I have to find the spectral density function, (notice: the problem clearly states that I'm looking for the spectral density function, not the spectral distribution function) of the following process:
$$X_t=A\cos\left(\frac{\pi t}{3}\right)+B\sin\left(\frac{\pi t}{3}\right)+Y_t$$
Where $A$ and $B$ are non-correlated and both have mean zero and variance 1. Furthermore, $Y_t=Z_t+2.5Z_{t-1}$ is an $\operatorname{MA}(1)$ process. Again, the values of $Z_t$ are not correlated (white noise).
Now, the first part of the equation i.e. $A\cos\left(\frac{\pi t}{3}\right)+B\sin\left(\frac{\pi t}{3}\right)$ yields an autocovariance function $\gamma(h)=\cos\left(\frac{\pi h}{3}\right)$ (this is confirmed by an almost similar example we saw in class). The sum of the absolute value of the terms of this function is not bounded. How can I find the spectral density function then? Can a process not admit such a function? In this case, is it equal to the distribution function?