I need to convert a yearly data into a quarterly and monthly data? discusses how to convert (with some risk !) annual data to quarterly data. After this conversion you next task is to develop a PDL/ADL (lag models) also generally called a Transfer Function or Dynamic Regression or often ARMAX. Your challenge is to form a model (ARMAX) between Y and it's lags and X (contemporaneous and lag structure) while identifying appropriate latent structure such as Pulses, Level Shifts, Seasonal Pulses and Local Time Trends. If you wish to post your quarterly data matrix I might try and take this further.
edited after receipt of data
You posted two time series with different frequencies of measurement and inconsistent time ranges . The overlapping period is 2007/1 to 2015/4 .. thus 36 quarterly periods or 9 annual periods. You need to either convert your annual data for refugees for 2007 to 2015 ( 9 points ) to quarterly data (36 periods) using the methodology I referred to (cubic smoothing ). when this is accomplished you will have a 36 by 2 data matrix. OR if you elect not to do this then simply sum the quarterly data from 2007/1 to 2015/4 to 9 annual sums and thus you will have a 9 by 2 data matrix (less informative) but still possibly useful. Please post either of these two approaches.
edit after receipt of 52 data points:
There is no evidence that thefts and refugees are relatable.
To answer the question regarding a relationship between these two time series I followed the guidelines https://onlinecourses.science.psu.edu/stat510/node/75 using AUTOBOX . Following are the steps ... determine stationary conditions i.e. the need for differencing and then filter appropriately . Here are some pix from that procedure.
- pre-whitening filters leading to cross-correlations ..
3 leading to a possible model
- revised here due to omitted structure
5 and simplifying here
with an acf suggesting that more ARIMA structure needs to be added to the univariate model such as data segmentation or weighted least squares.