psv245b - Derive a Lagrange Multiplier (LM) test for the...

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University of California D. Steigerwald Department of Economics Economics 245B Problem Set V 1. If the sample autocorrelations in a series are $ ρ 1 = .8 and $ ρ 2 = .5, find asymptotically efficient estimates of the parameters in an AR(2) model. If the variance of the observations is 2.0, estimate the variance of the disturbance term, ε t . Compute asymptotic standard errors for the estimates of φ 1 and φ 2 . 2.
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Unformatted text preview: Derive a Lagrange Multiplier (LM) test for the null hypothesis that a model is ARMA(1,1) against the alternative that it is ARMA(1,3). How would you carry out a modified LM test based on the F distribution? 3. Given the accompanying graphs of the autocorrelations and partial autocorrelations of the original data for some time series, identify a potential model for each....
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