Econ226_V

Econ226_V - 1 V. Estimation of continuous-time models y t...

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Unformatted text preview: 1 V. Estimation of continuous-time models y t asset price or interest rate at instant t dy t a ¡ y t , t ; 2 ¢ dt b ¡ y t , t ; 2 ¢ dW t W t L standard Brownian motion W t " W s L N 0, t " s y t 1 y t ; s t t 1 a ¡ y s , s ; 2 ¢ ds ; s t t 1 b ¡ y s , s ; 2 ¢ dW s Presumptions: (1) y . is only observed at discrete points t , t 1, t 2,. .. (2) the solution to these integrals is not known analytically 2 Can approximate using fact that for small , y t " y t X N A t , B t A t a ¡ y t , t ; 2 ¢ B t b 2 ¡ y t , t ; 2 ¢ 2 with accuracy arbitrarily good as v Consider dividing the interval between observations t , t 1 into M subintervals each of length A t 1 t A t 2 t 2 B A tM t M A t , M 1 t 1 with M 1 1 3 Consider unobserved latent variables y tj ' "missing" value of y A tj y t j y tj ' j 1,2, .. , M missing between each pair y t , y t 1 of observed data y t , j 1 ' " y tj ' L N A tj , B tj A tj a ¡ y tj ' , A tj ; 2 ¢ B tj b 2 ¡ y tj '...
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This note was uploaded on 03/02/2012 for the course ECON 226 taught by Professor Jameshamilton during the Winter '09 term at UCSD.

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Econ226_V - 1 V. Estimation of continuous-time models y t...

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