No, that is a problem. mu_z and mu_A contain frequency components that will not be fully removed by the one-sided HP-filter. As such, you cannot simply map to y_d. Your best hope may be something along the lines of
No, that is a problem. mu_z and mu_A contain frequency components that will not be fully removed by the one-sided HP-filter. As such, you cannot simply map to y_d. Your best hope may be something along the lines of