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

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

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),

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

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

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

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.

D bo trung bnh di ng bc k k hiu MA(k) theo cng thc:Trung bnh di ng

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

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:

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

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

Phng trnh trn c th c vit:

Lp li qu trnh ny vi gi tr Ft-1, Ft-2 cho n ht:

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.

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.

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

V d:Chn gi tr V th thi gian Yt v SESTnh sai s MSETm gi tr cho MES nh.

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

Vi l mt tham s nm trong khong (0,1)

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.

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.

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

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)

C 3 phng trnh:

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

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

V d:Chn gi tr , V th thi gian Yt v LESTnh sai s MSETm gi tr , cho MES nh.

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

Phng php nhn

Cp :

Xu hng:

Ma v:

D bo:

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

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 :

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.

Phng php cngCp :

Xy hng:

Ma v:

D bo:

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.

V d:Chn gi tr , , V th thi gian Yt v Holt-WinterSo snh kt qu vi SES v LES

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

40181174.8601234362-0.4157035455196.1002592886-15.1002592886228.0178305839181181.65014064561.07522932540.9962348288186.452820087-5.45282008729.733246901540181178.38289211631.46637696472.2499623463183.4932542726-2.49325427266.216316868

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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

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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

52235228.5422321299-0.7687138722250.8820732389-15.8820732389252.2402503663235233.77391277361.71720404821.0055371607223.973373601611.0266263984121.586489730452235217.85879260322.377008810220.1282687045214.715119459620.2848805404411.4763785394

53229229.4986965032-0.7786938348227.77351825781.22648174221.504257464229234.8974098611.7066661070.9748747853229.7158959326-0.71589593260.512506986353229221.53700714712.4503222888.1836165042224.10630577174.893694228323.9482431998

54243248.806352015-0.8948911133228.720002668414.2799973316203.9183237912243227.59442363271.54675020031.0673617851255.0030733586-12.0030733586144.07377005354243219.6994628892.208732199320.9258641699259.1262029709-16.1262029709260.0544222582

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LESPlot

LESPlot

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Airline Data

LES

Airline -LES

HWMultPlot

HWMultPlot

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Data

HW Forecast

Airline Data -Holt-Winter's F'cast, Multiplicative Model

HWAddPlot

HWAddPlot

118

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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

A-1: Phng php SESB-1: Phng php tuyn tnh HoltB-3: Phng php Holt-Winter

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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