How to compare short (9 points) time-series I need to compare two time series to assess whether they are really different (eg. don't overlap) between themselves and from 0 (don't overlap zero). 
The easy way is to simply perform a paired t-test, but being consequent in time the values are not independent so I assume a t-test would give false results.
I was wondering, is this also true for very short time series like mine?
If still they are worth being considered time-series which test should be used for the two above mentioned cases?
 A: Instead of a series of t-tests, you can do model-based comparisons of time series data. You can perform hypothesis testing for m observations in arbitrarily number of time series using spline basis functions. See this paper for details.
A: Positive autocorrelation in the series being compared will increase the probability of a type I error, possibly quite dramatically. 
Here's an example - I simulated two series, each of length 9, from an AR1 with parameter 0.8. This is the distribution of p-values under the null hypothesis in an equal-variance two-sample t-test (which should look uniform):

At a nominal significance level of 1% the probability of a type I error is actually around 40%. Similar results occur with a one-sample test, so autocorrelation will also affect a paired test.
So yes, doing something would seem to be necessary.
If the series are thought to be stationary (or at least their pair-differences if you're treating them as paired), it might be possible to assume a very simple, common model for the time-structure that should capture most of the dependence, such as an AR(1) (which are at least sometimes used in repeated measures or in mixed models more generally). 
An individual series doesn't have much data to estimate another parameter (you're already estimating two means and at least one variance), but with a common model across more than one series, there's more to go on. 
Things you know about the series might help in choosing a model. 
