A new method of forecasting south-west monsoon rainfall

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1 Curre Bioica 6): 8-86, ISSN 97-4 A ew mehod of forecasig souh-wes mosoo raifall K Raga Rao *, Navee Kumar Boiroju ad M Krisha Redd Sri Veaeshwara Veeriar Uiversi, Dair Techolog Programme, Kamaredd-5, AP, Idia Deparme of Saisics, Osmaia Uiversi, Hderabad 5 7, A P, Idia * rrollu@ahoocom ABSTRACT I his paper, a ew mehod of forecasig of mohl seasoal raifall i Idia is discussed This mehodolog uses ol he hisorical daa The parameers of he model are esimaed usig leas squares priciple The performace of he proposed model has bee evaluaed o he basis of mea absolue error MSE), roo mea square error RMSE) ad mea absolue perce error MAPE) KEY WORDS: Forecas, Leas square mehod, raifall, ime series INTRODUCTION The uow fuure is a source of axie, givig rise o a srog huma eed o predic i i order o reduce, or ideall elimiae, is ihere ucerai Forecasig is a serious professioal ad scieific edeavor wih a cerai purpose, amel o provide predicios o be used i formulaig decisios ad aig acios The forecas raslaes io a decisio, ad, accordigl, he ucerai aached o he forecas ie error, eeds o be edogeous o he decisio iself I oher words he use of he forecas eeds o be deermied- or- modified- based o he esimaed accurac abou wha we should or should o forecas- as some forecass ca be harmful o decisio maers Box e al, 994; Salas e al, 98) The mai objecive of his paper is o forecas he fuure mosoo raifall usig he proposed algorihm wih he help of previous mosoo raifall daa METHODOLOGY The mosoo raifall ca be prediced usig muliple regressio aalsis ad auoregressive models Predicio performace of he models is measured usig he mea absolue error MAE), roo mea squared error RMSE) ad mea absolue perceage errors MAPE) Salas e al, 98) Daa Source: The daa of souh-wes mosoo mohl seasoal Jue Sepember) raifall i mm) i Idia for he ears 99 5 is colleced from Idia Meeorological Deparme, Pue, Idia wwwropmeresi) The daa o souhwes mosoo raifall i mm) for he period observaios) is uilized for model fiig ad daa for subseque periods 5 observaios) is used for validaio The daa o souh-wes mosoo raifall is give i Table wwwcurrebioicacom 8

2 Curre Bioica 6): 8-86, ISSN 97-4 Table : Souh-Wes Mosoo Raifall i mm) i Idia durig 99-5 Year Ju Jul Aug Sep Sice give daa is par or parial ime series daa, ha is raifall for he mohs of Jue o Sepember, herefore he ARIMA echique does o applicable o he give daa ad i leads o formulae some ew echiques o forecas he souhwes mosoo raifall based o he give hisorical daa A ew mehod proposed i his paper o forecas he mosoo raifall i Idia Box e al, 994) The performace of he model have bee evaluaed o he basis of MAE, RMSE ad MAPE which are give b MAE Y Y ) RMSE Y Y ) ) MAPE Y Y Y ) where Y is he origial raifall i differe ears ad Y is he forecased raifall i he correspodig ears ad is he umber of ears used as forecasig period wwwcurrebioicacom 8

3 Curre Bioica 6): 8-86, ISSN 97-4 Proposed mehod of forecasig The purpose of ime series sud is o measure chroological variaios The mai objecive i aalzig ime series is o udersad, ierpre ad evaluae chage i he pheomea i he hope of more correcl aicipaig he course of fuure eves I a mahemaical approach, he objecive is o build a model from pas observaios ad use his model for fuure occurreces Box e al, 994) Oe ca expec curre moh raifall i he mosoo period ma deped o is previous moh raifall raifall ma spread i he curre ad previous mohs) ad also i ma deped o he raifall i he same moh of previous ear mosoo seasoali) Assumig ha he mohl raifall moderael correlaed wih he previous moh raifall, a saisical recurrece model is developed o forecas he raifall i Jue o Sepember i each ear b combiig he aïve mehod ad regressio mehods Salas e al, 98) Model Developme: I his mehod, he curre moh figure is expressed i erms same moh figure of previous ear ad previous moh figure i he curre ear For he give daa we have four mohs amel Jue, Jul, Augus ad Sepember i each ear Le represes he raifall of Jue for he h ear, represes he raifall of Jul for he h ear, represes he raifall of Augus for he h ear, ad A 44 4 B represes he raifall of Sepember for he h ear, ad 99, 99,, 5 Le he aual ime series Y [ ] T 4 where 99, 99,, 5 The recurrece forecasig model for mohl-seasoal raifall is give b Ŷ CAY BY ) 4) where C is he earl icreme cosa represes he average growh over he ears, A ad B are he coefficie marices ad Y is he vecor of ime series values for he ear The earl icreme cosa C) is calculaed as follows Calculae he earl icremes T I where T is he oal T- raifall of he ear Now compue earl icreme cosa C as geomeric mea of I values The coefficie marices A ad B are calculaed as follows: 4 wwwcurrebioicacom 8

4 Curre Bioica 6): 8-86, ISSN 97-4 wwwcurrebioicacom 8 The above coefficies are esimaed usig leas squares mehod from he give daa ad are give below ) ) 5) ) ) ) ) ) 6) ) ) ) 7) ) ) ) ) ) 8) ) ) ) 9) )4 )4 )4 4 )4 )4 4 4 ) )4 ) 4 ) ) Model Validaio: The give daa is divided i o wo idepede ses amel i-sample se ad ou-of-sample se I-sample se coais he mosoo raifall durig 99- is used for he model buildig ad he obaied model is esed o he ou-ofsample se cosiss of he mosoo raifall durig he -5 ears For he give daa, he model parameers are C 99 ad he coefficie marices

5 Curre Bioica 6): 8-86, ISSN A ad 7 79 B Therefore he model is + ) + ) + ) + ) ) ) ) + ) + ) + )4 For example,, Ju, Jul, Aug, Sep *94) 895 5* *895) * * 8786) * * 4744) The obaied MAE, RMSE ad MAPE values usig his mehod ad he values for he fied daa ad validaio se are give i Table Table : Measures of errors for he proposed mehod Daa MAE RMSE MAPE Fiig Validaio MSE : Mea absolue error, RMSE : Roo mea square error, MAPE: Mea absolue perce error Ou-of-Sample forecass usig he proposed mehod are preseed i Table wwwcurrebioicacom 84

6 Curre Bioica 6): 8-86, ISSN 97-4 Table : Forecass of Souh-Wes Mosoo Raifall i mm) i Idia Year Moh Observed raifall Forecass of raifall Ju Jul Aug Sep Ju Jul Aug Sep Ju Jul Aug 5 58 Sep Ju Jul Aug Sep Ju Jul Aug 9 99 Sep Figure : Origial ad Prediced Raifall wwwcurrebioicacom 85

7 Curre Bioica 6): 8-86, ISSN 97-4 Forecass usig he proposed mehod are preseed i figure I ca be observed ha he forecased raifall is ver close o he origial raifall Fig ) Therefore he proposed mehod ca be used o forecas he mosoo raifall i Idia CONCLUSION From he above sud i is observed ha, he proposed mehod ca be reaed as a aleraive mehod for forecasig mosoo raifall i Idia The proposed mehod performs well a forecasig of srucural chages ad seasoal variaios i he hisorical raifall MAE, RMSE ad MAPE values are useful i comparig his mehod wih a oher mehod However, his echique does o guaraee perfec forecass Neverheless, i ca be successfull used for forecasig log ime series daa ad i should be updaed from ime o ime wih icorporaio of curre daa REFERENCES Box, G E P, Jeis, GM ad Reisel, GC 994 Time Series Aalsis, Forecasig ad Corol, Preice Hall, rd ediio Salas JD, Delleur, JW, Yevjevich, V, ad Lae, WL 98 Applied Modelig of Hdrologic Time Series, Waer Resources Publicaios hp://wwwropmeresi/~olli/mol/fore casig/frameidexhml [MS received March ; MS acceped 7 Ma ] Disclaimer: Saemes, iformaio, scieific ames, spelligs, ifereces, producs, sle, ec meioed i Curre Bioica are aribued o he auhors ad do i o wa impl edorseme/cocurrece b Curre Bioica Queries relaed o aricles should be direced o auhors ad o o ediorial board wwwcurrebioicacom 86

Advanced Forecasting Techniques and Models: Time-Series Forecasts

Advanced Forecasting Techniques and Models: Time-Series Forecasts Advanced Forecasing Techniques and Models: Time-Series Forecass Shor Examples Series using Risk Simulaor For more informaion please visi: www.realopionsvaluaion.com or conac us a: admin@realopionsvaluaion.com