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We propose a new algorithm for estimating NARMAX models with $L_1$regularization for models represented as a linear combination of basisfunctions. Due to the $L_1$-norm penalty the Lasso estimation tends to producesome coefficients that are exactly zero and hence gives interpretable models.The novelty of the contribution is the inclusion of error regressors in theLasso estimation (which yields a nonlinear regression problem). The proposedalgorithm uses cyclical coordinate descent to compute the parameters of theNARMAX models for the entire regularization path. It deals with the error termsby updating the regressor matrix along with the parameter vector. Incomparative timings we find that the modification does not reduce thecomputational efficiency of the original algorithm and can provide the mostimportant regressors in very few inexpensive iterations. The method isillustrated for linear and polynomial models by means of two examples.

Lasso Regularization Paths for NARMAX Models via Coordinate Descent