[/C][C]6529[/C][C]6714.06885067956[/C][C]-185.068850679557[/C][/ROW]
[ROW][C]202[/C][C]6369[/C][C]6484.80958194382[/C][C]-115.809581943824[/C][/ROW]
[ROW][C]203[/C][C]6028[/C][C]6142.29189553415[/C][C]-114.291895534149[/C][/ROW]
[ROW][C]204[/C][C]6187[/C][C]6144.90106347[/C][C]42.0989365300011[/C][/ROW]
[ROW][C]205[/C][C]6164[/C][C]6149.98096643486[/C][C]14.0190335651405[/C][/ROW]
[ROW][C]206[/C][C]5866[/C][C]5702.78455830863[/C][C]163.215441691365[/C][/ROW]
[ROW][C]207[/C][C]6198[/C][C]6192.83701132614[/C][C]5.16298867386013[/C][/ROW]
[ROW][C]208[/C][C]5898[/C][C]6067.01662146601[/C][C]-169.016621466008[/C][/ROW]
[ROW][C]209[/C][C]6462[/C][C]6225.42958626592[/C][C]236.570413734081[/C][/ROW]
[ROW][C]210[/C][C]6063[/C][C]6308.12398159432[/C][C]-245.12398159432[/C][/ROW]
[ROW][C]211[/C][C]6496[/C][C]6622.87584866627[/C][C]-126.875848666266[/C][/ROW]
[ROW][C]212[/C][C]6678[/C][C]6628.31411750681[/C][C]49.6858824931924[/C][/ROW]
[ROW][C]213[/C][C]6554[/C][C]6573.93792450893[/C][C]-19.9379245089294[/C][/ROW]
[ROW][C]214[/C][C]6513[/C][C]6420.03188876787[/C][C]92.9681112321259[/C][/ROW]
[ROW][C]215[/C][C]6210[/C][C]6158.34610575941[/C][C]51.6538942405896[/C][/ROW]
[ROW][C]216[/C][C]5928[/C][C]6255.01095610729[/C][C]-327.010956107295[/C][/ROW]
[ROW][C]217[/C][C]6268[/C][C]6106.12071826393[/C][C]161.879281736067[/C][/ROW]
[ROW][C]218[/C][C]5582[/C][C]5740.18276516698[/C][C]-158.182765166985[/C][/ROW]
[ROW][C]219[/C][C]5869[/C][C]6063.75460054164[/C][C]-194.754600541636[/C][/ROW]
[ROW][C]220[/C][C]5764[/C][C]5828.51539564603[/C][C]-64.5153956460317[/C][/ROW]
[ROW][C]221[/C][C]6082[/C][C]6081.33111784636[/C][C]0.668882153639061[/C][/ROW]
[ROW][C]222[/C][C]6062[/C][C]5986.48106295366[/C][C]75.5189370463404[/C][/ROW]
[ROW][C]223[/C][C]6810[/C][C]6432.69967074362[/C][C]377.300329256375[/C][/ROW]
[ROW][C]224[/C][C]6727[/C][C]6668.3563874811[/C][C]58.6436125189039[/C][/ROW]
[ROW][C]225[/C][C]6537[/C][C]6605.66064915672[/C][C]-68.6606491567245[/C][/ROW]
[ROW][C]226[/C][C]6175[/C][C]6450.26095149715[/C][C]-275.260951497151[/C][/ROW]
[ROW][C]227[/C][C]6014[/C][C]6037.70471874967[/C][C]-23.7047187496737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295746&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295746&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
1424662418.8715557470647.1284442529359
1525442511.4571607152232.5428392847839
1625372514.3812680163522.6187319836481
1725642546.6805018072917.3194981927149
1825822565.9234171800316.0765828199742
1927162903.19653865057-187.196538650573
2029042762.26138736027141.738612639727
2128512810.5198193580440.4801806419623
2229322855.1732747172376.8267252827718
2327722747.7823498407924.2176501592098
2428112713.6447493912497.3552506087599
2529352828.51440288086106.485597119136
2627832816.21461311075-33.2146131107465
2730032885.7619791768117.238020823199
2829952920.3495070782474.6504929217613
2931272978.02370693601148.976293063988
3029853054.41360637161-69.4136063716064
3132873377.53033110378-90.5303311037833
3232363329.65436541663-93.6543654166258
3332523264.72768708578-12.7276870857772
3432283300.05204562167-72.05204562167
3528563105.5148279563-249.514827956303
3631762969.26897726121206.731022738793
3733623135.301529376226.698470623995
3830363137.90199160562-101.901991605622
3933303214.95072918377115.049270816233
4032513238.1874724263112.8125275736857
4133183285.0518856002532.9481143997514
4232383274.99549479158-36.9954947915758
4335973632.98809528392-35.9880952839162
4437083602.91661192252105.083388077483
4539023628.19241126853273.807588731469
4637453773.47465793808-28.4746579380781
4734263536.87356041602-110.873560416022
4835263539.8435398954-13.8435398953998
4934833633.87440299178-150.87440299178
5034583416.3868966898541.6131033101542
5138243602.97779575899221.022204241005
5236963646.4943454806349.5056545193725
5335183717.31033915846-199.310339158465
5438143598.29358949956215.706410500438
5539964106.68913651519-110.689136515185
5641364070.8516945405565.1483054594455
5740374107.54819074036-70.5481907403637
5839154061.74164289702-146.741642897023
5937603745.0734604029414.9265395970615
6039553816.58599150221138.414008497795
6141603953.98117536004206.018824639958
6241153894.14597613083220.854023869168
6342024214.61493560334-12.6149356033438
6440184127.84409067052-109.84409067052
6542334093.79114404108139.208855958917
6640294183.41166699764-154.411666997637
6744014529.19061579571-128.190615795713
6846454518.33422553574126.665774464262
6944914555.0412236549-64.0412236549046
7043794494.86238369967-115.862383699669
7143944189.68948397888204.310516021123
7244724369.66159029704102.338409702965
7346144516.2716742943697.7283257056361
7441604398.113780788-238.113780787996
7543284507.42798669214-179.427986692135
7642024328.05481648302-126.05481648302
7746354326.34642649875308.653573501249
7845424430.00877293521111.991227064789
7949204922.18773341951-2.18773341950782
8047745011.21789460591-237.217894605906
8146984864.98482549915-166.984825499148
8249164748.45306697256167.546933027438
8347034588.63583585208114.364164147923
8446164719.53767475634-103.537674756341
8548734785.1939638589187.8060361410908
8643754591.15995281967-216.159952819666
8748014726.6639580447974.3360419552082
8844274647.13781791477-220.137817914774
8946844684.37432731938-0.374327319377699
9046484625.4188596934722.5811403065263
9152255070.67619896187154.323801038131
9251745179.74986254931-5.74986254931173
9351815131.3981535325849.6018464674216
9452665155.10027277311110.899727226885
9548394944.75562175031-105.755621750308
9650324951.1701640272680.8298359727432
9752215129.3031250602591.6968749397474
9846584864.86184104109-206.861841041089
9950145069.10940524168-55.1094052416847
10049804876.76958328232103.230416717675
10149525092.98788133182-140.98788133182
10249464976.56117087254-30.5611708725437
10353655452.62434839262-87.62434839262
10454565436.4010463496319.5989536503721
10553975401.98332234346-4.98332234346071
10654365410.8233453338125.1766546661884
10749955114.92834732154-119.928347321542
10850195145.14852526803-126.148525268029
10952495239.537589747189.46241025281779
11047994882.12646943242-83.1264694324209
11151375161.86723814019-24.8672381401893
11249794999.36825730398-20.3682573039769
11349515121.28078843785-170.280788437847
11452655004.9684070524260.0315929476
11556125597.3589547487514.6410452512455
11655725637.54338670744-65.5433867074416
11754035559.82663572657-156.826635726567
11853735508.38288489001-135.382884890008
11952525116.68331060745135.316689392546
12054375245.1941690498191.805830950198
12152965495.29694800208-199.29694800208
12250115024.30095814418-13.3009581441775
12352945351.33965060026-57.3396506002637
12453355168.80543744446166.194562555538
12553985343.9976366246354.0023633753735
12653965389.573915924156.42608407585067
12757245860.00852750824-136.008527508238
12858985825.0586225978572.9413774021459
12957185782.58972938018-64.5897293801772
13056255771.28844668693-146.28844668693
13153805403.9582944637-23.9582944637004
13254885479.180849637548.81915036246119
13356785590.3331404485987.6668595514111
13452245246.90942096546-22.9094209654577
13555965575.8440445112920.1559554887108
13651845454.02839623972-270.028396239716
13756205434.18505013048185.814949869517
13855315521.552351700619.44764829939413
13958165976.9000465735-160.900046573496
14060865964.11542741521121.884572584791
14161755912.85080987747262.149190122531
14261126017.4497113394294.5502886605809
14358135749.1445487049163.8554512950923
14457405873.49016838516-133.490168385157
14558215949.49098319247-128.490983192465
14652945482.92059154852-188.920591548517
14758815762.2073189084118.792681091598
14855895622.39915135456-33.399151354557
14958455781.9117079214563.0882920785452
15057065790.22511343835-84.2251134383505
15163556196.27884136198158.721158638023
15264046365.0994742375838.9005257624167
15364266299.61903145977126.380968540229
15463756320.6417662108754.3582337891303
15558696016.55102398436-147.55102398436
15659946023.38416565748-29.3841656574787
15761056144.57414408384-39.5741440838356
15857925683.92121179677108.078788203235
15960116160.41866491474-149.418664914742
16059685878.3872198188689.6127801811444
16162556113.87178152102141.128218478977
16262086127.5840741272580.4159258727532
16368976676.76800075162220.231999248379
16468146860.14020339454-46.1402033945351
16568976772.93112970146124.068870298538
16665966780.61480909149-184.614809091486
16761886328.05866999653-140.058669996534
16864066362.7731732424543.2268267575491
16965486520.4705055748227.5294944251818
17058426084.30210755662-242.30210755662
17165556393.61356894278161.386431057215
17264246264.36140285158159.638597148416
17365966551.7824214970844.2175785029222
17466456514.48112999067130.518870009329
17572037141.9798666003961.0201333996138
17671287220.60405025475-92.6040502547503
17771337140.32594467915-7.32594467915169
17867787038.78601804642-260.786018046419
17965936546.6721337946746.3278662053317
18065916691.53108919322-100.531089193219
18161206793.46664057831-673.466640578313
18256126026.9648153711-414.964815371103
18360706318.19919471719-248.19919471719
18459836021.3537722308-38.3537722307992
18561456185.75930605852-40.7593060585241
18663036116.87106250872186.128937491285
18765886706.05164711712-118.05164711712
18866406669.54279193069-29.5427919306867
18967196614.88189962841104.118100371589
19065756510.3069090641864.6930909358225
19164876204.78932124865282.210678751353
19265106406.00037095128103.99962904872
19363656481.37572706052-116.375727060523
19458445973.25442356329-129.254423563293
19559746415.75188630406-441.75188630406
19658806073.14609168585-193.146091685849
19762796172.14896627977106.851033720225
19863426197.10155138895144.898448611053
19965986719.45833088263-121.458330882633
20068016693.8330266688107.166973331202
20165296714.06885067956-185.068850679557
20263696484.80958194382-115.809581943824
20360286142.29189553415-114.291895534149
20461876144.9010634742.0989365300011
20561646149.9809664348614.0190335651405
20658665702.78455830863163.215441691365
20761986192.837011326145.16298867386013
20858986067.01662146601-169.016621466008
20964626225.42958626592236.570413734081
21060636308.12398159432-245.12398159432
21164966622.87584866627-126.875848666266
21266786628.3141175068149.6858824931924
21365546573.93792450893-19.9379245089294
21465136420.0318887678792.9681112321259
21562106158.3461057594151.6538942405896
21659286255.01095610729-327.010956107295
21762686106.12071826393161.879281736067
21855825740.18276516698-158.182765166985
21958696063.75460054164-194.754600541636
22057645828.51539564603-64.5153956460317
22160826081.331117846360.668882153639061
22260625986.4810629536675.5189370463404
22368106432.69967074362377.300329256375
22467276668.356387481158.6436125189039
22565376605.66064915672-68.6606491567245
22661756450.26095149715-275.260951497151
22760146037.70471874967-23.7047187496737







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
2286035.936110401395874.596677725046197.27554307775
2296096.00826446575896.15327739966295.8632515318
2305617.690837206285394.088557195245841.29311721733
2315994.258863082955729.400238104476259.11748806144
2325857.706612113215569.302892411336146.11033181508
2336151.564339273125824.403907259616478.72477128662
2346069.101697725755720.125311809946418.07808364156
2356537.401315215976139.897705312056934.9049251199
2366566.579390795546143.575252930176989.58352866091
2376458.036762371786017.961774320656898.11175042291
2386294.876865356015841.855605050816747.89812566122
2396033.22250619555555.544722418996510.900289972

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
228 & 6035.93611040139 & 5874.59667772504 & 6197.27554307775 \tabularnewline
229 & 6096.0082644657 & 5896.1532773996 & 6295.8632515318 \tabularnewline
230 & 5617.69083720628 & 5394.08855719524 & 5841.29311721733 \tabularnewline
231 & 5994.25886308295 & 5729.40023810447 & 6259.11748806144 \tabularnewline
232 & 5857.70661211321 & 5569.30289241133 & 6146.11033181508 \tabularnewline
233 & 6151.56433927312 & 5824.40390725961 & 6478.72477128662 \tabularnewline
234 & 6069.10169772575 & 5720.12531180994 & 6418.07808364156 \tabularnewline
235 & 6537.40131521597 & 6139.89770531205 & 6934.9049251199 \tabularnewline
236 & 6566.57939079554 & 6143.57525293017 & 6989.58352866091 \tabularnewline
237 & 6458.03676237178 & 6017.96177432065 & 6898.11175042291 \tabularnewline
238 & 6294.87686535601 & 5841.85560505081 & 6747.89812566122 \tabularnewline
239 & 6033.2225061955 & 5555.54472241899 & 6510.900289972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295746&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]228[/C][C]6035.93611040139[/C][C]5874.59667772504[/C][C]6197.27554307775[/C][/ROW]
[ROW][C]229[/C][C]6096.0082644657[/C][C]5896.1532773996[/C][C]6295.8632515318[/C][/ROW]
[ROW][C]230[/C][C]5617.69083720628[/C][C]5394.08855719524[/C][C]5841.29311721733[/C][/ROW]
[ROW][C]231[/C][C]5994.25886308295[/C][C]5729.40023810447[/C][C]6259.11748806144[/C][/ROW]
[ROW][C]232[/C][C]5857.70661211321[/C][C]5569.30289241133[/C][C]6146.11033181508[/C][/ROW]
[ROW][C]233[/C][C]6151.56433927312[/C][C]5824.40390725961[/C][C]6478.72477128662[/C][/ROW]
[ROW][C]234[/C][C]6069.10169772575[/C][C]5720.12531180994[/C][C]6418.07808364156[/C][/ROW]
[ROW][C]235[/C][C]6537.40131521597[/C][C]6139.89770531205[/C][C]6934.9049251199[/C][/ROW]
[ROW][C]236[/C][C]6566.57939079554[/C][C]6143.57525293017[/C][C]6989.58352866091[/C][/ROW]
[ROW][C]237[/C][C]6458.03676237178[/C][C]6017.96177432065[/C][C]6898.11175042291[/C][/ROW]
[ROW][C]238[/C][C]6294.87686535601[/C][C]5841.85560505081[/C][C]6747.89812566122[/C][/ROW]
[ROW][C]239[/C][C]6033.2225061955[/C][C]5555.54472241899[/C][C]6510.900289972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295746&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295746&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
2286035.936110401395874.596677725046197.27554307775
2296096.00826446575896.15327739966295.8632515318
2305617.690837206285394.088557195245841.29311721733
2315994.258863082955729.400238104476259.11748806144
2325857.706612113215569.302892411336146.11033181508
2336151.564339273125824.403907259616478.72477128662
2346069.101697725755720.125311809946418.07808364156
2356537.401315215976139.897705312056934.9049251199
2366566.579390795546143.575252930176989.58352866091
2376458.036762371786017.961774320656898.11175042291
2386294.876865356015841.855605050816747.89812566122
2396033.22250619555555.544722418996510.900289972



Parameters (Session):
par1 = 12 ;
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')