I have a task which is related to finding correlations between time series. I have two financial time series given, which contain daily interest rate offers of two financial contributors and I want to find correlations (over time) between these quotes. The frequency and length is equal. The shape of the two time series is very similiar and looks like a upside down V. (upward trend followed by a downward trend)
My background in statistics, and particularly in time series analysis, is not very distinct. I know a few basics because I study mathematics but not more. I use the software R. My first approach was to calculate the Pearson correlation coefficient, but then I read a few topics about spurious correlation and fake correlations in trending time series so this could be not appropriate. Furthermore I read a few topics how to handle such problems, but I am still not sure how to solve my problem with my knowledge.
I would start as follows:
1) Use first differences or link relatives (which I found here: http://svds.com/avoiding-common-mistakes-with-time-series/) instead of absolute interest rates.
2) The hope is to get weak-stationary series so that I can calculate correlation coefficients (Pearson/Spearman) and cross correlation for different lags. Am I getting this right?
Would this course of action be appropriate to get meaningful results? How should I go on to solve the task? Im not looking for the perfect scientific solution, but I want to do a meaningful and solid analysis. Many thanks in advance!
Best Answer
Find correlation between two time series. Theory and practice (R) discusses my road-map which is quite consistent with the very clear presentation that you cited http://svds.com/avoiding-common-mistakes-with-time-series/ . The simple though profound idea is that to identify the intra-relationship one needs to adjust for any inter-relationship in the candidate X. I strongly suggest reading the seminal article on this subject https://www.jstor.org/stable/2341482?seq=1#page_scan_tab_contents . If you have problems obtaining it please feel free to contact me and I will try and help you.
Finally care must be taken to deal with possible anomalies as their untreated presence induces obfuscation yielding a downwards bias in statistical tests of significance much like a pebble affecting your glasses which will affect your vision.
I wonder about Google's econometricians/statisticians scholarship http://people.ischool.berkeley.edu/~hal/Papers/2015/primer.pdf as they continue to apply ordinary correlation tests (GOOGLE CORRELATE ; GOOGLE TRENDS) to time series data where angels fear to thread suggesting search processes based upon the naive assumption of no intra-correlation which is functionally equivalent to the assumption when analyzing cross-sectional data when trying to identify/short list significant predictors.