utocovariance r₁(h) and r2(h), respectively. That is Cov[Xt, Xt+h] = r₁(h), Cov[Yt, Yt+h] = r2(h) and cov[Xt, Ys] = 0 = r₁(0)] and Var[Y] = t, s,h, (in particular, Var[Xt r2(0)). Consider the ti oXtYt−2+5X0, t = 0±1, ±2,..., where ßo and ß₁ are nonrandom constants. ind the mean and variance of Zt.
utocovariance r₁(h) and r2(h), respectively. That is Cov[Xt, Xt+h] = r₁(h), Cov[Yt, Yt+h] = r2(h) and cov[Xt, Ys] = 0 = r₁(0)] and Var[Y] = t, s,h, (in particular, Var[Xt r2(0)). Consider the ti oXtYt−2+5X0, t = 0±1, ±2,..., where ßo and ß₁ are nonrandom constants. ind the mean and variance of Zt.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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PLEASE DO PART D ONLY. I HAVE SOLVED THE REST, I JUST CAN'T SOLVE PART D.
beta 1 is a non random constant.
Please solve d part explain step by step
![Let X₁, t = 0, ±1, ±2, · · · and Yt, t = 0, ±1, ±2, . be two independent time series with means
0 and autocovariance r₁(h) and r2(h), respectively. That is
Cov[Xt, Xt+h] = r₁(h),
Cov[Yt, Yt+h] = r₂(h) and cov[Xt, Ys] = 0
r₁(0)] and Var[Yt]
for all t,s,h, (in particular, Var [X₁
r2(0)). Consider the time series
Zt = BoXtYt-2 +5Xo, t = 0±1,±2,..., where ßo and ß₁ are nonrandom constants.
=
=
(a) Find the mean and variance of Zt.
(b) Find the autocovariance function of the time series {Zt, t = 0±1, ±2, · · · }.
(c) Is {Zt,t=0±1, ±2, · · · }. stationary?
(d) Let Z, be: 1.6, 28.1, 7.8, 4.0, 9.6, 0.2, 18.7, 16.5, 4.6, 9.3, 3.5, 0.1, 11.5, 0.0, 9.3, 5.5, 70.2, 0.7,
38.6, 11.3, 3.3, 8.9, 11.1, 64.3, 16.6, 7.3, 3.2, 23.9, 0.6.
Find the estimate of the trend Î; using ordinary linear least square method.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34b44b37-e66b-4c48-a846-aeedd1db2b78%2Fd8e2da5d-907f-4fb4-b944-7d361d0399dd%2F0dh72hr_processed.png&w=3840&q=75)
Transcribed Image Text:Let X₁, t = 0, ±1, ±2, · · · and Yt, t = 0, ±1, ±2, . be two independent time series with means
0 and autocovariance r₁(h) and r2(h), respectively. That is
Cov[Xt, Xt+h] = r₁(h),
Cov[Yt, Yt+h] = r₂(h) and cov[Xt, Ys] = 0
r₁(0)] and Var[Yt]
for all t,s,h, (in particular, Var [X₁
r2(0)). Consider the time series
Zt = BoXtYt-2 +5Xo, t = 0±1,±2,..., where ßo and ß₁ are nonrandom constants.
=
=
(a) Find the mean and variance of Zt.
(b) Find the autocovariance function of the time series {Zt, t = 0±1, ±2, · · · }.
(c) Is {Zt,t=0±1, ±2, · · · }. stationary?
(d) Let Z, be: 1.6, 28.1, 7.8, 4.0, 9.6, 0.2, 18.7, 16.5, 4.6, 9.3, 3.5, 0.1, 11.5, 0.0, 9.3, 5.5, 70.2, 0.7,
38.6, 11.3, 3.3, 8.9, 11.1, 64.3, 16.6, 7.3, 3.2, 23.9, 0.6.
Find the estimate of the trend Î; using ordinary linear least square method.
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