Subset regression time series and its modeling procedures

Consider the linear regression model y(n) = x1(n)[theta]1 + ... + xk(n)[theta]k + w(n) with w(n) assumed a linear time series, especially an ARMA series. Procedures which use recursions only are suggested to identify the non-zero [theta]k and the order of ARMA or subset ARMA residuals. The consistency of these procedures is proved. The convergence rate of LS estimation of regression parameters under these assumption is also discussed. Simulations show good results.