chuong 4-phuong phap san bang mu
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S dng Y1, Y2, ...,Yt-1, Yt d bo Ft+1, Ft+2, ..., Ft+mXt hai nhm phng php:Phng php trung bnhPhng php san bng mNi dung
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a. Thi im tham chiuHin tib. D liu qu kh c ctYt-n-1 . Yt-2 Yt-1 Ytn kFt+1 Ft+2 Ft+mm k tip theoc. D bo tng laiFt-n-1 . Ft-2 Ft-1 Ftd. Gi tr hiu chnh theo m hnh
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Sai s hiu chnh theo m hnh:(Yt-n+1 Ft-n+1),, (Yt-1 Ft-1), (Yt Ft)Sai s d bo (khi c cc gi tr thc t:(Yt+1 Ft+1), (Yt+2 Ft+2),
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Bc 1: Phn chui thi gian thnh d liu xy dng m hnh v d liu kim traBc 2: Chn phng php san bngBc 3: Xy dng m hnh san bng da trn d liu chnBc 4: Dng m hnh san d bo gi tr ca d liu kim traBc 5: nh gi kt qu v a vo ng dng
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Cc phng php san bng chui thi gianCc phng php trung bnhCc phng php san bng mTrung bnh gin nTrung bnh di ngSan bng m gin nPhng php tuyn tnh ca HoltPhng php Holt-WinterPhn loi ca PegelsMt tham sTham s thch nghi
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Ly trung bnh ca tt c cc quan st trc lm d bo.
Cho kt qu tt nu cc gi tr quan st khng c tnh xu hng v thi v ng k.Trung bnh gin n
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Ch c 2 i tng cn c lu tr theo thi gian.
Khi d bo mt chui ln, cch lu tr ny cng hiu qu.
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D bo trung bnh di ng bc k k hiu MA(k) theo cng thc:Trung bnh di ng
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Ph hp khi d liu khng c tnh xu th v thi v (d liu n nh)D liu c cho l n nh nu Yt l mt bin ngu nhin, c phn phi xc sut khng ph thuc vo t.Trung bnh di ng cng bao gm nhiu quan st th d liu cng phng hn
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Mi d bo mi Ft+2 l s iu chnh ca d bo Ft+1. S iu chnh ny l 1/k sai bit gia Yt+1 v Yt-k+1C th biu din di dng:
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MonthTime periodObserved values (shipments)Three-month moving averageFive month moving averageJan1200.0Feb2135.0Mar3195.0Apr4197.5176.7May5310.0175.8Jun6175.0234.2207.5Jul7155.0227.5202.5Aug8130.0213.3206.5Sep9220.0153.3193.5Oct10277.5168.3198Nov11235.0209.2191.5Dec12244.2203.5
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San bng m gin n mt tham s (SES): Bng gi tr d bo ca k trc cng sai s d bo.
San bng m gin n
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Phng trnh trn c th c vit:
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Lp li qu trnh ny vi gi tr Ft-1, Ft-2 cho n ht:
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Tng qut:C th s dng gi tr quan st u tin Y1 nh l gi tr d bo ca F1: F1 = Y1F1 nh hng rt nh n mi gi tr d bo.
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S ph thuc ca gi tr d bo Ft+1 vo Yt, Yt-1, Yt-2, gim theo hm m.Mc gim c iu khin bi . cng ln gim cng nhanh.
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a = 0.2 a = 0.4 a = 0.6a = 0.8Yt0.20.40.60.8Yt-10.160.240.240.16Yt-20.1280.1440.0960.032Yt-30.10240.08640.03840.0064
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V d:Chn gi tr V th thi gian Yt v SESTnh sai s MSETm gi tr cho MES nh.
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San bng m gin n vi tham s thch ng (ARRSES):ARRSES tng t SES ch khc l c iu chnh khi c s thay i trong hnh mu ca d liu.
San bng m gin n
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Vi l mt tham s nm trong khong (0,1)
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Et l sai s d boAt l c lng ca sai s d boMt l c lng gi tr tuyt i ca sai s d boC hai c lng trn u dng phng php SES.
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Mt cch iu khin s thay i ca l iu khin gi tr ca (gi tr cng nh thay i cng t)
ARRSES l phng php san bng m n vi gi tr t ng thay i qua cc k khi c s thay i trong hnh mu ca d liu.
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F2 = Y1 2 = 3 = 4 = = 0.2A1 = M1 = 0
PeriodObserved valueForecastError (Et)Smoothed errorAbsolute smoothed error
YtFtEtAtMt t1200.02135.0200-65.0-1313.00.20003195.01878.0-8.812.00.20004197.5188.68.9-5.311.40.20005310.0190.4119.619.733.0-0.46496175.0245.7-70.71.640.60.59707155.0203.5-48.5-8.442.10.03948130.0201.5-71.5-2148.0-0.19959220.0187.332.7-10.345.0-0.437510277.5201.675.9751.1-0.228911235.0218.916.18.844.10.137012221.10.1995
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M rng phng php san bng m gin n xem xt yu t xu th.S dng 2 h s san bng , (0, 1)Phng php tuyn tnh Holt (LES)
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C 3 phng trnh:
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Lt l c lng cp ca chui thi gian ti tbt l c lng yu t xu th ca chui thi gian ti t hng s san bng m cho c lng cp hng s san bng m cho c lng yu t xu thm s k d bo
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C th gn gi tr bt u cho L1 v b1:L1= Y1 ; b1= 0Hoc:L1= Y1 ; b1= Y2 - Y1 hoc b1= (Y4 - Y1) / 3Hoc:L1= trung bnh ca 5 hay 6 quan st ub1= h s gc ca ng hi quy tuyn tnh cho 5 hay 6 quan st uChn , c MSE nh
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V d:Chn gi tr , V th thi gian Yt v LESTnh sai s MSETm gi tr , cho MES nh.
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M rng ca phng php tuyn tnh Holt xem xt yu t ma v.Da trn 3 phng trnh san bng:Cp Xu hngThi vPhng php Holt- Winter
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Phng php nhn
Cp :
Xu hng:
Ma v:
D bo:
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Trong :s: s k trong mt ma (s thng hoc qu trong nm)Lt: c lng cp ca chuibt: c lng yu t xu hngSt: c lng yu t ma v: hng s san bng m cho c lng cp : hng s san bng m cho c lng xu th: hng s san m cho c lng ma v
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khi to gi tr ban u cn c gi tr s, sau thit lp: to yu t xu th ta s dng k+s thi k :
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Ch s thi v ban u:
Cc trng s , , nm trong khong (0, 1) v c chn bng cch ti thiu ha cc gi tr MAD, MSE, v MAPE.
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Phng php cngCp :
Xy hng:
Ma v:
D bo:
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Nhng gi tr ban u ca Ls v bs c tnh nh trong phng php nhn.Ch s thi v ban u c tnh l:
Cc trng s , , nm trong khong (0, 1) v cng c chn bng cch ti thiu ha cc gi tr MAD, MSE, v MAPE.
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V d:Chn gi tr , , V th thi gian Yt v Holt-WinterSo snh kt qu vi SES v LES
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Chart1
118
115112.5454545455
126119.7803309725
141136.1095107413
135135.158534559
125127.86267634
149141.804915686
170157.5292480378
170161.8431777012
158153.1322568592
133138.6197130924
114123.234423658
140135.7496601706
145134.077435687
150147.4980440665
178162.2272212071
163160.4428046091
172152.249436717
178182.1714213748
199200.4554409284
199197.987921261
184185.0949267998
162160.2809179489
146144.2982634062
166172.4073036037
171174.4232401402
180177.0341936752
193204.0164543764
181183.4932542726
183189.0669304688
218190.6098659086
230219.7221011676
242222.7673823039
209213.3532552011
191190.595381211
172174.6705862777
194194.8272100664
196201.397649229
196209.5258464996
236219.9637531868
235214.7151194596
229224.1063057717
243259.1262029709
264262.0085371097
272271.0416101357
237236.0057926764
211218.9682925886
180198.0864931959
201215.5175173113
204213.9631986995
188213.1887925223
235245.8809720934
227236.1170326555
234222.581995632
264239.3650647249
302268.2189308102
293284.435584917
259251.209096605
229227.9367846921
203200.5311105649
229226.8736840061
242234.3086434378
233225.6235001704
267280.8870962536
269273.1356088108
270280.3556124031
315304.0036176167
364338.0933229565
347330.6744786631
312299.6293906811
274272.5133922513
237247.3336639554
278270.6528433867
284285.1416839805
277274.458931106
317310.2520130928
313317.4471071662
318319.9627953279
374365.6475373186
413413.1222997017
405390.8947981072
355356.2971304355
306316.2729578204
271277.6910633914
306317.7591141502
Data
Airline Data -Holt-Winter's F'cast Additive Model
AirlineData
Airline Data
1112
2118
3132
4129
5121
6135
7148
8148
9136
10119
11104
12118
1115
2126
3141
4135
5125
6149
7170
8170
9158
10133
11114
12140
1145
2150
3178
4163
5172
6178
7199
8199
9184
10162
11146
12166
1171
2180
3193
4181
5183
6218
7230
8242
9209
10191
11172
12194
1196
2196
3236
4235
5229
6243
7264
8272
9237
10211
11180
12201
1204
2188
3235
4227
5234
6264
7302
8293
9259
10229
11203
12229
1242
2233
3267
4269
5270
6315
7364
8347
9312
10274
11237
12278
1284
2277
3317
4313
5318
6374
7413
8405
9355
10306
11271
12306
Timeplot
Timeplot
112
118
132
129
121
135
148
148
136
119
104
118
115
126
141
135
125
149
170
170
158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
201
204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
318
374
413
405
355
306
271
306
Airline Passenger Traffic
LES&HW
Note: In both F'casts, Ft is the forecast obtain at time period t-1
Note This block can be copied for carrying out the H-W forecastNote This block can be copied for carrying out the H-W forecast
Note the MSE's in row 7 are directly comparable so that we can see whichJust put the new data in the left-hand columnJust put the new data in the left-hand column
method has done best.Holt-Winter's Forecast, Multiplicative ModelHolt-Winter's Forecast Additive Model
Holt'sLinExpSmthgAlphaHW0.8089818259AlphaHWA0.2658943679
AlphaLES1.4066073599MSE(LES)489.2420419983BetaHW0.0177493982BetaHWA0.0563427257
Orig. DataBetaLES-0.0057848879MSE538.4094770747Orig. DataGammaHW1.0324535703MSE(HW)90.3730682094Orig. DataGammaHWA1.2005917771MSE(HW)118.5619443658
Month tYtLtbtFtEtEt*EtYtLtbtStFtEtEt*EtYtLtbtStFtEtEt*Et
111211201120.88421052631112-14.6666666667
2118120.4396441596-0.0488223951126361180.93157894742118-8.6666666667
3132136.7203773134-0.1432870427120.390821764611.6091782354134.77301930111321.042105263231325.3333333333
4129125.919099329-0.0816317603136.5770902707-7.577090270757.41229697021291.018421052641292.3333333333
5121119.0330500831-0.0422689682125.8374675687-4.837467568723.40109247851210.95526315795121-5.6666666667
6135141.5094662256-0.1725370363118.990781114916.0092188851256.29508931071351.065789473761358.3333333333
7148150.7092536314-0.2267548822141.33692918936.663070810744.39651262841481.1684210526714821.3333333333
8148146.9905977375-0.2065546264150.4824987493-2.48249874936.16280004021481.1684210526814821.3333333333
9136131.6151287011-0.1188041576146.7840431111-10.7840431111116.29558582241361.073684210591369.3333333333
10119113.9189024684-0.017120742131.4963245435-12.4963245435156.15812709721190.939473684210119-7.6666666667
1110499.97386267350.0634507078113.9017817264-9.901781726498.04528135691040.821052631611104-22.6666666667
12118125.3037605834-0.0827128558100.037313381317.9626866187322.6581105599118126.66666666670.54545454550.931578947412118126.66666666670.5454545455-8.6666666667
13115110.84404676770.0004564825125.2210477276-10.2210477276104.4698166498115129.51561816450.58634023010.8880443103112.48229665072.51770334936.33883015513115127.86477102430.5822266148-12.5033255753112.54545454552.45454545456.0247933884
14126132.1623365221-0.1228647924110.844503250115.1554967499229.6890817358126134.27005838150.66032149640.9386288817121.20024545184.799754548223.037643723414126130.1007726040.675404804-3.1848917999119.78033097256.219669027538.6842828122
15141144.6434167437-0.1957772009132.03947172968.960528270480.2910668841141135.23184729920.66567236171.042671606140.61165903060.38834096940.150808708515141132.07653095830.74867026749.6436207434136.10951074134.890489258723.9168851895
16135131.1585202278-0.1189011359144.4476395428-9.447639542889.2578929301135133.19602182910.6177224011.0133854994138.4008950231-3.400895023111.56608695816135132.78304777930.74629522732.1936071265135.158534559-0.1585345590.0251332064
17125122.544246426-0.0697563577131.0396190919-6.039619091936.4769987754125131.41936048140.57522353040.9510202472127.827339883-2.8273398837.993850813817125132.76817349060.7034088621-8.189718479127.86267634-2.862676348.1949158275
18149159.7854675644-0.2855961785122.474490068326.5255099317703.602677139149138.3110211760.68733648871.0776551712140.67843822318.321561776969.248390406218149135.38471474860.811199955914.6748013731141.8049156867.19508431451.7692382849
19170174.2694295748-0.3710364163159.499871385910.5001286141110.2527009116170144.25442409030.78062850451.1787996229162.40860737667.591392623457.629241962519170139.51181741510.998026952732.3245700652157.529248037812.4707519622155.5196545023
20170168.4148846498-0.3393149345173.8983931585-3.898393158515.197469218170145.40754253330.78723997681.1691507343169.46200882130.53799117870.289434508420170142.67869747741.120226048628.5224399035161.84317770128.156822298866.5337500142
21158153.9031991982-0.2573293604168.0755697153-10.0755697153101.5171050879158146.97308793530.80105442971.0750703127156.96702964241.03297035761.067027759621158145.09322901161.193150747513.623573198153.13225685924.867743140823.6949232844
22133124.6052373716-0.0893325582153.6458698378-20.6458698378426.2519413587133142.75399357910.711949810.9314195401138.8299179587-5.829917958733.987943404622133144.79212969841.1089606262-12.6196636593138.6197130924-5.619713092431.5811752412
23114109.7241557064-0.0037639484124.5159048134-10.5159048134110.5842540441114139.72861760930.64561452660.8156989437117.7930903616-3.793090361614.387534490923114143.44570908290.9706177544-30.8055292481123.234423658-9.23442365885.2745802947
24140152.3119115673-0.2501511142109.720391758130.2796082419916.8546752849140148.3898293380.78788655290.9438464983130.76967941089.230320589285.198818179424140145.54646825971.0342930026-4.9205821164135.74966017064.250339829418.0653886651
25145142.1286362257-0.1926891045152.061760453-7.06176045349.8684606963145160.58632132860.99038243350.9034246207132.476421815112.5235781849156.840010552125145149.48500959651.1979262698-2.8766013451134.07743568710.922564313119.302411171
26150153.2789032515-0.2583068337141.93594712128.064052878865.0289488325150160.14550608530.9649795360.9365839197151.6605607589-1.66056075892.757462034126150151.34819185791.2354086057-0.9797649526147.49804406652.50195593356.2597834934
27178188.1568093434-0.4615658853153.020596417824.9794035822623.9706033229178168.88060897731.10289454941.0543666573167.985328793310.0146712067100.293639378127178156.77749351131.471703971323.545135757162.227221207115.7727787929248.7805508512
28163152.9587322544-0.2606190633187.6952434582-24.6952434582609.8550494589163162.5922243150.97170379161.0021549507172.2588176089-9.258817608985.725703514328163158.92914133481.51001386124.4474198875160.44280460912.55719539096.5392482674
29172179.8482892373-0.4176797871152.698113191119.3018868089372.5628343853172177.55484132081.22003408110.9692890363155.552607342516.4473926575270.516725230229172165.69071873641.80590126539.2176613879152.24943671719.750563283390.0847499973
30178177.4183036684-0.4060388238179.4306094501-1.43060945012.0466433988178167.77155252441.02473172211.0604249122192.6576689606-14.6576689606214.847259359930178166.38746255191.743408311310.9982724855182.1714213748-4.171421374817.4007562864
31199207.9403749426-0.5849544724177.012264844521.9877351555483.4604972664199168.81207118411.02501193071.1788264975198.97699622480.02300377520.000529173731199167.74387731741.721604040131.0418009233200.4554409284-1.45544092842.1183082959
32199195.6026245414-0.516965866207.3554204702-8.355420470269.8130512335199170.1379727981.03035254151.1696547952198.56515043620.43484956380.189094143132199169.73458739421.736766207729.4144468205197.9879212611.0120787391.0243033739
33184179.4924895928-0.4267611314195.0856586755-11.0856586755122.8918282689184171.15479172891.03011232811.075049589184.0179850556-0.01798505560.000323462233184171.18021873251.720362875612.6585472158185.0949267998-1.09492679981.198864697
34162155.0609492049-0.2878961754179.0657284613-17.0657284613291.2390879155162173.59509104611.05514229840.9332640928160.37638414761.62361585242.636128436234162173.35767584351.7461168108-11.1045314649160.28091794891.71908205112.9552430985
35146142.4328120691-0.2165092653154.7730530295-8.773053029576.9664594587146178.15908785081.11742235420.8196154041142.46201086013.537989139912.517367154335146175.55627483031.7716108899-29.3056846666144.29826340621.70173659382.8959074346
36166175.6706263266-0.4100387752142.216302803823.7836971962565.6642523206166176.52560490421.06859544070.9402607834169.2095063846-3.209506384610.300931233136166175.62421977831.675621707-10.5677308156172.4073036037-6.407303603741.0535394704
37171169.267613744-0.3753700938175.2605875513-4.260587551318.1526062825171187.04760986241.23638777030.9145556336160.442973087710.5570269123111.450817226937171176.3896212121.6243374159-5.8937123329174.4232401402-3.423240140211.7185730575
38180184.5164954843-0.4657546386168.892243650111.1077563499123.3822511279180191.44210016771.29244218970.940350454176.34376452423.656235475813.368057854238180178.8025498261.66876879341.6341816254177.03419367522.96580632488.7960071561
39193196.6388346381-0.5385753495184.05074084578.949259154380.0892394106193184.89852976671.15335768211.0434733492203.2128751686-10.2128751686104.302819208939193177.54210544611.503728939113.8356604693204.0164543764-11.0164543764121.3622670264
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237242.7577640645
278271.637924463
284280.0620190835
277278.3953379817
317326.4370393197
313307.3660858567
318305.0757357813
374348.4903040731
413406.2655511198
405405.3225759162
355367.4660082382
306319.8319636987
271272.1496325899
306312.3295755315
Data
HW Forecast
Airline Data -Holt-Winter's F'cast, Multiplicative Model
HWAddPlot
HWAddPlot
118
115112.5454545455
126119.7803309725
141136.1095107413
135135.158534559
125127.86267634
149141.804915686
170157.5292480378
170161.8431777012
158153.1322568592
133138.6197130924
114123.234423658
140135.7496601706
145134.077435687
150147.4980440665
178162.2272212071
163160.4428046091
172152.249436717
178182.1714213748
199200.4554409284
199197.987921261
184185.0949267998
162160.2809179489
146144.2982634062
166172.4073036037
171174.4232401402
180177.0341936752
193204.0164543764
181183.4932542726
183189.0669304688
218190.6098659086
230219.7221011676
242222.7673823039
209213.3532552011
191190.595381211
172174.6705862777
194194.8272100664
196201.397649229
196209.5258464996
236219.9637531868
235214.7151194596
229224.1063057717
243259.1262029709
264262.0085371097
272271.0416101357
237236.0057926764
211218.9682925886
180198.0864931959
201215.5175173113
204213.9631986995
188213.1887925223
235245.8809720934
227236.1170326555
234222.581995632
264239.3650647249
302268.2189308102
293284.435584917
259251.209096605
229227.9367846921
203200.5311105649
229226.8736840061
242234.3086434378
233225.6235001704
267280.8870962536
269273.1356088108
270280.3556124031
315304.0036176167
364338.0933229565
347330.6744786631
312299.6293906811
274272.5133922513
237247.3336639554
278270.6528433867
284285.1416839805
277274.458931106
317310.2520130928
313317.4471071662
318319.9627953279
374365.6475373186
413413.1222997017
405390.8947981072
355356.2971304355
306316.2729578204
271277.6910633914
306317.7591141502
Data
Airline Data -Holt-Winter's F'cast Additive Model
-
Chart2
118
115112.4822966507
126121.2002454518
141140.6116590306
135138.4008950231
125127.827339883
149140.6784382231
170162.4086073766
170169.4620088213
158156.9670296424
133138.8299179587
114117.7930903616
140130.7696794108
145132.4764218151
150151.6605607589
178167.9853287933
163172.2588176089
172155.5526073425
178192.6576689606
199198.9769962248
199198.5651504362
184184.0179850556
162160.3763841476
146142.4620108601
166169.2095063846
171160.4429730877
180176.3437645242
193203.2128751686
181186.452820087
183177.1136977668
218200.2088451645
230240.217158977
242231.6428440551
209222.1194749056
191184.7597329921
172167.7815073608
194197.7105920853
196190.6149856086
196201.813864231
236220.1246136906
235223.9733736016
229229.7158959326
243255.0030733586
264267.7711314853
272268.9872663336
237245.9719311617
211212.4870865055
180186.4027211833
201207.3159166191
204199.5850900353
188207.7183938045
235217.9234947966
227221.5408164792
234220.2957946514
264254.8944870365
302288.1724936609
293305.7721842496
259265.097045365
229232.951560736
203201.5163648989
229232.1292456821
242229.0779642657
233239.0695042212
267275.934856573
269254.4791324069
270261.4891923567
315294.3128134882
364342.7369674096
347361.4536941262
312315.2840401987
274280.4907485014
237242.7577640645
278271.637924463
284280.0620190835
277278.3953379817
317326.4370393197
313307.3660858567
318305.0757357813
374348.4903040731
413406.2655511198
405405.3225759162
355367.4660082382
306319.8319636987
271272.1496325899
306312.3295755315
Data
HW Forecast
Airline Data -Holt-Winter's F'cast, Multiplicative Model
AirlineData
Airline Data
1112
2118
3132
4129
5121
6135
7148
8148
9136
10119
11104
12118
1115
2126
3141
4135
5125
6149
7170
8170
9158
10133
11114
12140
1145
2150
3178
4163
5172
6178
7199
8199
9184
10162
11146
12166
1171
2180
3193
4181
5183
6218
7230
8242
9209
10191
11172
12194
1196
2196
3236
4235
5229
6243
7264
8272
9237
10211
11180
12201
1204
2188
3235
4227
5234
6264
7302
8293
9259
10229
11203
12229
1242
2233
3267
4269
5270
6315
7364
8347
9312
10274
11237
12278
1284
2277
3317
4313
5318
6374
7413
8405
9355
10306
11271
12306
Timeplot
Timeplot
112
118
132
129
121
135
148
148
136
119
104
118
115
126
141
135
125
149
170
170
158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
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204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
318
374
413
405
355
306
271
306
Airline Passenger Traffic
LES&HW
Note: In both F'casts, Ft is the forecast obtain at time period t-1
Note This block can be copied for carrying out the H-W forecastNote This block can be copied for carrying out the H-W forecast
Note the MSE's in row 7 are directly comparable so that we can see whichJust put the new data in the left-hand columnJust put the new data in the left-hand column
method has done best.Holt-Winter's Forecast, Multiplicative ModelHolt-Winter's Forecast Additive Model
Holt'sLinExpSmthgAlphaHW0.8089818259AlphaHWA0.2658943679
AlphaLES1.4066073599MSE(LES)489.2420419983BetaHW0.0177493982BetaHWA0.0563427257
Orig. DataBetaLES-0.0057848879MSE538.4094770747Orig. DataGammaHW1.0324535703MSE(HW)90.3730682094Orig. DataGammaHWA1.2005917771MSE(HW)118.5619443658
Month tYtLtbtFtEtEt*EtYtLtbtStFtEtEt*EtYtLtbtStFtEtEt*Et
111211201120.88421052631112-14.6666666667
2118120.4396441596-0.0488223951126361180.93157894742118-8.6666666667
3132136.7203773134-0.1432870427120.390821764611.6091782354134.77301930111321.042105263231325.3333333333
4129125.919099329-0.0816317603136.5770902707-7.577090270757.41229697021291.018421052641292.3333333333
5121119.0330500831-0.0422689682125.8374675687-4.837467568723.40109247851210.95526315795121-5.6666666667
6135141.5094662256-0.1725370363118.990781114916.0092188851256.29508931071351.065789473761358.3333333333
7148150.7092536314-0.2267548822141.33692918936.663070810744.39651262841481.1684210526714821.3333333333
8148146.9905977375-0.2065546264150.4824987493-2.48249874936.16280004021481.1684210526814821.3333333333
9136131.6151287011-0.1188041576146.7840431111-10.7840431111116.29558582241361.073684210591369.3333333333
10119113.9189024684-0.017120742131.4963245435-12.4963245435156.15812709721190.939473684210119-7.6666666667
1110499.97386267350.0634507078113.9017817264-9.901781726498.04528135691040.821052631611104-22.6666666667
12118125.3037605834-0.0827128558100.037313381317.9626866187322.6581105599118126.66666666670.54545454550.931578947412118126.66666666670.5454545455-8.6666666667
13115110.84404676770.0004564825125.2210477276-10.2210477276104.4698166498115129.51561816450.58634023010.8880443103112.48229665072.51770334936.33883015513115127.86477102430.5822266148-12.5033255753112.54545454552.45454545456.0247933884
14126132.1623365221-0.1228647924110.844503250115.1554967499229.6890817358126134.27005838150.66032149640.9386288817121.20024545184.799754548223.037643723414126130.1007726040.675404804-3.1848917999119.78033097256.219669027538.6842828122
15141144.6434167437-0.1957772009132.03947172968.960528270480.2910668841141135.23184729920.66567236171.042671606140.61165903060.38834096940.150808708515141132.07653095830.74867026749.6436207434136.10951074134.890489258723.9168851895
16135131.1585202278-0.1189011359144.4476395428-9.447639542889.2578929301135133.19602182910.6177224011.0133854994138.4008950231-3.400895023111.56608695816135132.78304777930.74629522732.1936071265135.158534559-0.1585345590.0251332064
17125122.544246426-0.0697563577131.0396190919-6.039619091936.4769987754125131.41936048140.57522353040.9510202472127.827339883-2.8273398837.993850813817125132.76817349060.7034088621-8.189718479127.86267634-2.862676348.1949158275
18149159.7854675644-0.2855961785122.474490068326.5255099317703.602677139149138.3110211760.68733648871.0776551712140.67843822318.321561776969.248390406218149135.38471474860.811199955914.6748013731141.8049156867.19508431451.7692382849
19170174.2694295748-0.3710364163159.499871385910.5001286141110.2527009116170144.25442409030.78062850451.1787996229162.40860737667.591392623457.629241962519170139.51181741510.998026952732.3245700652157.529248037812.4707519622155.5196545023
20170168.4148846498-0.3393149345173.8983931585-3.898393158515.197469218170145.40754253330.78723997681.1691507343169.46200882130.53799117870.289434508420170142.67869747741.120226048628.5224399035161.84317770128.156822298866.5337500142
21158153.9031991982-0.2573293604168.0755697153-10.0755697153101.5171050879158146.97308793530.80105442971.0750703127156.96702964241.03297035761.067027759621158145.09322901161.193150747513.623573198153.13225685924.867743140823.6949232844
22133124.6052373716-0.0893325582153.6458698378-20.6458698378426.2519413587133142.75399357910.711949810.9314195401138.8299179587-5.829917958733.987943404622133144.79212969841.1089606262-12.6196636593138.6197130924-5.619713092431.5811752412
23114109.7241557064-0.0037639484124.5159048134-10.5159048134110.5842540441114139.72861760930.64561452660.8156989437117.7930903616-3.793090361614.387534490923114143.44570908290.9706177544-30.8055292481123.234423658-9.23442365885.2745802947
24140152.3119115673-0.2501511142109.720391758130.2796082419916.8546752849140148.3898293380.78788655290.9438464983130.76967941089.230320589285.198818179424140145.54646825971.0342930026-4.9205821164135.74966017064.250339829418.0653886651
25145142.1286362257-0.1926891045152.061760453-7.06176045349.8684606963145160.58632132860.99038243350.9034246207132.476421815112.5235781849156.840010552125145149.48500959651.1979262698-2.8766013451134.07743568710.922564313119.302411171
26150153.2789032515-0.2583068337141.93594712128.064052878865.0289488325150160.14550608530.9649795360.9365839197151.6605607589-1.66056075892.757462034126150151.34819185791.2354086057-0.9797649526147.49804406652.50195593356.2597834934
27178188.1568093434-0.4615658853153.020596417824.9794035822623.9706033229178168.88060897731.10289454941.0543666573167.985328793310.0146712067100.293639378127178156.77749351131.471703971323.545135757162.227221207115.7727787929248.7805508512
28163152.9587322544-0.2606190633187.6952434582-24.6952434582609.8550494589163162.5922243150.97170379161.0021549507172.2588176089-9.258817608985.725703514328163158.92914133481.51001386124.4474198875160.44280460912.55719539096.5392482674
29172179.8482892373-0.4176797871152.698113191119.3018868089372.5628343853172177.55484132081.22003408110.9692890363155.552607342516.4473926575270.516725230229172165.69071873641.80590126539.2176613879152.24943671719.750563283390.0847499973
30178177.4183036684-0.4060388238179.4306094501-1.43060945012.0466433988178167.77155252441.02473172211.0604249122192.6576689606-14.6576689606214.847259359930178166.38746255191.743408311310.9982724855182.1714213748-4.171421374817.4007562864
31199207.9403749426-0.5849544724177.012264844521.9877351555483.4604972664199168.81207118411.02501193071.1788264975198.97699622480.02300377520.000529173731199167.74387731741.721604040131.0418009233200.4554409284-1.45544092842.1183082959
32199195.6026245414-0.516965866207.3554204702-8.355420470269.8130512335199170.1379727981.03035254151.1696547952198.56515043620.43484956380.189094143132199169.73458739421.736766207729.4144468205197.9879212611.0120787391.0243033739
33184179.4924895928-0.4267611314195.0856586755-11.0856586755122.8918282689184171.15479172891.03011232811.075049589184.0179850556-0.01798505560.000323462233184171.18021873251.720362875612.6585472158185.0949267998-1.09492679981.198864697
34162155.0609492049-0.2878961754179.0657284613-17.0657284613291.2390879155162173.59509104611.05514229840.9332640928160.37638414761.62361585242.636128436234162173.35767584351.7461168108-11.1045314649160.28091794891.71908205112.9552430985
35146142.4328120691-0.2165092653154.7730530295-8.773053029576.9664594587146178.15908785081.11742235420.8196154041142.46201086013.537989139912.517367154335146175.55627483031.7716108899-29.3056846666144.29826340621.70173659382.8959074346
36166175.6706263266-0.4100387752142.216302803823.7836971962565.6642523206166176.52560490421.06859544070.9402607834169.2095063846-3.209506384610.300931233136166175.62421977831.675621707-10.5677308156172.4073036037-6.407303603741.0535394704
37171169.267613744-0.3753700938175.2605875513-4.260587551318.1526062825171187.04760986241.23638777030.9145556336160.442973087710.5570269123111.450817226937171176.3896212121.6243374159-5.8937123329174.4232401402-3.423240140211.7185730575
38180184.5164954843-0.4657546386168.892243650111.1077563499123.3822511279180191.44210016771.29244218970.940350454176.34376452423.656235475813.368057854238180178.8025498261.66876879341.6341816254177.03419367522.96580632488.7960071561
39193196.6388346381-0.5385753495184.05074084578.949259154380.0892394106193184.89852976671.15335768211.0434733492203.2128751686-10.2128751686104.302819208939193177.54210544611.503728939113.8356604693204.0164543764-11.0164543764121.3622670264
40181174.8601234362-0.4157035455196.1002592886-15.1002592886228.0178305839181181.65014064561.07522932540.9962348288186.452820087-5.45282008729.733246901540181178.38289211631.46637696472.2499623463183.4932542726-2.49325427266.216316868
41183186.478761841-0.4853208641174.44441989078.555580109373.197951006183187.6381579531.16242835550.975475844177.11369776685.886302233234.648553980441183178.23610643861.37548698443.8705043583189.0669304688-6.066930468836.8076453137
42218231.0141024652-0.7457603422185.993440976832.00655902321024.4198205026218202.37318419631.40333379971.0777628082200.208845164517.7911548355316.525190380242218186.89447581491.785824429335.1388735358190.609865908627.3901340914750.2194455455
43230229.8908901178-0.7435768247230.268342123-0.2683421230.072007495230196.76488741041.27888157661.1685858417240.217158977-10.217158977104.39033756143230191.4131356581.939799825440.1003420214219.722101167610.2778988324105.63520441
44242247.22599701-0.8481599826229.147313293112.8526867069165.1915555847242205.20720811611.406028311.1796086918231.642844055110.3571559449107.270679267844242198.46678020942.22792777646.365329551222.767382303919.2326176961369.8935834454
45209193.801896366-0.5440140618246.3778370274-37.37783702741397.1027008466209196.74074601021.23079754661.0618983292222.1194749056-13.1194749056172.120621799945209199.53720194522.16271073078.8217570515213.3532552011-4.353255201118.9508308463
46191190.0819284372-0.5256415248193.2578823042-2.25788230425.0980324997191203.38079763331.3268085510.9393152501184.75973299216.240267007938.9409323346191201.80749853312.1687724112-10.7479161694190.5953812110.4046187890.1637163644
47172164.8614845282-0.3827848623189.5562869124-17.5562869124308.2232101504172208.87136867691.40071282940.823598526167.78150736084.218492639217.795680147347172203.26617709392.1287637881-31.6594357539174.6705862777-2.67058627777.1320310664
48194206.0035779909-0.6230016268164.478699665929.5213003341871.5071734184194207.07956128921.34404751690.9367269083197.7105920853-3.710592085313.768493623348194205.17499038432.1163711776-11.2968016603194.8272100664-0.82721006640.684276494
49196192.1857886099-0.5466712593205.3805763641-9.380576364187.9952129219196213.1869918251.42859469880.9195372627190.61498560865.385014391428.998379995549196205.85615703182.0355078424-10.6509908556201.397649229-5.39764922929.1346171991
50196197.7731669811-0.5821560486191.63911735064.360882649419.0172974822196209.6139294491.33981829580.9348804208201.813864231-5.81386423133.801017296650196204.29521846841.8328742491-10.2869744787209.5258464996-13.5258464996182.9485235315
51236251.7800205867-0.8979473478197.191010932538.80898906751506.1376324388236223.26158388961.55827498021.0574968202220.124613690615.8753863094252.027890474251236210.3920404282.073116685327.9693859695219.963753186816.0362468132257.1612118542
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LESPlot
LESPlot
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Airline Data
LES
Airline -LES
HWMultPlot
HWMultPlot
118
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125127.827339883
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Data
HW Forecast
Airline Data -Holt-Winter's F'cast, Multiplicative Model
HWAddPlot
HWAddPlot
118
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355356.2971304355
306316.2729578204
271277.6910633914
306317.7591141502
Data
Airline Data -Holt-Winter's F'cast Additive Model
-
Phn loi ca Pegels
Thnh phn xu hngThnh phn ma v1 23(khng)(cng)(nhn) A (khng)A 1A 2A 3B (cng)B 1B 2B 3C (nhn)C 1C 2C 3
-
C th tm tt 9 m hnh san bng m trn bng cng thc sau:
Trong P, Q, R v T bin i da vo tng ng.
-
Xu hngThnh phn ma v1(Khng)2(Cng)3(Nhn)A (Khng)Pt = YtQt = Lt-1 Ft+m = LtPt = Yt St sQt = Lt-1Tt = Yt LtFt+m = Lt + St+m s Pt = Yt /St sQt = Lt-1Tt = Yt /LtFt+m = Lt St+m s B (Cng)Pt = YtQt = Lt-1 + bt-1Rt = Lt Lt-1
Ft+m = Lt + mbtPt = Yt St-sQt = Lt-1 + bt-1Rt = Lt Lt-1Tt = Yt LtFt+m = Lt + mbt + St+m sPt = Yt /St sQt = Lt-1 + bt-1Rt = Lt Lt-1Tt = Yt /LtFt+m = (Lt + mbt )St+m sC (Nhn)Pt = YtQt = Lt-1 bt-1Rt = Lt /Lt-1
Ft+m = Lt btmPt = Yt St-sQt = Lt-1 bt-1Rt = Lt /Lt-1Tt = Yt LtFt+m = Lt btm + St+m sPt = Yt /St sQt = Lt-1 bt-1Rt = Lt /Lt-1Tt = Yt /LtFt+m = Lt btm St+m s
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A-1: Phng php SESB-1: Phng php tuyn tnh HoltB-3: Phng php Holt-Winter
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V d: Xt m hnh san bng m cho php xu hng s nhn v tnh thi v s nhn, c th hin trong C 3 trong bng phn loi ca Pegels. Ta c:
V kt qu d bo cho m thi k u l:
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