How to correlate time series to a variable

Question

In an experiment, heart rate of participants is collected for 60 seconds (1 reading per seconds) and pupil diameter whilst performing one of three tasks. The success of the task is measured with a binary value (success/failure) indicating whether they achieved the expected result or not.

What is a good statistical model to find a correlation between two time series and the success/failure variable? I'm not trying to correlate the two time series, I'm trying to correlate both of them individually or together with the success/failure variable.

Data look like this

```

Time, HR Reading, pupil size
0, 75, 0.01
1, 78, 0.012
2, 76, 0.011
...
...
59, 98, 0.04

```

Observation for this data is true.

Answer 1

As I've understood it, you basically want the probability of success depending the twao variables. In this case, a probit/logit model would be a good point to start:

$\pi_t=\alpha+\beta_1HR+\beta_2PS$

$P(y_t=1)=\Phi(\pi_t)$

with HR as the heart rate and PS as the pupil size.

Best wishes,

Richard