Calibration

[Ann]

Hi everyone :)

In doing my thesis, I'm having some struggles and I have decided to ask you, hoping that you can help me. I'm trying to calibrate a model to the data.
For my thesis I'm analyzing the data by finding the means and standard deviations and correlations. In doing this I'm struggling with some problems.

Question 1:
The way that I analyze the data (like GDP, consumption, investment....) is that I take logs, later I take HP filter and then conduct an AR(1) process on cyclical component. From the AR(1) regression I'm getting standard error of regression which I take a standard deviation of my time series and from cyclical component I take the empirical mean, which I take as a mean of my series (I hope this is correct way to do).

However I have one time series (a ratio of Financial Aid to GDP) where I'm getting negative mean. It makes me suspicious , as all the numbers that I've got are positive (like 0.06, 0.03 etc). Of course for this series I don't take logarithm as the numbers are already small, and I take directly HP filter. Now I'm wondering if this is true? Should I find the mean with some other technique (it's just can't be negative mean)?
I've attached this time series to the e-mail. Maybe you can help me by telling what should I do? Or maybe overall I do the analysis wrong way?


Question 2:

When I want to find the correlation between series should I find it from cyclical component series or maybe from trend series?

Question 3: Sometimes I conduct this analyse (especially for Financial Aid) and I logarithmize, Take HP Filter, then regress it with AR(1) process, and then at the end the coefficient value for AR(1) is negative. I also find this strange, isn't this mean that my series negatively correlated from the previous time? Is this ok to leave like that or should I also do something more?

I have attached the series of Financial Aid /GDP and just Financial Aid, so it'll also possible for you to view the series.