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I have a multivariate (multi-response) dataset with, for example, 10 different binary responses. I'm interested in an AR(p) model, determining how the responses at previous time steps relate to the current responses. That is, I'm looking for:

$P(Y_t \mid Y_{t-1}, ... Y_{t-p}) = \ell(\beta_0 + \beta_1Y_{t-1} + ... + \beta_p Y_{t-p})$

where each $Y_t$ is a length-10 binary vector, that is (I hope this notation works) $Y_t \in \{0, 1\}^{10}$, and $\ell$ is a link function (which I think I need - so something like probit or logit?).

I was thinking of using the VAR package in Python, but this requires stationary data and I'm all but certain my data are non-stationary.

How can I transform my binary multivariate time series data to be stationary?

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  • $\begingroup$ This looks like an implausible model for binary responses. Maybe you shouldn't be asking about transformations or stationarity, but rather about what kinds of models might be suitable for such data in the first place. You would need to say more about the nature of your data in order for such a question not to be overly broad, though. $\endgroup$
    – whuber ♦
    Feb 22, 2018 at 20:59
  • $\begingroup$ Thank you for the comment. I'm a student, and my advisor told me I needed to use an AR(p) baseline to compare to another time series model I'm using. I see what you mean, though - I should have included a link function, I think? I'll modify the question. $\endgroup$
    – StatsSorceress
    Feb 22, 2018 at 21:02
  • $\begingroup$ Yes, that has a better chance of working. $\endgroup$
    – whuber ♦
    Feb 22, 2018 at 21:06
  • $\begingroup$ Two things that spring to my mind are 1) Estimate a model with an AR(p) latent variable and a logit or something that is a function of the latent variable and its lags and 2) Some vague sense that Markov chains might be useful. $\endgroup$
    – John
    Mar 1, 2018 at 19:48

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