carx: A package to fit Censored Auto-Regressive model with eXogenous covariates (CARX)


carx is a package to estimate the parameters of the Censored AutoRegressive model with eXogenous covariates (CARX), which can also be viewed as regression models with censored responses and autoregressive residuals. carx allows left, right, or interval censoring for the response variable. The regression errors are assumed to follow an autoregressive model with normal innovations. In addition to the estimation method, the package also contains functions to predict future values, diagnose whether the model is adequate, and plot functions to illustrate the data and model.


More specifically, we estimate the parameters assumed in the following model. Let (Y_t) be a censored time series with the latent process denoted by (Y_t^*). For each Y_t^*, it can be censored by either (-∞,c_{l,t}) or (c_{u,t},∞), and if it is censored, Y_t will be recorded as c_{l,t} or c_{u,t} respectively.

The latent process (Y_t^*) is modelled as

Y_t^* = X_t' β + η_t,


η_t = ∑_{i=1}^p ψ_i η_{t-i} + \varepsilon_t,

where (X_t) is a covariate process with all values observable, and the innovations (\varepsilon_t) are independent and identically normally distributed with mean 0 and variance σ^2.

In this package we implemented the quasi-maximum likelihood estimator proposed by Wang and Chan (2015), for more details, please refer to the paper.


Wang C, Chan KS (2015). "Quasi-likelihood estimation of a censored autoregressive model with exogenous variables." Submitted.

Questions? Problems? Suggestions? or email at

All documentation is copyright its authors; we didn't write any of that.