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Math Help - Stationary process

  1. #1
    J13
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    Stationary process

    I dont get this question and cant find an I(1) process anywhere
    any help would be so useful

    What is meant by a stationary process?
    (a) Consider the processes


    and show that the first is stationary and the second is not.
    (b) What is an I(1) process? How would you test that a data series
    has been generated from an I(1) process?
    (c) What is meant by saying that series are cointegrated?
    (d) How can cointegration come about?

    Thanks in advance
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  2. #2
    Ond
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    a) Well, the first process is a MA(1) process, and MA processes are always stationary, no matter what.

    The second process is an AR(1) process, and they are either stationary or not. This particular AR process is called a random walk process and is not stationary.

    b) An I(1) process is a non-stationary process that has ben first differenced (excuse my English) in order to make that particular process stationary. You could test this with a Dickey-Fuller unit root test.

    c) If two series are cointegrated then there exists some long-term equilibrium between those two series.

    d) It can for example come about because of arbitrage opportunities that arise in markets.
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