[25 marks] Question One You are given the MA (3) process as follows: y = y + - €-1 - Q26t-2 - Q3€ -3 where & is a white

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25 Marks Question One You Are Given The Ma 3 Process As Follows Y Y 1 Q26t 2 Q3 3 Where Is A White 1 (77.67 KiB) Viewed 100 times

You are given the MA (3) process as follows;
Ye = M + E•
- 01Et-1 - 02Et-2 - 03Et-3
where 8 is a white noise error term with
E(€+) = 0
fort # S
a). Determine the following characteristics:
(i) Mathematical expectation (the Mean)
(¡i) The Variance - Covariances
(ti) The Correlations and by mathematical induction give the
general correlation
formula.
b). Consider a stationary AR(2) process.
G) Write down the model with a constant term;
() Derive the mean, variance, the autocovariance and
autocorrelation functions;
(ili) Discuss the autocorrelation and partial autocorrelation
properties and write
down the general formula for an AR(p).
[25 marks] Question One You are given the MA (3) process as follows: y = y + - €-1 - Q26t-2 - Q3€ -3 where & is a white noise error term with E(E-) = 0 E(EE) = So, for t = s = a). Determine the following characteristics: (i) Mathematical expectation (the Mean) (ii) The Variance - Covariances (iii) The Correlations and by mathematical induction give the general correlation formula b). Consider a stationary AR(2) process. (i) Write down the model with a constant term; (ii) Derive the mean, variance, the autocovariance and autocorrelation functions; (iii) Discuss the autocorrelation and partial autocorrelation properties and write down the general formula for an AR(p).