I am interested in analyzing the correlation between nationwide home prices and nationwide unemployment rates, both of which are leading economic indicators. I have data on nationwide home prices by using the Case-Shiller nationwide home price index (found here: http://us.spindices.com/indices/real-estate/sp-case-shiller-us-national-home-price-index), and I have data on nationwide unemployment rates from the Bureau of Labor Statistics.
Preliminary hypothesis/background info: Home prices are high when economy is doing well, and unemployment rates are low when the economy is doing well. So common sense tells me that as the unemployment rate rises, then the Case Shiller home price index decreases, which means there should be a negative correlation. But I don't know how to prove this. Here is a summary of the data I have:
I have the data for the Case-Shiller nationwide Home Price index for every month over the last ten years (1/1/2005-12/31/2014) which means 120 data points. I also have all the data for the nationwide Unemployment Rate over the same time period (1/1/2005-12/31/2014), which also means 120 data points. Both data are collected for the end of the month over the same time period, which means there is zero lag in the data sets.
What kind of correlation analysis do I need to do to determine if there is any correlation between these two data sets? Cross-correlation? Time-series analysis?
Thank you so much for any advice on how to start this research! Any help on what direction I should go would be incredibly appreciate.