Discrete choice models and time series

Some outcomes are choices, not quantities: a person works or not, a loan defaults or not, a commuter takes the bus or the train. Discrete choice models estimate the probability of each choice, usually with a logit or probit link that keeps probabilities between 0 and 1. Time series, by contrast, follow one variable over time, where today's value often depends on yesterday's. Worked example: in a logit model with index 0, the probability is 1/(1 + e^0) = 0.5; and in an AR(1) process Y_t = 0.8 Y_{t-1} + shock, a shock of 10 today still contributes 0.8^2 x 10 = 6.4 two periods later.