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Unformatted text preview: 1. An ARCH(1) process is given by 1 ~ (0, ), t t t N h where 2 1 1 1 ; t t t t h V , o 1 and 1 1 . a. Find the unconditional mean and variance of t . t E and . 1 / 1 2 t E (Show the derivation) b. Show that t 's are correlated but not independent. t 's are uncorrelated as, for j > 0, 1 ( ) [ ( ) ] t t j t t t j E E E . t 's are not independent as 2 2 2 2 1 1 1 ( ) [ ( ) ] t t t t t E E E = 2 4 1 1 1 ( ) o t t E c. Discuss the properties of this process. If t follows the ARCH process, then i) high (low) volatility tends to be followed by high (low) volatility, ii) its distribution is leptokurtic, iii) .. d. Discuss how you would test for the presence of ARCH effects in t ....
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This note was uploaded on 09/29/2010 for the course ECON Econometri taught by Professor Fairlie during the Winter '09 term at UCSC.
- Winter '09