# What measurement of error should I use to compare predicted model results to actual measurements (and why)?

Lets say I have a time-series dataset of measurements g that varies with time t and I also have a time-series dataset of predictions of these measurements (lets call this g1) that again varies with time t.

I want to be able to quantitatively say how well the predicted data g1 matches the measured data g using a statistic that estimates error (for example $MSE$ or $R^2$). However as someone with only a brief introductory background in statistics I do not understand the differences in what different error statistics are telling me.

So what would be the best error measurement to find this (with an explanation of what that statistic is actually telling me)?