Autoregressive continuous logit: Formulation and application to time-of-day choice modeling

Abstract

In this paper, we formulate the autoregressive continuous logit model as a novel continuous choice model capable of representing correlations across alternatives in the continuous spectrum. We formulate this model by considering two approaches: combining a discrete-time autoregressive process of order one (i.e., a linear stochastic difference equation) with the continuous logit model, which leads to the discrete-time autoregressive continuous logit; and combining a continuous-time autoregressive process (i.e., a linear stochastic differential equation), known in the stochastic process literature as Ornstein-Uhlenbeck process with the continuous logit model, which leads to the continuous-time autoregressive continuous logit. The autoregressive nature of the model is in its error structure, allowing correlations in unobserved heterogeneity. For both approaches, we study their properties numerically. We also compare both approaches to highlight their relation to each other.