1. Define a Stochastic process and briefly discuss the meaning of measurability of a stochastic process. 2. Consider the ARMA(1,1) model yt = 0.8yt-1 + et + 0.5et-1 with et ~ WN(0, σe2). Derive the Wold representation of yt. 3. Consider the ARMA(2,1) process Φ(L)Xt = Θ(L)et with Φ(L) = 1 − 1.3L + 0.4L2 , Θ(L) = 1 + 0.4L and et ∼ WN(0, σe2). Obtain its Wold representation. 4.Consider the ARMA(2,2) process given by Xt =0.4Xt−1+0.45Xt−2+et+et−1+0.25et−2 with et ∼WN(0,σe2). 5. Consider the MA(1) process yt = et+1.5et−1 with et ∼ WN(0,σe2). Is the above MA(1) a Wold representation? Why or Why not? If not, obtain a suitable Wold representation.

1. Define a Stochastic process and briefly discuss the meaning of measurability of a stochastic process. 2. Consider the ARMA(1,1) model yt = 0.8yt-1 + et + 0.5et-1 with et ~ WN(0, σe2). Derive the Wold representation of yt. 3. Consider the ARMA(2,1) process Φ(L)Xt = Θ(L)et with Φ(L) = 1 − 1.3L + 0.4L2 , Θ(L) = 1 + 0.4L and et ∼ WN(0, σe2). Obtain its Wold representation. 4.Consider the ARMA(2,2) process given by Xt =0.4Xt−1+0.45Xt−2+et+et−1+0.25et−2 with et ∼WN(0,σe2). 5. Consider the MA(1) process yt = et+1.5et−1 with et ∼ WN(0,σe2). Is the above MA(1) a Wold representation? Why or Why not? If not, obtain a suitable Wold representation.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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