I = = = = = Suppose that {xi: t e T} is an AR(1) time series with d= 0, $i = 0.7 and Ou = 1.4. Thus {xt: t e T} satisfies the equation (1) with {ut: t e T} denoting a white noise time series with standard deviation Ou 1.4. Suppose the {zi: t e T} is an MA(1) time series with mean u = 0, Q1 = -0.4 and 0 = 2.0 and is independent of {xi: t e T}. Thus {zi: t e T} satisfies the equation (2) with {vi: t e T} denoting a white noise time series with standard deviation on = 2.0. x, = 0.7x7-1 +u, (1) z, = V, 0.4v-1 (2) Suppose that y: = x+ + z for t e T. a) Determine the spectral density of {xt: t e T} b) Determine the spectral density of {zt: t e T} c) Determine the spectral density of {yi: t e T} d) Determine the squared coherency function of{y: t e T}with {x: t e T} E I = = = = = Suppose that {xi: t e T} is an AR(1) time series with d= 0, $i = 0.7 and Ou = 1.4. Thus {xt: t e T} satisfies the equation (1) with {ut: t e T} denoting a white noise time series with standard deviation Ou 1.4. Suppose the {zi: t e T} is an MA(1) time series with mean u = 0, Q1 = -0.4 and 0 = 2.0 and is independent of {xi: t e T}. Thus {zi: t e T} satisfies the equation (2) with {vi: t e T} denoting a white noise time series with standard deviation on = 2.0. x, = 0.7x7-1 +u, (1) z, = V, 0.4v-1 (2) Suppose that y: = x+ + z for t e T. a) Determine the spectral density of {xt: t e T} b) Determine the spectral density of {zt: t e T} c) Determine the spectral density of {yi: t e T} d) Determine the squared coherency function of{y: t e T}with {x: t e T} E