EXERCISE 1.
Are the following series stationary?
1) Yt = Yt-i + εt.
2) yt = εi + εt.
3) yt = εi - θ1εt-i - θ2et-i.
4) yt = sin(Πt) + εt.
EXERCISE 2.
Manually sketch (by-hand) the autocorrelation function (ACF) for the following processes :
1) AFtMA(1,1) with Φ = 0.7 and θ = 0.4
2) ARMA(1,1) with Φ = 0.7 and θ = -0.4
Discus the important characteristics of the ACF for an ARMA(1,1) model
EXERCISE 3.
Consider the following AREvIA (p, d, q) time seres :
yt = 0.8yt-1- 0.2yt-2 + εt.
1) Identify p, d and q
2) Calculate the autocovariance function of the saies using the Yule-Walker equations
EXERCISE 4.
Suppose that {xt} is a time series such that : xt = μ + yt where μ is a constant and the estimator of μ is x' = 1/n Σt=1nxt
Compute :
1) Var(x') if yt is white noise
2) Var(x') if yt is εt - (1/3)et-1
3) Var(x') if yt is εt + (1/3)yt-1