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Unformatted text preview: Stat 5101 (Geyer) Fall 2009 Homework Assignment 5 Due Wednesday, October 21, 2009 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 5-1. Suppose X 1 , X 2 , ... are IID random variables having mean and variance 2 . For each i 1 define Y i = 5 X j =1 X i + j Then Y 1 , Y 2 , ... is called a moving average of order 5 time series, MA(5) for short. It is a weakly stationary time series. (So far this repeats the setup for Problem 4-6.) If Y n = 1 n n X i =1 Y i show that Y n- 5 = O p ( n- 1 / 2 ) . 5-2. Suppose that X 1 , X 2 , ... are IID random variables. For some subset A of the real numbers, define Y i = I A ( X i ) , i = 1 , 2 ,... and Y n = 1 n n X i =1 Y i . Show that Y n converges in probability to Pr( X i A ), and in fact Y n- Pr( X i A ) = O p ( n- 1 / 2 ) ....
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This note was uploaded on 10/28/2010 for the course STAT 5101 taught by Professor Staff during the Fall '02 term at Minnesota.
- Fall '02