The Linear Regression Of Weighted Segments

Transcription

1 The Lear Regresso Of Weghed Segmes George Dael Maeescu Absrac. We proposed a regresso model where he depede varable s made o up of pos bu segmes. Ths suao correspods o he markes hroughou he da are observed values. Currec marke or he sock echage are eamples whch values are dffere ad varable hroughou he da. Kewords: regresso, weghed segmes, ceer of mass JEL Classfcao: C0, C, C58 The Model I a prevous paper ([]) we roduced he oo of mulple pos regresso. Such regresso refers o a se of daa of he form: The ( [ ]),,, = values ca be varables of me, ad [, ] s a rage of correspodg values. Such a suao s foud for eample dal values of radg o he currec marke, he sock marke, ec. For such daa ses we used a calculao scheme for deermg a regresso sragh shape f ( ) = a + b Where he coeffces a ad b are obaed from he codo: ( + - ) a b d a, b = m ò e-mal: da@maeescu.ro

2 Ths model foud some properes of classcal regresso, for eample f equdsa ervals are ake, bu also oher suaos, cludg he case of hgher order regressos. I he followg we aalze a form for calculag weghed regresso, o eflece beer real. Thus, f foreg echage rasacos ma be of eres o ol echage rae level or rage durg he da bu he volume of rasacos carred ou a a cera value. I fac, he volume level ca be repored eve he mos mpora dcaor. I hs arcle, we pu he queso of reporg he "ceer of grav" or "weghed average" of rasacos. Mahemacall, each erval [, ] assocae a des fuco :[, ] ceer of mass: G = f [, ds M ò, ] f + where M s he oal mass of he segme [, ] [, ] R for whch we calculae "" coordae of he, M = ò f [, ds ], ad he oao ò Fds s he le egral of he fuco F, alog he [, ] segme. We used parameerzao ì = í î =, Î, [ ] ad go: = ò ( ) s ( ) M f d I applcaos, we wll use he model: m ( ) + - G a b a, b = M = G f d ò Ths ormalzed form correspods o he lm, wh classcal regresso whe =

3 We oce ha, mahemacall we oba he lear regresso model for he daa sere of ceers of grav ( ) m,, = G ( ) + - G a b a, b = For applcaos, we wll use he soluos b applg he kow seps: or j ( a, b) = ( a ) + b - G = = j = é ( a + b) - G ù = 0 a ë û j = ( a + b - G ) = 0 b = a + b = G = = = a + b = G = = ad b applg Cramer's rule, resuls: a = G = = = G = = = ; b = G = = = = G = = = Applcaos Frs, we cosder he case of uforml dsrbued values. Ths correspods cu equal volumes for each value o he erval [, ] represes he case of cosa des,.e. G. I our model of weghed segmes hs + =. We calculae he regresso le b usg Mahcad fucos, as s show ha follow 0 0

4 a a.. b b a 0.88 b.9 f u ( ) a u b

5 f Bu, oe sgfca case s he suao of varable volumes,.e. varable des. I such a case, G ma o be equal o dsrbued ceer of mass +. As for eample, we geeraed a ormal g rorm 0. 0 g rorm 0. 0 g rorm 0. 0 g rorm g rorm g rorm g rorm g rorm g rorm g rorm g ad he correspodg regresso le.

6 Due o lack of real daa (socks, fore marke) we cao calculae some real values for he cere of mass, bu we beleve such daa ma be obaed ad used. Refereces.. Dolado, J.J. ad Lükepohl, H., 996. Makg Wald Tes Work for Coegraed VAR Ssems. Ecoomerc Revews, 5, pp Lükepohl, H. ad Krazg, M., 00. Appled Tme Seres Ecoomercs (Themes Moder Ecoomercs). Cambrdge Uvers Press.. Maeescu, G.D., 0. Mulple Pos Regresso, Romaa Joural of Ecomomc Forecasg, /0, p.-