statistics - Correlating paired time series data - Stack Overflow

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I am looking to analyze a dataset with many paired time series, but it’s the first time I deal with such data type and was wondering what’s the best way to analyze them. I am looking for the effect of temperature on degradation of 100s of materials of different (and known) compositions. This is observational data so I don’t control the temperature.

One example of my data looks like this:

Material #1 (comp: A20%, B34%, C11%, D13%, E22%)

T1 temp 214 deg 2%

T2 temp 217 deg 2%

T3 temp 224 deg -

T4 temp 224 deg 2%

T5 temp 230 deg 4%

T6 temp 210 deg 6%

T7 temp 214 deg -

T8 temp 212 deg 7%

T9 temp 218 deg 7%

T10 temp 217 deg 10%

T11 temp 209 deg 11%

T12 temp 207 deg 11%

T13 temp 210 deg -

T14 temp 213 deg -

T15 temp 212 deg 11%

Each material is made of multiple components and I know the proportion (all materials have slightly different proportions). T is time points and interval between each time point may not be the same. Temp is temperature. Deg is proportion of degenerated material with some missing data (this only goes in one direction as material does not self regenerate).

I would like to study the correlation between these two time series. Specifically, I would like to find:

1. At what temperature does each materials starts to degrade, then see if that correlate with their composition (I.e. Can I predict the temperature from composition?)
2. What’s the time lag between temperature increase and degeneration? Does that time lag dependent on composition or absolute temperature?

I feel like I have the data to answer these questions, I just having problem finding the best models or methods.

Thank you so much!

My current difficulty in approaching this problem is how to best correlate the two series. I can try to find when degeneration is happening by looking at the slope of the deg series. But I can’t find what temperature caused the degeneration unless I know the lag time between the temperature elevation and degeneration. But conversely, I also can’t predict the lag time if I don’t know at what temperature the degeneration start…

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