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Solutions to Quiz 4

# Solutions to Quiz 4 - Solutions to Quiz 4 Q1 A Keeping In...

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Solutions to Quiz 4 Q1) A) Keeping In order to calculate, we need and Thus, Now we have, Here, Thus we have, B) Using the above derived equation: C) In that case, we will have a 4×4 martrix. In order to identify our equations, we need to put restrictions on all the elements above principle diagonal, i.e., 6 restrictions. D) For a shock in t 0 1 0 1 0.2 0.8 2 0.68 0.32 3 0.392 0.608 4 0.5648 0.4352 5 0.46112 0.53888 6 0.523328 0.476672 7 0.486002 0.513997 8 0.508398 0.491602

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.2 .4 .6 .8 1 yt 0 5 10 15 20 25 t For a shock in t 0 1 0 1 0.8 0.2 2 0.32 0.68 3 0.608 0.392 4 0.4352 0.5648 5 0.53888 0.46112 6 0.476672 0.523328 7 0.513997 0.486003 8 0.491602 0.508398
0 .2 .4 .6 .8 yt2 0 5 10 15 20 25 t Q2) ACF or correlogram is a correlation coefficient between pairs of values of , separated by an interval of length k. First ACF depict a white noise series where all the coefficients are zero Second ACF depict a non-stationary time series where coefficients are slowly decreasing Third ACF depict a AR(1) process where coefficients are fatly decreasing B) PACF is the correlation between the current value and the value k period ago, after controlling for observation at the intermediate lags, i.e., all lags < k

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