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

Two hundred observations of a time seriesX1, . . . , X200, gave the following sample statistics:

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a. Based on these sample statistics, is it reasonable to suppose that {Xt− μ} is white noise?

b. Assuming that {Xt − μ} can be modeled as the AR(2) process Xt− μ − φ1(Xt−1 − μ) − φ2(Xt−2 − μ) Zt ,where {Zt} ∼ IID(02), find estimates of μ, φ1, φ2, and σ2.

c. Would you conclude that μ = 0?

d. Construct 95% confidence intervals for φ1 and φ2.

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

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