Consider an MA(1) process:
x_t = ω_t + θω_t-1,
where θ is a parameter.
(a) Derive a formula for the power spectrum of x_t, expressed in terms of θ and ω.
(b) Use arma. spec() to plot the spectral density of x_t for θ > 0 and for θ < 0 (just select arbitrary values).
(c) How should we interpret the spectra exhibited in part (b)?