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Thread: How would you solve these questions? Time series

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    How would you solve these questions? Time series




    Question 1

    For the AR(3) process,

    xt = 0.6xt−1 − 0.4xt−2 + 0.4xt−3
    find the values of the autocovariance function γ(1) and γ(2)


    Question 2

    For the AR(3) model from the previous question, what is the value of the partial autocorrelation function pi(4) and why?

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    Re: How would you solve these questions? Time series


    1) Assume 0 means.
    2) Multiply both sides of the equation by X_{t-s} and take expectation. Do this for several s.
    3) Solve the resulting system of equations for autocovariances.

    The process is similar for partial autocovariances. In an AR(p) process, the partial autocovariance is 0 beyond lag p.

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