Table 2: ARCH(1) Relative Efficiency of OLS Sample Size:512
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1 Table 1: ARCH(1) Relative Efficiency of OLS Sample Size:256 γ 1 φ (0.002) (0.002) (0.003) (0.006) (0.003) (0.004) (0.005) (0.008) (0.004) (0.005) (1.761) (0.019) Table 2: ARCH(1) Relative Efficiency of OLS Sample Size:512 γ 1 φ (0.001) (0.002) (0.002) (0.004) (0.002) (0.004) (0.006) (0.008) (0.005) (0.007) (0.020) (0.019) Table 3: ARCH(1) Relative Efficiency of OLS Sample Size:1024 γ 1 φ (0.001) (0.001) (0.001) (0.002) (0.003) (0.004) (0.008) (0.016) (0.005) (0.093) (0.019) (0.045) Relative Efficiency is defined as SIV 2 /S2 OLS where S2 is the estimated variance of the estimator ˆφ. Numbers in parenthesis are asymptotic standard deviations of the variance ratio. Results are based on 10,000 replications. 52
2 Table 4: ARCH(1) Sample Size N=32 t h t =0.1+γ 1 ε 2 t 1 φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD
3 Table 5: ARCH(1) Sample Size N=256 t h t =0.1+γ 1 ε 2 t 1 φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD
4 Table 6: ARCH(1) Sample Size N=1024 t h t =0.1+γ 1 ε 2 t 1 φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD
5 Table 7: IGARCH(1,1) Sample Size N=1024 t h t =0.1+γ 1 ε 2 t 1 + β 1 h t 1 ; β 1 + γ 1 =1 φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD
6 Table 8: Stochastic Volatility Sample Size N=1024 Model:y t = φy t 1 + ε t ε t = u t exp(h t /2) h t =0.1+γ 1 h t 1 + v t φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD φ OLS φ FD
7 Relative Efficiency AR Figure 3.1: Asymptotic efficiency of OLS relative to the IV estimator as a function of the parameter φ. Generating mechanisms considered are from bottom to top: γ 1 =.5, γ 1 =.4, γ 1 =.3 and γ 1 =.2. 58
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