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exponential smoothing

*The author of this computation has been verified*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Wed, 08 Dec 2010 09:17:39 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/08/t12917997521dy5fzj8ca1z5py.htm/, Retrieved Wed, 22 May 2013 08:18:53 +0000
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
System-generated keywords (parent):
t1228161348uwzsdsk5ig48muz (pk = 27281)
Estimated Impact
47
 
Dataseries X:
» Textfile « » CSV « » Stem and Leaf « » Histogram « » Kernel Density « » Harrell-Davis Quantiles « » Central Tendency « » Variability «
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.859089779897674
beta0.0739551466119535
gamma1


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13299.5239.39449786324860.105502136752
14347.4339.4925684547857.90743154521482
15338.3339.929368367977-1.62936836797678
16327.7329.223847139343-1.52384713934293
17351.6353.166328513730-1.56632851373035
18396.6400.389465951146-3.78946595114559
19438.8384.59946838781954.2005316121809
20395.6427.763334305495-32.1633343054951
21363.5393.901916821003-30.4019168210031
22378.8345.07632301571533.7236769842847
23357410.295475302627-53.2954753026268
24369383.104615914129-14.1046159141288
25464.8456.9764119326667.82358806733362
26479.1502.592180774858-23.4921807748580
27431.3470.502913550706-39.202913550706
28366.5420.938862378819-54.4388623788188
29326.3389.460350164271-63.1603501642712
30355.1369.585850194136-14.4858501941362
31331.6338.228916187246-6.62891618724552
32261.3298.551363583577-37.2513635835773
33249241.8299002121887.17009978781158
34205.5217.967924422901-12.4679244229012
35235.6211.95764480809523.6423551919051
36240.9241.98904722745-1.08904722745021
37264.9316.562591234604-51.6625912346038
38253.8289.312575917534-35.5125759175336
39232.3226.5700985522315.72990144776912
40193.8198.202426353210-4.40242635320968
41177196.401736377519-19.4017363775191
42213.2211.6796915975861.52030840241380
43207.2186.89868700696220.301312993038
44180.6159.47067126989821.1293287301018
45188.6156.30113556351232.2988644364878
46175.4149.99459343855425.4054065614463
47199182.75022833916716.2497716608326
48179.6203.617164709325-24.0171647093253
49225.8250.581684813321-24.7816848133213
50234249.622954887637-15.6229548876367
51200.2211.965074818564-11.7650748185640
52183.6168.21451159180715.3854884081933
53178.2183.631681264515-5.43168126451542
54203.2217.078693406992-13.8786934069917
55208.5183.95603276270324.5439672372974
56191.8162.80010060119228.999899398808
57172.8170.9766299555431.82337004445708
58148138.5919464650259.40805353497475
59159.4156.3723218196683.02767818033197
60154.5159.424241468732-4.92424146873239
61213.2223.114591521913-9.91459152191297
62196.4237.594179120147-41.1941791201465
63182.8178.2628823647034.53711763529682
64176.4153.12984918555223.2701508144476
65153.6173.674936082875-20.0749360828750
66173.2193.709097448662-20.5090974486619
67171160.24050332241710.7594966775835
68151.2126.93060898447624.2693910155242
69161.9125.97345677823335.9265432217675
70157.2124.88163560193832.3183643980615
71201.7163.82696635807237.8730336419277
72236.4200.28953826207236.1104617379277
73356.1305.73216475881350.367835241187
74398.3378.62511951616419.6748804838356
75403.7392.93004242907410.7699575709265
76384.6391.087477668013-6.4874776680125
77365.8393.365923368252-27.5659233682523
78368.1419.833142168581-51.7331421685811
79367.9374.89222873197-6.99222873197033
80347338.0537245328588.94627546714219
81343.3334.4197455565918.88025444340911
82292.9316.710436241821-23.8104362418211
83311.5311.778835654345-0.278835654344562
84300.9316.353255060838-15.4532550608384
85366.9377.367067087161-10.4670670871610
86356.9387.667374574820-30.7673745748205
87329.7348.173219823229-18.4732198232289
88316.2307.7085947446378.49140525536296
89269309.768950771735-40.7689507717352
90289.3310.533206458106-21.2332064581061
91266.2289.081745239821-22.8817452398206
92253.6230.81190883849522.7880911615046
93233.8229.9127075754743.88729242452641
94228.4193.84303814983334.5569618501666
95253.6236.61393143854516.9860685614551
96260.1249.22294884163110.8770511583691
97306.6330.573061287800-23.9730612877995
98309.2322.565493664962-13.3654936649622
99309.5297.01460930371812.4853906962820
100271286.173849460292-15.1738494602924
101279.9258.68683658454221.2131634154579
102317.9317.1145548083720.785445191628298
103298.4317.408207348347-19.0082073483469
104246.7272.208947367314-25.5089473673142
105227.3227.393941712298-0.0939417122979478
106209.1192.21176394506616.8882360549335
107259.9216.19120960679443.7087903932063
108266251.45791817299314.5420818270065
109320.6331.840035391451-11.2400353914510
110308.5337.869127744946-29.3691277449465
111282.2302.798694924629-20.5986949246292
112262.7258.1226538880034.57734611199737
113263.5252.47025616613311.0297438338667
114313.1298.36329682943914.7367031705608
115284.3307.831853745127-23.5318537451273
116252.6257.521597984580-4.92159798457968
117250.3234.97345006809615.3265499319041
118246.5217.41079095030329.0892090496972
119312.7258.40540546960554.2945945303951
120333.2302.08308994734031.1169100526596
121446.4397.55128294514348.8487170548572
122511.6460.94489352261250.6551064773881
123515.5509.2400341400556.25996585994528
124506.4506.2737247486130.126275251387142
125483.2512.512040675153-29.312040675153
126522.3536.512509971341-14.2125099713409
127509.8526.121695403856-16.3216954038557
128460.7495.489111659899-34.7891116598992
129405.8459.098776494406-53.2987764944056
130375389.123568567087-14.1235685670874
131378.5398.404206937121-19.9042069371205
132406.8372.21631495799834.5836850420023
133467.8470.525458397287-2.72545839728718
134469.8483.954127951157-14.1541279511571
135429.8460.286358805320-30.4863588053195
136355.8412.522482908257-56.7224829082571
137332.7349.797741990305-17.0977419903055
138378371.2183831210156.78161687898495
139360.5364.699360233611-4.19936023361089
140334.7328.782042485915.91795751409
141319.5314.2441603400195.2558396599814
142323.1293.30265421721629.7973457827839
143363.6335.50106876385228.0989312361477
144352.1357.280238295066-5.18023829506632
145411.9412.695151719774-0.79515171977448
146388.6422.818141734829-34.2181417348292
147416.4374.98388595275241.4161140472477
148360.7385.233692068623-24.5336920686227
149338357.730570008506-19.7305700085058
150417.2382.07197348015535.1280265198452
151388.4401.97644570551-13.5764457055102
152371.1362.4519545440128.64804545598793
153331.5353.362568993653-21.8625689936526
154353.7314.05552532243539.6444746775654
155396.7366.57327341646630.1267265835342
156447387.63304999694859.3669500030517
157533.5505.44656882013928.0534311798609
158565.4543.80518184257321.5948181574265
159542.3566.284677040684-23.9846770406839
160488.7518.608917065626-29.908917065626
161467.1494.375879818437-27.2758798184374
162531.3526.6970137951974.60298620480307
163496.1518.307088803149-22.2070888031488
164444478.743728919878-34.7437289198785
165403.4429.564768896736-26.1647688967365
166386.3396.442496697389-10.142496697389
167394.1402.898223963434-8.79822396343422
168404.1390.21576298085313.8842370191471
169462.1457.230992686724.86900731328035
170448.1465.976857378014-17.8768573780137
171432.3436.831062875644-4.53106287564430
172386.3394.975926168384-8.67592616838436
173395.2380.64698357067714.5530164293227
174421.9447.344541882730-25.4445418827305
175382.9401.403825092133-18.5038250921331
176384.2355.53119012633028.6688098736704
177345.5358.342846127191-12.8428461271914
178323.4336.074088928867-12.6740889288669
179372.6337.53461588687935.0653841131211
180376365.50820114785510.4917988521452
181462.7427.90022661763134.7997733823692
182487460.61734907009126.3826509299093
183444.2475.650160482946-31.4501604829458
184399.3412.649923436822-13.3499234368217
185394.9399.846709607714-4.94670960771367
186455.4445.18520671303610.2147932869642
187414434.151681288589-20.1516812885894
188375.5396.700404236917-21.2004042369169
189347350.842023269268-3.84202326926834
190339.4336.9229316773052.47706832269495
191385.8359.68262900308226.1173709969177
192378.8377.493880647921.30611935207986
193451.8435.82370311175615.9762968882444
194446.1450.391656203322-4.29165620332213
195422.5428.182330339259-5.68233033925878
196383.1388.765698048713-5.66569804871318
197352.8383.132449695987-30.3324496959868
198445.3406.57029449603738.7297055039631
199367.5415.337928552713-47.8379285527133
200355.1351.7781189917553.32188100824504
201326.2328.814772864798-2.61477286479806
202319.8316.3006133267893.49938667321084
203331.8342.794875426611-10.9948754266111
204340.9322.39446423404718.5055357659534
205394.1395.827304834317-1.72730483431701
206417.2389.46552762670227.7344723732983
207369.9393.743527649005-23.8435276490048
208349.2336.74325083479812.4567491652016
209321.4342.370518648668-20.9705186486678
210405.7383.34497256658122.3550274334191
211342.9364.568979412128-21.6689794121277
212316.5331.084163280832-14.5841632808317
213284.2291.148314350786-6.94831435078623
214270.9274.744405521449-3.84440552144861
215288.8291.392324176541-2.59232417654061
216278.8281.406239980988-2.60623998098799
217324.4331.548709542247-7.14870954224693
218310.9322.03403410479-11.1340341047900
219299280.53626376238618.4637362376139
220273262.56839299437910.4316070056209
221279.3259.18856063514920.1114393648514
222359.2341.61414514437917.5858548556214
223305312.287595026467-7.28759502646739
224282.1292.819733659708-10.7197336597077
225250.3258.189000392346-7.88900039234625
226246.5242.2638191405454.23618085945469
227257.9267.392999763603-9.49299976360294
228266.5252.40110826626614.0988917337345
229315.9318.240504504690-2.34050450469039
230318.4314.5862200790173.81377992098322
231295.4293.3415725670232.05842743297711
232266.4262.3469431020544.05305689794619
233245.8256.644778866016-10.8447788660155
234362.8311.94696422909550.8530357709055
235324.9309.63523892573215.264761074268
236294.2312.431349656668-18.2313496566681
237289.5274.64219613100514.8578038689951
238295.2284.30817491018410.891825089816
239290.3317.984481049331-27.6844810493308
240272294.296944379872-22.2969443798723
241307.4327.848325620151-20.4483256201514
242328.7309.65028918122419.0497108187762
243292.9302.360618874707-9.4606188747066
244249.1262.132597556559-13.0325975565586
245230.4238.948982446017-8.548982446017
246361.5304.35909464105757.1409053589425
247321.7302.27573537003919.4242646299612
248277.2304.030832271001-26.8308322710011
249260.7263.075734057070-2.37573405706956
250251255.841975116547-4.84197511654668
251257.6268.030371034543-10.4303710345427
252241.8258.485679976229-16.6856799762290
253287.5296.035494145975-8.53549414597478
254292.3293.311561388790-1.01156138878952
255274.7263.16972014140711.5302798585933
256254.2240.20473499258413.9952650074159
257230242.322756684355-12.3227566843547
258339314.95796026780124.0420397321986
259318.2278.23286239281239.9671376071882
260287291.531307526183-4.53130752618301
261295.8275.00924875418120.7907512458190
262284290.631696408165-6.631696408165
263271303.683025011475-32.6830250114747
264262.7275.913992861356-13.2139928613565
265340.6319.58943645807821.010563541922
266379.4347.18029544373332.2197045562672
267373.3353.33756420628519.9624357937149
268355.2344.48282462450710.7171753754927
269338.4346.386849258154-7.986849258154
270466.9434.45729055863732.4427094413634
271451414.31299279400136.6870072059986
272422425.434687129450-3.43468712944951
273429.2420.403994813748.7960051862596
274425.9428.076834263778-2.17683426377778
275460.7447.78648534599112.9135146540092
276463.6471.33139000913-7.73139000913011
277541.4534.2868337377447.11316626225619
278544.2560.382466783197-16.1824667831972
279517.5529.019964978043-11.5199649780434
280469.4495.60527322686-26.2052732268602
281439.4464.597184716138-25.1971847161378
282549543.9290707007975.07092929920282
283533499.47870955281333.521290447187
284506.1500.6367694584595.46323054154055
285484503.948495371552-19.9484953715518
286457482.529665212826-25.5296652128258
287481.5479.96844320831.53155679170021
288469.5485.767924492514-16.2679244925141
289544.7537.8808856118936.81911438810675
290541.2554.822043823008-13.6220438230080
291521.5520.859578471720.64042152827983
292469.7491.138448912611-21.4384489126114
293434.4459.986404812567-25.5864048125666
294542.6538.8431380313833.75686196861693
295517.3492.78346925494424.5165307450561
296485.7477.1905028680348.5094971319661
297465.8474.670553357688-8.87055335768804
298447457.818133261494-10.8181332614943
299426.6468.479232017238-41.8792320172377
300411.6428.489344879765-16.8893448797654
301467.5477.294693840822-9.79469384082205
302484.5470.00023157989314.4997684201068
303451.2456.910849666036-5.71084966603627
304417.4412.9229418897434.47705811025679
305379.9399.397346773819-19.4973467738193
306484.7483.9539477293680.746052270631992
307455434.37573751807220.6242624819278
308420.8409.0788817230311.7211182769699
309416.5402.96849697543413.5315030245664
310376.3402.609835981495-26.3098359814953
311405.6392.12390876907813.4760912309223
312405.8403.2660595989422.53394040105781
313500.8471.04701943701129.7529805629895
314514504.9530805808859.04691941911528
315475.5487.787069745690-12.2870697456895
316430.1442.623105111373-12.5231051113732
317414.4413.0724408709741.32755912902644
318538521.65293537020716.3470646297931
319526492.55056275417533.4494372458245
320488.5482.104099932256.39590006775046
321520.2476.42260377340843.7773962265922
322504.4503.1041020041121.29589799588808
323568.5530.36440157454438.1355984254559
324610.6571.14032108460539.4596789153952
325818686.81618934528131.183810654720
326830.9823.7240048436867.17599515631389
327835.9820.60691796682215.2930820331775
328782819.518193452945-37.5181934529445
329762.3789.272837104078-26.9728371040779
330856.9892.685744440066-35.7857444400662
331820.9834.922887967442-14.0228879674422
332769.6790.581584409861-20.9815844098612
333752.2775.608670422403-23.4086704224034
334724.4743.27748562043-18.8774856204301
335723.1761.808687252763-38.7086872527631
336719.5735.283368875808-15.7833688758084
337817.4811.4438751605175.95612483948332
338803.3810.35817559438-7.05817559438037
339752.5782.314361775406-29.8143617754065
340689718.3247066874-29.3247066873996
341630.4680.416867311052-50.0168673110519
342765.5745.13960087803720.3603991219634
343757.7724.59367249399633.1063275060045
344732.2708.67009870465223.5299012953485
345702.6723.332597474981-20.7325974749814
346683.3685.846963279467-2.54696327946715
347709.5708.5587494206820.94125057931842
348702.2714.791441256038-12.5914412560384
349784.8792.42495525268-7.6249552526806
350810.9772.64271726707838.2572827329222
351755.6778.006125333704-22.4061253337040
352656.8718.604237548373-61.8042375483727
353615.1645.968699821164-30.8686998211639
354745.3734.36573785287210.9342621471280
355694.1704.226495241626-10.126495241626
356675.7643.7744221432331.9255778567701
357643.7653.907727436926-10.2077274369261
358622.1623.190336538489-1.0903365384886
359634.6642.901459588552-8.30145958855155
360588633.956150404699-45.956150404699
361689.7676.1756266859713.5243733140298
362673.9674.920955045504-1.02095504550380
363647.9629.39034644573118.509653554269
364568.8593.584347262271-24.7843472622714
365545.7553.460535954125-7.76053595412498
366632.6665.417366198776-32.8173661987756
367643.8589.76149029783954.0385097021606
368593.1589.4727700074793.62722999252139
369579.7566.6746161344113.0253838655896
370546555.993757927082-9.9937579270819
371562.9565.266721418102-2.36672141810209
372572.5554.71781238170517.782187618295


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
373662.72907376386615.085169490331710.37297803739
374649.600323407577584.775983773264714.424663041891
375609.557892278852529.497099827506689.618684730198
376552.432900405948458.035476354263646.830324457633
377538.257577684042429.980386344299646.534769023785
378656.101380491767534.16990139446778.032859589073
379625.713210163436490.217064183838761.209356143034
380573.299566371783424.242410480975722.356722262591
381549.881611806264387.209851343412712.553372269115
382525.111610517392348.732107793196701.491113241588
383545.02424463445354.815823879371735.23266538953
384540.477524462648336.298754010789744.656294914508
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/08/t12917997521dy5fzj8ca1z5py/17zte1291799853.png (opens in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t12917997521dy5fzj8ca1z5py/17zte1291799853.ps (opens in new window)
Click here to open pdf file.


http://www.freestatistics.org/blog/date/2010/Dec/08/t12917997521dy5fzj8ca1z5py/2i8t01291799853.png (opens in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t12917997521dy5fzj8ca1z5py/2i8t01291799853.ps (opens in new window)
Click here to open pdf file.


http://www.freestatistics.org/blog/date/2010/Dec/08/t12917997521dy5fzj8ca1z5py/3i8t01291799853.png (opens in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t12917997521dy5fzj8ca1z5py/3i8t01291799853.ps (opens in new window)
Click here to open pdf file.


 
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):