34] pea —— Mobuce - 4 classmate a — I —— [ime Senter Model — Have onty a eal OTe eae | utiva rca Time Series Takin g | Mowing Atteenpe = Unvaariate Li Have only Q Average V variables ( date monthaCsay 3 Umonthe) variable (Date _¢ Yy variable) by 4 varvable> Aatect of v 2 See dato follows ‘Teautar trilervals of time — Time Serves coal T U | Moclet . Bei] Mont Gales . | arch to Sime Should be |_ dont $0 equally phased . IL May 20° oh a, it pracely | dune is everyone Ghouigt be month in series, | July 20 mo Aste or anything or nul : — eae Aug 25 allewee \ ep 30 bx: Nomth Soles i [Tan Net Mor Ok. il So May June xamples of Forecasting Roumfalt " Forecaching > Bock pice forecasting. > Gaz{* price forecaxting q 2b Ain cot. "Petrol!Cases Time ie Qualitative L- moving ! TY] Aen e Ez Exponential Smoothing i ARIMA || t~_ARIMAK I Trenel projections } —_Deco position. Combining technique 2 bur belomg model i 1 euten | dechnigu Teme Lrw ¢ Orderecl Lequenc “ values Lot faualty Spectre dime _ inter val . vatrable | Accumption. =} Time Series vy \ | Shout be equally Spaced over time. Patterns of, post Mata wilt propegale intin futfire Cannot be used to predict random _owente (x: Texnanv’) Looe Force, Management ugel in cat centre. Predicting : of alle le _ unde no. 2) Catt) “Volume forecasting 3) Economic Gerree Foreeacting -GDP- 4) Inventory & kogictich “Fore tatting 5) Workload projection. oe duane] Cater Forecasting ) Weather Perecacti Pa ats is piven act chaste, weekly monthly. ja at ibpeitan be. “4 ete requdtemenl 4 dol He dole Che guilt, tov esr agate gation seggeegeli g os ion, | ab ons is, icing in ae Comatder ‘tag. SOMES Zs hades averahe 0 t_ two | tree yen gput it. But it te moteee —_ re Qa: | en Teo 2) Jana pa Eos ey Lop 14 mA jer 0 CMuIccImg ) seh a0 aoe : 2ep 20 uo Do2u 3 Ton 21 £00 rob. _panaassone 21 sep a 600 siitrarce 2. : Miccing yeasty ri Jaorbat oe 23 550 (kieroge f a ai Tinto Tan 24 9 ican © Time Gees Plot = BD aptow sof. hime Senet. Vertical axe "meaty (Finttll cee row data -tooke.) sty» variable of inforect 9 horizonta anc || Corresponds to dime periods Components 04 Time Servex ¢ Season Cycles Trenc Cancreasing | decreasing.) reegular. 1 Fem —||Prce (Product drfe Cycle) ¢ ea Taleh oe Period x_& | = ‘Puriotre _ Pluctertion . * Thend = dong Jerm change in __mean - & Onereal ! A —_ OsceQlatiry movement in dali a eas where the! period of ocerttation c..—rt—S—ES typically” snot bln, 0 Vv Tclassmate, s SS ULL remain ter avs own been accounted for oinle 1 neces or mext anontht. o 0 td = Mini O 4g & inl 1c meced sa toe ean crecast for meet 41 rweebt. 7 ig recomm no. 0. ie 30 /21 Joe model. dala i nececar clot ear o, Normal a eit not goo for dime~ feriee forecactin, becauce im “average ual _tarportance it oven Lo. data int. Rut a trend 6 rrent —_ugilh end or _previove, 2/3 pointe on Creeent: sor | Yrelt | aa | tao [ua y [buna error ( itretd Ser qT [Peasy aera £3 of Sufi) oy there) | Coke a ee ) ol6 ASG twit el7 90 SJ 170 14 Dole 13. 1ee 14 2014 bo. Mies lea a 20 kal 172 oot 186 no a2 lan] 1918 [}eod3 Podt} 144 oau | 2 ooo a2 l6 le 1a,abs MAp_err | Maden abe MAderr. | any enr = | (Yrela - Ha) Cuvetd = Hau), 4 ' . by -3 3 2 4 =13 es a 6 2 ~4 . = 4 tell ty “ly ‘to to. ri 1 2 7 . y a 7 a tal. 19 | 4 22 a tan 1310 Mean 12.83 Mean 13.73 | a llwe nave: 3% moving dverages NAC, HA(9), MACH). te know wivelvl| yo better fimel_ MAS _ ern, MAd-erh, MAG-enr fy find trere chbcolute £ find re mean of absolute of errone. Yhe one usin Deis meow cL. ‘absolute errors’ re Oia befler one. Heap fe VO NAS. Me 9e » ef AMSA. ; | : oe © wu Mua - Rogrincinre 1 2 : oe aye iitme iene tannot | be epretenlid in Unenir regivession. || Becauce time Series hae. slate os + is _all, . d y Hla ie hate, imlérvab') Hien svce dime Srmredlet zB Component to --first__eleek, _for_miseing volute _or i data ict equally —{paced Plot _eimpte. trend chart cet Resi underttand better. 2 1g terme evmpunit_of otal, lovidat ean be —_forceata.Saee ter} Be i one ppieeeeseats penta WON oa Bor ENKI Je wes pme Model, of dala Tt requires good good _anount i I | dime it. < Rea ese ofeer eae wilhin i I AR - Ma | Zoe! Nr || Auto Regressive Inleq-valeZl Moving Average | Ceatuatily) CStationarity? ¢ Recency) Rinear Regression | Apa _modele are able to moolel_c wide Spectrus Gries behaviour & have a £4 sternatie Approach. Foy iderdil ying the Correct form. | Aulo- Regressive cap tires Leoeonoli ty She “ARIMA model aun Sequential iy first _rnodlet. Auth - Peqreucive rune to predict & the Crror( aeftal - = pres oil be pasted to rtibdet t Movie Arerage. Calculates Trey other! value? “both ) Auto - regressive 6, Moving Arerage willl qct_rtigrali. . a . pra dee —cdafe—for_A&_melel_€| error gentnaléa om || AR q { ! smodel te__data for MA model 4 AR MA _#\_0 on 4a s 4 1 © 6 5 ! \ a 2: cong _ = | 2 3 | I 3 2 [4 6 3 ' { . 1 | Zclassmate 5) Gz egrets on : AU ata cience wmoctele tikes Aimear, | gt te trite to find reason: Por model atl rows one b one. But works vertrcalty 1c trier te fine by examining att uoorks horizontal by examiniay Series model weacon for model. _annwertifg — values of Coleman + tric. fe far. autho regretsive. mode). v Time Gerier Model u z 3 Xo X ———— orm i t pee = oo 10 F do \/Ate 3 M te |\ thee Whenever, there etre _onany bia ia [Nfe date || pvinte _§ Fue Con observe Lore May 2h Be) ee Sea rrcality | Gyebicat. [a those. + tune - 5) dala points Can be comidered igri ficant v : For He mat oll hota porate Shave ty be contidered im that eae. Auto- regressive (AR) Process. Yee et BY ye ee Mo yi CMA) Process ae a a Be + B2 Oyen a uhere Ct = (fy? «2 ye) i 2s wurxedt Aipring Models (‘ARMA) _ Procese! ep hfe + ha Yea onsets Cet On Cua + By Opo24. y oe AR Woebke em _ Cemawitic. process’ ~ Seaton, hl | MA -: works: om inrequbar Comnpoment (noise GB recluces : extulgivorie the ___ error. : trendCIASSMAte : es ——$—_— — in Three Gloge of Aen ed etm h Identuficaiton 2. Gettmation 4:| Toenripicntyon Gage e | ior iclentify : I = whether Shafionary | mon = ttationanty I = Seaonality I = Oreler AR 6 MA processes : : i = White Noise C Tovegutar trends vole Canna I be predicted ) omeng YH date’ ie mot » Streamlined average. Jen Variance —_Nen Ctationanly \ 1 de 1 mst Gationary Time SoNex - Gtastictical propertier euch ae mean, Varvance, autocorrelation. cre OR hpinitont ever time eae : er fn | a Sobor Chart 2 Non. Stettona ny In _ aR, i x ce IMA Assumption 1¢ daly « Shouta be Sockiomany : : T ADP CAvamented Dik Bll 7 - ,.¢ ler)Tect ak an data ic aa : ebostinnes : : Gllonaiy te chatcomany tare fog Cu.) Bi it becomec Oye bhCz meen) Care ya) Yi lags Cy) hago. ty) — aoe 2 - = Deloig Cbe.- 20 1 oa 1 tranelormation) (fn i _ dat le) toppers Ub J loo -14J 4 te t HY sya _forecat te -May 5 Unia-a] wo esr) Valuer Tune ost 6 es | 19-28) | Joi-25) I =| How To Detect Seasonality | veing | Autocorrelation Plot (ACE) Gequence plot , multiple. I box _plott . - : ; [ | Auto Correlation, function ACE Plot - Bar chart of Cocfticrenls™ of Correlation duc | time Serie $s itself. Pack Plot ( Partial Autocorrelation funclion) Correlation =~ Rilatiorship. bw 2 Coniinuove vanablec. Autocorrelation fs Correlation’ Clortimucve | varvable), but |_insthad of 2: dit forent variables , 't 1c Correlation Lita sbetw va t fame ‘variable: ine” Yew Ye~ Ye Yt-o, Yt ~ Yeo considering - ooffect: other [- 2 a} : varrablee on Me af wen. Portal Sorrefation = ‘ —— een : (prrefetion in _blw 2 valuee of Lame variable h the “fis of other _variablec oni Yt is not er Ge the, orher variables cre Contint Ale im Ye ew Yer) here we cure. finding Correlation =o Ye 6 Ye-1 keeping other van eens.) ant.a classmate, | pd ood = os al — Tnputr oo Agima ic pda & - == Agi map, a a4) ————_ P> Comes from. PACE Curve t= Comes from Cationarity (ie ot whieh 4eg | dlata becomes Stationary ) 4 =) Comes from ACF curve | | Ge: ARIMA (3,2, 4) | “ Here, Aata becomer Stationary ot fag BLD. th “eu aa 2 the Pst bars that * Croceee’ ‘vexomen niin PACE curve | ig Comesderea ac ps TéKe sve Of that © value - =Cmodelue) i ws) ¢ ae 7 iE ° 7 By — ve Here Pp (RT le woe () eas 6 & = 36) Ae Dy the: iven data itset, ig. shatienlery then .d=o0 [Thicmedel 10° ARMA rnodel : The. bare that eroce UC or dtu Pe Comerdered Bei: 4 walue. det'c fey = 4,6, 6,4 “dhe mo. 4 modele Can be -permufation ». Combbinabio Pig, de fe Models (3, 9 a fet M5 C35 2n6) in ACP curve i | C612, 4yclassmate. =o Testing the Forecasting Gerformance ___ —||_Mape $y 3 Rust CRoot Mean Square Error) (Mean Absetule Percentage Error) Chooce the model with Smallect maple, Rmse as bert ombdet - Stratepiec Larmptieng C Shic te for logsetic regvetsion) Dyeide ample evhere y= ao \ Cain m0) Cee in no) * Train Test Trai? \ rect ! i Bor 20+- Ceor) (20s) data Cannot be _Qpuit__irendomly im time - Serves motict _becauce data will not be Spaced. equally . Usualty dost 2 quarters Cé smenths) ioiumbentoalrde ca foil tact _datroet . Insbial CFrnet) omen for train eet. Im Linear regression, Aolh can be epuit, randomly bat it ig mot _ accurate. Fimel Lome echnrguec. @ 2 p of al ead for matter ammount f Io. A | Smeching Techav gue | Seahtea Smoothing 3) Expomentiol . pees Ymnootiung 2\_Werghleat some eng nting I Wludesehtza Avenaet. + Gixing omore worghbage, to recear anonthc[“bme erick lata “while taling forecast T th Key Months 0¢| Momth2.0q| Months | Month4 | Months” Lon : tooo || 49.eu ee 14~ | o2¢.03 [isd 213.06 tooul G&.9o0. No 82 D3e ob] Yo. 14 65 A> teol2 || 817.44 HS6.66 bs.0¢ | 2545.99 | 4p 30.4 loots || 446.qy 743.5) | 345.67 5VS2 | 363.4 loorulll 363.04 355.5 521-6] Atom orl 454.25° | Thy ic ume Serves dat but in Jer of 2acW customop = a a = Here | wergnta average, if we wont i inet Menthe og of ___toorg lowe tamer. : E be || take Gov. ph 454.95 + Qp'/ ef Low, OT+ loys of 52.6 y . eee OS a St 355-5 +0571 of 30, 04. tones ae = cdhille pereenlin 16 not tied , butt may Cure w give! amore wiih 092 Lo Ye cent Cala. Percentage tho Th Go4 204 10406 +65 _ i Tt [rs better Hor dogeCy) iL 6 lng polnle Sin —— Sein behind Hoe writ Cause Lat ay dats Docs , ic mot Stationary pen Otter 6 ty db tata tranctormeteon AS than atdhe fen Stat added. ty fe too Vv loO ve we,a a oF derm Memory? Orophtt >), ethic vs when dels hat no feaconalily dre or yet Weighted Average will 4 4 mol_qure good retultt for nore 6 ornte , it'S better fbr Ymatler “no } data _poinlt t ate gee _ExpoNentias Smooth in Here, any number blu Ol te 0-4 cam be taker & amulti'p Wed # wif} previeve value im powers Month, Geter Single. onential ingle Exes oT, lo to. F ies Jo» 0.47 M 1p rn x 0.4 4 lia Ip x 0-47 NY : May to A tax 0-4 o ~ 7 June to Fyie x 0-4 July 9 12 x 0.4! o weight Reduane weight in exponent’, Thc fechnique 1S applrcable for Smaller Cet 04 ata Point becauce exponents become ap Es exponent power ic Augh. Werghte dont even add up| to 4 . oneNTIAA — QmoorHiNG tan be blw 0 to 0-4 Here, weight is added r Un = C+ Yo + Cine) Dans det'c take Sar 0-4 U q TR Were Bae Month Gale 9 z 3 3 E. lo (0-4 st0) +(1-0.4)S = © M Jo G-4 ey + C 1-0-9) Y= IT A 13. (41 + Cl-oed tet = — Moy a Tune ° Tile—— to Caploine | Scponcatial Cmooihing faite f Hoare HETHOP Pinan Capone on Savona e__ Adding Slope to -Cepomentind- Cn nga p—tes Salas) Lucre : li mn Puy stn which? fc _7ruse! ni exponential Smoothing Glope 2 ms AY a am: | fp = x - Ya Two medele of Double Exponential Looting [aaartive . Mubtipvreative T 1 | | Gage Exponential Werghted Gmoothin = 3 if Alpha tan be nyt: i +2 . blu _o+! to0-4 | i aa (eee) Se 7 aie 3262 (0.9% 68+ Coty 4a) OF [13> Oa xa) + Otx85) = 197 — 2 273) (03.4153) + (14127) 2 135 ; (0.3x973) +Yxissy = He Formula = - mele = Oye Yay ECB) ae (alta ne vata i af But Oy + es = 4. douse bx ONENTIAL Lmoorn ING ln 2 %a + OO) Che eee aes. devel Qa eds \ + (162) bn ee|| P_tan be anything blue 0:1 “to 0.4. 0% G Pp Mean alto Gy Sorte _Ps06 Cin ba) 4 dx bx gant a = 10 3 ogfa-0) +Ci-0.6)0 = @ (C12) 5 Joy pie (i= 6) 4 Clec6)o - 66 16.6 is bo. 0-6 (12-") + (1-0-6) 5:6, = 9 C4 lub & lo 4 OtGGe iso Cibo et ces 8.336 ened) 0-6 (7-4) + C06) (= 0,664) = - 0:4 344 | 6. 0656 | Teipae Exponent 1A Smoorning I Hosrs Winter HeTHoe. |_ Alto fap tines eas aug Requires more dala poinls Wits = ot Cys 9.24 3 Cie df ee) Kevel bas p (ty = bas) + Up) bent — Ly = b (yx — tad + (1-3) Seng Qatonimecas Giuem = 4x4 mby + Sx-g¢4+ 6n-1)modé Poreath.