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 \((-\infty,c_{l,t})\) or \((c_{u,t},\infty)\), 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 $$ Y_t^* = X_t' \beta + \eta_t, $$ and $$ \eta_t = \sum_{i=1}^p \psi_i \eta_{t-i} + \varepsilon_t, $$ 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 \(\sigma^2\).
In this package we implemented the quasi-maximum likelihood estimator proposed by Wang and Chan (2017), for more details, please refer to the paper.
Wang C, Chan KS (2017). "Quasi-likelihood estimation of a censored autoregressive model with exogenous variables." Journal of the American Statistical Association. 2017 Mar 20(just-accepted).