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

### Description

`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.

### Details

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,
*

and

*
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.

### References

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