Let Pt Be A Random Walk With Increment E T And Let E T Be I Normal With Mean U A

Let Pt be a random walk with increment Et, and let Et be i.i.d. normal with mean u and variance sigma2. Assume t0 = 1.

1. Derive the unconditional mean and variance of Pt.

2. Derive the conditional mean and variance of Pt given a value of Pt-1 = x.

3. Compare and contrast the behavior of the unconditional and conditional variance, as t –infinity .

 

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