# Two hundred observations of a time series, X 1 , . . . , X 200 , gave the following sample… 1 answer below »

Two hundred observations of a time series, *X*_{1}*, . . . , X*_{200}, gave the following sample statistics:

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Two hundred observations of a time series, X 1 , . . . , X 200 , gave the following sample…
1 answer below »

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a. Based on these sample statistics, is it reasonable to suppose that {*X _{t}*−

*μ*} is white noise?

b. Assuming that {*Xt *− *μ*} can be modeled as the AR(2) process *X _{t}*−

*μ*−

*φ*

_{1}

*(X*

_{t}_{−1}−

*μ)*−

*φ*

_{2}

*(X*

_{t}_{−2 }−

*μ)*=

*Z*where {

_{t},*Z*} ∼ IID(0

_{t}*,σ*

^{2}), find estimates of

*μ, φ*

_{1}

*, φ*

_{2}, and

*σ*

^{2}.

c. Would you conclude that *μ *= 0?

d. Construct 95% confidence intervals for *φ*_{1} and *φ*_{2}.

e. Assuming that the data were generated from an AR(2) model, derive estimates of the PACF for all lags *h *≥ 1.