Demonstrating the Continuous Mapping Theorem Gauss file(s) nts cmt g Matlab file(s) nts cmt m Simulate the random walk yt yt1 vt , vt N(0, 2 ), with 2 1 and y0 0 for a sample size of T 500 The number of draws is 10000 (a) Given that m 1T 1 2y d R 1 0 B(s)ds , simulate the sampling distribution of m and verify that the functional can be expressed as N(0, 1 3) (b) Given that m 1T 5 2 PT t 1 tyt d R 1 0 sB(s)ds , simulate the sampling distribution of m and verify that the functional can be expressed as N(0, 2 15)

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Question: Demonstrating the Continuous Mapping Theorem Gauss file(s) nts_cmt.g Matlab file(s) nts_cmt.m Simulate the random walk yt = yt1 + vt , vt N(0, 2

Demonstrating the Continuous Mapping Theorem Gauss file(s) nts_cmt.g Matlab file(s) nts_cmt.m Simulate the random walk yt = yt−1 + vt , vt ∼ N(0, σ2 ), with σ 2 = 1 and y0 = 0 for a sample size of T = 500. The number of draws is 10000.

(a) Given that m = σ −1T −1/2y d → R 1 0 B(s)ds , simulate the sampling distribution of m and verify that the functional can be expressed as N(0, 1/3).

(b) Given that m = σ −1T −5/2 PT t=1 tyt d → R 1 0 sB(s)ds , simulate the sampling distribution of m and verify that the functional can be expressed as N(0, 2/15).

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