hw13 - ORIE 4630 D Ruppert Homework#13 Friday Dec 3 2010...

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ORIE 4630 — D. Ruppert Homework #13 — Friday, Dec 3, 2010 Note: Students are required to work independently on homework. 1. The problem uses the same data set that was used in the lectures this week. You can obtain the data with the following R code. options(digits=4) library("Ecdat") data(Capm) r = Capm$rf n = length(r) lagr = r[1:(n-1)] diffr = r[2:n] - lagr Fit the model ∆( r t ) = β ( r t - 1 - α ) + θ 1 / 2 ( r t - 1 ) γ/ 2 ϵ t by estimating ( α, β, θ, γ ) simultaneously by maximum likelihood. Assume that ϵ 1 , . . . , ϵ n are independent N (0 , 1). Find standard errors for all four parameters using the Fisher information matrix. Include your R program with your homework. 2. This problem uses monthly observations of the 2-month yield, i.e., Y T with T equal to 2 months. The rates were log-transformed to stabilize the variance. To fit a GARCH model to the changes in the log-rates, the following R code was run: library(fGarch) library(Ecdat) data(Irates) r = as.numeric(log(Irates[,2])) n = length(r) lagr = r[1:(n-1)] diffr = r[2:n] - lagr garchFit(~arma(1,0)+garch(1,1),data=diffr, cond.dist = "std")
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