I am using complex demodulation to estimate slow amplitude and phase changes over time of a single sinusoid. The time series consists of continuous blocks with large gaps (~30% of block lengths) between them. The amplitude results are fine, but although the estimated phase evolution is smooth within blocks, there are sometimes large jumps (of different sizes) when going from one block to the next. This is not due to +/- 2pi ambiguities: the results lie roughly in (-2,2) and the jumps vary in size from ~0.2 to ~1.5. Within a block the phase typically varies by ~0.1; the blocks are long enough that independent statistical testing (Nyblom statistic) confirms that changes within blocks are significant.
Additional requested information: the gaps between data are due to extraneous circumstances, not connected to the source of the sinusoids. The same time zeropoint is used throughout. Besides all this, I replicated the problem using simulated data with no changes in phase: using the observed times (blocks and gaps), and generating a pure sinusoid with constant amplitude and phase, I still obtain apparent phase jumps after some gaps using complex demodulation. The result should therefore be reproducible.
The model is $$y(t)=A\cos(2\pi f t+\phi)+\sigma e(t),\;\; t=1,2,...$$ where $e$ is standard normal. Here are some specific parameter values: block lengths 500; gap lengths 167; $A=15$, $f=0.105269$, $\phi=1.7$; $\sigma=1.5$. With these fixed block and gap lengths I get phase jumps after every gap; in my application the block and gap lengths vary somewhat and I don't get noticeable jumps after each gap.
The low pass filtering is performed by two passes of a moving average filter with length $2P+1$, where $P=9$ is the nearest integer to $1/f$.
