FIR Filter phase shift and stability I designed an FIR highpass filter which is causing a phase shift to the output. The output signal is also not stable (?) on start. 
Are these normal or am I doing something wrong?
If these are normal, what causes these?
(Attached is a diagram showing the input in blue and the output in red).
Thanks.
This is perfectly normal. At the beginning you see the transient effect because the signal suddenly starts and the filter was at rest before (zero initial condition). A causal filter will always add some phase shift to your signal. This phase shift is usually frequency dependent, but for a linear phase FIR filter the resulting delay is independent of frequency.

If $H(e^{j\omega})$ is the frequency response of the filter and $\phi(\omega)=\arg\{H(e^{j\omega})\}$ is its phase response, then the phase shift experienced by a sinusoid with frequency $\omega_0$ is simply $\phi(\omega_0)$, i.e. the corresponding time delay equals $-\phi(\omega_0)/\omega_0$.