Consider the model for the time series {y| t e T} y, = x, + v, and x, = Bx,1 +u, where {v| t e T} and {u:|t e T} are independent white noise time series wit variances o and o respectively. a. Assuming that E(x,) = 0 and Var(x,)= o, determine a means of
Consider the model for the time series {y| t e T} y, = x, + v, and x, = Bx,1 +u, where {v| t e T} and {u:|t e T} are independent white noise time series wit variances o and o respectively. a. Assuming that E(x,) = 0 and Var(x,)= o, determine a means of
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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time series
![Consider the model for the time series {y| t e T}
y, = x, + v, and x, = Bx, +u,
where {v| t e T} and {u| t e T} are independent white noise time series with
variances o and o, respectively.
a. Assuming that E(x,) = 0 and Var(x,) = o , determine a means of
calculating:
i. î, (1 –1) = E[x, .Y-3, Yr2»Yr1]
X,
1.
iii. £ (T)= E[x, .. Y7-2, Yr-1» Yr] for t<T
b. Assuming that ß = 0.9,0 = 2.0,o; = 1.5 and o =15, Suppose that the
first T= 15 observations on {y| t e T} are given below:
t
2
3
4
5
6
7
8
0.89
0.19
1.9
2.96
2.43
0.25
0.18
-1.03
t
9
10
11
12
13
14
15
-1.79
-4.74
-2.69
-0.78
-2.31
-0.89
-4.21
Compute
i. î, (1– 1) = E[x, ... y,-3» Yr-2, Yr-1] ! = 1, 2,...,15
ii. i, (1) = E[x, ...y,3» Y,2»Y;1»9%] t = 1,2,.,15
iii. , (15) = E[x, ..Yr-2, Yr-1» Vis] t = 1,2,.,15
= E] x,
1» Yi5| t = 1,2,...,15](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc67afd47-73a6-45ab-b513-dac9a3557eea%2F48921bb4-d147-4512-83d1-5ed8496c0ade%2Fn94d9sf_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the model for the time series {y| t e T}
y, = x, + v, and x, = Bx, +u,
where {v| t e T} and {u| t e T} are independent white noise time series with
variances o and o, respectively.
a. Assuming that E(x,) = 0 and Var(x,) = o , determine a means of
calculating:
i. î, (1 –1) = E[x, .Y-3, Yr2»Yr1]
X,
1.
iii. £ (T)= E[x, .. Y7-2, Yr-1» Yr] for t<T
b. Assuming that ß = 0.9,0 = 2.0,o; = 1.5 and o =15, Suppose that the
first T= 15 observations on {y| t e T} are given below:
t
2
3
4
5
6
7
8
0.89
0.19
1.9
2.96
2.43
0.25
0.18
-1.03
t
9
10
11
12
13
14
15
-1.79
-4.74
-2.69
-0.78
-2.31
-0.89
-4.21
Compute
i. î, (1– 1) = E[x, ... y,-3» Yr-2, Yr-1] ! = 1, 2,...,15
ii. i, (1) = E[x, ...y,3» Y,2»Y;1»9%] t = 1,2,.,15
iii. , (15) = E[x, ..Yr-2, Yr-1» Vis] t = 1,2,.,15
= E] x,
1» Yi5| t = 1,2,...,15
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