Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Aug 2016 12:24:57 +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/Aug/15/t14712603706nmtuwd3terf9l7.htm/, Retrieved Sun, 28 Apr 2024 09:30:49 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 28 Apr 2024 09:30:49 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.384610233695977
beta0.0225408714425909
gamma0.451381968305457

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.384610233695977 \tabularnewline
beta & 0.0225408714425909 \tabularnewline
gamma & 0.451381968305457 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.384610233695977[/C][/ROW]
[ROW][C]beta[/C][C]0.0225408714425909[/C][/ROW]
[ROW][C]gamma[/C][C]0.451381968305457[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.384610233695977
beta0.0225408714425909
gamma0.451381968305457







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325132426.3683226495786.6316773504263
1424662416.6571870824449.3428129175591
1525442509.8654810260834.1345189739218
1625372512.4371036484324.5628963515705
1725642544.8736623881619.1263376118391
1825822564.1350798249217.8649201750777
1927162884.52455556911-168.524555569109
2029042757.97404964201146.02595035799
2128512807.918851959743.0811480402999
2229322852.3935196518979.6064803481081
2327722757.8980149932614.1019850067414
2428112725.0810675248185.9189324751892
2529352837.7780435059197.2219564940851
2627832825.61800598944-42.6180059894414
2730032882.27139559397120.728604406031
2829952919.2786115757175.721388424291
2931272974.11400867223152.885991327767
3029853049.86289255575-64.8628925557491
3132873291.33523241962-4.33523241961575
3232363321.40690524362-85.4069052436162
3332523257.83704054694-5.83704054694272
3432283297.31139053312-69.3113905331243
3528563129.72220949365-273.72220949365
3631763006.03609431466169.963905685338
3733623154.80790760238207.192092397618
3830363147.66330021222-111.663300212224
3933303224.10027498021105.899725019787
4032513243.739045909597.26095409040818
4133183293.921618873424.0783811266015
4232383258.77100340011-20.7710034001134
4335973533.523515059363.4764849407002
4437083567.25326440808140.746735591918
4539023614.82436673625287.175633263754
4637453753.96038325931-8.96038325931249
4734263557.9232742296-131.923274229597
4835263618.36992930194-92.3699293019367
4934833680.66242948243-197.662429482433
5034583429.8023115485628.197688451442
5138243622.24353215317201.75646784683
5236963653.9598700677742.0401299322266
5335183725.10141185893-207.101411858926
5438143589.48547181299224.514528187006
5539963985.0125821595310.9874178404739
5641364022.59661278383113.403387216171
5740374102.66684690088-65.6668469008846
5839154023.11890532629-108.118905326293
5937603753.210945881886.78905411812229
6039553877.6199580673677.3800419326358
6141603977.04917243164182.950827568365
6241153939.71185184109175.288148158913
6342024242.60775703655-40.6077570365533
6440184140.3135808071-122.313580807097
6542334081.18323279899151.816767201008
6640294208.76073399299-179.760733992985
6744014391.2392783689.76072163199933
6846454458.54206701112186.457932988885
6944914519.34365995771-28.3436599577053
7043794445.0572314968-66.0572314968003
7143944226.30871905992167.691280940082
7244724436.6692206978735.3307793021286
7346144553.3447036168160.6552963831873
7441604469.87635918569-309.876359185691
7543284525.02984942226-197.029849422257
7642024337.34962491708-135.349624917082
7746354346.71064777664288.28935222336
7845424433.21420183483108.785798165169
7949204780.35823763848139.641762361524
8047744948.86587786416-174.865877864165
8146984810.06852019559-112.068520195594
8249164691.41546452062224.584535479377
8347034650.2108745562352.7891254437691
8446164779.446577021-163.446577020997
8548734824.8157990159748.1842009840257
8643754631.62908822172-256.629088221721
8748014737.0725707257863.9274292742202
8844274667.61933106796-240.619331067957
8946844753.98346011311-69.9834601131097
9046484649.53808273831-1.53808273830964
9152254958.57322894552266.426771054479
9251745085.3319745847988.6680254152097
9351815064.47165481966116.528345180336
9452665128.37080143688137.629198563117
9548395006.36525087883-167.365250878829
9650324989.3172220180442.6827779819605
9752215172.9937990429848.0062009570192
9846584895.30929344235-237.309293442351
9950145097.63415041071-83.634150410714
10049804885.9601324905994.0398675094075
10149525150.46609708487-198.466097084874
10249465016.53354127671-70.5335412767145
10353655373.78442493753-8.78442493753209
10454565343.24904638118112.750953618822
10553975337.5309806420559.4690193579527
10654365382.9919505596953.0080494403064
10749955140.63264723115-145.632647231152
10850195187.39037612535-168.390376125351
10952495286.63579570339-37.6357957033933
11047994891.28729987078-92.2872998707753
11151375187.86215350933-50.8621535093253
11249795034.21605771771-55.2160577177146
11349515154.84153454556-203.841534545561
11452655049.10746176013215.89253823987
11556125530.8856738518381.1143261481666
11655725566.677754169875.32224583013158
11754035501.90161282824-98.9016128282365
11853735480.34446833197-107.344468331973
11952525115.43174320595136.568256794046
12054375261.14919168118175.85080831882
12152965528.84205055288-232.842050552878
12250115041.27032585937-30.270325859371
12352945371.77806253457-77.7780625345695
12453355204.91069231954130.089307680456
12553985355.4687063963442.5312936036635
12653965463.1668124369-67.1668124368989
12757245798.26808255543-74.2680825554316
12858985751.52692193006146.473078069942
12957185711.593297577316.40670242269334
13056255728.61188538009-103.611885380094
13153805433.33847025125-53.3384702512494
13254885515.73186243202-27.7318624320214
13356785588.6390596443289.3609403556829
13452245281.09207776265-57.092077762647
13555965587.687506072498.31249392751306
13651845512.01845041032-328.018450410321
13756205458.43696041831161.563039581685
13855315578.85127894424-47.8512789442429
13958165916.98326349836-100.983263498361
14060865918.62645104781167.373548952189
14161755845.34821952391329.651780476088
14261125956.4559367929155.544063207099
14358135777.3943019632335.6056980367675
14457405904.45353563049-164.453535630487
14558215959.46053563178-138.460535631781
14652945523.79369040973-229.793690409726
14758815780.82061174745100.179388252546
14855895646.54281781483-57.5428178148304
14958455834.8107365538810.1892634461192
15057065839.35038611994-133.350386119943
15163556129.61400053669225.385999463307
15264046333.9288719127470.0711280872611
15364266270.06423308609155.935766913914
15463756266.25018021057108.749819789426
15558696035.72344406456-166.723444064555
15659946027.48753846972-33.4875384697161
15761056139.31537374473-34.3153737447292
15857925718.4663056650973.5336943349057
15960116186.5769015435-175.576901543502
16059685902.8006501109565.1993498890488
16162556158.5265582255896.4734417744176
16262086158.5639343672549.4360656327453
16368976622.54584484645274.454155153549
16468146806.783959345457.2160406545463
16568976746.24466192045150.755338079546
16665966730.93506409469-134.935064094692
16761886331.65621285165-143.656212851654
16864066370.9933001797835.0066998202192
16965486511.2199587836.7800412200049
17058426150.57432987924-308.574329879237
17165556402.11424600921152.885753990791
17264246313.98639300911110.013606990891
17365966598.46049851554-2.46049851554471
17466456549.3483072993895.6516927006196
17572037095.97776008979107.022239910207
17671287142.50396060284-14.5039606028431
17771337114.2107843099918.7892156900125
17867786968.37180545445-190.371805454445
17965936544.4523183830448.5476816169557
18065916708.11096053577-117.11096053577
18161206789.77515391471-669.775153914708
18256126054.77557184146-442.775571841459
18360706375.04483772257-305.04483772257
18459836087.07539623869-104.075396238686
18561456244.30210695207-99.302106952071
18663036170.69329169306132.306708306945
18765886720.39333365735-132.393333657347
18866406624.8194419590915.1805580409118
18967196601.1872543113117.812745688704
19065756420.18831766601154.811682333989
19164876183.24300397246303.756996027543
19265106389.10132469697120.898675303031
19363656400.91264323002-35.9126432300163
19458445970.37625550628-126.376255506284
19559746450.95540078604-476.955400786035
19658806151.56267717805-271.562677178049
19762796243.1167709949235.8832290050832
19863426284.4277369193557.5722630806522
19965986729.79974575042-131.799745750417
20068016673.39463930466127.605360695336
20165296720.4336079616-191.433607961603
20263696427.01445821176-58.0144582117637
20360286143.98404592628-115.98404592628
20461876128.3697209777458.6302790222571
20561646062.89142690934101.108573090656
20658665651.33193972321214.668060276795
20761986160.0602123759837.9397876240228
20858986114.58085401025-216.58085401025
20964626311.98549726295150.014502737049
21060636403.50959565428-340.509595654279
21164966640.01351434151-144.013514341512
21266786647.7026893830130.2973106169875
21365546564.58640961739-10.5864096173909
21465136375.24314796835137.756852031645
21562106150.5626514226659.4373485773422
21659286251.59845598318-323.598455983184
21762686048.27443445069219.72556554931
21855825712.27259456159-130.272594561593
21958696034.64412626134-165.644126261336
22057645833.80147463697-69.8014746369736
22160826184.39964986149-102.399649861493
22260626035.3079907190626.6920092809369
22368106463.52775932699346.472240673005
22467276708.438843401318.561156598701
22565376609.50719445678-72.5071944567826
22661756437.07290650122-262.072906501221
22760146032.91038939781-18.9103893978054
22861095992.78738895536116.212611044644

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2513 & 2426.36832264957 & 86.6316773504263 \tabularnewline
14 & 2466 & 2416.65718708244 & 49.3428129175591 \tabularnewline
15 & 2544 & 2509.86548102608 & 34.1345189739218 \tabularnewline
16 & 2537 & 2512.43710364843 & 24.5628963515705 \tabularnewline
17 & 2564 & 2544.87366238816 & 19.1263376118391 \tabularnewline
18 & 2582 & 2564.13507982492 & 17.8649201750777 \tabularnewline
19 & 2716 & 2884.52455556911 & -168.524555569109 \tabularnewline
20 & 2904 & 2757.97404964201 & 146.02595035799 \tabularnewline
21 & 2851 & 2807.9188519597 & 43.0811480402999 \tabularnewline
22 & 2932 & 2852.39351965189 & 79.6064803481081 \tabularnewline
23 & 2772 & 2757.89801499326 & 14.1019850067414 \tabularnewline
24 & 2811 & 2725.08106752481 & 85.9189324751892 \tabularnewline
25 & 2935 & 2837.77804350591 & 97.2219564940851 \tabularnewline
26 & 2783 & 2825.61800598944 & -42.6180059894414 \tabularnewline
27 & 3003 & 2882.27139559397 & 120.728604406031 \tabularnewline
28 & 2995 & 2919.27861157571 & 75.721388424291 \tabularnewline
29 & 3127 & 2974.11400867223 & 152.885991327767 \tabularnewline
30 & 2985 & 3049.86289255575 & -64.8628925557491 \tabularnewline
31 & 3287 & 3291.33523241962 & -4.33523241961575 \tabularnewline
32 & 3236 & 3321.40690524362 & -85.4069052436162 \tabularnewline
33 & 3252 & 3257.83704054694 & -5.83704054694272 \tabularnewline
34 & 3228 & 3297.31139053312 & -69.3113905331243 \tabularnewline
35 & 2856 & 3129.72220949365 & -273.72220949365 \tabularnewline
36 & 3176 & 3006.03609431466 & 169.963905685338 \tabularnewline
37 & 3362 & 3154.80790760238 & 207.192092397618 \tabularnewline
38 & 3036 & 3147.66330021222 & -111.663300212224 \tabularnewline
39 & 3330 & 3224.10027498021 & 105.899725019787 \tabularnewline
40 & 3251 & 3243.73904590959 & 7.26095409040818 \tabularnewline
41 & 3318 & 3293.9216188734 & 24.0783811266015 \tabularnewline
42 & 3238 & 3258.77100340011 & -20.7710034001134 \tabularnewline
43 & 3597 & 3533.5235150593 & 63.4764849407002 \tabularnewline
44 & 3708 & 3567.25326440808 & 140.746735591918 \tabularnewline
45 & 3902 & 3614.82436673625 & 287.175633263754 \tabularnewline
46 & 3745 & 3753.96038325931 & -8.96038325931249 \tabularnewline
47 & 3426 & 3557.9232742296 & -131.923274229597 \tabularnewline
48 & 3526 & 3618.36992930194 & -92.3699293019367 \tabularnewline
49 & 3483 & 3680.66242948243 & -197.662429482433 \tabularnewline
50 & 3458 & 3429.80231154856 & 28.197688451442 \tabularnewline
51 & 3824 & 3622.24353215317 & 201.75646784683 \tabularnewline
52 & 3696 & 3653.95987006777 & 42.0401299322266 \tabularnewline
53 & 3518 & 3725.10141185893 & -207.101411858926 \tabularnewline
54 & 3814 & 3589.48547181299 & 224.514528187006 \tabularnewline
55 & 3996 & 3985.01258215953 & 10.9874178404739 \tabularnewline
56 & 4136 & 4022.59661278383 & 113.403387216171 \tabularnewline
57 & 4037 & 4102.66684690088 & -65.6668469008846 \tabularnewline
58 & 3915 & 4023.11890532629 & -108.118905326293 \tabularnewline
59 & 3760 & 3753.21094588188 & 6.78905411812229 \tabularnewline
60 & 3955 & 3877.61995806736 & 77.3800419326358 \tabularnewline
61 & 4160 & 3977.04917243164 & 182.950827568365 \tabularnewline
62 & 4115 & 3939.71185184109 & 175.288148158913 \tabularnewline
63 & 4202 & 4242.60775703655 & -40.6077570365533 \tabularnewline
64 & 4018 & 4140.3135808071 & -122.313580807097 \tabularnewline
65 & 4233 & 4081.18323279899 & 151.816767201008 \tabularnewline
66 & 4029 & 4208.76073399299 & -179.760733992985 \tabularnewline
67 & 4401 & 4391.239278368 & 9.76072163199933 \tabularnewline
68 & 4645 & 4458.54206701112 & 186.457932988885 \tabularnewline
69 & 4491 & 4519.34365995771 & -28.3436599577053 \tabularnewline
70 & 4379 & 4445.0572314968 & -66.0572314968003 \tabularnewline
71 & 4394 & 4226.30871905992 & 167.691280940082 \tabularnewline
72 & 4472 & 4436.66922069787 & 35.3307793021286 \tabularnewline
73 & 4614 & 4553.34470361681 & 60.6552963831873 \tabularnewline
74 & 4160 & 4469.87635918569 & -309.876359185691 \tabularnewline
75 & 4328 & 4525.02984942226 & -197.029849422257 \tabularnewline
76 & 4202 & 4337.34962491708 & -135.349624917082 \tabularnewline
77 & 4635 & 4346.71064777664 & 288.28935222336 \tabularnewline
78 & 4542 & 4433.21420183483 & 108.785798165169 \tabularnewline
79 & 4920 & 4780.35823763848 & 139.641762361524 \tabularnewline
80 & 4774 & 4948.86587786416 & -174.865877864165 \tabularnewline
81 & 4698 & 4810.06852019559 & -112.068520195594 \tabularnewline
82 & 4916 & 4691.41546452062 & 224.584535479377 \tabularnewline
83 & 4703 & 4650.21087455623 & 52.7891254437691 \tabularnewline
84 & 4616 & 4779.446577021 & -163.446577020997 \tabularnewline
85 & 4873 & 4824.81579901597 & 48.1842009840257 \tabularnewline
86 & 4375 & 4631.62908822172 & -256.629088221721 \tabularnewline
87 & 4801 & 4737.07257072578 & 63.9274292742202 \tabularnewline
88 & 4427 & 4667.61933106796 & -240.619331067957 \tabularnewline
89 & 4684 & 4753.98346011311 & -69.9834601131097 \tabularnewline
90 & 4648 & 4649.53808273831 & -1.53808273830964 \tabularnewline
91 & 5225 & 4958.57322894552 & 266.426771054479 \tabularnewline
92 & 5174 & 5085.33197458479 & 88.6680254152097 \tabularnewline
93 & 5181 & 5064.47165481966 & 116.528345180336 \tabularnewline
94 & 5266 & 5128.37080143688 & 137.629198563117 \tabularnewline
95 & 4839 & 5006.36525087883 & -167.365250878829 \tabularnewline
96 & 5032 & 4989.31722201804 & 42.6827779819605 \tabularnewline
97 & 5221 & 5172.99379904298 & 48.0062009570192 \tabularnewline
98 & 4658 & 4895.30929344235 & -237.309293442351 \tabularnewline
99 & 5014 & 5097.63415041071 & -83.634150410714 \tabularnewline
100 & 4980 & 4885.96013249059 & 94.0398675094075 \tabularnewline
101 & 4952 & 5150.46609708487 & -198.466097084874 \tabularnewline
102 & 4946 & 5016.53354127671 & -70.5335412767145 \tabularnewline
103 & 5365 & 5373.78442493753 & -8.78442493753209 \tabularnewline
104 & 5456 & 5343.24904638118 & 112.750953618822 \tabularnewline
105 & 5397 & 5337.53098064205 & 59.4690193579527 \tabularnewline
106 & 5436 & 5382.99195055969 & 53.0080494403064 \tabularnewline
107 & 4995 & 5140.63264723115 & -145.632647231152 \tabularnewline
108 & 5019 & 5187.39037612535 & -168.390376125351 \tabularnewline
109 & 5249 & 5286.63579570339 & -37.6357957033933 \tabularnewline
110 & 4799 & 4891.28729987078 & -92.2872998707753 \tabularnewline
111 & 5137 & 5187.86215350933 & -50.8621535093253 \tabularnewline
112 & 4979 & 5034.21605771771 & -55.2160577177146 \tabularnewline
113 & 4951 & 5154.84153454556 & -203.841534545561 \tabularnewline
114 & 5265 & 5049.10746176013 & 215.89253823987 \tabularnewline
115 & 5612 & 5530.88567385183 & 81.1143261481666 \tabularnewline
116 & 5572 & 5566.67775416987 & 5.32224583013158 \tabularnewline
117 & 5403 & 5501.90161282824 & -98.9016128282365 \tabularnewline
118 & 5373 & 5480.34446833197 & -107.344468331973 \tabularnewline
119 & 5252 & 5115.43174320595 & 136.568256794046 \tabularnewline
120 & 5437 & 5261.14919168118 & 175.85080831882 \tabularnewline
121 & 5296 & 5528.84205055288 & -232.842050552878 \tabularnewline
122 & 5011 & 5041.27032585937 & -30.270325859371 \tabularnewline
123 & 5294 & 5371.77806253457 & -77.7780625345695 \tabularnewline
124 & 5335 & 5204.91069231954 & 130.089307680456 \tabularnewline
125 & 5398 & 5355.46870639634 & 42.5312936036635 \tabularnewline
126 & 5396 & 5463.1668124369 & -67.1668124368989 \tabularnewline
127 & 5724 & 5798.26808255543 & -74.2680825554316 \tabularnewline
128 & 5898 & 5751.52692193006 & 146.473078069942 \tabularnewline
129 & 5718 & 5711.59329757731 & 6.40670242269334 \tabularnewline
130 & 5625 & 5728.61188538009 & -103.611885380094 \tabularnewline
131 & 5380 & 5433.33847025125 & -53.3384702512494 \tabularnewline
132 & 5488 & 5515.73186243202 & -27.7318624320214 \tabularnewline
133 & 5678 & 5588.63905964432 & 89.3609403556829 \tabularnewline
134 & 5224 & 5281.09207776265 & -57.092077762647 \tabularnewline
135 & 5596 & 5587.68750607249 & 8.31249392751306 \tabularnewline
136 & 5184 & 5512.01845041032 & -328.018450410321 \tabularnewline
137 & 5620 & 5458.43696041831 & 161.563039581685 \tabularnewline
138 & 5531 & 5578.85127894424 & -47.8512789442429 \tabularnewline
139 & 5816 & 5916.98326349836 & -100.983263498361 \tabularnewline
140 & 6086 & 5918.62645104781 & 167.373548952189 \tabularnewline
141 & 6175 & 5845.34821952391 & 329.651780476088 \tabularnewline
142 & 6112 & 5956.4559367929 & 155.544063207099 \tabularnewline
143 & 5813 & 5777.39430196323 & 35.6056980367675 \tabularnewline
144 & 5740 & 5904.45353563049 & -164.453535630487 \tabularnewline
145 & 5821 & 5959.46053563178 & -138.460535631781 \tabularnewline
146 & 5294 & 5523.79369040973 & -229.793690409726 \tabularnewline
147 & 5881 & 5780.82061174745 & 100.179388252546 \tabularnewline
148 & 5589 & 5646.54281781483 & -57.5428178148304 \tabularnewline
149 & 5845 & 5834.81073655388 & 10.1892634461192 \tabularnewline
150 & 5706 & 5839.35038611994 & -133.350386119943 \tabularnewline
151 & 6355 & 6129.61400053669 & 225.385999463307 \tabularnewline
152 & 6404 & 6333.92887191274 & 70.0711280872611 \tabularnewline
153 & 6426 & 6270.06423308609 & 155.935766913914 \tabularnewline
154 & 6375 & 6266.25018021057 & 108.749819789426 \tabularnewline
155 & 5869 & 6035.72344406456 & -166.723444064555 \tabularnewline
156 & 5994 & 6027.48753846972 & -33.4875384697161 \tabularnewline
157 & 6105 & 6139.31537374473 & -34.3153737447292 \tabularnewline
158 & 5792 & 5718.46630566509 & 73.5336943349057 \tabularnewline
159 & 6011 & 6186.5769015435 & -175.576901543502 \tabularnewline
160 & 5968 & 5902.80065011095 & 65.1993498890488 \tabularnewline
161 & 6255 & 6158.52655822558 & 96.4734417744176 \tabularnewline
162 & 6208 & 6158.56393436725 & 49.4360656327453 \tabularnewline
163 & 6897 & 6622.54584484645 & 274.454155153549 \tabularnewline
164 & 6814 & 6806.78395934545 & 7.2160406545463 \tabularnewline
165 & 6897 & 6746.24466192045 & 150.755338079546 \tabularnewline
166 & 6596 & 6730.93506409469 & -134.935064094692 \tabularnewline
167 & 6188 & 6331.65621285165 & -143.656212851654 \tabularnewline
168 & 6406 & 6370.99330017978 & 35.0066998202192 \tabularnewline
169 & 6548 & 6511.21995878 & 36.7800412200049 \tabularnewline
170 & 5842 & 6150.57432987924 & -308.574329879237 \tabularnewline
171 & 6555 & 6402.11424600921 & 152.885753990791 \tabularnewline
172 & 6424 & 6313.98639300911 & 110.013606990891 \tabularnewline
173 & 6596 & 6598.46049851554 & -2.46049851554471 \tabularnewline
174 & 6645 & 6549.34830729938 & 95.6516927006196 \tabularnewline
175 & 7203 & 7095.97776008979 & 107.022239910207 \tabularnewline
176 & 7128 & 7142.50396060284 & -14.5039606028431 \tabularnewline
177 & 7133 & 7114.21078430999 & 18.7892156900125 \tabularnewline
178 & 6778 & 6968.37180545445 & -190.371805454445 \tabularnewline
179 & 6593 & 6544.45231838304 & 48.5476816169557 \tabularnewline
180 & 6591 & 6708.11096053577 & -117.11096053577 \tabularnewline
181 & 6120 & 6789.77515391471 & -669.775153914708 \tabularnewline
182 & 5612 & 6054.77557184146 & -442.775571841459 \tabularnewline
183 & 6070 & 6375.04483772257 & -305.04483772257 \tabularnewline
184 & 5983 & 6087.07539623869 & -104.075396238686 \tabularnewline
185 & 6145 & 6244.30210695207 & -99.302106952071 \tabularnewline
186 & 6303 & 6170.69329169306 & 132.306708306945 \tabularnewline
187 & 6588 & 6720.39333365735 & -132.393333657347 \tabularnewline
188 & 6640 & 6624.81944195909 & 15.1805580409118 \tabularnewline
189 & 6719 & 6601.1872543113 & 117.812745688704 \tabularnewline
190 & 6575 & 6420.18831766601 & 154.811682333989 \tabularnewline
191 & 6487 & 6183.24300397246 & 303.756996027543 \tabularnewline
192 & 6510 & 6389.10132469697 & 120.898675303031 \tabularnewline
193 & 6365 & 6400.91264323002 & -35.9126432300163 \tabularnewline
194 & 5844 & 5970.37625550628 & -126.376255506284 \tabularnewline
195 & 5974 & 6450.95540078604 & -476.955400786035 \tabularnewline
196 & 5880 & 6151.56267717805 & -271.562677178049 \tabularnewline
197 & 6279 & 6243.11677099492 & 35.8832290050832 \tabularnewline
198 & 6342 & 6284.42773691935 & 57.5722630806522 \tabularnewline
199 & 6598 & 6729.79974575042 & -131.799745750417 \tabularnewline
200 & 6801 & 6673.39463930466 & 127.605360695336 \tabularnewline
201 & 6529 & 6720.4336079616 & -191.433607961603 \tabularnewline
202 & 6369 & 6427.01445821176 & -58.0144582117637 \tabularnewline
203 & 6028 & 6143.98404592628 & -115.98404592628 \tabularnewline
204 & 6187 & 6128.36972097774 & 58.6302790222571 \tabularnewline
205 & 6164 & 6062.89142690934 & 101.108573090656 \tabularnewline
206 & 5866 & 5651.33193972321 & 214.668060276795 \tabularnewline
207 & 6198 & 6160.06021237598 & 37.9397876240228 \tabularnewline
208 & 5898 & 6114.58085401025 & -216.58085401025 \tabularnewline
209 & 6462 & 6311.98549726295 & 150.014502737049 \tabularnewline
210 & 6063 & 6403.50959565428 & -340.509595654279 \tabularnewline
211 & 6496 & 6640.01351434151 & -144.013514341512 \tabularnewline
212 & 6678 & 6647.70268938301 & 30.2973106169875 \tabularnewline
213 & 6554 & 6564.58640961739 & -10.5864096173909 \tabularnewline
214 & 6513 & 6375.24314796835 & 137.756852031645 \tabularnewline
215 & 6210 & 6150.56265142266 & 59.4373485773422 \tabularnewline
216 & 5928 & 6251.59845598318 & -323.598455983184 \tabularnewline
217 & 6268 & 6048.27443445069 & 219.72556554931 \tabularnewline
218 & 5582 & 5712.27259456159 & -130.272594561593 \tabularnewline
219 & 5869 & 6034.64412626134 & -165.644126261336 \tabularnewline
220 & 5764 & 5833.80147463697 & -69.8014746369736 \tabularnewline
221 & 6082 & 6184.39964986149 & -102.399649861493 \tabularnewline
222 & 6062 & 6035.30799071906 & 26.6920092809369 \tabularnewline
223 & 6810 & 6463.52775932699 & 346.472240673005 \tabularnewline
224 & 6727 & 6708.4388434013 & 18.561156598701 \tabularnewline
225 & 6537 & 6609.50719445678 & -72.5071944567826 \tabularnewline
226 & 6175 & 6437.07290650122 & -262.072906501221 \tabularnewline
227 & 6014 & 6032.91038939781 & -18.9103893978054 \tabularnewline
228 & 6109 & 5992.78738895536 & 116.212611044644 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2426.36832264957[/C][C]86.6316773504263[/C][/ROW]
[ROW][C]14[/C][C]2466[/C][C]2416.65718708244[/C][C]49.3428129175591[/C][/ROW]
[ROW][C]15[/C][C]2544[/C][C]2509.86548102608[/C][C]34.1345189739218[/C][/ROW]
[ROW][C]16[/C][C]2537[/C][C]2512.43710364843[/C][C]24.5628963515705[/C][/ROW]
[ROW][C]17[/C][C]2564[/C][C]2544.87366238816[/C][C]19.1263376118391[/C][/ROW]
[ROW][C]18[/C][C]2582[/C][C]2564.13507982492[/C][C]17.8649201750777[/C][/ROW]
[ROW][C]19[/C][C]2716[/C][C]2884.52455556911[/C][C]-168.524555569109[/C][/ROW]
[ROW][C]20[/C][C]2904[/C][C]2757.97404964201[/C][C]146.02595035799[/C][/ROW]
[ROW][C]21[/C][C]2851[/C][C]2807.9188519597[/C][C]43.0811480402999[/C][/ROW]
[ROW][C]22[/C][C]2932[/C][C]2852.39351965189[/C][C]79.6064803481081[/C][/ROW]
[ROW][C]23[/C][C]2772[/C][C]2757.89801499326[/C][C]14.1019850067414[/C][/ROW]
[ROW][C]24[/C][C]2811[/C][C]2725.08106752481[/C][C]85.9189324751892[/C][/ROW]
[ROW][C]25[/C][C]2935[/C][C]2837.77804350591[/C][C]97.2219564940851[/C][/ROW]
[ROW][C]26[/C][C]2783[/C][C]2825.61800598944[/C][C]-42.6180059894414[/C][/ROW]
[ROW][C]27[/C][C]3003[/C][C]2882.27139559397[/C][C]120.728604406031[/C][/ROW]
[ROW][C]28[/C][C]2995[/C][C]2919.27861157571[/C][C]75.721388424291[/C][/ROW]
[ROW][C]29[/C][C]3127[/C][C]2974.11400867223[/C][C]152.885991327767[/C][/ROW]
[ROW][C]30[/C][C]2985[/C][C]3049.86289255575[/C][C]-64.8628925557491[/C][/ROW]
[ROW][C]31[/C][C]3287[/C][C]3291.33523241962[/C][C]-4.33523241961575[/C][/ROW]
[ROW][C]32[/C][C]3236[/C][C]3321.40690524362[/C][C]-85.4069052436162[/C][/ROW]
[ROW][C]33[/C][C]3252[/C][C]3257.83704054694[/C][C]-5.83704054694272[/C][/ROW]
[ROW][C]34[/C][C]3228[/C][C]3297.31139053312[/C][C]-69.3113905331243[/C][/ROW]
[ROW][C]35[/C][C]2856[/C][C]3129.72220949365[/C][C]-273.72220949365[/C][/ROW]
[ROW][C]36[/C][C]3176[/C][C]3006.03609431466[/C][C]169.963905685338[/C][/ROW]
[ROW][C]37[/C][C]3362[/C][C]3154.80790760238[/C][C]207.192092397618[/C][/ROW]
[ROW][C]38[/C][C]3036[/C][C]3147.66330021222[/C][C]-111.663300212224[/C][/ROW]
[ROW][C]39[/C][C]3330[/C][C]3224.10027498021[/C][C]105.899725019787[/C][/ROW]
[ROW][C]40[/C][C]3251[/C][C]3243.73904590959[/C][C]7.26095409040818[/C][/ROW]
[ROW][C]41[/C][C]3318[/C][C]3293.9216188734[/C][C]24.0783811266015[/C][/ROW]
[ROW][C]42[/C][C]3238[/C][C]3258.77100340011[/C][C]-20.7710034001134[/C][/ROW]
[ROW][C]43[/C][C]3597[/C][C]3533.5235150593[/C][C]63.4764849407002[/C][/ROW]
[ROW][C]44[/C][C]3708[/C][C]3567.25326440808[/C][C]140.746735591918[/C][/ROW]
[ROW][C]45[/C][C]3902[/C][C]3614.82436673625[/C][C]287.175633263754[/C][/ROW]
[ROW][C]46[/C][C]3745[/C][C]3753.96038325931[/C][C]-8.96038325931249[/C][/ROW]
[ROW][C]47[/C][C]3426[/C][C]3557.9232742296[/C][C]-131.923274229597[/C][/ROW]
[ROW][C]48[/C][C]3526[/C][C]3618.36992930194[/C][C]-92.3699293019367[/C][/ROW]
[ROW][C]49[/C][C]3483[/C][C]3680.66242948243[/C][C]-197.662429482433[/C][/ROW]
[ROW][C]50[/C][C]3458[/C][C]3429.80231154856[/C][C]28.197688451442[/C][/ROW]
[ROW][C]51[/C][C]3824[/C][C]3622.24353215317[/C][C]201.75646784683[/C][/ROW]
[ROW][C]52[/C][C]3696[/C][C]3653.95987006777[/C][C]42.0401299322266[/C][/ROW]
[ROW][C]53[/C][C]3518[/C][C]3725.10141185893[/C][C]-207.101411858926[/C][/ROW]
[ROW][C]54[/C][C]3814[/C][C]3589.48547181299[/C][C]224.514528187006[/C][/ROW]
[ROW][C]55[/C][C]3996[/C][C]3985.01258215953[/C][C]10.9874178404739[/C][/ROW]
[ROW][C]56[/C][C]4136[/C][C]4022.59661278383[/C][C]113.403387216171[/C][/ROW]
[ROW][C]57[/C][C]4037[/C][C]4102.66684690088[/C][C]-65.6668469008846[/C][/ROW]
[ROW][C]58[/C][C]3915[/C][C]4023.11890532629[/C][C]-108.118905326293[/C][/ROW]
[ROW][C]59[/C][C]3760[/C][C]3753.21094588188[/C][C]6.78905411812229[/C][/ROW]
[ROW][C]60[/C][C]3955[/C][C]3877.61995806736[/C][C]77.3800419326358[/C][/ROW]
[ROW][C]61[/C][C]4160[/C][C]3977.04917243164[/C][C]182.950827568365[/C][/ROW]
[ROW][C]62[/C][C]4115[/C][C]3939.71185184109[/C][C]175.288148158913[/C][/ROW]
[ROW][C]63[/C][C]4202[/C][C]4242.60775703655[/C][C]-40.6077570365533[/C][/ROW]
[ROW][C]64[/C][C]4018[/C][C]4140.3135808071[/C][C]-122.313580807097[/C][/ROW]
[ROW][C]65[/C][C]4233[/C][C]4081.18323279899[/C][C]151.816767201008[/C][/ROW]
[ROW][C]66[/C][C]4029[/C][C]4208.76073399299[/C][C]-179.760733992985[/C][/ROW]
[ROW][C]67[/C][C]4401[/C][C]4391.239278368[/C][C]9.76072163199933[/C][/ROW]
[ROW][C]68[/C][C]4645[/C][C]4458.54206701112[/C][C]186.457932988885[/C][/ROW]
[ROW][C]69[/C][C]4491[/C][C]4519.34365995771[/C][C]-28.3436599577053[/C][/ROW]
[ROW][C]70[/C][C]4379[/C][C]4445.0572314968[/C][C]-66.0572314968003[/C][/ROW]
[ROW][C]71[/C][C]4394[/C][C]4226.30871905992[/C][C]167.691280940082[/C][/ROW]
[ROW][C]72[/C][C]4472[/C][C]4436.66922069787[/C][C]35.3307793021286[/C][/ROW]
[ROW][C]73[/C][C]4614[/C][C]4553.34470361681[/C][C]60.6552963831873[/C][/ROW]
[ROW][C]74[/C][C]4160[/C][C]4469.87635918569[/C][C]-309.876359185691[/C][/ROW]
[ROW][C]75[/C][C]4328[/C][C]4525.02984942226[/C][C]-197.029849422257[/C][/ROW]
[ROW][C]76[/C][C]4202[/C][C]4337.34962491708[/C][C]-135.349624917082[/C][/ROW]
[ROW][C]77[/C][C]4635[/C][C]4346.71064777664[/C][C]288.28935222336[/C][/ROW]
[ROW][C]78[/C][C]4542[/C][C]4433.21420183483[/C][C]108.785798165169[/C][/ROW]
[ROW][C]79[/C][C]4920[/C][C]4780.35823763848[/C][C]139.641762361524[/C][/ROW]
[ROW][C]80[/C][C]4774[/C][C]4948.86587786416[/C][C]-174.865877864165[/C][/ROW]
[ROW][C]81[/C][C]4698[/C][C]4810.06852019559[/C][C]-112.068520195594[/C][/ROW]
[ROW][C]82[/C][C]4916[/C][C]4691.41546452062[/C][C]224.584535479377[/C][/ROW]
[ROW][C]83[/C][C]4703[/C][C]4650.21087455623[/C][C]52.7891254437691[/C][/ROW]
[ROW][C]84[/C][C]4616[/C][C]4779.446577021[/C][C]-163.446577020997[/C][/ROW]
[ROW][C]85[/C][C]4873[/C][C]4824.81579901597[/C][C]48.1842009840257[/C][/ROW]
[ROW][C]86[/C][C]4375[/C][C]4631.62908822172[/C][C]-256.629088221721[/C][/ROW]
[ROW][C]87[/C][C]4801[/C][C]4737.07257072578[/C][C]63.9274292742202[/C][/ROW]
[ROW][C]88[/C][C]4427[/C][C]4667.61933106796[/C][C]-240.619331067957[/C][/ROW]
[ROW][C]89[/C][C]4684[/C][C]4753.98346011311[/C][C]-69.9834601131097[/C][/ROW]
[ROW][C]90[/C][C]4648[/C][C]4649.53808273831[/C][C]-1.53808273830964[/C][/ROW]
[ROW][C]91[/C][C]5225[/C][C]4958.57322894552[/C][C]266.426771054479[/C][/ROW]
[ROW][C]92[/C][C]5174[/C][C]5085.33197458479[/C][C]88.6680254152097[/C][/ROW]
[ROW][C]93[/C][C]5181[/C][C]5064.47165481966[/C][C]116.528345180336[/C][/ROW]
[ROW][C]94[/C][C]5266[/C][C]5128.37080143688[/C][C]137.629198563117[/C][/ROW]
[ROW][C]95[/C][C]4839[/C][C]5006.36525087883[/C][C]-167.365250878829[/C][/ROW]
[ROW][C]96[/C][C]5032[/C][C]4989.31722201804[/C][C]42.6827779819605[/C][/ROW]
[ROW][C]97[/C][C]5221[/C][C]5172.99379904298[/C][C]48.0062009570192[/C][/ROW]
[ROW][C]98[/C][C]4658[/C][C]4895.30929344235[/C][C]-237.309293442351[/C][/ROW]
[ROW][C]99[/C][C]5014[/C][C]5097.63415041071[/C][C]-83.634150410714[/C][/ROW]
[ROW][C]100[/C][C]4980[/C][C]4885.96013249059[/C][C]94.0398675094075[/C][/ROW]
[ROW][C]101[/C][C]4952[/C][C]5150.46609708487[/C][C]-198.466097084874[/C][/ROW]
[ROW][C]102[/C][C]4946[/C][C]5016.53354127671[/C][C]-70.5335412767145[/C][/ROW]
[ROW][C]103[/C][C]5365[/C][C]5373.78442493753[/C][C]-8.78442493753209[/C][/ROW]
[ROW][C]104[/C][C]5456[/C][C]5343.24904638118[/C][C]112.750953618822[/C][/ROW]
[ROW][C]105[/C][C]5397[/C][C]5337.53098064205[/C][C]59.4690193579527[/C][/ROW]
[ROW][C]106[/C][C]5436[/C][C]5382.99195055969[/C][C]53.0080494403064[/C][/ROW]
[ROW][C]107[/C][C]4995[/C][C]5140.63264723115[/C][C]-145.632647231152[/C][/ROW]
[ROW][C]108[/C][C]5019[/C][C]5187.39037612535[/C][C]-168.390376125351[/C][/ROW]
[ROW][C]109[/C][C]5249[/C][C]5286.63579570339[/C][C]-37.6357957033933[/C][/ROW]
[ROW][C]110[/C][C]4799[/C][C]4891.28729987078[/C][C]-92.2872998707753[/C][/ROW]
[ROW][C]111[/C][C]5137[/C][C]5187.86215350933[/C][C]-50.8621535093253[/C][/ROW]
[ROW][C]112[/C][C]4979[/C][C]5034.21605771771[/C][C]-55.2160577177146[/C][/ROW]
[ROW][C]113[/C][C]4951[/C][C]5154.84153454556[/C][C]-203.841534545561[/C][/ROW]
[ROW][C]114[/C][C]5265[/C][C]5049.10746176013[/C][C]215.89253823987[/C][/ROW]
[ROW][C]115[/C][C]5612[/C][C]5530.88567385183[/C][C]81.1143261481666[/C][/ROW]
[ROW][C]116[/C][C]5572[/C][C]5566.67775416987[/C][C]5.32224583013158[/C][/ROW]
[ROW][C]117[/C][C]5403[/C][C]5501.90161282824[/C][C]-98.9016128282365[/C][/ROW]
[ROW][C]118[/C][C]5373[/C][C]5480.34446833197[/C][C]-107.344468331973[/C][/ROW]
[ROW][C]119[/C][C]5252[/C][C]5115.43174320595[/C][C]136.568256794046[/C][/ROW]
[ROW][C]120[/C][C]5437[/C][C]5261.14919168118[/C][C]175.85080831882[/C][/ROW]
[ROW][C]121[/C][C]5296[/C][C]5528.84205055288[/C][C]-232.842050552878[/C][/ROW]
[ROW][C]122[/C][C]5011[/C][C]5041.27032585937[/C][C]-30.270325859371[/C][/ROW]
[ROW][C]123[/C][C]5294[/C][C]5371.77806253457[/C][C]-77.7780625345695[/C][/ROW]
[ROW][C]124[/C][C]5335[/C][C]5204.91069231954[/C][C]130.089307680456[/C][/ROW]
[ROW][C]125[/C][C]5398[/C][C]5355.46870639634[/C][C]42.5312936036635[/C][/ROW]
[ROW][C]126[/C][C]5396[/C][C]5463.1668124369[/C][C]-67.1668124368989[/C][/ROW]
[ROW][C]127[/C][C]5724[/C][C]5798.26808255543[/C][C]-74.2680825554316[/C][/ROW]
[ROW][C]128[/C][C]5898[/C][C]5751.52692193006[/C][C]146.473078069942[/C][/ROW]
[ROW][C]129[/C][C]5718[/C][C]5711.59329757731[/C][C]6.40670242269334[/C][/ROW]
[ROW][C]130[/C][C]5625[/C][C]5728.61188538009[/C][C]-103.611885380094[/C][/ROW]
[ROW][C]131[/C][C]5380[/C][C]5433.33847025125[/C][C]-53.3384702512494[/C][/ROW]
[ROW][C]132[/C][C]5488[/C][C]5515.73186243202[/C][C]-27.7318624320214[/C][/ROW]
[ROW][C]133[/C][C]5678[/C][C]5588.63905964432[/C][C]89.3609403556829[/C][/ROW]
[ROW][C]134[/C][C]5224[/C][C]5281.09207776265[/C][C]-57.092077762647[/C][/ROW]
[ROW][C]135[/C][C]5596[/C][C]5587.68750607249[/C][C]8.31249392751306[/C][/ROW]
[ROW][C]136[/C][C]5184[/C][C]5512.01845041032[/C][C]-328.018450410321[/C][/ROW]
[ROW][C]137[/C][C]5620[/C][C]5458.43696041831[/C][C]161.563039581685[/C][/ROW]
[ROW][C]138[/C][C]5531[/C][C]5578.85127894424[/C][C]-47.8512789442429[/C][/ROW]
[ROW][C]139[/C][C]5816[/C][C]5916.98326349836[/C][C]-100.983263498361[/C][/ROW]
[ROW][C]140[/C][C]6086[/C][C]5918.62645104781[/C][C]167.373548952189[/C][/ROW]
[ROW][C]141[/C][C]6175[/C][C]5845.34821952391[/C][C]329.651780476088[/C][/ROW]
[ROW][C]142[/C][C]6112[/C][C]5956.4559367929[/C][C]155.544063207099[/C][/ROW]
[ROW][C]143[/C][C]5813[/C][C]5777.39430196323[/C][C]35.6056980367675[/C][/ROW]
[ROW][C]144[/C][C]5740[/C][C]5904.45353563049[/C][C]-164.453535630487[/C][/ROW]
[ROW][C]145[/C][C]5821[/C][C]5959.46053563178[/C][C]-138.460535631781[/C][/ROW]
[ROW][C]146[/C][C]5294[/C][C]5523.79369040973[/C][C]-229.793690409726[/C][/ROW]
[ROW][C]147[/C][C]5881[/C][C]5780.82061174745[/C][C]100.179388252546[/C][/ROW]
[ROW][C]148[/C][C]5589[/C][C]5646.54281781483[/C][C]-57.5428178148304[/C][/ROW]
[ROW][C]149[/C][C]5845[/C][C]5834.81073655388[/C][C]10.1892634461192[/C][/ROW]
[ROW][C]150[/C][C]5706[/C][C]5839.35038611994[/C][C]-133.350386119943[/C][/ROW]
[ROW][C]151[/C][C]6355[/C][C]6129.61400053669[/C][C]225.385999463307[/C][/ROW]
[ROW][C]152[/C][C]6404[/C][C]6333.92887191274[/C][C]70.0711280872611[/C][/ROW]
[ROW][C]153[/C][C]6426[/C][C]6270.06423308609[/C][C]155.935766913914[/C][/ROW]
[ROW][C]154[/C][C]6375[/C][C]6266.25018021057[/C][C]108.749819789426[/C][/ROW]
[ROW][C]155[/C][C]5869[/C][C]6035.72344406456[/C][C]-166.723444064555[/C][/ROW]
[ROW][C]156[/C][C]5994[/C][C]6027.48753846972[/C][C]-33.4875384697161[/C][/ROW]
[ROW][C]157[/C][C]6105[/C][C]6139.31537374473[/C][C]-34.3153737447292[/C][/ROW]
[ROW][C]158[/C][C]5792[/C][C]5718.46630566509[/C][C]73.5336943349057[/C][/ROW]
[ROW][C]159[/C][C]6011[/C][C]6186.5769015435[/C][C]-175.576901543502[/C][/ROW]
[ROW][C]160[/C][C]5968[/C][C]5902.80065011095[/C][C]65.1993498890488[/C][/ROW]
[ROW][C]161[/C][C]6255[/C][C]6158.52655822558[/C][C]96.4734417744176[/C][/ROW]
[ROW][C]162[/C][C]6208[/C][C]6158.56393436725[/C][C]49.4360656327453[/C][/ROW]
[ROW][C]163[/C][C]6897[/C][C]6622.54584484645[/C][C]274.454155153549[/C][/ROW]
[ROW][C]164[/C][C]6814[/C][C]6806.78395934545[/C][C]7.2160406545463[/C][/ROW]
[ROW][C]165[/C][C]6897[/C][C]6746.24466192045[/C][C]150.755338079546[/C][/ROW]
[ROW][C]166[/C][C]6596[/C][C]6730.93506409469[/C][C]-134.935064094692[/C][/ROW]
[ROW][C]167[/C][C]6188[/C][C]6331.65621285165[/C][C]-143.656212851654[/C][/ROW]
[ROW][C]168[/C][C]6406[/C][C]6370.99330017978[/C][C]35.0066998202192[/C][/ROW]
[ROW][C]169[/C][C]6548[/C][C]6511.21995878[/C][C]36.7800412200049[/C][/ROW]
[ROW][C]170[/C][C]5842[/C][C]6150.57432987924[/C][C]-308.574329879237[/C][/ROW]
[ROW][C]171[/C][C]6555[/C][C]6402.11424600921[/C][C]152.885753990791[/C][/ROW]
[ROW][C]172[/C][C]6424[/C][C]6313.98639300911[/C][C]110.013606990891[/C][/ROW]
[ROW][C]173[/C][C]6596[/C][C]6598.46049851554[/C][C]-2.46049851554471[/C][/ROW]
[ROW][C]174[/C][C]6645[/C][C]6549.34830729938[/C][C]95.6516927006196[/C][/ROW]
[ROW][C]175[/C][C]7203[/C][C]7095.97776008979[/C][C]107.022239910207[/C][/ROW]
[ROW][C]176[/C][C]7128[/C][C]7142.50396060284[/C][C]-14.5039606028431[/C][/ROW]
[ROW][C]177[/C][C]7133[/C][C]7114.21078430999[/C][C]18.7892156900125[/C][/ROW]
[ROW][C]178[/C][C]6778[/C][C]6968.37180545445[/C][C]-190.371805454445[/C][/ROW]
[ROW][C]179[/C][C]6593[/C][C]6544.45231838304[/C][C]48.5476816169557[/C][/ROW]
[ROW][C]180[/C][C]6591[/C][C]6708.11096053577[/C][C]-117.11096053577[/C][/ROW]
[ROW][C]181[/C][C]6120[/C][C]6789.77515391471[/C][C]-669.775153914708[/C][/ROW]
[ROW][C]182[/C][C]5612[/C][C]6054.77557184146[/C][C]-442.775571841459[/C][/ROW]
[ROW][C]183[/C][C]6070[/C][C]6375.04483772257[/C][C]-305.04483772257[/C][/ROW]
[ROW][C]184[/C][C]5983[/C][C]6087.07539623869[/C][C]-104.075396238686[/C][/ROW]
[ROW][C]185[/C][C]6145[/C][C]6244.30210695207[/C][C]-99.302106952071[/C][/ROW]
[ROW][C]186[/C][C]6303[/C][C]6170.69329169306[/C][C]132.306708306945[/C][/ROW]
[ROW][C]187[/C][C]6588[/C][C]6720.39333365735[/C][C]-132.393333657347[/C][/ROW]
[ROW][C]188[/C][C]6640[/C][C]6624.81944195909[/C][C]15.1805580409118[/C][/ROW]
[ROW][C]189[/C][C]6719[/C][C]6601.1872543113[/C][C]117.812745688704[/C][/ROW]
[ROW][C]190[/C][C]6575[/C][C]6420.18831766601[/C][C]154.811682333989[/C][/ROW]
[ROW][C]191[/C][C]6487[/C][C]6183.24300397246[/C][C]303.756996027543[/C][/ROW]
[ROW][C]192[/C][C]6510[/C][C]6389.10132469697[/C][C]120.898675303031[/C][/ROW]
[ROW][C]193[/C][C]6365[/C][C]6400.91264323002[/C][C]-35.9126432300163[/C][/ROW]
[ROW][C]194[/C][C]5844[/C][C]5970.37625550628[/C][C]-126.376255506284[/C][/ROW]
[ROW][C]195[/C][C]5974[/C][C]6450.95540078604[/C][C]-476.955400786035[/C][/ROW]
[ROW][C]196[/C][C]5880[/C][C]6151.56267717805[/C][C]-271.562677178049[/C][/ROW]
[ROW][C]197[/C][C]6279[/C][C]6243.11677099492[/C][C]35.8832290050832[/C][/ROW]
[ROW][C]198[/C][C]6342[/C][C]6284.42773691935[/C][C]57.5722630806522[/C][/ROW]
[ROW][C]199[/C][C]6598[/C][C]6729.79974575042[/C][C]-131.799745750417[/C][/ROW]
[ROW][C]200[/C][C]6801[/C][C]6673.39463930466[/C][C]127.605360695336[/C][/ROW]
[ROW][C]201[/C][C]6529[/C][C]6720.4336079616[/C][C]-191.433607961603[/C][/ROW]
[ROW][C]202[/C][C]6369[/C][C]6427.01445821176[/C][C]-58.0144582117637[/C][/ROW]
[ROW][C]203[/C][C]6028[/C][C]6143.98404592628[/C][C]-115.98404592628[/C][/ROW]
[ROW][C]204[/C][C]6187[/C][C]6128.36972097774[/C][C]58.6302790222571[/C][/ROW]
[ROW][C]205[/C][C]6164[/C][C]6062.89142690934[/C][C]101.108573090656[/C][/ROW]
[ROW][C]206[/C][C]5866[/C][C]5651.33193972321[/C][C]214.668060276795[/C][/ROW]
[ROW][C]207[/C][C]6198[/C][C]6160.06021237598[/C][C]37.9397876240228[/C][/ROW]
[ROW][C]208[/C][C]5898[/C][C]6114.58085401025[/C][C]-216.58085401025[/C][/ROW]
[ROW][C]209[/C][C]6462[/C][C]6311.98549726295[/C][C]150.014502737049[/C][/ROW]
[ROW][C]210[/C][C]6063[/C][C]6403.50959565428[/C][C]-340.509595654279[/C][/ROW]
[ROW][C]211[/C][C]6496[/C][C]6640.01351434151[/C][C]-144.013514341512[/C][/ROW]
[ROW][C]212[/C][C]6678[/C][C]6647.70268938301[/C][C]30.2973106169875[/C][/ROW]
[ROW][C]213[/C][C]6554[/C][C]6564.58640961739[/C][C]-10.5864096173909[/C][/ROW]
[ROW][C]214[/C][C]6513[/C][C]6375.24314796835[/C][C]137.756852031645[/C][/ROW]
[ROW][C]215[/C][C]6210[/C][C]6150.56265142266[/C][C]59.4373485773422[/C][/ROW]
[ROW][C]216[/C][C]5928[/C][C]6251.59845598318[/C][C]-323.598455983184[/C][/ROW]
[ROW][C]217[/C][C]6268[/C][C]6048.27443445069[/C][C]219.72556554931[/C][/ROW]
[ROW][C]218[/C][C]5582[/C][C]5712.27259456159[/C][C]-130.272594561593[/C][/ROW]
[ROW][C]219[/C][C]5869[/C][C]6034.64412626134[/C][C]-165.644126261336[/C][/ROW]
[ROW][C]220[/C][C]5764[/C][C]5833.80147463697[/C][C]-69.8014746369736[/C][/ROW]
[ROW][C]221[/C][C]6082[/C][C]6184.39964986149[/C][C]-102.399649861493[/C][/ROW]
[ROW][C]222[/C][C]6062[/C][C]6035.30799071906[/C][C]26.6920092809369[/C][/ROW]
[ROW][C]223[/C][C]6810[/C][C]6463.52775932699[/C][C]346.472240673005[/C][/ROW]
[ROW][C]224[/C][C]6727[/C][C]6708.4388434013[/C][C]18.561156598701[/C][/ROW]
[ROW][C]225[/C][C]6537[/C][C]6609.50719445678[/C][C]-72.5071944567826[/C][/ROW]
[ROW][C]226[/C][C]6175[/C][C]6437.07290650122[/C][C]-262.072906501221[/C][/ROW]
[ROW][C]227[/C][C]6014[/C][C]6032.91038939781[/C][C]-18.9103893978054[/C][/ROW]
[ROW][C]228[/C][C]6109[/C][C]5992.78738895536[/C][C]116.212611044644[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1325132426.3683226495786.6316773504263
1424662416.6571870824449.3428129175591
1525442509.8654810260834.1345189739218
1625372512.4371036484324.5628963515705
1725642544.8736623881619.1263376118391
1825822564.1350798249217.8649201750777
1927162884.52455556911-168.524555569109
2029042757.97404964201146.02595035799
2128512807.918851959743.0811480402999
2229322852.3935196518979.6064803481081
2327722757.8980149932614.1019850067414
2428112725.0810675248185.9189324751892
2529352837.7780435059197.2219564940851
2627832825.61800598944-42.6180059894414
2730032882.27139559397120.728604406031
2829952919.2786115757175.721388424291
2931272974.11400867223152.885991327767
3029853049.86289255575-64.8628925557491
3132873291.33523241962-4.33523241961575
3232363321.40690524362-85.4069052436162
3332523257.83704054694-5.83704054694272
3432283297.31139053312-69.3113905331243
3528563129.72220949365-273.72220949365
3631763006.03609431466169.963905685338
3733623154.80790760238207.192092397618
3830363147.66330021222-111.663300212224
3933303224.10027498021105.899725019787
4032513243.739045909597.26095409040818
4133183293.921618873424.0783811266015
4232383258.77100340011-20.7710034001134
4335973533.523515059363.4764849407002
4437083567.25326440808140.746735591918
4539023614.82436673625287.175633263754
4637453753.96038325931-8.96038325931249
4734263557.9232742296-131.923274229597
4835263618.36992930194-92.3699293019367
4934833680.66242948243-197.662429482433
5034583429.8023115485628.197688451442
5138243622.24353215317201.75646784683
5236963653.9598700677742.0401299322266
5335183725.10141185893-207.101411858926
5438143589.48547181299224.514528187006
5539963985.0125821595310.9874178404739
5641364022.59661278383113.403387216171
5740374102.66684690088-65.6668469008846
5839154023.11890532629-108.118905326293
5937603753.210945881886.78905411812229
6039553877.6199580673677.3800419326358
6141603977.04917243164182.950827568365
6241153939.71185184109175.288148158913
6342024242.60775703655-40.6077570365533
6440184140.3135808071-122.313580807097
6542334081.18323279899151.816767201008
6640294208.76073399299-179.760733992985
6744014391.2392783689.76072163199933
6846454458.54206701112186.457932988885
6944914519.34365995771-28.3436599577053
7043794445.0572314968-66.0572314968003
7143944226.30871905992167.691280940082
7244724436.6692206978735.3307793021286
7346144553.3447036168160.6552963831873
7441604469.87635918569-309.876359185691
7543284525.02984942226-197.029849422257
7642024337.34962491708-135.349624917082
7746354346.71064777664288.28935222336
7845424433.21420183483108.785798165169
7949204780.35823763848139.641762361524
8047744948.86587786416-174.865877864165
8146984810.06852019559-112.068520195594
8249164691.41546452062224.584535479377
8347034650.2108745562352.7891254437691
8446164779.446577021-163.446577020997
8548734824.8157990159748.1842009840257
8643754631.62908822172-256.629088221721
8748014737.0725707257863.9274292742202
8844274667.61933106796-240.619331067957
8946844753.98346011311-69.9834601131097
9046484649.53808273831-1.53808273830964
9152254958.57322894552266.426771054479
9251745085.3319745847988.6680254152097
9351815064.47165481966116.528345180336
9452665128.37080143688137.629198563117
9548395006.36525087883-167.365250878829
9650324989.3172220180442.6827779819605
9752215172.9937990429848.0062009570192
9846584895.30929344235-237.309293442351
9950145097.63415041071-83.634150410714
10049804885.9601324905994.0398675094075
10149525150.46609708487-198.466097084874
10249465016.53354127671-70.5335412767145
10353655373.78442493753-8.78442493753209
10454565343.24904638118112.750953618822
10553975337.5309806420559.4690193579527
10654365382.9919505596953.0080494403064
10749955140.63264723115-145.632647231152
10850195187.39037612535-168.390376125351
10952495286.63579570339-37.6357957033933
11047994891.28729987078-92.2872998707753
11151375187.86215350933-50.8621535093253
11249795034.21605771771-55.2160577177146
11349515154.84153454556-203.841534545561
11452655049.10746176013215.89253823987
11556125530.8856738518381.1143261481666
11655725566.677754169875.32224583013158
11754035501.90161282824-98.9016128282365
11853735480.34446833197-107.344468331973
11952525115.43174320595136.568256794046
12054375261.14919168118175.85080831882
12152965528.84205055288-232.842050552878
12250115041.27032585937-30.270325859371
12352945371.77806253457-77.7780625345695
12453355204.91069231954130.089307680456
12553985355.4687063963442.5312936036635
12653965463.1668124369-67.1668124368989
12757245798.26808255543-74.2680825554316
12858985751.52692193006146.473078069942
12957185711.593297577316.40670242269334
13056255728.61188538009-103.611885380094
13153805433.33847025125-53.3384702512494
13254885515.73186243202-27.7318624320214
13356785588.6390596443289.3609403556829
13452245281.09207776265-57.092077762647
13555965587.687506072498.31249392751306
13651845512.01845041032-328.018450410321
13756205458.43696041831161.563039581685
13855315578.85127894424-47.8512789442429
13958165916.98326349836-100.983263498361
14060865918.62645104781167.373548952189
14161755845.34821952391329.651780476088
14261125956.4559367929155.544063207099
14358135777.3943019632335.6056980367675
14457405904.45353563049-164.453535630487
14558215959.46053563178-138.460535631781
14652945523.79369040973-229.793690409726
14758815780.82061174745100.179388252546
14855895646.54281781483-57.5428178148304
14958455834.8107365538810.1892634461192
15057065839.35038611994-133.350386119943
15163556129.61400053669225.385999463307
15264046333.9288719127470.0711280872611
15364266270.06423308609155.935766913914
15463756266.25018021057108.749819789426
15558696035.72344406456-166.723444064555
15659946027.48753846972-33.4875384697161
15761056139.31537374473-34.3153737447292
15857925718.4663056650973.5336943349057
15960116186.5769015435-175.576901543502
16059685902.8006501109565.1993498890488
16162556158.5265582255896.4734417744176
16262086158.5639343672549.4360656327453
16368976622.54584484645274.454155153549
16468146806.783959345457.2160406545463
16568976746.24466192045150.755338079546
16665966730.93506409469-134.935064094692
16761886331.65621285165-143.656212851654
16864066370.9933001797835.0066998202192
16965486511.2199587836.7800412200049
17058426150.57432987924-308.574329879237
17165556402.11424600921152.885753990791
17264246313.98639300911110.013606990891
17365966598.46049851554-2.46049851554471
17466456549.3483072993895.6516927006196
17572037095.97776008979107.022239910207
17671287142.50396060284-14.5039606028431
17771337114.2107843099918.7892156900125
17867786968.37180545445-190.371805454445
17965936544.4523183830448.5476816169557
18065916708.11096053577-117.11096053577
18161206789.77515391471-669.775153914708
18256126054.77557184146-442.775571841459
18360706375.04483772257-305.04483772257
18459836087.07539623869-104.075396238686
18561456244.30210695207-99.302106952071
18663036170.69329169306132.306708306945
18765886720.39333365735-132.393333657347
18866406624.8194419590915.1805580409118
18967196601.1872543113117.812745688704
19065756420.18831766601154.811682333989
19164876183.24300397246303.756996027543
19265106389.10132469697120.898675303031
19363656400.91264323002-35.9126432300163
19458445970.37625550628-126.376255506284
19559746450.95540078604-476.955400786035
19658806151.56267717805-271.562677178049
19762796243.1167709949235.8832290050832
19863426284.4277369193557.5722630806522
19965986729.79974575042-131.799745750417
20068016673.39463930466127.605360695336
20165296720.4336079616-191.433607961603
20263696427.01445821176-58.0144582117637
20360286143.98404592628-115.98404592628
20461876128.3697209777458.6302790222571
20561646062.89142690934101.108573090656
20658665651.33193972321214.668060276795
20761986160.0602123759837.9397876240228
20858986114.58085401025-216.58085401025
20964626311.98549726295150.014502737049
21060636403.50959565428-340.509595654279
21164966640.01351434151-144.013514341512
21266786647.7026893830130.2973106169875
21365546564.58640961739-10.5864096173909
21465136375.24314796835137.756852031645
21562106150.5626514226659.4373485773422
21659286251.59845598318-323.598455983184
21762686048.27443445069219.72556554931
21855825712.27259456159-130.272594561593
21958696034.64412626134-165.644126261336
22057645833.80147463697-69.8014746369736
22160826184.39964986149-102.399649861493
22260626035.3079907190626.6920092809369
22368106463.52775932699346.472240673005
22467276708.438843401318.561156598701
22565376609.50719445678-72.5071944567826
22661756437.07290650122-262.072906501221
22760146032.91038939781-18.9103893978054
22861095992.78738895536116.212611044644







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
2296108.727044016225808.307675853926409.14641217853
2305588.276119605935265.458920944955911.09331826691
2315949.336509909525604.673914982236293.99910483682
2325838.671143921265472.598138806496204.74414903603
2336207.51192144465820.373790435536594.65005245366
2346135.001735225345727.073637273076542.92983317761
2356642.890277625846214.391487123817071.38906812786
2366661.562660458286212.66719366897110.45812724766
2376528.138543990296058.983260996826997.29382698375
2386329.506018198475840.196915109026818.81512128791
2396094.527653054085585.144827415786603.91047869238
2406100.219186788925570.820811118476629.61756245936

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
229 & 6108.72704401622 & 5808.30767585392 & 6409.14641217853 \tabularnewline
230 & 5588.27611960593 & 5265.45892094495 & 5911.09331826691 \tabularnewline
231 & 5949.33650990952 & 5604.67391498223 & 6293.99910483682 \tabularnewline
232 & 5838.67114392126 & 5472.59813880649 & 6204.74414903603 \tabularnewline
233 & 6207.5119214446 & 5820.37379043553 & 6594.65005245366 \tabularnewline
234 & 6135.00173522534 & 5727.07363727307 & 6542.92983317761 \tabularnewline
235 & 6642.89027762584 & 6214.39148712381 & 7071.38906812786 \tabularnewline
236 & 6661.56266045828 & 6212.6671936689 & 7110.45812724766 \tabularnewline
237 & 6528.13854399029 & 6058.98326099682 & 6997.29382698375 \tabularnewline
238 & 6329.50601819847 & 5840.19691510902 & 6818.81512128791 \tabularnewline
239 & 6094.52765305408 & 5585.14482741578 & 6603.91047869238 \tabularnewline
240 & 6100.21918678892 & 5570.82081111847 & 6629.61756245936 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]6108.72704401622[/C][C]5808.30767585392[/C][C]6409.14641217853[/C][/ROW]
[ROW][C]230[/C][C]5588.27611960593[/C][C]5265.45892094495[/C][C]5911.09331826691[/C][/ROW]
[ROW][C]231[/C][C]5949.33650990952[/C][C]5604.67391498223[/C][C]6293.99910483682[/C][/ROW]
[ROW][C]232[/C][C]5838.67114392126[/C][C]5472.59813880649[/C][C]6204.74414903603[/C][/ROW]
[ROW][C]233[/C][C]6207.5119214446[/C][C]5820.37379043553[/C][C]6594.65005245366[/C][/ROW]
[ROW][C]234[/C][C]6135.00173522534[/C][C]5727.07363727307[/C][C]6542.92983317761[/C][/ROW]
[ROW][C]235[/C][C]6642.89027762584[/C][C]6214.39148712381[/C][C]7071.38906812786[/C][/ROW]
[ROW][C]236[/C][C]6661.56266045828[/C][C]6212.6671936689[/C][C]7110.45812724766[/C][/ROW]
[ROW][C]237[/C][C]6528.13854399029[/C][C]6058.98326099682[/C][C]6997.29382698375[/C][/ROW]
[ROW][C]238[/C][C]6329.50601819847[/C][C]5840.19691510902[/C][C]6818.81512128791[/C][/ROW]
[ROW][C]239[/C][C]6094.52765305408[/C][C]5585.14482741578[/C][C]6603.91047869238[/C][/ROW]
[ROW][C]240[/C][C]6100.21918678892[/C][C]5570.82081111847[/C][C]6629.61756245936[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
2296108.727044016225808.307675853926409.14641217853
2305588.276119605935265.458920944955911.09331826691
2315949.336509909525604.673914982236293.99910483682
2325838.671143921265472.598138806496204.74414903603
2336207.51192144465820.373790435536594.65005245366
2346135.001735225345727.073637273076542.92983317761
2356642.890277625846214.391487123817071.38906812786
2366661.562660458286212.66719366897110.45812724766
2376528.138543990296058.983260996826997.29382698375
2386329.506018198475840.196915109026818.81512128791
2396094.527653054085585.144827415786603.91047869238
2406100.219186788925570.820811118476629.61756245936



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
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')