Time Series Analysis Assignment
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Time Series Analysis
Assignment
(1) Let
where Yt is stationary time series. Is Xt stationary ?
(2) Suppose that
Xt = (1 + 2t)St + Zt
where St = St−12. Suggest a transform for Xt so that the transformed series is stationary.
(3) Derive ACFs ρk, k = 1, 2, ... for the following models.
(a) Xt = Zt − θ1Zt−1 − θ2Zt−3
(b) Xt − 0.5Xt−1 = Zt, where {Zt} ∼ WN(0, 1).
(4) If the ACF of some stationary time series is
ρ1 = 0.5467, ρ2 = 0.3667, ρ3 = 0.2, ρk = 0,fork ≥ 4
what kind of model you would like to choose for the time series ?
(5)
(a) Suppose R calculations of fitting an AR(2) model to the data are
{\sf
Call: arima(x = x, order = c(2, 0, 0))
Coefficients:
\begint{rrrr}
& ar1 & ar2 & intercept \\
& 1.1503 & -0.8009 & 0.8738\\
s.e. & 0.1250 & 0.1184 & 0.0623
\endt
sigma\^{}2 estimated as 0.03005: log likelihood = 5.38, aic = 1-2.77 }
write down the estimated AR model
(6) Based on the time plot of International Airline Passengers. Answer the following questions.
⊲ (a) Is it stationary ? Justify it .
⊲ (b) What kind of time series components do the data contain ?
⊲ (c) Suggest a transformation so that it may equalize the seasonal vari-ation.
2024-01-17