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    Calculations Regarding Time Series Analysis

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    Suppose Cov(X(t), X(t-k)) = y(k) is free of t but that E(X(t)) = 3t.
    (a) Is {X(t)} stationary?
    (b) Let Y(t) = 7 - 3 t + X(t). Is {Y(t)} stationary?

    © BrainMass Inc. brainmass.com December 24, 2021, 10:58 pm ad1c9bdddf
    https://brainmass.com/statistics/regression-analysis/calculations-regarding-time-series-analysis-522971

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    2.11 Suppose C0v(X,,X,_ k) = yk is free oft but that E(X,) = 3:.
    (a) Is {X,} stationary?
    (b) Let Y, = 7 — 3! +X,. Is {Y,} stationary?
    Solution
    a) In order to show that {XI} is stationary, we have to show that its mean and autocovariance
    functions are free of t.

    It is given that the autocovariance function C01/(XI, X ,_k) = 7/k is free of t.
    However, E (X I) = 3t , which varies with t.

    Since E (X I) is not free of t, {Xt} is not stationary.
    b) In order to show that {I/I} is stationary, we have to show that its mean and autocovariance
    functions are free of t.

    We have,
    E(Y,) = E(7—3t+ XI)
    : 7 — 3t + E (X I)
    = 7—3t+3t (Since E(X,)=3t)
    = 7, which is free of t.
    Also,

    C0v(Y,,Y,_k) = C0v(7 —3t+X,,7 —3(t—k)+X,_k)
    = C0v(X[,X,_k)
    = 7/,6 , which is free of t.
    Therefore, the mean and autocovariance functions of are free of t.
    Thus, is stationary.
    [Note that: If a and b are constants, then C01/(a + X ,b + Y) = Cot/(X ,Y) . Applying this result, we
    get C01/(7 —3t+ X,,7 —3(t—k)+ X,_k)= Cot/(XI, X,_k) since 7 —3t and 7 —3(t—k) are
    constants.]

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 10:58 pm ad1c9bdddf>
    https://brainmass.com/statistics/regression-analysis/calculations-regarding-time-series-analysis-522971

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