# Correlating Two Time Series with Gaps in Data and of Different Lengths

I am attempting to correlate the time series from 4 separate tilt monitors that sample every 5 minutes. The time series have slightly different base times and end times, and the resulting arrays are slightly different lengths, though they span the same period of time. My goal is to correlate each of these time series with a single "wind speed" time series that also covers the same period of time as the tilt monitors, sampling every 5 minutes, but also has a slightly different array length and base time and end time.

The different array lengths in the tilt measurements are due to instrument error. There are some times within each of the arrays where the instrument missed a measurement and so the sample interval is 10 minutes.

My arrays sizes look something like this:

Tilt_a = 6236x2
Tilt_b = 6310x2
Tilt_c = 6304x2
Tilt_d = 6309x2
Wind_speed = 6283x2


What is the best method to correlate the tilt data with the wind data without creating artifacts (false data) within the data? I know that I could interpolate through each time series to get an interval of 5 minutes throughout each series, but I do not know if this is the best way. I also do not know how to reconcile their slightly different base times and end times.

I am using MATLAB to do the correlation. This post is similar to: How to correlate two time series with gaps and different time bases?

• Welcome to CrossValidated! Do you need an answer specific to MATLAB? If so, StackOverflow is a more appropriate place to ask. – Hack-R Apr 9 '19 at 18:53
• +1. I believe your problem differs from the one you reference in that (a) it really concerns missing data and (b) there will be systematic differences between the time series to account for due to their different times of origin. It could be important to know why some of the data are missing (for instance, were those when the wind speed was extremely large?) and to understand how rapidly the time series values can change from one time interval to the next. – whuber Apr 9 '19 at 19:36
• I do not need any answer specific to MATLAB. I wanted to give that piece of information so my use of "array" made sense. – geojasm Apr 9 '19 at 20:09