Hello, I am sure I am missing something fairly obvious here but could somebody point me in the right direction to solve Q7iii in the Sep 2021 paper. I have tried expressing the autocorrelations in terms of autocovariances but don't seem to be getting anywhere. Cheers Jamie
Hi Jamie It's worth first writing down the defining equation for Yt, if you haven't already done so for the prior parts. As: \(Y_t = X_t - X_{t-3} \) We have: \( (1 - (a + b)B + abB^2) Y_t = e_t \) or: \( Y_t = (a+b)Y_{t-1} - abY_{t-2} + e_t \) We can then start with our equations for the autocovariances, for example: \( \gamma_1 = cov(Y_t, Y_{t-1}) \) \( \gamma_1 = cov((a+b)Y_{t-1} - abY_{t-2} + e_t, Y_{t-1}) \) \( \gamma_1 = (\alpha + \beta) * \gamma_0 - \alpha \beta \gamma_1 \) Dividing by \( \gamma_0 \), we can write this in terms of autocorrelations: \( \rho_1 = (\alpha + \beta) - \alpha \beta \rho_1 \) Hope this helps! Andy
