Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.476329705578366
beta0.00583226902366792
gamma0.787059048256216


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310.19459.629373771367520.565126228632481
1410.301410.00272708958730.298672910412705
1510.06759.907190515320130.160309484679869
169.67159.600192684262860.0713073157371422
179.50199.485640240584620.0162597594153819
189.45979.454378848238490.00532115176150683
199.43629.430046854730350.00615314526965349
209.59199.496507425059830.0953925749401741
2110.01679.989765395139770.0269346048602319
2210.32210.6689062937212-0.346906293721227
2311.16611.1989869326756-0.0329869326755912
2411.545411.28780921468240.257590785317616
2511.371211.5475966827094-0.176396682709438
2611.072311.4589796199638-0.386679619963772
2710.81310.9791177783629-0.166117778362912
2810.301610.4781993129901-0.176599312990149
2910.422710.22043395467720.202266045322812
3010.316210.27134191920680.0448580807931744
3110.451910.26437277823240.187527221767622
3210.856710.45269927971680.404000720283179
3311.271611.06428941401550.207310585984477
3411.434111.6753163293582-0.241216329358149
3512.127312.3854683180792-0.258168318079164
3611.981412.4865120460467-0.505112046046674
3711.835212.2017282923085-0.366528292308509
3811.984711.93294642281170.0517535771883288
3911.54511.7511186119019-0.20611861190195
4011.528511.22500400123050.303495998769465
4111.553911.35158648473260.202313515267432
4211.62211.33715126147590.284848738524092
4311.657811.50347732749210.154322672507881
4411.676711.7652949613966-0.0885949613966055
4511.875212.0598968205952-0.184696820595162
4613.264312.29696270765890.967337292341057
4714.229713.57678357531340.652916424686619
4814.30814.0135407204530.294459279547038
4913.791514.1724732985381-0.380973298538088
5013.763314.0749076915119-0.311607691511915
5113.977513.61840423421390.359095765786126
5213.647813.57781928615660.0699807138433535
5313.224713.5570782519601-0.332378251960144
5413.097113.3260957755452-0.228995775545213
5513.103913.1965620292357-0.0926620292357363
5613.20613.2426237165744-0.0366237165743701
5713.790113.52452711565060.265572884349405
5814.645714.4542978451630.191402154836963
5915.576415.23617688272090.340223117279081
6015.610215.37662938672470.233570613275305
6115.885515.22838578242690.657114217573103
6216.013715.65697849319310.356721506806888
6315.618615.8002102307539-0.181610230753856
6415.38415.3863607103684-0.00236071036841778
6515.275115.16857554368460.10652445631543
6615.091215.193735121429-0.102535121428984
6714.922215.1854504928658-0.263250492865808
6815.623115.17769954899360.445400451006449
6916.673715.81944466558950.854255334410547
7017.680517.00637368013760.67412631986242
7119.191918.0881891034741.10371089652601
7219.171118.55913927359940.611960726400639
7318.565818.7775364095943-0.211736409594273
7418.128518.6778811181326-0.549381118132573
7516.79118.1745345751706-1.38353457517058
7616.946817.2656169481082-0.318816948108239
7717.316416.94465796274390.371742037256055
7817.181617.0134051081160.16819489188401
7916.762717.0720114140829-0.309311414082945
8017.23917.338444047844-0.0994440478439707
8117.883817.8917099067047-0.00790990670470393
8218.903818.59385992556580.309940074434166
8320.027419.67838601646760.349013983532441
8420.008719.58420159565830.42449840434173
8519.636619.37031896379120.266281036208753
8619.816319.3570307565210.459269243478992
8718.860218.9909688632289-0.130768863228869
8817.920619.1217332152506-1.20113321525055
8917.688918.6667890731234-0.977889073123421
9017.8418.0066914475159-0.16669144751588
9117.67817.705960863279-0.0279608632790413
9217.725818.190677708724-0.464877708723996
9318.586518.6043578849005-0.0178578849004687
9419.980419.42950118601440.550898813985615
9521.158420.64230409481490.516095905185093
9621.292120.65667787267490.635422127325061
9720.944520.47650015612160.467999843878374
9820.573120.6378453756735-0.0647453756735281
9919.327419.776541073742-0.449141073741966
10017.786619.3111611426841-1.52456114268413
10117.748318.7899389767934-1.04163897679344
10217.564818.4294091620754-0.864609162075372
10317.476317.8470709071887-0.370770907188717
10417.726417.9811175351567-0.254717535156662
10518.573618.6724303228626-0.0988303228625647
10619.923619.68648117890210.237118821097919
10721.328620.72766398963440.600936010365604
10820.724920.8240537330693-0.09915373306929
10920.333420.21535299926710.118047000732943
11019.765819.9798390740421-0.214039074042145
11118.756918.8779844446256-0.121084444625627
11217.696318.1155294754083-0.419229475408283
11317.797818.3128276328719-0.515027632871938
11418.177118.2705430090492-0.0934430090492384
11518.373818.2556566192510.118143380748961
11618.199618.6683608018858-0.468760801885811
11718.844319.3193148426882-0.475014842688207
11820.100120.2889434102163-0.188843410216311
11921.245821.2722960493976-0.0264960493976325
12020.838120.7746472095350.0634527904649609
12120.196720.3267484052807-0.130048405280721
12219.815919.8293239054349-0.0134239054348733
12318.578418.8550347429995-0.276634742999505
12419.2117.888865498791.32113450121003
12519.341918.87376371993140.468136280068567
12619.1219.4743777865566-0.354377786556554
12719.156319.4225112705314-0.266211270531358
12818.978319.4092735756887-0.4309735756887
12920.291320.07478987061680.216510129383174
13022.543921.49282243438641.05107756561364
13123.282123.13820571971990.143894280280083
13222.619122.7637719325874-0.144671932587364
13322.159922.14138542074280.0185145792572285
13421.276621.767608118465-0.491008118464975
13519.084620.4608341534551-1.37623415345512
13618.909619.6298615273214-0.720261527321423
13718.809519.2855725384251-0.4760725384251
13820.116419.08956349744121.02683650255878
13920.776219.72792470809391.04827529190612
14020.904420.27253509209160.631864907908355
14122.002621.71375952764940.288840472350582
14223.640123.51300104727210.127098952727877
14325.0424.3445758394240.695424160576025
14424.718524.11566314936680.602836850633174
14524.175223.92041910078990.254780899210136
14624.138223.45365720374520.684542796254796
14722.394922.34972389802470.0451761019753043
14821.374322.477870416737-1.10357041673696
14921.491122.0622738550886-0.571173855088571
15021.218722.4507682265026-1.23206822650258
15121.213722.0260716278822-0.812371627882225
15221.673521.51169352445490.161806475545131
15322.509622.5852489277214-0.075648927721371
15424.309724.14081196507390.168888034926095
15525.798925.22325077446880.575649225531187
15625.437624.89551028062680.542089719373152
15723.87824.5240925509798-0.646092550979763
15823.696623.7990621211054-0.102462121105393
15923.354422.04826143704151.30613856295848
16021.199322.2986056291484-1.09930562914841
16122.043122.099515152551-0.0564151525510397
16222.020322.4572829406797-0.43698294067968
16321.88622.582972223452-0.696972223451994
16421.977122.5240808032375-0.546980803237481
16523.075923.1591830278017-0.0832830278016559
16624.985924.80890947078460.176990529215445
16726.261426.0598922500960.201507749904039
16826.112725.53609983910140.576600160898625
16925.629624.68749043657870.942109563421312
17025.292624.94353294702250.34906705297751
17122.814623.9901341604274-1.17553416042737
17222.297422.06182014725630.235579852743683
17322.886822.9269836324203-0.0401836324203195
17422.461223.1342446551806-0.673044655180572
17522.316523.0382941810491-0.721794181049141
17622.731923.0272912360853-0.295391236085269
17723.269223.9719409295977-0.70274092959767
17824.943225.4307449389783-0.487544938978338
17927.827226.37031816568941.45688183431055
18027.405926.59760656275890.808293437241076
18126.623226.0091623260990.614037673900999
18226.877925.86274959178191.01515040821815
18325.10524.59834095367330.506659046326682
18423.60124.0576764218647-0.456676421864749
18523.537424.4822829296312-0.944882929631159
18623.524823.9980996004789-0.473299600478878
18722.946523.9780864052642-1.03158640526419
18823.663323.9952909466309-0.331990946630924
18925.593224.75453713552910.838662864470901
19027.768327.04045781544850.727842184551491
19129.469129.36795153141320.101148468586846
19228.347228.6859573226121-0.338757322612057
19328.387927.47170308758850.916196912411518
19427.969627.63600829887750.333591701122469
19526.007525.83694818220.170551817800032
19624.253324.737778945383-0.484478945383046
19724.499924.9464870877212-0.446587087721181
19823.898824.893972424939-0.995172424938978
19923.668324.3937707482777-0.725470748277729
20023.942724.8444807862001-0.901780786200089
20126.015525.81258088932810.202919110671903
20228.952927.746001712911.20689828709001
20330.30230.04071677402610.261283225973859
20429.87429.25146347471210.622536525287902
20528.225729.0127891422302-0.787089142230229
20628.081128.1213563467421-0.0402563467420549
20726.339826.07169826883690.268101731163132
20825.484724.74396423736480.74073576263519
20925.482325.5502461746277-0.0679461746277248
21024.969725.451386841879-0.481686841879036
21125.228225.3077622430438-0.0795622430437568
21225.925725.996092777663-0.0703927776630131
21328.781827.82045278144720.96134721855277
21427.955230.5359745178161-2.58077451781605
21533.347530.63328143697592.71421856302407
21632.783431.16465962872011.61874037127992
21731.658630.82561535248580.832984647514227
21831.661331.02428581940770.637014180592306
21929.183929.4368058216401-0.252905821640098
22028.882528.06673490858130.815765091418729
22127.633428.5866919976225-0.953291997622536
22227.751127.9043718132665-0.153271813266503
22327.379228.0926156501799-0.713415650179883
22427.774828.4907365133578-0.715936513357818
22531.432930.43898712182740.993912878172551
22633.273531.71633327513281.55716672486724
22735.096235.9847728236153-0.888572823615291
22834.953734.35624081335240.597459186647647
22931.830733.2117541657466-1.38105416574664
23030.998432.2737711509282-1.27537115092818
23128.62929.4019935661006-0.772993566100631
23226.437928.2166246605336-1.77872466053355
23325.440826.7563803575192-1.31558035751916
23424.668126.2149856052307-1.54688560523067
23524.099425.488427913921-1.38902791392103
23624.604325.5417053730366-0.937405373036572
23727.249228.0665888838137-0.817388883813699
23829.551128.68567117283180.865428827168174
23929.852231.58702163426-1.73482163425999
24031.698930.13596822757711.56293177242295
24129.635728.60667397711421.02902602288576
24230.519728.83770949126551.68199050873449
24332.782327.56735406671025.21494593328982
24424.994228.822015330372-3.82781533037195
24523.518726.5732433048479-3.05454330484788
24624.024925.0999889530405-1.07508895304048
24724.569224.6563300019965-0.0871300019965453
24824.40225.5126028273958-1.11060282739576
24926.708928.0006942403101-1.29179424031011
25031.687429.08231550457712.60508449542285
25132.880131.74035389059041.13974610940958
25232.790633.0254845231796-0.234884523179652
25330.878530.42253000973410.455969990265849
25430.302430.6508827349147-0.348482734914658
25528.367929.8650080498423-1.49710804984231
25625.657824.17232704255451.48547295744549
25725.159824.76477206339690.395027936603096
25824.614325.7517135975505-1.13741359755051
25924.52825.6866028634125-1.15860286341254
26025.290525.6087293904743-0.318229390474308
26130.001628.39983538100941.60176461899064
26234.272832.47418192627591.79861807372405
26334.440834.15018478493930.290615215060676
26434.190734.4679846355662-0.277284635566232
26533.663632.13316059338471.53043940661526
26633.907332.54832188945221.35897811054778
26730.217532.1136578811878-1.89615788118785
26828.527427.47040104554081.05699895445921
26925.950527.418328153444-1.46782815344404
27026.239826.8901647716637-0.650364771663668
27126.281927.0535085943215-0.771608594321471
27226.736227.5126070417817-0.776407041781688
27328.839530.8818074047264-2.04230740472638
27431.095133.2963800073389-2.20128000733894
27533.701532.42933372398321.2721662760168
27633.809132.96709579871670.842004201283338
27732.112631.90008787384580.212512126154209
2783231.60274561262810.397254387371913
27929.12229.3516109877461-0.229610987746145
28026.812426.70724322703690.105156772963142
28125.465425.1463958023260.319004197673973
28223.833125.7964904786171-1.96339047861709
28324.71425.2709931498161-0.556993149816055
28428.328825.81750158627912.51129841372089
28529.639130.227274453255-0.588174453255004
28632.454233.2693049406338-0.815104940633844
28733.565734.4983328388712-0.93263283887125
28833.185633.80664725701-0.621047257009963
28933.29731.77728789801691.5197121019831
29033.5132.17637313365351.33362686634647
29131.378930.11311942192731.26578057807269
29229.455528.3234104714311.13208952856902
29327.269927.3470954558095-0.0771954558095125
29427.258626.87389186899370.384708131006349
29527.859128.0591807336772-0.200080733677197
29629.636230.0539711656321-0.417771165632093
29730.958731.7965756377964-0.837875637796394
29831.863334.6309522670717-2.76765226707166
29933.818834.880877077543-1.06207707754302
30033.753134.2549901312807-0.501890131280739
30133.610333.16408789707980.446212102920249
30232.905232.9715189950188-0.0663189950188325
30329.500530.2059594170856-0.705459417085581
30427.363427.4092054253926-0.0458054253926043
30527.229825.35715069087821.87264930912183
30626.521125.9922557066970.528844293302985
30726.522826.9947367708277-0.47193677082775
30827.299128.7591178074658-1.46001780746584
30929.172629.8180306485655-0.645430648565544
31030.29731.9351449398479-1.63814493984789
31132.528733.4156404876455-0.886940487645489
31232.48733.0941331093994-0.607133109399349
31332.419732.33364790161680.0860520983831776
31430.85431.7470570980797-0.893057098079748
31528.699528.31075063473460.388749365265426
31627.788126.29660400762391.49149599237613
31726.560925.7613121868520.799587813148033
31825.943125.32223450103210.620865498967852
31925.557825.9471325673605-0.389332567360494
32027.127527.3349089259084-0.207408925908421
32130.255629.3209916445190.934608355481036
32234.097631.78073362663692.31686637336313
32334.561435.4648866545652-0.903486654565249
32434.294835.2609292289445-0.966129228944489
32533.341834.6242551438542-1.28245514385424
32631.818732.9875615694042-1.16886156940421
32729.081829.9527306567994-0.870930656799434
32827.344427.7941097309204-0.449709730920436
32926.623326.04463591786990.578664082130139
33026.186925.4216983107710.765201689228963
33126.295325.69442100118530.600878998814689
33228.704327.62703266218561.07726733781439
33332.065330.69749356357751.36780643642254
33434.540133.93625032485010.603849675149881
33534.663635.47534376811-0.811743768109977
33634.255735.2877224121335-1.03202241213355
33732.052634.487556612849-2.43495661284898
33830.689232.3437811521206-1.65458115212057
33928.01229.1941033782195-1.18210337821945
34026.152827.0537281257153-0.900928125715268
34123.227625.5047823456402-2.27718234564018
34224.24423.58207248798360.661927512016447
34324.814123.72125756831781.09284243168221
34427.863226.06930279138491.7938972086151
34529.623329.58760389082980.0356961091702068
34632.424531.86000389496290.564496105037062
34733.341732.77983148688240.561868513117588
34833.044233.1424581789294-0.0982581789293846
34932.052632.1981791548532-0.145579154853174
35030.218231.4622410932519-1.24404109325192
35128.929228.69969222840890.229507771591077
35226.822127.3483602151292-0.526260215129245
35326.103225.4124464559430.690753544057017
35425.979226.1248824211871-0.14568242118715
35527.144326.06478885688581.07951114311419
35629.499328.70319760608370.796102393916346
35731.65631.0265555198060.629444480194046
35833.366533.8063702163256-0.439870216325616
35935.052134.25055988787950.801540112120513
36034.407634.4597922402601-0.0521922402601405
36133.06933.5226003872809-0.453600387280893
36231.581632.1909938761108-0.609393876110815
36330.069530.3436391907877-0.274139190787693
36429.003528.44506485959110.558435140408879
36528.681327.53459741144631.14670258855368
36628.35928.12790711106050.231092888939543
36730.044728.76174127228351.28295872771652
36831.507331.39029710677540.117002893224576
36934.1633.32965207710630.830347922893672
37035.5735.7731549823104-0.203154982310359
37136.4236.8511358375616-0.431135837561641
37235.1236.1272873862051-1.00728738620513
37333.1434.5730110712064-1.4330110712064
37430.2932.7112494016535-2.42124940165354
37528.230.1345780088238-1.93457800882378
37626.527.7791733974942-1.2791733974942
37725.4726.2216860507305-0.751686050730459
37824.9625.5139134343944-0.553913434394357
37925.626.1857351607658-0.585735160765751
38027.7627.41679844816290.343201551837151
38130.1329.73172041861350.398279581386493
38232.3531.5160580031050.833941996894968
38332.832.9695652836361-0.169565283636132
38432.5432.10906180920230.430938190797747
38529.7831.0446019864125-1.26460198641252
38628.7928.8364276243664-0.0464276243664337
38726.827.5788188700187-0.778818870018679
38825.4126.0345569337433-0.624556933743349
38924.3424.9985993894524-0.658599389452377
39024.3924.4092468127578-0.019246812757828
3912525.3166821029955-0.316682102995458
39226.2727.0535724388792-0.783572438879169
39327.8828.8461481905897-0.966148190589735
39429.3530.1480089558361-0.79800895583606
39529.8330.393909102959-0.563909102959027
39629.4629.5753201969181-0.115320196918113


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
39727.532559895975725.716335122861629.3487846690898
39826.413079776990724.399162253683428.426997300298
39924.860097574847922.664223788151727.0559713615441
40023.736928002705221.371189844678126.1026661607323
40122.972706917436820.446745567168925.4986682677047
40222.950681998258520.272398268734825.6289657277821
40323.734849824699620.91085674267526.5588429067242
40425.421187232860622.457113813704428.3852606520167
40527.504963563138224.405667260276430.604259866
40629.332225694518726.101946006890632.5625053821467
40730.052840722353426.695313356436233.4103680882706
40829.687428258107326.205971961196433.1688845550182