Exercises
Exhibit 4.14 indicates a realization of 50 consecutive terms of a variance 1 Gaussian white noise.5

Use this to generate a corresponding realization of the MA(2) process
[4.59]
where tW is a variance 1 Gaussian white noise.
Use the white noise realization of Exhibit 4.14 to generate and graph a realization of the AR(2) process
[4.60]
where tW is a variance 1 Gaussian white noise. Initialize the realization with terms 0x = 1x= 0.
Use the white noise realization of Exhibit 4.14 to generate and graph a realization of the ARMA(1,1) process
[4.61]
where tW is a variance 1 Gaussian white noise. Initialize the realization with term 0x = 0.
Solution
Derive expressions for the unconditional and conditional means, E(tX) and t–1E(tX), of an MA(q) process [4.53].
Solution
Derive expressions for the unconditional and conditional means, E(tX) and t–1E(tX), of an AR(p) process [4.55], assuming they exist.
Solution