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Dual Algorithm for Arma Spectrum Estimation



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DUAL ALGORITHH FOR AR8A SPECIRUHESII8ATION M I s a b e l RIBEIRO Y Jose H F MOURA Ifept of E l e c t r i c a l and Computer Eng Carnegie MellonUniversity P i t t s b u r g h PA 15213 USA CAPS InstitcltoSuperiorTQcnico Av Rovisco P a i s 1 P 1096 Lisboa PORTUGAL ABSTRACT The p r e s e n t work describes an ANMA e s t i m a t i o na l g o r i t h mt h adt i f f e r s from t h e known a v atiel ac b h lnei q u e s It s u b s t it thuet e s a u t o c o r r e l a t i o ne s t i m a t i o ns e q u e n c e by t h e sequence of e s t i m a t erde f l e c t i ocno e f f i c i e n t s These a r e by t h e Burg technique Ell Then r e l i a b l yp r o v i d e d i t f i t st ot h ep r o c e s sb o t h a sequence of higher o r d e rl i n e a rp r e d i c t o r s e g Levinsonalgorithm and a sequenceofhigherorderlinearinnovations f i l t e r s e g by r e c u r s i vien v e r s i o n F i n a l l y i t o b t a i ntsh e MA c o e f f i c i e n t s from t hlei n e a r r e l ast ai ot inssf i e d by corresponding the c o e f f i c i e n t s of t h es u c c e s s i v eh i g h e ro r d e rl i n e a r predictors and l i k eow bttihaseien s AR c o e f f i c i e n t s from t h e l i n e a r r e l a t i o n s s a t i s f i e d by t h e c o r r e s p o n d i n cgo e f f i c i e n t s of t hseu c c e s s i v e h i g h e ro r d e ri n n o v a t i o nf i l t e r s We s t r e s st h a t h ep r o c e d u r ed o e s n o t use t h e sample a u t o c o r r e l a t i o n lags i t u s eisn s t e a d t hse q u e n c e of s a m p lree f l e c t i ocno e f f i c i e n t s from which i t e s t i m a t e si n d e p e n d e n t l y o f eachother and i n a dual way t h e MA and the A R components of t h ep r o c e s s 1 INIRODUCT ION The use of autoregressive moving average A R H A models i n s p e c t r a el s t i n a t i o nh a sr e c e i v e d i n c r e a s e da t e n t i o n i n t h e l a s t few y e a r s s e e e g C21 C4lf Most of t h er e p o r t e dt e c h n i q u e si n v o l v e s e v e r aslt e p st h ef i r s t of u h i ccho n s t r u c t s a sample autocovar function iance Another c h a r a c t e r i s t i c t ha loogsfoe r i t h m s is the dependence of t h e MA component e s t i m a t i o n upon t h e A R component e s t i m a t i o n T h i s work a d d r e s s et sh e ARMA e s t i m a t i o n problem presenting an estimation procedure that d o ensos ht a rt eh e two above mentioned common i t d e p a r t s from the features On the one hand usualapproach of usingthesampleautocovariance l a gs e q u e n c e e s t i m a t i n gi n s t e a d from t h ed a t at h e r seef ql eocucofeteni focfnei c i e n t s The s i n i u l a t i orne s u l pt sr e s e n t ehde rues e the Burg of the r e f l e c t i o n technique C11 f o rt h ee s t i m a t i o n On t hoet h ehra n dt h e AR and MA coefficients c o e f f i c i e nat ors eb t a i n e d i n a dual way The Thework of t h ef i r s ta u t h o r INIC P o r t u g a l was supported by a l g ocroi tnhsm tructs from the reflection c o e f f i c i e n t s two sequences of s u c c e s s i v e l yh i g h e r o r d e rl i n e a rf i l t e r s one is a sequence of l i n e a r p r e d i c t o r s t h eo t h e r is a sequence of i n n o v a t i o n s f i l t e r s The MA p a r t is thenobtained by e x p l o r i n g lt ihnereealra t i ot sahnarasetti s f i e d by c o r r e s p o n …


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