Abstarct: Forecasting financial time series is especially important‎. ‎There are many statistical models to predict time series‎, ‎e.g‎. ‎AR‎, ‎MA‎, ARMA models‎. ‎They are not good for modeling variance and instabilities in risk management‎, ‎securities management‎, ‎asset specialization and more‎. ‎Instead‎, ‎Autoregressive Conditional Heteroscedastic (or ARCH) and Generalized Autoregressive Conditional Heteroscedastic (or GARCH) models have been used‎. ‎If there are explanatory and response variables‎, ‎it is better to use times series regression for modeling the data‎. ‎In this dissertation‎, ‎integrating penalized techniques like adaptive LASSO method in order to select important variables in time series regression models with errors ARMA and ARMA-GARCH is considered and verified efficiency of the proposed algorithm via some numerical studies‎. ‎