The Economist is an international weekly journal written in the event you percentage an unusual curiosity in being good and extensively proficient. each one factor explores the shut hyperlinks among family and overseas concerns, enterprise, politics, finance, present affairs, technology, know-how and the humanities.
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Additional resources for The Economist (7 September 2013)
Example text
F u r t h e r m o r e , — (Χι η + (- X ) n ~* Έ,Χχ = μ b y t h e l a w of l a r g e n u m b e r s . B u t (Yi + · • • + Y )/n = Y. T h e r e is a s m u c h r a n d o m n e s s in t h e n t h s a m p l e a v e r a g e a s t h e r e is in t h e first o b s e r v a t i o n for t h e p r o c e s s {Yt}T o p r e v e n t s i t u a t i o n s like t h i s , w e i n t r o d u c e t h e following d e f i n i t i o n . n D e f i n i t i o n 2 . 7 / / the sample average formed from a sample path of a process converges to the underlying parameter of the process, the process is called e r g o d i c .
T If Yo = 0, then Y = Σΐ=ι ^i, which implies that v a r Y addition to being noncausal, this process is also nonstationary, changes with time. t = to . Thus, in as its variance • 2 t A s a n o t h e r i l l u s t r a t i o n of A R I M A m o d e l , let P d e n o t e t h e p r i c e of a s t o c k a t t h e e n d of d a y t. Define t h e r e t u r n o n t h i s s t o c k a s r = (P -Pt-\)/Pt-ιA s i m p l e T a y l o r ' s e x p a n s i o n of t h e l o g f u n c t i o n l e a d s t o t h e following e q u a t i o n : t t Pt - ι = Pt-i ' S-5— P L = t O logP -logP _!.
T S h o w t h a t {Y } + Z, \φ\>1, t {Z }~WN(0,a ). 2 t a l s o satisfies t h e c a u s a l A R ( 1 ) e q u a t i o n t Y t = φ - ^ - ι + W, t {W } ~ WN(0, σ ) 2 t for a s u i t a b l y c h o s e n w h i t e n o i s e p r o c e s s {Wt}. Determine σ. 2 3 . S h o w t h a t for a n M A ( 2 ) p r o c e s s w i t h m o v i n g a v e r a g e p o l y n o m i a l θ(ζ) = 1 — Θ\Ζ — # z t o b e i n v e r t i b l e , t h e p a r a m e t e r s ( # i , 0 ) m u s t lie i n t h e t r i a n g u l a r r e g i o n d e t e r m i n e d b y t h e i n t e r s e c t i o n of t h e t h r e e r e g i o n s 2 2 2 0 + 0 i < 1, 2 0 - 0i < 1, 2 | 0 | < 1.
