3
$\begingroup$

I like to know if we can model binary outcome with time series predictors. For example lets say Y is binary. $X_1, X_2, X_3,...,X_n$ is the same predictor variable but is a historical snapshot over time period $1,...,n$. I am interested in predicting $Y$ but include the auto correlation among $X_1,...,X_n$ and seasonality if any among $X_1,...,X_n$.

$\endgroup$
1
$\begingroup$

Your question sounds very much like you are interested in discrete time event history analysis (aka discrete time survival analysis, aka a logit hazard model) to answer the question whether and when will an event occur?

For example, equation 1 gives the logit hazard where discrete time periods (up to period $T$ are indicated $d_{1}, \dots, d_{T}$, and you may condition your model on $p$ number of predictors $X_{1}, \dots, X_{p}$. This gives you a hazard estimate as in equation 2. These equations specify a conditional hazard function with a fully discrete parameterization of time. Although you could instead specify a conditional hazard function that is constant over time, or is a linear or polynomial function of time period, or even a hybrid of polynomial functions of period plus some discrete time indicators. Your predictors can be constant over time, or time-varying, so I see no reason why you could not also include lagged or differenced functions of the predictors to model auto-correlation.

  1. $\mathrm{logit}\left(h\left(t,{X_{1t},\dots,X_{pt}}\right)\right) = \alpha_{1}d_{1} + \dots + \alpha_{T}d_{T} + \beta_{1}X_{1t} + \dots + \beta_{p}X_{pt}$

  2. $\hat{h}\left(t,{X_{1t},\dots,X_{pt}}\right) = \frac{e^{\hat{\alpha}_{1}d_{1} + \dots + \hat{\alpha}_{T}d_{T} + \hat{\beta}_{1}X_{1t} + \dots + \hat{\beta}_{p}X_{pt}}}{1 + e^{\hat{\alpha}_{1}d_{1} + \dots + \hat{\alpha}_{T}d_{T} + \hat{\beta}_{1}X_{1t} + \dots + \hat{\beta}_{p}X_{pt}}}$

One need not use a logit hazard model (indeed one could use probit, complimentary log-log, robit, etc. binomial link functions).

If you are using Stata see also the dthaz package by typing net describe dthaz, from(https://alexisdinno.com/stata).

References

Singer, J. and Willett, J. (1993). It’s about time: Using discrete-time survival analysis to study duration and the timing of events. Journal of Educational and Behavioral Statistics, 18(2):155–195.

Singer, J. D. and Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. Oxford University Press, New York, NY.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.