Financial statistics Model

a_t is white noise with average 0 and variance 1.

a) calculate average and variance MA(2) model

y_t = 0,5 + a_t + 2a_t-1 -a_t-2.

Also calculate first three autocorrelation functions, p_1, p₂ and p3.

b) Calculate average and variance AR(1) model

y_t = 1 + 0,5y_t-1 +a_t

Also calculate the first three autocorrelation functions p_1, p₂ and p3. Hint: To calculate the variance, note that the AR representation z_t := y_t − E[yt] has μ = 0.

c) c) Calculate average AR(2) model,

y_t= 1 + 0,75_yt-1 + 0,75_yt-2 + a_t.

d) Calculate the average and variance ARMA (1,1) model,

y_t = 1 + 0,5_yt-1 – a_t-1 + a_t.

 

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