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Wk10 Univariate Time Series

Wk10 Univariate Time Series - I nt r oduct i on t o Econom...

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I nt r oduct i on t o Economet r i cs Spr i ng 2010 Wk10. Uni var i at e Ti mes Ser i es: Anal ysi s and For ecast i ng
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2 I nt r oduct i on t o Ti me Ser i es A r andom or st ochast i c pr ocess i s a col l ect i on of r andom var i abl es or der ed i n t i me and i s of t en denot ed by Y t , wher e t = 1, , T ( wher e t he subscr i pt t r epr esent s t i me) .
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3 AR( 1) A ser i es t hat f ol l ows t he above i s cal l ed a aut or egr essi ve ser i es of or der 1. OLS “ wor ks” i f cov( u t | y t - s ) =0, wher e s t , i . e. no endogenei t y pr obl em and hence est i mat es ar e consi st ent . Consi der t he f ol l owi ng model : t t t u Y Y + + = - 1 1 0 β β
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4 Anot her common way i s t o r epr esent t he AR( 1) model i s aut or egr essi ve er r or s as wher e ε t sat i sf i es t he usual cl assi cal assumpt i ons. Fur t her mor e under AR( 1) , ( see Appendi x 12A) And ,
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5 AR( 1) I n gener al , gi ven We consi der t he case wher e - 1< ρ <1, t hat i s ρ 1 or l ar ger t han | 1| , and est i mat e t he model usi ng GLS ( Cochr ane –Or cut t , Hi l dr et h- Lu, et c. ) . However i f ρ =1, t he ser i es i s non- st at i onar y and t he “ usual ” est i mat i on pr ocedur es do not appl y.
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6 St at i onar y Ti me Ser i es A st ochast i c pr ocess i s sai d t o be st at i onar y i f i t s mean and var i ance
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