How to normalise(?) an [x,y] time series data set

Problem:

I’m currently parsing a time series dataset, of [x,y] coordinates. The data isn’t complete – it contains gaps and jitter, and I would like to fill these gaps / normalise the jitter using statistical analysis.

Background:

I’m currently reading up on non-linear regression (specifically polynomial regression -> PR) – which seems to be the best fit (pun intended) for my problem.

I realise that PR deals with arcs "turning in one direction" so, I’m going to try to refactor my code to work with smaller sample sizes – and work my way along the time series.

Questions:

1. Am I on the right track?
2. Is there a name for what I’m trying to do? i.e. using polynomial regression across an ongoing graph (curve fitting? trendline? continuous regression?)
3. Is there another technique I can/should use, that provides a better "fit" for my data?