![]() This method has been implemented in the R package RlmDataDriven. To obtain the parameters of the proposed AEN-PAC model, we convert the optimization problem of the proposed AEN-PAC model into an adaptive lasso model, thereby proposing an effective method to solve the optimization problem. Finally, we illustrate the proposed method using an air quality dataset from Beijing. Our estimation procedure outperforms the other methods providing estimates with lower biases and mean squared errors. We compare the efficiency of our procedure on simulated data to other usual regression methods. Therefore, we introduce a new estimation procedure which adapts the weighted M-estimation to environmental time series data, while selecting optimal value for the tuning parameter present in the M-estimation. However, this method is limited to the independent errors case, and is not applicable to time series data. It assumes a parametric function for the variance, and, estimates alternately and robustly, mean and variance parameters. To solve this problem, the weighted M-estimation was developed. This can have significant effects on parameter estimation. In environmental data, the response variable often contains outliers and errors can be heteroscedastic. However, this method relies on strong assumptions that are not always satisfied. The classical approach is the ordinary least squares method which consists in minimizing the sum of the squares of the residuals. In this paper, we study the Lasso estimator for fitting autoregressive time series models. Under this double asymptotic framework, the Lasso estimator was shown to possess several consistency properties. The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. We defined the Lasso procedure for fitting an autoregressive model, where the maximal lag may increase with the sample size. We adopt a double asymptotic framework where the maximal lag may increase with the sample size. In this paper, we study the Lasso estimator for tting autoregressive time series models. Therefore, an iteratively reweighted adaptive lasso algorithm for the estimation of time series models under conditional heteroscedasticity is presented in a high-dimensional setting. In environmental studies, regression analysis is frequently performed. Autoregressive Process Modeling via the Lasso Procedure. The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. However, currently lasso type estimators for autoregressive time series models still focus on models with homoscedastic residuals.
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