Sorry I think this problem description is kind of vague but: I generate a time series of 1000 points using an underlying process. Now I need to estimate this underlying unobserved process using particle filtering with resampling and the time series acting as the observable. My resulting series is close to the true underlying in the sense that most of it is within 1 standard deviation of the true underlying. However there are a couple stretches where it is over 1 standard deviation but less than 2 standard deviations. I guess maybe covering around 150-200 points. Is this typical/expected or does this indicate an implementation issue? Thanks.