# Compare quarterly time series with another annually time series

I have the following time series: 1) Criminality series in UK (for example, theft) every quarter year. 2) Refugee count in UK every year. I would like to compare both series to identify if the entrance of refugee are statistically increasing the number of the criminality levels in UK.

How can I go on with the comparison?

EDIT The data is adjusted, thanks to IrishStat answer (Cubic Spline method). Main problem is going through the comparison, if you have any other suggestion please feel free to comment!

Expected results: according to Becker (1968) and Elrich (1996) criminality study, the entrance of low income refugees with relatively lower scholarity than UK population would increase crime in the region.

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.

1. pre-whitening filters leading to cross-correlations ..

2

3 leading to a possible model

1. 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.

• Hi! First, thank you for this awesome reply. I added the google drive link to the spreadsheet with the data, since I don't know how to add it here. I'll study the methods you proposed! Aug 28, 2017 at 21:20